Minnesota State Standards Alignment Grades One through ...

Minnesota State Standards Alignment Grades One through Eleven

Trademark of Renaissance Learning, Inc., and its subsidiaries, registered, common law, or pending registration in the United States and other countries. P.O. Box 8036 • Wisconsin Rapids, WI 54495-8036 Phone: (800) 338-4204 • Fax: (715) 424-4242 www.renlearn.com

© 2009 by Renaissance Learning, Inc. All rights reserved. No portion of this document may be reproduced, by any process or technique, without the express written consent of Renaissance Learning, Inc.

ii

Minnesota State Standards Alignment

Standards List with Aligned Product Skills

The Standards List with Aligned Product Skills Report is a standards-oriented document showing the entire list of standards for the subject and grade on the left side of the report with the aligning product objectives on the right side. This alignment report shows the breadth of standards coverage for the purpose and focus of this product.

Note to Educator .....................................................iii

Grade 1 ..................................................... 1

Grade 2 ..................................................... 7

Grade 3 ....................................................14

Grade 4 ....................................................22

Grade 5 ....................................................32

Grade 6 ....................................................46

Grade 7 ....................................................61

Grade 8 ....................................................93

Grades 9 - 11 ..................................................123

iii

Note to Educator: Thank you for your interest in Renaissance Learning technology. The attached document contains the alignment between the software and/or instructional materials and the skills described in the state standards documentation. At Renaissance Learning, we recognize the impact that the standards-based reform movement and high-stakes standardized testing have on schools, and we share the concerns of educators and administrators that students perform well on high-stakes assessments. We hope this report answers your questions regarding the alignment of Renaissance Learning technology and materials to your state standards. If you have any questions about the attached document, please feel free to call us at (800) 338-4204. Sincerely, Renaissance Sales and Funding Staff

P.O. Box 8036 Wisconsin Rapids, WI 54495-8036

Phone: (800) 338-4204 Fax: (715) 424-4242

www.renlearn.com

Agency Tag Set NameMinnesota, Math, 2007, Grade 1, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 1.1 - Number & OperationMN 1.1.1 - Count, compare and represent whole numbers up to 120, with an emphasis on groups of tens and ones.MN 1.1.1.1 - Use place value to describe whole numbers between 10 and 100 in terms of groups of tens and ones. Example: Recognize the numbers 11 to 19 as one group of ten and a particular number of ones.

Topic 1 - Numbers and Operations

Obj. 19 - Count objects grouped in tens and ones

Obj. 20 - Model a number to 100 using tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

Obj. 22 - Represent a 2-digit number as tens and onesObj. 23 - Determine the 2-digit number represented as tens and ones

MN 1.1.1.2 - Read, write and represent whole numbers up to 120. Representations may include numerals, addition and subtraction, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.


Obj. 1 - Read a whole number to 30

Obj. 2 - Read a whole number from 31 to 100Obj. 3 - Determine the word form of a whole number to 30Obj. 4 - Determine the word form of a whole number from 31 to 100Obj. 9 - Identify a number to 20 represented by a point on a number lineObj. 10 - Locate a number to 20 on a number lineObj. 19 - Count objects grouped in tens and onesObj. 20 - Model a number to 100 using tens and onesObj. 21 - Recognize a number from a model of tens and ones to 100

Obj. 30 - Determine equivalent forms of a number, up to 10

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Grade 1

Accelerated Math Grade 1

081309Page 1 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 1, Academic Standards, State Department of EducationStandard Topic Description Objective Description


MN 1.1.1.3 - Count, with and without objects, forward and backward from any given number up to 120.


Obj. 5 - Count objects to 20

Obj. 6 - Count on by ones from a number less than 100Obj. 7 - Count back by ones from a number less than 20Obj. 8 - Count back by ones from a number between 20 and 100

MN 1.1.1.4 - Find a number that is 10 more or 10 less than a given number. Example: Using a hundred grid, find the number that is 10 more than 27.


Obj. 12 - Determine ten more than or ten less than a given number

MN 1.1.1.5 - Compare and order whole numbers up to 100.


Obj. 11 - Determine one more than or one less than a given numberObj. 28 - Order whole numbers to 100 in ascending orderObj. 29 - Order whole numbers to 100 in descending order

MN 1.1.1.6 - Use words to describe the relative size of numbers. Example: Use the words equal to, not equal to, more than, less than, fewer than, is about, and is nearly to describe numbers.


Obj. 27 - Compare whole numbers to 100 using words

MN 1.1.1.7 - Use counting and comparison skills to create and analyze bar graphs and tally charts. Example: Make a bar graph of students' birthday months and count to compare the number in each month.

Topic 4 - Data Analysis and Statistics

Obj. 88 - Read a 2-category tally chart

Obj. 89 - Use a 2-category tally chart to represent groups of objects (1 symbol = 1 object)Obj. 97 - Read a bar graphObj. 98 - Use a bar graph to represent groups of objects

MN 1.1.2 - Use a variety of models and strategies to solve addition and subtraction problems in real-world and mathematical contexts.MN 1.1.2.1 - Use words, pictures, objects, length-based models (connecting cubes), numerals and number lines to model and solve addition and subtraction problems in part-part-total, adding to, taking away from and comparing situations.


Obj. 26 - Compare sets of objects using words


081309Page 2 of 198



Obj. 31 - Determine the missing portion in a partially screened (hidden) collection of up to 10 objects

Obj. 32 - Relate a picture model to a basic addition factObj. 33 - Determine the basic addition fact shown by a picture modelObj. 34 - Relate a number-line model to a basic addition factObj. 35 - Determine the basic addition fact shown by a number-line modelObj. 36 - Relate a picture model to a basic subtraction factObj. 37 - Determine the basic subtraction fact shown by a picture modelObj. 38 - Determine the basic subtraction fact shown by a number-line modelObj. 39 - Relate a number-line model to a basic subtraction fact

MN 1.1.2.2 - Compose and decompose numbers up to 12 with an emphasis on making ten. Example: Given 3 blocks, 7 more blocks are needed to make 10.MN 1.1.2.3 - Recognize the relationship between counting and addition and subtraction. Skip count by 2s, 5s, and 10s.


Obj. 13 - Count by 2s to 50 starting from a multiple of 2

Obj. 14 - Count by 5s or 10s to 100 starting from a multiple of 5 or 10, respectivelyObj. 40 - Apply the relationship between addition and counting onObj. 41 - Apply the relationship between subtraction and counting back

MN 1.2 - AlgebraMN 1.2.1 - Recognize and create patterns; use rules to describe patterns.


081309Page 3 of 198



MN 1.2.1.1 - Create simple patterns using objects, pictures, numbers and rules. Identify possible rules to complete or extend patterns. Patterns may be repeating, growing or shrinking. Calculators can be used to create and explore patterns. Example: Describe rules that can be used to extend the pattern 2, 4, 6, 8, __, __, __ and complete the pattern 33, 43, __, 63, __, 83 or 20, __, __, 17.

Topic 2 - Algebraic Thinking Obj. 66 - Extend a repeating picture pattern

Obj. 67 - Extend a pictorial growth pattern

MN 1.2.2 - Use number sentences involving addition and subtraction basic facts to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

MN 1.2.2.1 - Represent real-world situations involving addition and subtraction basic facts, using objects and number sentences. Example: One way to represent the number of toys that a child has left after giving away 4 of 6 toys is to begin with a stack of 6 connecting cubes and then break off 4 cubes.

MN 1.2.2.2 - Determine if equations involving addition and subtraction are true. Example: Determine if the following number sentences are true or false 7 = 7; 7 = 8 - 1; 5 + 2 = 2 + 5; 4 + 1 = 5 + 2.

MN 1.2.2.3 - Use number sense and models of addition and subtraction, such as objects and number lines, to identify the missing number in an equation such as: 2 + 4 = __; 3 + __ = 7; 5 = __ - 3.


081309Page 4 of 198



MN 1.2.2.4 - Use addition or subtraction basic facts to represent a given problem situation using a number sentence. Example: 5 + 3 = 8 could be used to represent a situation in which 5 red balloons are combined with 3 blue balloons to make 8 total balloons.

MN 1.3 - Geometry & Measurement

MN 1.3.1 - Describe characteristics of basic shapes. Use basic shapes to compose and decompose other objects in various contexts.

MN 1.3.1.1 - Describe characteristics of two- and three-dimensional objects, such as triangles, squares, rectangles, circles, rectangular prisms, cylinders, cones and spheres. Example: Triangles have three sides and cubes have eight vertices (corners).

Topic 3 - Geometry and Measurement

Obj. 82 - Determine the common attributes in a set of geometric shapes

MN 1.3.1.2 - Compose (combine) and decompose (take apart) two- and three-dimensional figures such as triangles, squares, rectangles, circles, rectangular prisms and cylinders. Example 1: Decompose a regular hexagon into 6 equilateral triangles; build prisms by stacking layers of cubes; model an ice cream cone by composing a cone and half of a sphere. Example 2: Use a drawing program to find shapes that can be made with a rectangle and a triangle.MN 1.3.2 - Use basic concepts of measurement in real-world and mathematical situations involving length, time and money.MN 1.3.2.1 - Measure the length of an object in terms of multiple copies of another object. Example: Measure a table by placing paper clips end-to-end and counting.MN 1.3.2.2 - Tell time to the hour and half-hour.


Obj. 76 - Tell time to the hour

Obj. 77 - Tell time to the half hour


081309Page 5 of 198



MN 1.3.2.3 - Identify pennies, nickels and dimes and find the value of a group of these coins, up to one dollar.


Obj. 17 - Determine the value of a collection of like coins

Obj. 18 - Determine the value of a collection of mixed coins


081309Page 6 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 2, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 2.1 - Number & OperationMN 2.1.1 - Compare and represent whole numbers up to 1000, with an emphasis on place value.MN 2.1.1.1 - Read, write and represent whole numbers up to 1000. Representations may include numerals, addition, subtraction, multiplication, words, pictures, tally marks, number lines and manipulatives, such as bundles of sticks and base 10 blocks.

Topic 1 - Number Sense and Operations

Obj. 1 - Read a whole number to 1,000

Obj. 2 - Determine the word form of a whole number to 1,000Obj. 12 - Model a number using hundreds, tens, and ones to 1,000Obj. 13 - Recognize a number from a model of hundreds, tens, and ones to 1,000

MN 2.1.1.2 - Use place value to describe whole numbers between 10 and 1000 in terms of groups of hundreds, tens and ones. Know that 100 is ten groups of 10, and 1000 is ten groups of 100. Example: Writing 853 is a shorter way of writing 8 hundreds + 5 tens + 3 ones.


Obj. 9 - Determine the value of a digit in a 3-digit number

Obj. 10 - Determine which digit is in a specified place in a 3-digit whole numberObj. 14 - Represent a 3-digit number as hundreds, tens, and ones

Obj. 15 - Determine the 3-digit number represented as hundreds, tens, and onesObj. 16 - Recognize equivalent forms of a 3-digit number using hundreds, tens, and ones

MN 2.1.1.3 - Find 10 more or 10 less than any given three-digit number. Find 100 more or 100 less than any given three-digit number. Example: Find the number that is 10 less than 382 and the number that is 100 more than 382.



081309Page 7 of 198



MN 2.1.1.4 - Round numbers up to the nearest 10 and 100 and round numbers down to the nearest 10 and 100. Example: If there are 17 students in the class and granola bars come 10 to a box, you need to buy 20 bars (2 boxes) in order to have enough bars for everyone.MN 2.1.1.5 - Compare and order whole numbers up to 1000.


Obj. 20 - Compare whole numbers to 1,000 using wordsObj. 21 - Compare whole numbers to 1,000 using the symbols <, >, and =

Obj. 22 - Order whole numbers to 1,000 in ascending orderObj. 23 - Order whole numbers to 1,000 in descending order

MN 2.1.1.6 - Use addition and subtraction to create and obtain information from tables, bar graphs and tally charts.

Topic 4 - Data Analysis and Statistics

Obj. 92 - Answer a question using information from a tally chart

Obj. 98 - Answer a question using information from a bar graph with a y-axis scale by 2s

MN 2.1.2 - Demonstrate mastery of addition and subtraction basic facts; add and subtract one- and two-digit numbers in real-world and mathematical problems.MN 2.1.2.1 - Use strategies to generate addition and subtraction facts including making tens, fact families, doubles plus or minus one, counting on, counting back, and the commutative and associative properties. Use the relationship between addition and subtraction to generate basic facts. Example: Use the associative property to make ten when adding 5 + 8 = (3 + 2) + 8 = 3 + (2 + 8) = 3 + 10 = 13.

MN 2.1.2.2 - Demonstrate fluency with basic addition facts and related subtraction facts.MN 2.1.2.3 - Estimate sums and differences up to 100. Example: Know that 23 + 48 is about 70.


Obj. 45 - Estimate the difference of two 2-digit numbers


081309Page 8 of 198



MN 2.1.2.4 - Use mental strategies and algorithms based on knowledge of place value to add and subtract two-digit numbers. Strategies may include decomposition, expanded notation, and partial sums and differences. Example: Using decomposition, 78 + 42, can be thought of as: 78 + 2 + 20 + 20 = 80 + 20 + 20 = 100 + 20 = 120 and using expanded notation, 34 - 21 can be thought of as: 30 + 4 - 20 - 1 = 30 - 20 + 4 - 1 = 10 + 3 = 13.


Obj. 24 - Determine a number pair that totals 100

Obj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 37 - Subtract money values using cents or dollars with one regroupingObj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

MN 2.1.2.5 - Solve real-world and mathematical addition and subtraction problems involving whole numbers with up to 2 digits.


Obj. 24 - Determine a number pair that totals 100

Obj. 29 - Add two 2-digit numbers with regrouping, given a modelObj. 30 - Add money values using cents or dollars with regroupingObj. 31 - Add a 2-digit number to a 1-digit number with regroupingObj. 32 - Add two 2-digit numbers with regroupingObj. 33 - Add three 2-digit numbers with one regrouping, sum less than 100Obj. 37 - Subtract money values using cents or dollars with one regrouping


081309Page 9 of 198



Obj. 38 - Subtract a 1- or 2-digit number from a 2-digit number with one regroupingObj. 42 - WP: Add or subtract up to 2-digit numbers with one regrouping

MN 2.2 - AlgebraMN 2.2.1 - Recognize, create, describe, and use patterns and rules to solve real-world and mathematical problems.MN 2.2.1.1 - Identify, create and describe simple number patterns involving repeated addition or subtraction, skip counting and arrays of objects such as counters or tiles. Use patterns to solve problems in various contexts. Example 1: Skip count by 5 beginning at 3 to create the pattern 3, 8, 13, 18, __. Example 2: Collecting 7 empty milk cartons each day for 5 days will generate the pattern 7, 14, 21, 28, 35, resulting in a total of 35 milk cartons.


Obj. 3 - Complete a skip pattern starting from a multiple of 2, 5, or 10

Obj. 4 - Complete a skip pattern of 2, 5, or 10 starting from any number

Obj. 5 - Count on by 100s from any number

Topic 2 - Algebraic Thinking Obj. 70 - Determine an addition or subtraction number pattern given a ruleObj. 71 - Determine the rule for an addition or subtraction number patternObj. 72 - Extend a number pattern involving additionObj. 73 - Extend a number pattern involving subtraction

MN 2.2.2 - Use number sentences involving addition, subtraction and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.


081309Page 10 of 198



MN 2.2.2.1 - Understand how to interpret number sentences involving addition, subtraction and unknowns represented by letters. Use objects and number lines and create real-world situations to represent number sentences. Example: One way to represent n + 16 = 19 is by comparing a stack of 16 connecting cubes to a stack of 19 connecting cubes; 24 = a + b can be represented by a situation involving a birthday party attended by a total of 24 boys and girls.MN 2.2.2.2 - Use number sentences involving addition, subtraction, and unknowns to represent given problem situations. Use number sense and properties of addition and subtraction to find values for the unknowns that make the number sentences true. Example: How many more players are needed if a soccer team requires 11 players and so far only 6 players have arrived? This situation can be represented by the number sentence 11 - 6 = p or by the number sentence 6 + p = 11.

Topic 2 - Algebraic Thinking Obj. 65 - Determine a missing addend in a number sentence involving 2-digit numbers

Obj. 66 - Determine a missing subtrahend in a number sentence involving 2-digit numbersObj. 67 - Determine equivalent addition expressions involving 2-digit numbersObj. 68 - WP: Determine a missing addend or a missing subtrahend involving 2-digit numbers

Obj. 69 - WP: Use an open sentence to represent a given situation


MN 2.3.1 - Identify, describe and compare basic shapes according to their geometric attributes.


081309Page 11 of 198



MN 2.3.1.1 - Describe, compare, and classify two- and three-dimensional figures according to number and shape of faces, and the number of sides, edges and vertices (corners).

MN 2.3.1.2 - Identify and name basic two- and three-dimensional shapes, such as squares, circles, and triangles, rectangles, trapezoids, hexagons, cubes, rectangular prisms, cones, cylinders and spheres. Example: Use a drawing program to show several ways that a rectangle can be decomposed into exactly three triangles.


Obj. 85 - Identify a parallelogram, a trapezoid, a pentagon, a hexagon, or an octagon

Obj. 86 - Decompose a plane shape composed of three or more simpler shapesObj. 87 - Name a 3-dimensional geometric shape

MN 2.3.2 - Understand length as a measurable attribute; use tools to measure length.MN 2.3.2.1 - Understand the relationship between the size of the unit of measurement and the number of units needed to measure the length of an object. Example: It will take more paper clips than whiteboard markers to measure the length of a table.MN 2.3.2.2 - Demonstrate an understanding of the relationship between length and the numbers on a ruler by using a ruler to measure lengths to the nearest centimeter or inch. Example: Draw a line segment that is 3 inches long.


Obj. 76 - Measure length in inches

Obj. 77 - Measure length in centimeters

MN 2.3.3 - Use time and money in real-world and mathematical situations.MN 2.3.3.1 - Tell time to the quarter-hour and distinguish between a.m. and p.m.


Obj. 78 - Tell time to the quarter hour


081309Page 12 of 198



MN 2.3.3.2 - Identify pennies, nickels, dimes and quarters. Find the value of a group of coins and determine combinations of coins that equal a given amount. Example: 50 cents can be made up of 2 quarters, or 4 dimes and 2 nickels, or many other combinations.


081309Page 13 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 3, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 3.1 - Number & OperationMN 3.1.1 - Compare and represent whole numbers up to 10,000, with an emphasis on place value.MN 3.1.1.1 - Read, write and represent whole numbers up to 10,000. Representations may include numerals, expressions with operations, words, pictures, number lines, and manipulatives such as bundles of sticks and base 10 blocks.


Obj. 1 - Read a 4- or 5-digit whole number

Obj. 2 - Determine the word form of a 4- or 5-digit whole number

MN 3.1.1.2 - Use place value to describe whole numbers between 1000 and 10,000 in terms of groups of thousands, hundreds, tens and ones. Example: Writing 4,873 is a shorter way of writing the following sums: 4 thousands + 8 hundreds + 7 tens + 3 ones; 48 hundreds + 7 tens + 3 ones; 487 tens + 3 ones.


Obj. 3 - Determine the value of a digit in a 4- or 5-digit whole number

Obj. 4 - Determine which digit is in a specified place in a 4- or 5-digit whole numberObj. 5 - Represent a 4-digit whole number as thousands, hundreds, tens, and onesObj. 6 - Determine the 4-digit whole number represented in thousands, hundreds, tens, and ones

Obj. 7 - Represent a 4- or 5-digit whole number in expanded formObj. 8 - Determine the 4- or 5-digit whole number represented in expanded formObj. 9 - Determine an equivalent form of a 4-digit whole number using thousands, hundreds, tens, and ones

MN 3.1.1.3 - Find 1000 more or 1000 less than any given four-digit number. Find 100 more or 100 less than a given four-digit number.



081309Page 14 of 198



MN 3.1.1.4 - Round numbers to the nearest 1000, 100 and 10. Round up and round down to estimate sums and differences. Example 1: 8726 rounded to the nearest 1000 is 9000, rounded to the nearest 100 is 8700, and rounded to the nearest 10 is 8730. Example 2: 473 - 291 is between 400 - 300 and 500 - 200, or between 100 and 300.


Obj. 27 - Round a 2- to 4-digit whole number to its greatest place

Obj. 28 - Estimate a sum or difference of whole numbers to 10,000 by roundingObj. 30 - Estimate a sum or difference of 2- to 4-digit whole numbers using any methodObj. 31 - Estimate a sum of three 2- to 4-digit numbers using any method

Obj. 32 - WP: Estimate a sum or difference of two 3- or 4-digit whole numbers using any method

MN 3.1.1.5 - Compare and order whole numbers up to 10,000.


Obj. 11 - Compare 4- or 5-digit whole numbers using the symbols <, >, and =Obj. 12 - Order 4- or 5-digit whole numbers in ascending or descending order

MN 3.1.2 - Add and subtract multi-digit whole numbers; represent multiplication and division in various ways; solve real-world and mathematical problems using arithmetic.MN 3.1.2.1 - Add and subtract multi-digit numbers, using efficient and generalizable procedures based on knowledge of place value, including standard algorithms.


Obj. 13 - Add 3- and 4-digit numbers with regrouping

Obj. 14 - Add three 2- to 3-digit whole numbersObj. 15 - Subtract 3- and 4-digit numbers with regroupingObj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping


081309Page 15 of 198



MN 3.1.2.2 - Use addition and subtraction to solve real-world and mathematical problems involving whole numbers. Assess the reasonableness of results based on the context. Use various strategies, including the use of a calculator and the relationship between addition and subtraction, to check for accuracy. Example: The calculation 117 - 83 = 34 can be checked by adding 83 and 34.


Obj. 10 - Determine the result of changing a digit in a 4- or 5-digit whole number

Obj. 16 - WP: Add or subtract 3- and 4-digit whole numbers with regrouping

Topic 2 - Algebraic Thinking Obj. 56 - Determine the missing addend in a number sentence involving 3-digit numbersObj. 57 - Determine the missing subtrahend in a number sentence involving 3-digit numbers

MN 3.1.2.3 - Represent multiplication facts by using a variety of approaches, such as repeated addition, equal-sized groups, arrays, area models, equal jumps on a number line and skip counting. Represent division facts by using a variety of approaches, such as repeated subtraction, equal sharing and forming equal groups. Recognize the relationship between multiplication and division.


Obj. 33 - Use a multiplication sentence to represent an area or an array model

Obj. 34 - Use a division sentence to represent objects divided into equal groups

MN 3.1.2.4 - Solve real-world and mathematical problems involving multiplication and division, including both "how many in each group" and "how many groups" division problems. Example 1: You have 27 people and 9 tables. If each table seats the same number of people, how many people will you put at each table? Example 2: If you have 27 people and tables that will hold 9 people, how many tables will you need?


Obj. 35 - Know basic multiplication facts to 10 x 10

Obj. 36 - Know basic multiplication facts for 11 and 12


081309Page 16 of 198



Obj. 37 - Know basic division facts to 100 ÷ 10Obj. 38 - Know basic division facts for 11 and 12Obj. 39 - WP: Multiply using basic facts to 10 x 10Obj. 40 - WP: Divide using basic facts to 100 ÷ 10Obj. 41 - Complete a multiplication and division fact family

MN 3.1.2.5 - Use strategies and algorithms based on knowledge of place value and properties of addition and multiplication to multiply a two- or three-digit number by a one-digit number. Strategies may include mental strategies, partial products, the standard algorithm, and the commutative, associative, and distributive properties. Example: 9 × 26 = 9 × (20 + 6) = 9 × 20 + 9 × 6 = 180 + 54 = 234.


Obj. 42 - Multiply a 1-digit whole number by a multiple of 10 to 100

Obj. 43 - Multiply a 2-digit whole number by a 1-digit number

MN 3.1.3 - Understand meanings and uses of fractions in real-world and mathematical situations.MN 3.1.3.1 - Read and write fractions with words and symbols. Recognize that fractions can be used to represent parts of a whole, parts of a set, points on a number line, or distances on a number line. Example: Parts of a shape (3/4 of a pie), parts of a set (3 out of 4 people), and measurements (3/4 of an inch).


Obj. 44 - Determine a pictorial model of a fraction of a whole

Obj. 45 - Determine a pictorial model of a fraction of a set of objects

Obj. 46 - Identify a fraction represented by a point on a number lineObj. 47 - Locate a fraction on a number lineObj. 55 - Estimate fractions of a whole


081309Page 17 of 198



MN 3.1.3.2 - Understand that the size of a fractional part is relative to the size of the whole. Example: One-half of a small pizza is smaller than one-half of a large pizza, but both represent one-half.


Obj. 53 - WP: Compare equal unit fractions of different-sized wholes

MN 3.1.3.3 - Order and compare unit fractions and fractions with like denominators by using models and an understanding of the concept of numerator and denominator.


Obj. 48 - Compare fractions using models

MN 3.2 - AlgebraMN 3.2.1 - Use single-operation input-output rules to represent patterns and relationships and to solve real-world and mathematical problems.

MN 3.2.1.1 - Create, describe, and apply single-operation input-output rules involving addition, subtraction and multiplication to solve problems in various contexts. Example: Describe the relationship between number of chairs and number of legs by the rule that the number of legs is four times the number of chairs.

Topic 2 - Algebraic Thinking Obj. 65 - Determine a rule for a table of related number pairs

Obj. 66 - WP: Find the missing number in a table of paired values

MN 3.2.2 - Use number sentences involving multiplication and division basic facts and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.MN 3.2.2.1 - Understand how to interpret number sentences involving multiplication and division basic facts and unknowns. Create real-world situations to represent number sentences. Example: The number sentence 8 × m = 24 could be represented by the question "How much did each ticket to a play cost if 8 tickets totaled $24?".


081309Page 18 of 198



MN 3.2.2.2 - Use multiplication and division basic facts to represent a given problem situation using a number sentence. Use number sense and multiplication and division basic facts to find values for the unknowns that make the number sentences true. Example 1: Find values of the unknowns that make each number sentence true 6 = p ÷ 9; 24 = a × b; 5 × 8 = 4 × t. Example 2: How many math teams are competing if there is a total of 45 students with 5 students on each team? This situation can be represented by 5 × n = 45 or 45/5 = n or 45/n = 5.

Topic 2 - Algebraic Thinking Obj. 58 - Determine the missing multiplicand in a number sentence involving basic facts

Obj. 59 - Determine the missing dividend or divisor in a number sentence involving basic factsObj. 60 - Recognize equivalent multiplication or division expressions involving basic factsObj. 63 - WP: Determine a multiplication or division sentence for a given situation


MN 3.3.1 - Use geometric attributes to describe and create shapes in various contexts.MN 3.3.1.1 - Identify parallel and perpendicular lines in various contexts, and use them to describe and create geometric shapes, such as right triangles, rectangles, parallelograms and trapezoids.


Obj. 92 - Identify parallel, perpendicular, and intersecting lines

MN 3.3.1.2 - Sketch polygons with a given number of sides or vertices (corners), such as pentagons, hexagons and octagons.MN 3.3.2 - Understand perimeter as a measurable attribute of real-world and mathematical objects. Use various tools to measure perimeter.

MN 3.3.2.1 - Use half units when measuring distances. Example: Measure a person's height to the nearest half inch.


081309Page 19 of 198



MN 3.3.2.2 - Find the perimeter of a polygon by adding the lengths of the sides.


Obj. 86 - Determine a method for finding the perimeter of a shape given the side lengthsObj. 88 - WP: Determine the perimeter of a shape given a model showing all side lengths

MN 3.3.2.3 - Measure distances around objects. Example: Measure the distance around a classroom, or measure a person's wrist size.MN 3.3.3 - Use time, money and temperature to solve real-world and mathematical problems.MN 3.3.3.1 - Tell time to the minute, using digital and analog clocks. Determine elapsed time to the minute. Example: Your trip began at 9:50 a.m. and ended at 3:10 p.m. How long were you traveling?


Obj. 74 - Tell time to the minute

Obj. 76 - Calculate elapsed time within an hour, given two clocks, without regroupingObj. 77 - Calculate elapsed time within an hour, given two clocks, with regroupingObj. 78 - WP: Calculate elapsed time within an hour given two clocks

Obj. 79 - WP: Calculate elapsed time within an hourObj. 80 - WP: Determine the end time given the start time and the elapsed time within an hourObj. 81 - WP: Determine the start time given the end time on a clock and the elapsed time within an hour

Obj. 82 - WP: Determine the start time given the end time and the elapsed time within an hour

MN 3.3.3.2 - Know relationships among units of time. Example: Know the number of minutes in an hour, days in a week and months in a year.


Obj. 75 - Convert hours to minutes or minutes to seconds


081309Page 20 of 198



MN 3.3.3.3 - Make change up to one dollar in several different ways, including with as few coins as possible. Example: A chocolate bar costs $1.84. You pay for it with $2. Give two possible ways to make change.MN 3.3.3.4 - Use an analog thermometer to determine temperature to the nearest degree in Fahrenheit and Celsius. Example: Read the temperature in a room with a thermometer that has both Fahrenheit and Celsius scales. Use the thermometer to compare Celsius and Fahrenheit readings.


Obj. 84 - Read a thermometer in degrees Fahrenheit or Celsius

MN 3.4 - Data AnalysisMN 3.4.1 - Collect, organize, display, and interpret data. Use labels and a variety of scales and units in displays.

MN 3.4.1.1 - Collect, display and interpret data using frequency tables, bar graphs, picture graphs and number line plots having a variety of scales. Use appropriate titles, labels and units.

Topic 4 - Data Analysis, Statistics, and Probability

Obj. 105 - Use a bar graph with a scale interval of 5 or 10 to represent data

Obj. 106 - Answer a question using information from a bar graph with a scale interval of 5 or 10Obj. 107 - Read a line plotObj. 108 - Use a line plot to represent dataObj. 109 - Answer a question using information from a line plotObj. 110 - Use a frequency table to represent dataObj. 111 - Answer a question using information from a frequency table


081309Page 21 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 4, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 4.1 - Number & OperationMN 4.1.1 - Compare and represent whole numbers up to 100,000, with an emphasis on place value.MN 4.1.1.1 - Read, write and represent whole numbers up to 100,000. Representations include numerals, words and expressions with operations.


Obj. 2 - Determine the word form of a 6-digit whole number

Obj. 5 - Determine the whole number represented in expanded form written in powers of tenObj. 6 - Represent a 6-digit whole number in expanded form using powers of tenObj. 7 - Convert between proper expanded form and improper expanded form up to a 5-digit whole numberObj. 8 - Convert between standard form and improper expanded form up to a 5-digit whole number

MN 4.1.1.2 - Find 10,000 more and 10,000 less than a given five-digit number. Find 1,000 more and 1,000 less than a given five-digit number.

MN 4.1.1.3 - Use an understanding of place value to multiply a number by 10, 100 and 1000.MN 4.1.2 - Demonstrate mastery of multiplication and division basic facts; multiply multi-digit numbers; solve real-world and mathematical problems using arithmetic.MN 4.1.2.1 - Demonstrate fluency with multiplication and division facts.

MN 4.1.2.2 - Multiply multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms.


Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000

Obj. 21 - Apply the distributive property to the multiplication of a 2-digit number by a 1- or 2-digit number

Obj. 22 - Apply the distributive property to multiply a multi-digit number by a 1-digit number



081309Page 22 of 198



Obj. 23 - Multiply a 3- or 4-digit whole number by a 1-digit whole number

Obj. 24 - Multiply a 2-digit whole number by a 2-digit whole numberObj. 25 - Multiply a 3-digit whole number by a 2-digit whole numberObj. 26 - Multiply three 1- and 2-digit whole numbersObj. 27 - WP: Multiply a multi-digit whole number by a 1-digit whole numberObj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number

Obj. 29 - WP: Multiply a 3-digit whole number by a 2-digit whole number

MN 4.1.2.3 - Estimate products and quotients of multi-digit whole numbers by using rounding, benchmarks and place value to assess the reasonableness of results in calculations. Example: 53 × 38 is between 50 × 30 and 60 × 40, or between 1500 and 2400, and 411/73 is between 400/80 and 500/70, or between 5 and 7.


Obj. 30 - Estimate a product of whole numbers by rounding

Obj. 31 - Estimate a product of whole numbers using any methodObj. 32 - WP: Estimate a product of two whole numbers using any method

MN 4.1.2.4 - Solve multi-step real-world and mathematical problems requiring the use of addition, subtraction and multiplication of multi-digit whole numbers. Use various strategies including the relationships between the operations and a calculator to check for accuracy.


Obj. 9 - Add up to 4-digit whole numbers in expanded form

Obj. 10 - Add a 5-digit or greater whole number and a 3-digit or greater whole numberObj. 11 - Add three multi-digit whole numbersObj. 12 - Subtract a smaller number from a 3- or 4-digit whole number in expanded form


081309Page 23 of 198



Obj. 13 - Subtract a 3-digit or greater whole number from a 5-digit or greater whole numberObj. 14 - WP: Add a 5-digit or greater whole number and a 3-digit or greater whole numberObj. 15 - WP: Add three multi-digit whole numbersObj. 16 - WP: Subtract a 3-digit or greater whole number from a 5-digit or greater whole numberObj. 19 - WP: Solve a 2-step problem involving addition and/or subtraction of multi-digit whole numbers

Obj. 20 - Multiply a 1- or 2-digit whole number by a multiple of 10, 100, or 1,000Obj. 21 - Apply the distributive property to the multiplication of a 2-digit number by a 1- or 2-digit number

Obj. 24 - Multiply a 2-digit whole number by a 2-digit whole numberObj. 25 - Multiply a 3-digit whole number by a 2-digit whole numberObj. 28 - WP: Multiply a 2-digit whole number by a 2-digit whole number

Obj. 29 - WP: Multiply a 3-digit whole number by a 2-digit whole number

Obj. 42 - WP: Solve a 2-step whole number problem using more than 1 operation

MN 4.1.2.5 - Use strategies and algorithms based on knowledge of place value and properties of operations to divide multi-digit whole numbers by one- or two-digit numbers. Strategies may include mental strategies, partial quotients, the commutative, associative, and distributive properties and repeated subtraction. Example: A group of 324 students are going to a museum in 6 buses. If each bus has the same number of students, how many students will be on each bus?


Obj. 33 - Divide a multi-digit whole number by 10 or 100 with no remainder


081309Page 24 of 198



Obj. 34 - Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 35 - Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotientObj. 36 - Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 37 - Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotientObj. 38 - WP: Divide a 2-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 39 - WP: Divide a 3-digit whole number by a 1-digit whole number with no remainder in the quotient

Obj. 40 - WP: Divide a 2-digit whole number by a 1-digit whole number with a remainder in the quotient

Obj. 41 - WP: Divide a 3-digit whole number by a 1-digit whole number with a remainder in the quotient

MN 4.1.3 - Represent and compare fractions and decimals in real-world and mathematical situations; use place value to understand how decimals represent quantities.MN 4.1.3.1 - Represent equivalent fractions using fraction models such as parts of a set, fraction circles, fraction strips, number lines and other manipulatives. Use the models to determine equivalent fractions.

MN 4.1.3.2 - Locate fractions on a number line. Use models to order and compare whole numbers and fractions, including mixed numbers and improper fractions. Example: Locate 5/3 and 1 3/4 on a number line and give a comparison statement about these two fractions, such as 5/3 " is less than 1 3/4.".


Obj. 43 - Identify a mixed number represented by a model


081309Page 25 of 198



Obj. 44 - Identify a mixed number represented by a point on a number lineObj. 45 - Locate a mixed number on a number lineObj. 47 - Identify an improper fraction represented by a model of a mixed numberObj. 48 - Identify an improper fraction represented by a point on a number lineObj. 49 - Locate an improper fraction on a number lineObj. 52 - Compare fractions on a number lineObj. 53 - Order fractions on a number line

MN 4.1.3.3 - Use fraction models to add and subtract fractions with like denominators in real-world and mathematical situations. Develop a rule for addition and subtraction of fractions with like denominators.


Obj. 54 - Add fractions with like denominators no greater than 10 using models

Obj. 58 - Subtract fractions with like denominators no greater than 10 using models

MN 4.1.3.4 - Read and write decimals with words and symbols; use place value to describe decimals in terms of groups of thousands, hundreds, tens, ones, tenths, hundredths and thousandths. Example: Writing 362.45 is a shorter way of writing the sum: 3 hundreds + 6 tens + 2 ones + 4 tenths + 5 hundredths, which can also be written as: three hundred sixty-two and forty-five hundredths.


Obj. 62 - Read a decimal number through the hundredths place

Obj. 63 - Determine the word form of a decimal number through the hundredths placeObj. 64 - Determine the decimal number from a pictorial model of tenths or hundredthsObj. 65 - Identify a pictorial model of tenths or hundredths of a decimal number


081309Page 26 of 198



MN 4.1.3.5 - Compare and order decimals and whole numbers using place value, a number line and models such as grids and base 10 blocks.MN 4.1.3.6 - Locate the relative position of fractions, mixed numbers and decimals on a number line.


Obj. 44 - Identify a mixed number represented by a point on a number line

Obj. 45 - Locate a mixed number on a number lineObj. 48 - Identify an improper fraction represented by a point on a number lineObj. 49 - Locate an improper fraction on a number lineObj. 66 - Identify a decimal number to tenths represented by a point on a number lineObj. 67 - Locate a decimal number to tenths on a number line

MN 4.1.3.7 - Read and write tenths and hundredths in decimal and fraction notations using words and symbols; know the fraction and decimal equivalents for halves and fourths. Example: 1/2 = 0.5 = 0.50 and 7/4 = 1 3/4 = 1.75, which can also be written as one and three-fourths or one and seventy-five hundredths.


Obj. 68 - Determine the decimal number equivalent to a fraction with a denominator of 10 or 100

Obj. 69 - Determine a fraction equivalent to a decimal, using a denominator of 10 or 100Obj. 70 - Determine the decimal number equivalent to a fraction modelObj. 71 - Determine the fraction equivalent to a decimal number model

MN 4.1.3.8 - Round decimal values to the nearest tenth. Example: The number 0.36 rounded to the nearest tenth is 0.4.


Obj. 80 - Round a decimal number to a specified place through hundredths

MN 4.2 - AlgebraMN 4.2.1 - Use input-output rules, tables and charts to represent patterns and relationships and to solve real-world and mathematical problems.


081309Page 27 of 198



MN 4.2.1.1 - Create and use input-output rules involving addition, subtraction, multiplication and division to solve problems in various contexts. Record the inputs and outputs in a chart or table. Example 1: If the rule is "multiply by 3 and add 4," record the outputs for given inputs in a table. Example 2: A student is given these three arrangements of dots: Identify a pattern that is consistent with these figures, create an input-output rule that describes the pattern, and use the rule to find the number of dots in the 10th figure.

Topic 2 - Algebra Obj. 90 - Generate a table of paired numbers based on a rule

Obj. 91 - Determine a rule that relates two variablesObj. 92 - Extend a number pattern in a table of related pairs

MN 4.2.2 - Use number sentences involving multiplication, division and unknowns to represent and solve real-world and mathematical problems; create real-world situations corresponding to number sentences.

MN 4.2.2.1 - Understand how to interpret number sentences involving multiplication, division and unknowns. Use real-world situations involving division to represent number sentences. Example: The number sentence a × b = 60 can be represented by the situation in which chairs are being arranged in equal rows and the total number of chairs is 60.


081309Page 28 of 198



MN 4.2.2.2 - Use multiplication, division and unknowns to represent a given problem situation using a number sentence. Use number sense, properties of multiplication, and the relationship between multiplication and division to find values for the unknowns that make the number sentences true. Example 1: If $84 is to be shared equally among a group of children, the amount of money each child receives can be determined using the number sentence 84 ÷ n = d. Example 2: Find values of the unknowns or variables that make each number sentence true: 12 × m = 36; s = 256 ÷ t.


MN 4.3.1 - Name, describe, classify and sketch polygons.MN 4.3.1.1 - Describe, classify and sketch triangles, including equilateral, right, obtuse and acute triangles. Recognize triangles in various contexts.


Obj. 125 - Classify a triangle by its sides

MN 4.3.1.2 - Describe, classify and draw quadrilaterals, including squares, rectangles, trapezoids, rhombuses, parallelograms and kites. Recognize quadrilaterals in various contexts.


Obj. 126 - Classify a quadrilateral

MN 4.3.2 - Understand angle and area as measurable attributes of real-world and mathematical objects. Use various tools to measure angles and areas.MN 4.3.2.1 - Measure angles in geometric figures and real-world objects with a protractor or angle ruler.MN 4.3.2.2 - Compare angles according to size. Classify angles as acute, right and obtuse. Example: Compare different hockey sticks according to the angle between the blade and the shaft.


Obj. 121 - Classify an angle given a picture

Obj. 122 - Classify an angle given its measure


081309Page 29 of 198



MN 4.3.2.3 - Understand that the area of a two-dimensional figure can be found by counting the total number of same size square units that cover a shape without gaps or overlaps. Justify why length and width are multiplied to find the area of a rectangle by breaking the rectangle into one unit by one unit squares and viewing these as grouped into rows and columns. Example: How many copies of a square sheet of paper are needed to cover the classroom door? Measure the length and width of the door to the nearest inch and compute the area of the door.


Obj. 114 - Determine the area of a polygon on a grid

Obj. 119 - Estimate the area of an irregular polygon on a grid

MN 4.3.2.4 - Find the areas of geometric figures and real-world objects that can be divided into rectangular shapes. Use square units to label area measurements.


Obj. 115 - Determine the area of a rectangle given a picture showing the length and width

Obj. 116 - Determine the area of a rectangle given the length and width

Obj. 117 - WP: Determine the area of a rectangle

MN 4.3.3 - Use translations, reflections and rotations to establish congruency and understand symmetries.MN 4.3.3.1 - Apply translations (slides) to figures.


Obj. 130 - Determine the result of a flip, a turn, or a slide

MN 4.3.3.2 - Apply reflections (flips) to figures by reflecting over vertical or horizontal lines and relate reflections to lines of symmetry.


Obj. 130 - Determine the result of a flip, a turn, or a slide

MN 4.3.3.3 - Apply rotations (turns) of 90° clockwise or counterclockwise.


Obj. 131 - Determine the result of a quarter or a half turn

MN 4.3.3.4 - Recognize that translations, reflections and rotations preserve congruency and use them to show that two figures are congruent.MN 4.4 - Data Analysis


081309Page 30 of 198



MN 4.4.1 - Collect, organize, display and interpret data, including data collected over a period of time and data represented by fractions and decimals.

MN 4.4.1.1 - Use tables, bar graphs, timelines and Venn diagrams to display data sets. The data may include fractions or decimals. Understand that spreadsheet tables and graphs can be used to display data.


081309Page 31 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 5, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 5.1 - Number & OperationMN 5.1.1 - Divide multi-digit numbers; solve real-world and mathematical problems using arithmetic.MN 5.1.1.1 - Divide multi-digit numbers, using efficient and generalizable procedures, based on knowledge of place value, including standard algorithms. Recognize that quotients can be represented in a variety of ways, including a whole number with a remainder, a fraction or mixed number, or a decimal. Example: Dividing 153 by 7 can be used to convert the improper fraction 153/7 to the mixed number 21 6/7.


Obj. 13 - Divide a multi-digit whole number by multiples of 100 or 1,000

Obj. 14 - Divide a multi-digit whole number by a 1-digit number with no remainder and at least one zero in the quotientObj. 15 - Divide a multi-digit whole number by a 1-digit number with a remainder and at least one zero in the quotientObj. 17 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimalObj. 18 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotientObj. 19 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotientObj. 20 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotientObj. 21 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientObj. 22 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed numberObj. 23 - WP: Divide a whole number, with no remainder



081309Page 32 of 198



Obj. 24 - WP: Divide a whole number and interpret the remainder

MN 5.1.1.2 - Consider the context in which a problem is situated to select the most useful form of the quotient for the solution and use the context to interpret the quotient appropriately. Example: If 77 amusement ride tickets are to be distributed evenly among 4 children, each child will receive 19 tickets, and there will be one left over. If $77 is to be distributed evenly among 4 children, each will receive $19.25, with nothing left over.


Obj. 16 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed number

MN 5.1.1.3 - Estimate solutions to arithmetic problems in order to assess the reasonableness of results of calculations.


Obj. 27 - Estimate a quotient using compatible numbers

Obj. 28 - Estimate a quotient using any methodObj. 29 - WP: Estimate a quotient using any methodObj. 56 - Estimate a fraction sum using benchmark numbers 0, 1/2, and 1Obj. 57 - Estimate a fraction difference using benchmark numbers 0, 1/2, and 1Obj. 58 - WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1Obj. 83 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 84 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 85 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any method


081309Page 33 of 198



MN 5.1.1.4 - Solve real-world and mathematical problems requiring addition, subtraction, multiplication and division of multi-digit whole numbers. Use various strategies, including the use of a calculator and the inverse relationships between operations, to check for accuracy. Example: The calculation 117 ÷ 9 = 13 can be checked by multiplying 9 and 13.


Obj. 11 - Multiply a 3- or 4-digit whole number by a 3-digit whole number

Obj. 12 - WP: Multiply a 3- or 4-digit whole number by a 3-digit whole numberObj. 13 - Divide a multi-digit whole number by multiples of 100 or 1,000

Obj. 14 - Divide a multi-digit whole number by a 1-digit number with no remainder and at least one zero in the quotientObj. 15 - Divide a multi-digit whole number by a 1-digit number with a remainder and at least one zero in the quotientObj. 16 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a mixed numberObj. 17 - Divide a multi-digit whole number by a 1-digit number and express the quotient as a decimalObj. 18 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and no zeros in the quotientObj. 19 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and no zeros in the quotientObj. 20 - Divide a multi-digit whole number by a 2-digit whole number, with no remainder and at least one zero in the quotientObj. 21 - Divide a multi-digit whole number by a 2-digit whole number, with a remainder and at least one zero in the quotientObj. 22 - Divide a multi-digit whole number by a 2-digit whole number and express the quotient as a mixed number


081309Page 34 of 198



Obj. 23 - WP: Divide a whole number, with no remainderObj. 24 - WP: Divide a whole number and interpret the remainderObj. 25 - WP: Solve a 2-step problem involving whole numbers

MN 5.1.2 - Read, write, represent and compare fractions and decimals; recognize and write equivalent fractions; convert between fractions and decimals; use fractions and decimals in real-world and mathematical situations.MN 5.1.2.1 - Read and write decimals using place value to describe decimals in terms of groups from millionths to millions. Example: Possible names for the number 0.37 are: 37 hundredths; 3 tenths + 7 hundredths; possible names for the number 1.5 are: one and five tenths; 15 tenths.


Obj. 69 - Determine the value of a digit in a decimal number to thousandths

Obj. 70 - Determine a decimal number represented in expanded formObj. 71 - Represent a decimal number in expanded form

MN 5.1.2.2 - Find 0.1 more than a number and 0.1 less than a number. Find 0.01 more than a number and 0.01 less than a number. Find 0.001 more than a number and 0.001 less than a number.

MN 5.1.2.3 - Order fractions and decimals, including mixed numbers and improper fractions, and locate on a number line. Example 1: Which is larger 1.25 or 6/5 ? Example 2: In order to work properly, a part must fit through a 0.24 inch wide space. If a part is 1/4 inch wide, will it fit?


Obj. 33 - Compare fractions with unlike denominators

Obj. 34 - Order fractions with unlike denominators in ascending or descending order


081309Page 35 of 198



MN 5.1.2.4 - Recognize and generate equivalent decimals, fractions, mixed numbers and improper fractions in various contexts. Example: When comparing 1.5 and 19/12 , note that 1.5 = 1 1/2 = 1 6/12 = 18/12, so 1.5 < 19/12.


Obj. 31 - Determine equivalent fractions not in simplest form

Obj. 32 - Determine the simplest form of a fractionObj. 47 - Convert a mixed number to an improper fractionObj. 48 - Convert an improper fraction to a mixed numberObj. 90 - Convert a decimal number through thousandths to a simplified fractionObj. 91 - Convert a fraction with a denominator that is a factor of 10, 100, or 1,000 to decimal notation

MN 5.1.2.5 - Round numbers to the nearest 0.1, 0.01 and 0.001. Example: Fifth grade students used a calculator to find the mean of the monthly allowance in their class. The calculator display shows 25.80645161. Round this number to the nearest cent.


Obj. 82 - Round a decimal number to a specified decimal place to thousandths

MN 5.1.3 - Add and subtract fractions, mixed numbers and decimals to solve real-world and mathematical problems.MN 5.1.3.1 - Add and subtract decimals and fractions, using efficient and generalizable procedures, including standard algorithms.


Obj. 35 - Add fractions with like denominators greater than 10 and simplify the sum

Obj. 37 - Add fractions with unlike denominators and do not simplify the sumObj. 38 - Add fractions with unlike denominators that have factors in common and simplify the sumObj. 39 - Add fractions with unlike denominators that have no factors in commonObj. 40 - Subtract fractions with like denominators greater than 10 and simplify the differenceObj. 42 - Subtract fractions with unlike denominators and do not simplify the difference


081309Page 36 of 198



Obj. 43 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceObj. 44 - Subtract fractions with unlike denominators that have no factors in commonObj. 45 - WP: Add or subtract fractions with like denominators and simplify the sum or differenceObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 49 - Add mixed numbers with like denominators and simplify the sumObj. 50 - Add mixed numbers with unlike denominators and simplify the sumObj. 51 - Subtract mixed numbers with like denominators and simplify the differenceObj. 52 - Subtract mixed numbers with unlike denominators and simplify the differenceObj. 53 - WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference

Obj. 54 - WP: Add or subtract mixed numbers with unlike denominators that have no factors in common

Obj. 75 - Add two decimal numbers of differing places to thousandths

Obj. 76 - Add three or more decimal numbersObj. 77 - Add decimal numbers and whole numbersObj. 78 - Subtract two decimal numbers of differing places to thousandthsObj. 79 - Subtract a decimal number from a whole number or a whole number from a decimal number

Obj. 80 - WP: Add or subtract decimal numbers through thousandths


081309Page 37 of 198



Obj. 81 - WP: Add or subtract a decimal number through thousandths and a whole number

MN 5.1.3.2 - Model addition and subtraction of fractions and decimals using a variety of representations. Example: Represent 2/3 + 1/4 and 2/3 - 1/4 by drawing a rectangle divided into 4 columns and 3 rows and shading the appropriate parts or by using fraction circles or bars.


Obj. 36 - Add fractions with unlike denominators using a model and do not simplify the sum

Obj. 41 - Subtract fractions with unlike denominators using a model and do not simplify the difference

MN 5.1.3.3 - Estimate sums and differences of decimals and fractions to assess the reasonableness of results in calculations. Example: Recognize that 12 2/3 - 3 3/4 is between 8 and 9 (since 2/5 < 3/4).


Obj. 56 - Estimate a fraction sum using benchmark numbers 0, 1/2, and 1

Obj. 57 - Estimate a fraction difference using benchmark numbers 0, 1/2, and 1Obj. 58 - WP: Estimate a fraction sum or difference using benchmark numbers 0, 1/2, and 1Obj. 83 - Estimate the sum of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 84 - Estimate the difference of two decimal numbers through thousandths and less than 1 by rounding to a specified placeObj. 85 - WP: Estimate the sum or difference of two decimal numbers through thousandths using any method

MN 5.1.3.4 - Solve real-world and mathematical problems requiring addition and subtraction of decimals, fractions and mixed numbers, including those involving measurement, geometry and data. Example: Calculate the perimeter of the soccer field when the length is 109.7 meters and the width is 73.1 meters.


Obj. 35 - Add fractions with like denominators greater than 10 and simplify the sum


081309Page 38 of 198



Obj. 37 - Add fractions with unlike denominators and do not simplify the sumObj. 38 - Add fractions with unlike denominators that have factors in common and simplify the sumObj. 39 - Add fractions with unlike denominators that have no factors in commonObj. 40 - Subtract fractions with like denominators greater than 10 and simplify the differenceObj. 42 - Subtract fractions with unlike denominators and do not simplify the differenceObj. 43 - Subtract fractions with unlike denominators that have factors in common and simplify the differenceObj. 44 - Subtract fractions with unlike denominators that have no factors in commonObj. 45 - WP: Add or subtract fractions with like denominators and simplify the sum or differenceObj. 46 - WP: Add or subtract fractions with unlike denominators that have no factors in commonObj. 49 - Add mixed numbers with like denominators and simplify the sumObj. 50 - Add mixed numbers with unlike denominators and simplify the sumObj. 51 - Subtract mixed numbers with like denominators and simplify the differenceObj. 52 - Subtract mixed numbers with unlike denominators and simplify the differenceObj. 53 - WP: Add or subtract mixed numbers with like denominators and simplify the sum or difference

Obj. 54 - WP: Add or subtract mixed numbers with unlike denominators that have no factors in common

Obj. 75 - Add two decimal numbers of differing places to thousandths


081309Page 39 of 198



Obj. 76 - Add three or more decimal numbersObj. 77 - Add decimal numbers and whole numbersObj. 78 - Subtract two decimal numbers of differing places to thousandthsObj. 79 - Subtract a decimal number from a whole number or a whole number from a decimal number

Obj. 80 - WP: Add or subtract decimal numbers through thousandthsObj. 81 - WP: Add or subtract a decimal number through thousandths and a whole number

MN 5.2 - AlgebraMN 5.2.1 - Recognize and represent patterns of change; use patterns, tables, graphs and rules to solve real-world and mathematical problems.

MN 5.2.1.1 - Create and use rules, tables, spreadsheets and graphs to describe patterns of change and solve problems. Example: An end-of-the-year party for 5th grade costs $100 to rent the room and $4.50 for each student. Know how to use a spreadsheet to create an input-output table that records the total cost of the party for any number of students between 90 and 150.

Topic 2 - Algebra Obj. 105 - WP: Extend a pattern to solve a problem

Obj. 106 - Generate a table of paired numbers based on a variable expression with one operation

Obj. 107 - Generate a table of paired numbers based on a variable expression with two operations

Obj. 108 - Determine the variable expression with one operation for a table of paired numbersObj. 109 - WP: Generate a table of paired numbers based on a variable expression with one operation


081309Page 40 of 198



Obj. 110 - WP: Determine the variable expression with one operation for a table of paired numbersObj. 111 - Use a first quadrant graph to represent the values from a table generated in context

MN 5.2.1.2 - Use a rule or table to represent ordered pairs of positive integers and graph these ordered pairs on a coordinate system.

Topic 2 - Algebra Obj. 111 - Use a first quadrant graph to represent the values from a table generated in context


Obj. 151 - Determine the ordered pair of a point in the first quadrant

MN 5.2.2 - Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving whole numbers.MN 5.2.2.1 - Apply the commutative, associative and distributive properties and order of operations to generate equivalent numerical expressions and to solve problems involving whole numbers. Example: Purchase 5 pencils at 19 cents and 7 erasers at 19 cents. The numerical expression is 5 × 19 + 7 × 19 which is the same as (5 + 7) × 19.

MN 5.2.3 - Understand and interpret equations and inequalities involving variables and whole numbers, and use them to represent and solve real-world and mathematical problems.

MN 5.2.3.1 - Determine whether an equation or inequality involving a variable is true or false for a given value of the variable. Example: Determine whether the inequality 1.5 + x < 10 is true for x = 2.8, x = 8.1, or x = 9.2.


081309Page 41 of 198



MN 5.2.3.2 - Represent real-world situations using equations and inequalities involving variables. Create real-world situations corresponding to equations and inequalities. Example: 250 - 27 × a = b can be used to represent the number of sheets of paper remaining from a packet of 250 when each student in a class of 27 is given a certain number of sheets.

Topic 2 - Algebra Obj. 98 - Use a variable expression with one operation to represent a verbal expression

Obj. 99 - Use a verbal expression to represent a variable expression with one operationObj. 100 - WP: Use a variable expression with one operation to represent a situation

MN 5.2.3.3 - Evaluate expressions and solve equations involving variables when values for the variables are given. Example: Using the formula, A= lw, determine the area when the length is 5, and the width 6, and find the length when the area is 24 and the width is 4.

Topic 2 - Algebra Obj. 101 - Evaluate a 1-variable expression, involving one operation, using whole number substitution

Obj. 102 - Evaluate a 2-variable expression, involving one operation, using whole number substitution

Obj. 103 - WP: Evaluate a 1-variable expression with one operation using a whole number value

Obj. 104 - WP: Evaluate a 2-variable expression with one operation using whole number values


MN 5.3.1 - Describe, classify, and draw representations of three-dimensional figures.MN 5.3.1.1 - Describe and classify three-dimensional figures including cubes, prisms and pyramids by the number of edges, faces or vertices as well as the types of faces.


Obj. 144 - Determine the number of faces, edges, and vertices in a 3-dimensional shape


081309Page 42 of 198



MN 5.3.1.2 - Recognize and draw a net for a three-dimensional figure.


Obj. 142 - Determine the 3-dimensional shape that can be formed from a netObj. 143 - Determine a net of a 3-dimensional shape

MN 5.3.2 - Determine the area of triangles and quadrilaterals; determine the surface area and volume of rectangular prisms in various contexts.MN 5.3.2.1 - Develop and use formulas to determine the area of triangles, parallelograms and figures that can be decomposed into triangles.


Obj. 126 - Use a formula to determine the area of a triangle

Obj. 127 - Determine the area of a complex figure divided into basic shapesObj. 128 - Use a formula to determine the area of a parallelogram

Obj. 129 - WP: Determine the area of a triangleObj. 130 - WP: Determine the area of a square or rectangle

MN 5.3.2.2 - Determine the surface area of a rectangular prism by applying various strategies. Example: Use a net or decompose the surface into rectangles.


Obj. 138 - Determine the surface area of a cube or a rectangular prism given a net

Obj. 139 - Determine the surface area of a rectangular prismObj. 140 - WP: Find the surface area of a rectangular prism

MN 5.3.2.3 - Understand that the volume of a three-dimensional figure can be found by counting the total number of same-size cubic units that fill a shape without gaps or overlaps. Use cubic units to label volume measurements. Example: Use cubes to find the volume of a small fish tank.


Obj. 136 - Determine the volume of an object composed of rectangular prisms by counting units

MN 5.3.2.4 - Develop and use the formulas V = lwh and V = Bh to determine the volume of rectangular prisms. Justify why base area B and height h are multiplied to find the volume of a rectangular prism by breaking the prism into layers of unit cubes.


Obj. 132 - Determine the volume of a rectangular prism given a diagram


081309Page 43 of 198



Obj. 133 - WP: Determine the volume of a rectangular prism given a diagramObj. 134 - Determine the volume of a rectangular prismObj. 135 - WP: Determine the volume of a rectangular prism

MN 5.3.2.5 - Use various tools to measure the volume and surface area of various objects that are shaped like rectangular prisms. Example 1: Measure the surface area of a cereal box by cutting it into rectangles. Example 2: Measure the volume of a cereal box by using a ruler to measure its height, width and length, or by filling it with cereal and then emptying the cereal into containers of known volume.

MN 5.4 - Data AnalysisMN 5.4.1 - Display and interpret data; determine mean, median and range.

MN 5.4.1.1 - Know and use the definitions of the mean, median and range of a set of data. Know how to use a spreadsheet to find the mean, median and range of a data set. Understand that the mean is a "leveling out" of data. Example: The set of numbers 1, 1, 4, 6 has mean 3. It can be leveled by taking one unit from the 4 and three units from the 6 and adding them to the 1s, making four 3s.


Obj. 160 - Determine the range from a graph

Obj. 161 - Determine the mean of a set of whole number data, whole number resultsObj. 162 - Determine the median of an odd number of data valuesObj. 164 - Determine the range of a set of whole number data

MN 5.4.1.2 - Create and analyze double-bar graphs and line graphs by applying understanding of whole numbers, fractions and decimals. Know how to create spreadsheet tables and graphs to display data.


Obj. 152 - Answer a question using information from a line graph that does not start at zero or has a broken vertical scale

Obj. 154 - Read a double- or stacked-bar graph


081309Page 44 of 198



Obj. 155 - Use a double- or stacked-bar graph to represent data

Obj. 156 - Answer a question using information from a double- or stacked-bar graph


081309Page 45 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 6, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 6.1 - Number & OperationMN 6.1.1 - Read, write, represent and compare positive rational numbers expressed as fractions, decimals, percents and ratios; write positive integers as products of factors; use these representations in real-world and mathematical situations.

MN 6.1.1.1 - Locate positive rational numbers on a number line and plot pairs of positive rational numbers on a coordinate grid.MN 6.1.1.2 - Compare positive rational numbers represented in various forms. Use the symbols < and >. Example: 1/2 > 0.36.


Obj. 76 - Compare numbers in decimal and fractional forms

MN 6.1.1.3 - Understand that percent represents parts out of 100 and ratios to 100. Example: 75% is equivalent to the ratio 75 to 100, which is equivalent to the ratio 3 to 4.


Obj. 78 - Determine a percent where a ratio, not in 100ths, is given in words

Obj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50

MN 6.1.1.4 - Determine equivalences among fractions, decimals and percents; select among these representations to solve problems. Example: Since 1/10 is equivalent to 10%, if a woman making $25 an hour gets a 10% raise, she will make an additional $2.50 an hour, because $2.50 is 1/10 of $25.


Obj. 68 - Convert a mixed number to a decimal number

Obj. 69 - Convert a decimal number to a mixed numberObj. 70 - Convert a fraction to a repeating decimal numberObj. 72 - Convert a decimal number to a percentageObj. 73 - Convert a percentage to a decimal numberObj. 74 - Convert a fraction to a percentageObj. 75 - Convert a percentage to a fractionObj. 79 - Calculate a percent of a whole number where the answer is a whole number



081309Page 46 of 198



Obj. 80 - WP: Calculate the percent of a whole number where the answer is a whole number

MN 6.1.1.5 - Factor whole numbers; express a whole number as a product of prime factors with exponents. Example: 24= 2³ x 3.


Obj. 1 - Determine the prime factorization of a number between 50 and 200

MN 6.1.1.6 - Determine greatest common factors and least common multiples. Use common factors and common multiples to do arithmetic with fractions and find equivalent fractions. Example: Factor the numerator and denominator of a fraction to determine an equivalent fraction.


Obj. 2 - Determine the greatest common factor of three numbers to 100

Obj. 3 - Determine the least common multiple of three numbersObj. 4 - WP: Determine the least common multiple of two or more numbersObj. 13 - Add fractions with unlike denominators and simplify the sumObj. 14 - Subtract fractions with unlike denominators and simplify the differenceObj. 15 - Subtract a fraction from a whole numberObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 17 - Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sumObj. 18 - Subtract a mixed number from a whole numberObj. 19 - Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the differenceObj. 20 - Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer

Obj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference


081309Page 47 of 198



MN 6.1.1.7 - Convert between equivalent representations of positive rational numbers. Example: Express 10/7 as (7+3)/7 = 7/7 + 3/7 = 1 3/7.

MN 6.1.2 - Understand the concept of ratio and its relationship to fractions and to the multiplication and division of whole numbers. Use ratios to solve real-world and mathematical problems.MN 6.1.2.1 - Identify and use ratios to compare quantities; understand that comparing quantities using ratios is not the same as comparing quantities using subtraction. Example: In a classroom with 15 boys and 10 girls, compare the numbers by subtracting (there are 5 more boys than girls) or by dividing (there are 1.5 times as many boys as girls). The comparison using division may be expressed as a ratio of boys to girls (3 to 2 or 3:2 or 1.5 to 1).


Obj. 81 - WP: Determine a ratio using whole numbers less than 50

MN 6.1.2.2 - Apply the relationship between ratios, equivalent fractions and percents to solve problems in various contexts, including those involving mixtures and concentrations. Example: If 5 cups of trail mix contains 2 cups of raisins, the ratio of raisins to trail mix is 2 to 5. This ratio corresponds to the fact that the raisins are 2/5 of the total, or 40% of the total. And if one trail mix consists of 2 parts peanuts to 3 parts raisins, and another consists of 4 parts peanuts to 8 parts raisins, then the first mixture has a higher concentration of peanuts.


Obj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50

Obj. 84 - WP: Determine a part given a ratio and another part where the whole is less than 50Obj. 85 - WP: Determine the whole given a ratio and a part where the whole is less than 50


081309Page 48 of 198



MN 6.1.2.3 - Determine the rate for ratios of quantities with different units. Example: 60 miles in 3 hours is equivalent to 20 miles in one hour (20 mph).


Obj. 86 - WP: Determine a unit rate with a whole number value

MN 6.1.2.4 - Use reasoning about multiplication and division to solve ratio and rate problems. Example: If 5 items cost $3.75, and all items are the same price, then 1 item costs 75 cents, so 12 items cost $9.00.


Obj. 81 - WP: Determine a ratio using whole numbers less than 50

Obj. 83 - WP: Determine a part given a ratio and the whole where the whole is less than 50Obj. 84 - WP: Determine a part given a ratio and another part where the whole is less than 50Obj. 85 - WP: Determine the whole given a ratio and a part where the whole is less than 50Obj. 86 - WP: Determine a unit rate with a whole number valueObj. 87 - WP: Use a unit rate, with a whole number or whole cent value, to solve a problem

MN 6.1.3 - Multiply and divide decimals, fractions and mixed numbers; solve real-world and mathematical problems using arithmetic with positive rational numbers.MN 6.1.3.1 - Multiply and divide decimals and fractions, using efficient and generalizable procedures, including standard algorithms.


Obj. 22 - Multiply a fraction by a fraction

Obj. 28 - Divide a fraction by a whole number resulting in a fractional quotientObj. 29 - Divide a fraction by a fractionObj. 30 - Divide a whole number by a fraction resulting in a fractional quotientObj. 33 - WP: Multiply or divide a fraction by a fractionObj. 43 - Multiply a decimal number through thousandths by a whole number


081309Page 49 of 198



Obj. 44 - WP: Multiply a decimal number through thousandths by a whole numberObj. 45 - WP: Multiply a money expression by a decimal numberObj. 46 - Multiply a decimal number greater than one, in tenths, by a decimal number in tenthsObj. 47 - Multiply decimal numbers to thousandths using basic facts

Obj. 48 - Multiply decimal numbers less than one in hundredths or thousandthsObj. 49 - Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digitObj. 50 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Obj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 53 - Divide a decimal number by 10, 100, or 1,000Obj. 55 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal placesObj. 56 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberObj. 57 - Divide a whole number or a decimal number by 0.1, 0.01, or 0.001Obj. 60 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberObj. 61 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Obj. 62 - Divide a 2- or 3-digit whole number by a decimal number to hundredths or thousandths, rounded quotient if needed


081309Page 50 of 198



Obj. 63 - Divide a decimal number by a decimal number through thousandths, rounded quotient if neededObj. 64 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if needed

MN 6.1.3.2 - Use the meanings of fractions, multiplication, division and the inverse relationship between multiplication and division to make sense of procedures for multiplying and dividing fractions. Example: Just as 12/4 = 3 means 12 = 3x4, 2/3 ÷ 4/5 = 5/6 means 5/6 x 4/5 = 2/3.


Obj. 54 - Relate division by a whole number power of ten to multiplication by the related decimal fraction power of ten

Obj. 58 - Relate division by a decimal fraction power of ten to multiplication by the related whole number power of ten

MN 6.1.3.3 - Calculate the percent of a number and determine what percent one number is of another number to solve problems in various contexts. Example: If John has $45 and spends $15, what percent of his money did he keep?


Obj. 79 - Calculate a percent of a whole number where the answer is a whole number

Obj. 80 - WP: Calculate the percent of a whole number where the answer is a whole number

MN 6.1.3.4 - Solve real-world and mathematical problems requiring arithmetic with decimals, fractions and mixed numbers.


Obj. 13 - Add fractions with unlike denominators and simplify the sum

Obj. 14 - Subtract fractions with unlike denominators and simplify the differenceObj. 15 - Subtract a fraction from a whole numberObj. 16 - WP: Add or subtract fractions with unlike denominators and simplify the sum or differenceObj. 17 - Add mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum


081309Page 51 of 198



Obj. 18 - Subtract a mixed number from a whole numberObj. 19 - Subtract mixed numbers with unlike denominators or a mixed number and a fraction and simplify the differenceObj. 20 - Add and subtract three unlike-denominator fractions, mixed numbers, or fractions and mixed numbers, and simplify the answer

Obj. 21 - WP: Add or subtract mixed numbers with unlike denominators or a mixed number and a fraction with unlike denominators and simplify the sum or difference

Obj. 22 - Multiply a fraction by a fractionObj. 23 - Multiply a mixed number by a whole numberObj. 24 - Multiply a mixed number by a fractionObj. 25 - Multiply a mixed number by a mixed numberObj. 28 - Divide a fraction by a whole number resulting in a fractional quotientObj. 29 - Divide a fraction by a fractionObj. 30 - Divide a whole number by a fraction resulting in a fractional quotientObj. 31 - Divide a mixed number by a fractionObj. 32 - Divide a mixed number by a mixed numberObj. 33 - WP: Multiply or divide a fraction by a fractionObj. 34 - WP: Multiply or divide two mixed numbers or a mixed number and a fractionObj. 35 - WP: Solve a 2-step problem involving fractionsObj. 40 - Add three decimal numbers

Obj. 41 - Add and subtract three decimal numbersObj. 42 - WP: Add and subtract three decimal numbers


081309Page 52 of 198



Obj. 43 - Multiply a decimal number through thousandths by a whole numberObj. 44 - WP: Multiply a decimal number through thousandths by a whole numberObj. 45 - WP: Multiply a money expression by a decimal numberObj. 46 - Multiply a decimal number greater than one, in tenths, by a decimal number in tenthsObj. 47 - Multiply decimal numbers to thousandths using basic facts

Obj. 48 - Multiply decimal numbers less than one in hundredths or thousandthsObj. 49 - Multiply a decimal number greater than one by a decimal number to thousandths that has only 1 nonzero digitObj. 50 - Multiply decimal numbers greater than one where the product has 2 or 3 decimal places

Obj. 51 - WP: Multiply two decimal numbers to thousandthsObj. 53 - Divide a decimal number by 10, 100, or 1,000Obj. 55 - Divide a decimal number through thousandths by a 1- or 2-digit whole number where the quotient has 2-5 decimal placesObj. 56 - WP: Divide a decimal number through thousandths by a 1- or 2-digit whole numberObj. 57 - Divide a whole number or a decimal number by 0.1, 0.01, or 0.001Obj. 60 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a whole numberObj. 61 - Divide a 1- to 3-digit whole number by a decimal number to tenths where the quotient is a decimal number to thousandths

Obj. 63 - Divide a decimal number by a decimal number through thousandths, rounded quotient if needed


081309Page 53 of 198



Obj. 64 - WP: Divide a whole number by a decimal number through thousandths, rounded quotient if neededObj. 65 - WP: Divide a decimal through thousandths by a decimal through thousandths, rounded quotient if neededObj. 67 - WP: Solve a 2-step problem involving decimals

MN 6.1.3.5 - Estimate solutions to problems with whole numbers, fractions and decimals and use the estimations to assess the reasonableness of computations and of results in the context of the problem. Example: The sum 1/3 + 0.25 can be estimated to be between 1/2 and 1, and this estimate can be used as a check on the result of a more detailed calculation.


Obj. 52 - WP: Estimate the product of two decimals

Obj. 66 - WP: Estimate the quotient of two decimals

MN 6.2 - AlgebraMN 6.2.1 - Recognize and represent relationships between varying quantities; translate from one representation to another; use patterns, tables, graphs and rules to solve real-world and mathematical problems.MN 6.2.1.1 - Understand that a variable can be used to represent a quantity that can change, often in relationship to another changing quantity. Use variables in various contexts. Example: If a student earns $7 an hour in a job, the amount of money earned can be represented by a variable and is related to the number of hours worked, which also can be represented by a variable.


081309Page 54 of 198



MN 6.2.1.2 - Represent the relationship between two varying quantities with function rules, graphs and tables; translate between any two of these representations. Example: Describe the terms in the sequence of perfect squares t = 1, 4, 9, 16, ... by using the rule t-n² for n = 1, 2, 3, 4, ....

Topic 2 - Algebra Obj. 103 - WP: Generate a table of paired numbers based on a variable expression with two operations

Obj. 104 - Use a 2-variable equation to construct an input-output table

Obj. 105 - Use a 2-variable equation to represent a relationship expressed in a tableObj. 106 - Use a first quadrant graph to represent the values in an input-output tableObj. 107 - Use a graph to determine the entries in an input-output table

MN 6.2.2 - Use properties of arithmetic to generate equivalent numerical expressions and evaluate expressions involving positive rational numbers.MN 6.2.2.1 - Apply the associative, commutative and distributive properties and order of operations to generate equivalent expressions and to solve problems involving positive rational numbers. Example 1: 30/15 x 5/6 = (32x5)/(15x6) = (2x16x5)/(3x5x3x2) = 16/9 x 2/2 x 5/5 = 16/9. Example 2: Use the distributive law to write: 1/2 + 1/3 (9/2 - 15/8) = 1/2 + 1/3 x 9/2 - 1/3 x 15/8 = 1/2 + 3/2 - 5/8 = 2 - 5/8 = 1 3/8.

Topic 2 - Algebra Obj. 92 - Determine which property of addition or multiplication justifies a step in the simplification of an expression

MN 6.2.3 - Understand and interpret equations and inequalities involving variables and positive rational numbers. Use equations and inequalities to represent real-world and mathematical problems; use the idea of maintaining equality to solve equations. Interpret solutions in the original context.


081309Page 55 of 198



MN 6.2.3.1 - Represent real-world or mathematical situations using equations and inequalities involving variables and positive rational numbers. Example: The number of miles m in a k kilometer race is represented by the equation m = 0.62 k.

Topic 2 - Algebra Obj. 96 - WP: Use a 2-variable equation to represent a situation involving a direct proportion

Obj. 97 - WP: Use a 2-variable linear equation to represent a situation

MN 6.2.3.2 - Solve equations involving positive rational numbers using number sense, properties of arithmetic and the idea of maintaining equality on both sides of the equation. Interpret a solution in the original context and assess the reasonableness of results. Example: A cellular phone company charges $0.12 per minute. If the bill was $11.40 in April, how many minutes were used?

Topic 2 - Algebra Obj. 101 - Solve a 1-step equation involving whole numbers


MN 6.3.1 - Calculate perimeter, area, surface area and volume of two- and three-dimensional figures to solve real-world and mathematical problems.MN 6.3.1.1 - Calculate the surface area and volume of prisms and use appropriate units, such as cm² and cm³. Justify the formulas used. Justification may involve decomposition, nets or other models. Example: The surface area of a triangular prism can be derived by decomposing the surface into two triangles and three rectangles.


Obj. 127 - Determine the volume of a prism with a right triangle base

Obj. 128 - Determine the surface area of a 3-dimensional shape made from cubes


081309Page 56 of 198



MN 6.3.1.2 - Calculate the area of quadrilaterals. Quadrilaterals include squares, rectangles, rhombuses, parallelograms, trapezoids and kites. When formulas are used, be able to explain why they are valid. Example: The area of a kite is one-half the product of the lengths of the diagonals, and this can be justified by decomposing the kite into two triangles.

MN 6.3.1.3 - Estimate the perimeter and area of irregular figures on a grid when they cannot be decomposed into common figures and use correct units, such as cm and cm².

MN 6.3.2 - Understand and use relationships between angles in geometric figures.MN 6.3.2.1 - Solve problems using the relationships between the angles formed by intersecting lines. Example 1: If two streets cross, forming four corners such that one of the corners forms an angle of 120°, determine the measures of the remaining three angles. Example 2: Recognize that pairs of interior and exterior angles in polygons have measures that sum to 180°.


Obj. 129 - Determine the measure of a missing angle using straight and right angle relationships

MN 6.3.2.2 - Determine missing angle measures in a triangle using the fact that the sum of the interior angles of a triangle is 180°. Use models of triangles to illustrate this fact. Example 1: Cut a triangle out of paper, tear off the corners and rearrange these corners to form a straight line. Example 2: Recognize that the measures of the two acute angles in a right triangle sum to 90°.

MN 6.3.2.3 - Develop and use formulas for the sums of the interior angles of polygons by decomposing them into triangles.


081309Page 57 of 198



MN 6.3.3 - Choose appropriate units of measurement and use ratios to convert within measurement systems to solve real-world and mathematical problems.

MN 6.3.3.1 - Solve problems in various contexts involving conversion of weights, capacities, geometric measurements and times within measurement systems using appropriate units.


Obj. 108 - WP: Add or subtract customary measures of capacity requiring unit conversion

Obj. 109 - WP: Add or subtract metric measures of capacity requiring unit conversionObj. 110 - WP: Add or subtract customary measures of weight requiring unit conversionObj. 111 - WP: Add or subtract metric measures of mass requiring unit conversionObj. 113 - WP: Multiply or divide metric measures of capacity requiring unit conversionObj. 114 - WP: Multiply or divide customary measures of weight requiring unit conversionObj. 115 - WP: Multiply or divide metric measures of mass requiring unit conversion

MN 6.3.3.2 - Estimate weights, capacities and geometric measurements using benchmarks in measurement systems with appropriate units. Example: Estimate the height of a house by comparing to a 6-foot man standing nearby.

MN 6.4 - Data Analysis & Probability

MN 6.4.1 - Use probabilities to solve real-world and mathematical problems; represent probabilities using fractions, decimals and percents.


081309Page 58 of 198



MN 6.4.1.1 - Determine the sample space (set of possible outcomes) for a given experiment and determine which members of the sample space are related to certain events. Sample space may be determined by the use of tree diagrams, tables or pictorial representations. Example: A 6 x 6 table with entries such as (1,1), (1,2), (1,3), ..., (6,6) can be used to represent the sample space for the experiment of simultaneously rolling two number cubes.


Obj. 157 - Determine the number of possible combinations of a set of objects

MN 6.4.1.2 - Determine the probability of an event using the ratio between the size of the event and the size of the sample space; represent probabilities as percents, fractions and decimals between 0 and 1 inclusive. Understand that probabilities measure likelihood. Example: Each outcome for a balanced number cube has probability 1/6 , and the probability of rolling an even number is 1/2.


Obj. 152 - Determine the probability of a single event

MN 6.4.1.3 - Perform experiments for situations in which the probabilities are known, compare the resulting relative frequencies with the known probabilities; know that there may be differences. Example: Heads and tails are equally likely when flipping a fair coin, but if several different students flipped fair coins 10 times, it is likely that they will find a variety of relative frequencies of heads and tails.


Obj. 156 - Compare predictions from experimental and theoretical probability


081309Page 59 of 198



MN 6.4.1.4 - Calculate experimental probabilities from experiments; represent them as percents, fractions and decimals between 0 and 1 inclusive. Use experimental probabilities to make predictions when actual probabilities are unknown. Example: Repeatedly draw colored chips with replacement from a bag with an unknown mixture of chips, record relative frequencies, and use the results to make predictions about the contents of the bag.


Obj. 151 - Determine an experimental probability given a list of results

Obj. 154 - Make a prediction based on an experimental probability

Obj. 155 - Make a prediction based on a theoretical probability


081309Page 60 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 7, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 7.1 - Number & OperationMN 7.1.1 - Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.MN 7.1.1.1 - Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

MN 7.1.1.2 - Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. Example: 125/30 gives 4.16666667 on a calculator. This answer is not exact. The exact answer can be expressed as 4 1/6 , which is the same as 4.16 repeating. The calculator expression does not guarantee that the 6 is repeated, but that possibility should be anticipated.

MN 7.1.1.3 - Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.


Obj. 34 - Determine the opposite of an integer

Obj. 57 - Identify a positive or negative rational number represented by a point on a number line

Obj. 58 - Locate a positive or negative rational number on a number line

MN 7.1.1.4 - Compare positive and negative rational numbers expressed in various forms using the symbols <, >, "less than or equal to", "greater than or equal to". Example: -1/2 < -36.


Obj. 59 - Compare rational numbers (positive and negative)



081309Page 61 of 198



MN 7.1.1.5 - Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. Example: -40/12 = -120/36 = -10/3 = -3.3 repeating.

MN 7.1.2 - Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.MN 7.1.2.1 - Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. Example: 3 to the 4th power x (1/2)² = 81/4.


Obj. 30 - WP: Answer a question involving a fraction and a decimal

Obj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbersObj. 37 - Add integersObj. 39 - Subtract integersObj. 40 - WP: Add and subtract using integersObj. 41 - Multiply integersObj. 42 - Divide integersObj. 43 - WP: Multiply or divide integers

MN 7.1.2.2 - Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. Example: Multiplying a distance by -1 can be thought of as representing that same distance in the opposite direction. Multiplying by -1 a second time reverses directions again, giving the distance in the original direction.


081309Page 62 of 198



MN 7.1.2.3 - Understand that calculators and other computing technologies often truncate or round numbers. Example: A decimal that repeats or terminates after a large number of digits is truncated or rounded.MN 7.1.2.4 - Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.


Obj. 30 - WP: Answer a question involving a fraction and a decimal

Obj. 31 - WP: Solve a multi-step problem involving decimal numbersObj. 32 - WP: Solve a multi-step problem involving fractions or mixed numbersObj. 40 - WP: Add and subtract using integersObj. 43 - WP: Multiply or divide integersObj. 50 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Obj. 51 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50

Obj. 52 - WP: Determine a unit rate

Obj. 53 - WP: Use a unit rate to solve a problem

MN 7.1.2.5 - Use proportional reasoning to solve problems involving ratios in various contexts. Example: A recipe calls for milk, flour and sugar in a ratio of 4:6:3 (this is how recipes are often given in large institutions, such as hospitals). How much flour and milk would be needed with 1 cup of sugar?


Obj. 46 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50

Obj. 47 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50

Obj. 48 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50


081309Page 63 of 198



Obj. 49 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50

Topic 2 - Algebra Obj. 71 - WP: Solve a proportionObj. 72 - WP: Use direct variation to solve a problem

MN 7.1.2.6 - Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. Example: |- 3| represents the distance from - 3 to 0 on a number line or 3 units; the distance between 3 and 9/2 on the number line is |3 - 9/2| or 3/2.MN 7.2 - AlgebraMN 7.2.1 - Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.MN 7.2.1.1 - Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy=k or y= k/x). Example: The radius and circumference of a circle are proportional, whereas the length x and the width y of a rectangle with area 12 are inversely proportional, since xy = 12 or equivalently, y = 12/x.MN 7.2.1.2 - Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.

Topic 2 - Algebra Obj. 82 - Use a graph to represent the ordered pairs in a function table

Obj. 83 - Determine the graph of a 1-operation linear function


081309Page 64 of 198



MN 7.2.2 - Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

MN 7.2.2.1 - Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. Example: Larry drives 114 miles and uses 5 gallons of gasoline. Sue drives 300 miles and uses 11.5 gallons of gasoline. Use equations and graphs to compare fuel efficiency and to determine the costs of various trips.

Topic 2 - Algebra Obj. 68 - Use a variable expression with two operations to represent a table of paired numbers

Obj. 69 - WP: Use a 2-variable expression to represent a situationObj. 81 - Use a table to represent a linear functionObj. 82 - Use a graph to represent the ordered pairs in a function table

MN 7.2.2.2 - Solve multi-step problems involving proportional relationships in numerous contexts. Example 1: Distance-time, percent increase or decrease, discounts, tips, unit pricing, lengths in similar geometric figures, and unit conversion when a conversion factor is given, including conversion between different measurement systems. Example 2: How many kilometers are there in 26.2 miles?


Obj. 22 - WP: Determine a percent of a whole number using less than 100%

Obj. 23 - WP: Determine the percent a whole number is of another whole number, with a result less than 100%

Obj. 24 - WP: Determine a whole number given a part and a percentage


081309Page 65 of 198



Obj. 25 - WP: Determine the percent of decrease applied to a number

Obj. 26 - WP: Determine the percent of increase applied to a number

Obj. 27 - WP: Determine the result of applying a percent of decrease to a valueObj. 28 - WP: Determine the result of applying a percent of increase to a valueObj. 46 - WP: Determine a part, given part to whole ratio and the whole, where the whole is greater than 50Obj. 47 - WP: Determine a part, given part to part ratio and the whole, where the whole is greater than 50

Obj. 48 - WP: Determine a part, given part to whole ratio and a part, where the whole is greater than 50Obj. 49 - WP: Determine a part, given part to part ratio and a part, where the whole is greater than 50Obj. 50 - WP: Determine the whole, given part to whole ratio and a part, where the whole is greater than 50

Obj. 51 - WP: Determine the whole, given part to part ratio and a part, where the whole is greater than 50

Obj. 52 - WP: Determine a unit rate

Obj. 53 - WP: Use a unit rate to solve a problem

Topic 2 - Algebra Obj. 71 - WP: Solve a proportionObj. 72 - WP: Use direct variation to solve a problem

MN 7.2.2.3 - Use knowledge of proportions to assess the reasonableness of solutions. Example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off.


081309Page 66 of 198



MN 7.2.2.4 - Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. Example 1: "Four-fifths is three greater than the opposite of a number" can be represented as 4/5 = -n + 3, and "height no bigger than half the radius" can be represented as h is less than or equal to r/2. Example 2: "x is at least -3 and less than 5" can be represented as -3 is less than or equal to x < 5, and also on a number line.

Topic 2 - Algebra Obj. 75 - WP: Use a 1-variable 1-step equation to represent a situation

Obj. 76 - Determine the graph of an inequality on a number lineObj. 79 - Determine the graph of the solution set of a 1-step linear inequalityObj. 80 - WP: Use a 1-variable linear inequality to represent a situation

MN 7.2.3 - Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.

MN 7.2.3.1 - Generate equivalent numerical and algebraic expressions containing rational numbers and whole number exponents. Properties of algebra include associative, commutative and distributive laws. Example: Combine like terms (use the distributive law) to write 3x - 7x + 1 = (3-7)x + 1 = -4x + 1.

MN 7.2.3.2 - Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. Example: Evaluate the expression 1/3 (2x - 5)² at x = 5.

Topic 2 - Algebra Obj. 62 - Evaluate a 1-variable expression, with two or three operations, using integer substitution

Obj. 64 - Evaluate an algebraic expression involving whole number exponents


081309Page 67 of 198



Obj. 65 - WP: Evaluate a variable expressionObj. 66 - WP: Evaluate a variable expression involving exponents

MN 7.2.3.3 - Apply understanding of order of operations and grouping symbols when using calculators and other technologies. Example: Recognize the conventions of using a carat (^ raise to a power), asterisk (* multiply), and also pay careful attention to the use of nested parentheses.


Obj. 10 - Evaluate an expression containing the fraction bar as the division sign

Obj. 11 - Evaluate a numerical expression, with parentheses and exponents, using order of operations

Topic 2 - Algebra Obj. 63 - Evaluate a 2-variable expression, with two or three operations, using integer substitution

MN 7.2.4 - Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.MN 7.2.4.1 - Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. Example 1: Solve for w in the equation P = 2w + 2l when P = 3.5 and l = 0.4. Example 2: To post an Internet website, Mary must pay $300 for initial set up and a monthly fee of $12. She has $842 in savings, how long can she sustain her website?


081309Page 68 of 198



MN 7.2.4.2 - Solve equations resulting from proportional relationships in various contexts. Example 1: Given the side lengths of one triangle and one side length of a second triangle that is similar to the first, find the remaining side lengths of the second triangle. Example 2: Determine the price of 12 yards of ribbon if 5 yards of ribbon cost $1.85.

Topic 2 - Algebra Obj. 71 - WP: Solve a proportion

Obj. 72 - WP: Use direct variation to solve a problem


MN 7.3.1 - Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.

MN 7.3.1.1 - Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.


Obj. 84 - Determine the circumference of a circle in terms of pi

Obj. 88 - Determine the area of a circle in terms of piObj. 89 - Determine the area of a circle using 3.14 for piObj. 90 - Determine the area of a circle using 22/7 for piObj. 91 - WP: Determine the area of a circle using 3.14 for pi

MN 7.3.1.2 - Calculate the volume and surface area of cylinders and justify the formulas used. Example: Justify the formula for the surface area of a cylinder by decomposing the surface into two circles and a rectangle.


Obj. 94 - Determine the volume of a cylinder

Obj. 95 - WP: Determine the volume of a cylinderObj. 99 - Determine the surface area of a cylinder


081309Page 69 of 198



MN 7.3.2 - Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.MN 7.3.2.1 - Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors. Example: Corresponding angles in similar geometric figures have the same measure.


Obj. 106 - Determine the scale for a drawing or map question

MN 7.3.2.2 - Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures. Example: If two similar rectangles have heights of 3 and 5, and the first rectangle has a base of length 7, the base of the second rectangle has length 35/3.


Obj. 104 - Determine a missing dimension given two similar shapes

Obj. 105 - WP: Solve a problem involving similar shapesObj. 107 - WP: Solve a problem involving a map or scale drawing

MN 7.3.2.3 - Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. Example 1: 1 square foot equals 144 square inches. Example 2: In a map where 1 inch represents 50 miles, 1/2 inch represents 25 miles.


Obj. 107 - WP: Solve a problem involving a map or scale drawing

MN 7.3.2.4 - Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. Example: The point (1, 2) moves to (-1, 2) after reflection about the y-axis.


Obj. 121 - Determine the coordinates of a translated, a rotated, or a reflected shape on the Cartesian plane


MN 7.4.1 - Use mean, median and range to draw conclusions about data and make predictions.


081309Page 70 of 198



MN 7.4.1.1 - Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. Example: By looking at data from the past, Sandy calculated that the mean gas mileage for her car was 28 miles per gallon. She expects to travel 400 miles during the next week. Predict the approximate number of gallons that she will use.


Obj. 132 - Determine the mean of a set of data

Obj. 134 - Determine the median of a set of dataObj. 135 - WP: Use the mean of a data set to solve a problem

MN 7.4.1.2 - Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact. Example: How does dropping the lowest test score affect a student's mean test score?

MN 7.4.2 - Display and interpret data in a variety of ways, including circle graphs and histograms.MN 7.4.2.1 - Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.


Obj. 125 - Answer a question using information from a circle graph using percentage calculations

Obj. 126 - Use a circle graph to represent percentage dataObj. 127 - Use a histogram to represent dataObj. 128 - Answer a question using information from a histogram

MN 7.4.3 - Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.


081309Page 71 of 198



MN 7.4.3.1 - Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities. Example: Use a spreadsheet function such as RANDBETWEEN(1, 10) to generate random whole numbers from 1 to 10, and display the results in a histogram.

MN 7.4.3.2 - Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. Example: Determine probabilities for different outcomes in game spinners by finding fractions of the area of the spinner.


Obj. 137 - Determine the probability for independent events

MN 7.4.3.3 - Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. Example: When rolling a number cube 600 times, one would predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.


Obj. 138 - Determine the probability for dependent events


081309Page 72 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 7, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 7.1 - Number & OperationMN 7.1.1 - Read, write, represent and compare positive and negative rational numbers, expressed as integers, fractions and decimals.MN 7.1.1.1 - Know that every rational number can be written as the ratio of two integers or as a terminating or repeating decimal. Recognize that pi is not rational, but that it can be approximated by rational numbers such as 22/7 and 3.14.

MN 7.1.1.2 - Understand that division of two integers will always result in a rational number. Use this information to interpret the decimal result of a division problem when using a calculator. Example: 125/30 gives 4.16666667 on a calculator. This answer is not exact. The exact answer can be expressed as 4 1/6 , which is the same as 4.16 repeating. The calculator expression does not guarantee that the 6 is repeated, but that possibility should be anticipated.

MN 7.1.1.3 - Locate positive and negative rational numbers on the number line, understand the concept of opposites, and plot pairs of positive and negative rational numbers on a coordinate grid.

MN 7.1.1.4 - Compare positive and negative rational numbers expressed in various forms using the symbols <, >, "less than or equal to", "greater than or equal to". Example: -1/2 < -36.


Obj. 19 - Compare rational numbers and/or irrational numbers in various forms

MN 7.1.1.5 - Recognize and generate equivalent representations of positive and negative rational numbers, including equivalent fractions. Example: -40/12 = -120/36 = -10/3 = -3.3 repeating.


Obj. 17 - Convert a repeating decimal to a fraction or a mixed number



081309Page 73 of 198



MN 7.1.2 - Calculate with positive and negative rational numbers, and rational numbers with whole number exponents, to solve real-world and mathematical problems.MN 7.1.2.1 - Add, subtract, multiply and divide positive and negative rational numbers that are integers, fractions and terminating decimals; use efficient and generalizable procedures, including standard algorithms; raise positive rational numbers to whole-number exponents. Example: 3 to the 4th power x (1/2)² = 81/4.


Obj. 6 - Add or subtract signed fractions or mixed numbers

Obj. 7 - Multiply or divide signed fractions or mixed numbersObj. 8 - Add or subtract signed decimalsObj. 9 - Multiply or divide signed decimalsObj. 11 - Determine the square of a fraction or a decimal

MN 7.1.2.2 - Use real-world contexts and the inverse relationship between addition and subtraction to explain why the procedures of arithmetic with negative rational numbers make sense. Example: Multiplying a distance by -1 can be thought of as representing that same distance in the opposite direction. Multiplying by -1 a second time reverses directions again, giving the distance in the original direction.

MN 7.1.2.3 - Understand that calculators and other computing technologies often truncate or round numbers. Example: A decimal that repeats or terminates after a large number of digits is truncated or rounded.MN 7.1.2.4 - Solve problems in various contexts involving calculations with positive and negative rational numbers and positive integer exponents, including computing simple and compound interest.


Obj. 21 - Determine a percent of a number given a percent that is not a whole percent


081309Page 74 of 198



Obj. 22 - Determine the percent one number is of another numberObj. 23 - Determine a number given a part and a decimal percentage or a percentage more than 100%

Obj. 24 - WP: Determine a given percent of a numberObj. 25 - WP: Determine the percent one number is of another number

Obj. 26 - WP: Determine a number given a part and a decimal percentage or a percentage more than 100%Obj. 27 - Solve a problem involving simple interestObj. 28 - Solve a problem involving annually compounded interestObj. 29 - WP: Find the result of two consecutive percentage changes applied to a given number

MN 7.1.2.5 - Use proportional reasoning to solve problems involving ratios in various contexts. Example: A recipe calls for milk, flour and sugar in a ratio of 4:6:3 (this is how recipes are often given in large institutions, such as hospitals). How much flour and milk would be needed with 1 cup of sugar?

MN 7.1.2.6 - Demonstrate an understanding of the relationship between the absolute value of a rational number and distance on a number line. Use the symbol for absolute value. Example: |- 3| represents the distance from - 3 to 0 on a number line or 3 units; the distance between 3 and 9/2 on the number line is |3 - 9/2| or 3/2.MN 7.2 - AlgebraMN 7.2.1 - Understand the concept of proportionality in real-world and mathematical situations, and distinguish between proportional and other relationships.


081309Page 75 of 198



MN 7.2.1.1 - Understand that a relationship between two variables, x and y, is proportional if it can be expressed in the form y/x = k or y = kx. Distinguish proportional relationships from other relationships, including inversely proportional relationships (xy=k or y= k/x). Example: The radius and circumference of a circle are proportional, whereas the length x and the width y of a rectangle with area 12 are inversely proportional, since xy = 12 or equivalently, y = 12/x.MN 7.2.1.2 - Understand that the graph of a proportional relationship is a line through the origin whose slope is the unit rate (constant of proportionality). Know how to use graphing technology to examine what happens to a line when the unit rate is changed.MN 7.2.2 - Recognize proportional relationships in real-world and mathematical situations; represent these and other relationships with tables, verbal descriptions, symbols and graphs; solve problems involving proportional relationships and explain results in the original context.

MN 7.2.2.1 - Represent proportional relationships with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another. Determine the unit rate (constant of proportionality or slope) given any of these representations. Example: Larry drives 114 miles and uses 5 gallons of gasoline. Sue drives 300 miles and uses 11.5 gallons of gasoline. Use equations and graphs to compare fuel efficiency and to determine the costs of various trips.

Topic 2 - Algebra Obj. 46 - Determine the slope of a line given its graph or a graph of a line with a given slope

Obj. 50 - WP: Determine a linear graph that can represent a situation


081309Page 76 of 198



MN 7.2.2.2 - Solve multi-step problems involving proportional relationships in numerous contexts. Example 1: Distance-time, percent increase or decrease, discounts, tips, unit pricing, lengths in similar geometric figures, and unit conversion when a conversion factor is given, including conversion between different measurement systems. Example 2: How many kilometers are there in 26.2 miles?


Obj. 29 - WP: Find the result of two consecutive percentage changes applied to a given number


Obj. 57 - WP: Solve a distance-rate-time problem that involves unit conversions

MN 7.2.2.3 - Use knowledge of proportions to assess the reasonableness of solutions. Example: Recognize that it would be unreasonable for a cashier to request $200 if you purchase a $225 item at 25% off.MN 7.2.2.4 - Represent real-world or mathematical situations using equations and inequalities involving variables and positive and negative rational numbers. Example 1: "Four-fifths is three greater than the opposite of a number" can be represented as 4/5 = -n + 3, and "height no bigger than half the radius" can be represented as h is less than or equal to r/2. Example 2: "x is at least -3 and less than 5" can be represented as -3 is less than or equal to x < 5, and also on a number line.

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situationObj. 53 - WP: Use a 2-step linear inequality in one variable to represent a situation

MN 7.2.3 - Apply understanding of order of operations and algebraic properties to generate equivalent numerical and algebraic expressions containing positive and negative rational numbers and grouping symbols; evaluate such expressions.


081309Page 77 of 198



MN 7.2.3.1 - Generate equivalent numerical and algebraic expressions containing rational numbers and whole number exponents. Properties of algebra include associative, commutative and distributive laws. Example: Combine like terms (use the distributive law) to write 3x - 7x + 1 = (3-7)x + 1 = -4x + 1.


Obj. 1 - Evaluate an integer raised to a whole number power

Obj. 10 - Evaluate a numerical expression involving nested parentheses

Topic 2 - Algebra Obj. 33 - Simplify an algebraic expression by combining like terms

Obj. 36 - Use the distributive property to simplify an algebraic expression

MN 7.2.3.2 - Evaluate algebraic expressions containing rational numbers and whole number exponents at specified values of their variables. Example: Evaluate the expression 1/3 (2x - 5)² at x = 5.

Topic 2 - Algebra Obj. 31 - Evaluate a 2-variable expression with two or three operations substituting fractions or decimals

MN 7.2.3.3 - Apply understanding of order of operations and grouping symbols when using calculators and other technologies. Example: Recognize the conventions of using a carat (^ raise to a power), asterisk (* multiply), and also pay careful attention to the use of nested parentheses.MN 7.2.4 - Represent real-world and mathematical situations using equations with variables. Solve equations symbolically, using the properties of equality. Also solve equations graphically and numerically. Interpret solutions in the original context.


081309Page 78 of 198



MN 7.2.4.1 - Represent relationships in various contexts with equations involving variables and positive and negative rational numbers. Use the properties of equality to solve for the value of a variable. Interpret the solution in the original context. Example 1: Solve for w in the equation P = 2w + 2l when P = 3.5 and l = 0.4. Example 2: To post an Internet website, Mary must pay $300 for initial set up and a monthly fee of $12. She has $842 in savings, how long can she sustain her website?

Topic 2 - Algebra Obj. 37 - Solve a 1-step equation involving rational numbers

Obj. 38 - Solve a 2-step equation involving rational numbersObj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operationsObj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situationObj. 41 - WP: Solve a problem involving a 1-variable, 2-step equation

MN 7.2.4.2 - Solve equations resulting from proportional relationships in various contexts. Example 1: Given the side lengths of one triangle and one side length of a second triangle that is similar to the first, find the remaining side lengths of the second triangle. Example 2: Determine the price of 12 yards of ribbon if 5 yards of ribbon cost $1.85.


MN 7.3.1 - Use reasoning with proportions and ratios to determine measurements, justify formulas and solve real-world and mathematical problems involving circles and related geometric figures.


081309Page 79 of 198



MN 7.3.1.1 - Demonstrate an understanding of the proportional relationship between the diameter and circumference of a circle and that the unit rate (constant of proportionality) is pi. Calculate the circumference and area of circles and sectors of circles to solve problems in various contexts.MN 7.3.1.2 - Calculate the volume and surface area of cylinders and justify the formulas used. Example: Justify the formula for the surface area of a cylinder by decomposing the surface into two circles and a rectangle.MN 7.3.2 - Analyze the effect of change of scale, translations and reflections on the attributes of two-dimensional figures.MN 7.3.2.1 - Describe the properties of similarity, compare geometric figures for similarity, and determine scale factors. Example: Corresponding angles in similar geometric figures have the same measure.MN 7.3.2.2 - Apply scale factors, length ratios and area ratios to determine side lengths and areas of similar geometric figures. Example: If two similar rectangles have heights of 3 and 5, and the first rectangle has a base of length 7, the base of the second rectangle has length 35/3.


Obj. 59 - Determine the ratio of the perimeters or areas of similar shapes

Obj. 70 - WP: Solve a problem involving scale

MN 7.3.2.3 - Use proportions and ratios to solve problems involving scale drawings and conversions of measurement units. Example 1: 1 square foot equals 144 square inches. Example 2: In a map where 1 inch represents 50 miles, 1/2 inch represents 25 miles.


Obj. 70 - WP: Solve a problem involving scale


081309Page 80 of 198



MN 7.3.2.4 - Graph and describe translations and reflections of figures on a coordinate grid and determine the coordinates of the vertices of the figure after the transformation. Example: The point (1, 2) moves to (-1, 2) after reflection about the y-axis.


MN 7.4.1 - Use mean, median and range to draw conclusions about data and make predictions.MN 7.4.1.1 - Determine mean, median and range for quantitative data and from data represented in a display. Use these quantities to draw conclusions about the data, compare different data sets, and make predictions. Example: By looking at data from the past, Sandy calculated that the mean gas mileage for her car was 28 miles per gallon. She expects to travel 400 miles during the next week. Predict the approximate number of gallons that she will use.


Obj. 89 - Compare the medians, the modes, or the ranges of the data in a double stem-and-leaf plot

Obj. 90 - Determine the median of the data in a frequency table or a bar graphObj. 91 - Determine the mean of the data in a frequency table or a bar graph

MN 7.4.1.2 - Describe the impact that inserting or deleting a data point has on the mean and the median of a data set. Know how to create data displays using a spreadsheet to examine this impact. Example: How does dropping the lowest test score affect a student's mean test score?


Obj. 88 - Analyze the effect that changing elements in a data set has on the mean, the median, or the range

MN 7.4.2 - Display and interpret data in a variety of ways, including circle graphs and histograms.


081309Page 81 of 198



MN 7.4.2.1 - Use reasoning with proportions to display and interpret data in circle graphs (pie charts) and histograms. Choose the appropriate data display and know how to create the display using a spreadsheet or other graphing technology.


Obj. 76 - Use a circle graph to organize data

MN 7.4.3 - Calculate probabilities and reason about probabilities using proportions to solve real-world and mathematical problems.MN 7.4.3.1 - Use random numbers generated by a calculator or a spreadsheet or taken from a table to simulate situations involving randomness, make a histogram to display the results, and compare the results to known probabilities. Example: Use a spreadsheet function such as RANDBETWEEN(1, 10) to generate random whole numbers from 1 to 10, and display the results in a histogram.

MN 7.4.3.2 - Calculate probability as a fraction of sample space or as a fraction of area. Express probabilities as percents, decimals and fractions. Example: Determine probabilities for different outcomes in game spinners by finding fractions of the area of the spinner.MN 7.4.3.3 - Use proportional reasoning to draw conclusions about and predict relative frequencies of outcomes based on probabilities. Example: When rolling a number cube 600 times, one would predict that a 3 or 6 would be rolled roughly 200 times, but probably not exactly 200 times.


081309Page 82 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 8, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 8.1 - Number & OperationMN 8.1.1 - Read, write, compare, classify and represent real numbers, and use them to solve problems in various contexts.MN 8.1.1.1 - Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational. Example: Classify the following numbers as whole numbers, integers, rational numbers, irrational numbers, recognizing that some numbers belong in more than one category: 6/3, 3/6, 3.6 repeating, pi/2, - the square root of 4, the square root of 10, -6.7.


Obj. 18 - Identify rational or irrational numbers

MN 8.1.1.2 - Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers. Example 1: Put the following numbers in order from smallest to largest: 2, square root of 3, -4, -6.8, - the square root of 37. Example 2: The square root of 68 is an irrational number between 8 and 9.


Obj. 14 - Determine the two closest integers to a given square root

Obj. 15 - Approximate the location of a square root on a number lineObj. 19 - Compare rational numbers and/or irrational numbers in various formsObj. 20 - Order rational numbers and irrational numbers



081309Page 83 of 198



MN 8.1.1.3 - Determine rational approximations for solutions to problems involving real numbers. Example 1: A calculator can be used to determine that the square root of 7 is approximately 2.65. Example 2: To check that 1 5/12 is slightly bigger than the square root of 2, do the calculation (1 5/12)² = (17/12)² = 289/144 = 2 1/144. Example 3: Knowing that the square root of 10 is between 3 and 4, try squaring numbers like 3.5, 3.3, 3.1 to determine that 3.1 is a reasonable rational approximation of the square root of 10.


Obj. 16 - Determine the square root of a whole number to the nearest tenth

MN 8.1.1.4 - Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. Example: 3² x 3 to the -5 power = 3 to the -3 power (1/3)³ = 1/27.


Obj. 1 - Evaluate an integer raised to a whole number power

Obj. 2 - Evaluate a zero or negative power of an integerObj. 3 - Evaluate a numerical expression involving integer exponents and/or integer basesObj. 10 - Evaluate a numerical expression involving nested parentheses

MN 8.1.1.5 - Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. Example: (4.2 x 10 to the 4th power) x (8.25 x 10³)= 3.465 x 10 to the 8th power, but if these numbers represent physical measurements, the answer should be expressed as 3.5 x 10 to the 8th power because the first factor, 4.2 x 10 to the 4th power, only has two significant digits.


Obj. 4 - Convert a number less than 1 to scientific notation


081309Page 84 of 198



Obj. 5 - Convert a number less than 1 from scientific notation to standard form

MN 8.2 - AlgebraMN 8.2.1 - Understand the concept of function in real-world and mathematical situations, and distinguish between linear and non-linear functions.MN 8.2.1.1 - Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships. Example: The relationship between the area of a square and the side length can be expressed as f(x)=x². In this case, f(5)=25 , which represents the fact that a square of side length 5 units has area 25 units squared.MN 8.2.1.2 - Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount. Example: Uncle Jim gave Emily $50 on the day she was born and $25 on each birthday after that. The function f(x)=50+25x represents the amount of money Jim has given after x years. The rate of change is $25 per year.

MN 8.2.1.3 - Understand that a function is linear if it can be expressed in the form f(x)=mx+b or if its graph is a straight line. Example: The function f(x)=x² is not a linear function because its graph contains the points (1,1), (-1,1) and (0,0), which are not on a straight line.


081309Page 85 of 198



MN 8.2.1.4 - Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x)=mx+b, where x = 0, 1, 2, 3, .... Example: The arithmetic sequence 3, 7, 11, 15, ..., can be expressed as f(x) = 4x + 3.

MN 8.2.1.5 - Understand that a geometric sequence is a non-linear function that can be expressed in the form , fx(x)=ab where x = 0, 1, 2, 3, .... Example: The geometric sequence 6, 12, 24, 48, ... , can be expressed in the form f(x) = 6(2 to the x power).MN 8.2.2 - Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.

MN 8.2.2.1 - Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.

Topic 2 - Algebra Obj. 42 - Determine the graph of a line for a given table of values

Obj. 43 - Determine the table of values that represents a linear equation with rational coefficients in two variablesObj. 44 - Determine a linear equation in two variables that represents a table of valuesObj. 45 - Determine the graph of a 2-operation linear functionObj. 50 - WP: Determine a linear graph that can represent a situation

MN 8.2.2.2 - Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

Topic 2 - Algebra Obj. 46 - Determine the slope of a line given its graph or a graph of a line with a given slope

Obj. 47 - Determine the x- or y-intercept of a line given its graph


081309Page 86 of 198



Obj. 48 - WP: Interpret the meaning of the slope of a graphed line

Obj. 49 - WP: Interpret the meaning of the y-intercept of a graphed line

MN 8.2.2.3 - Identify how coefficient changes in the equation f(x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.

MN 8.2.2.4 - Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl starts with $100 in savings and adds $10 at the end of each month, she will have 100 + 10x dollars after x months.

MN 8.2.2.5 - Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl invests $100 at 10% annual interest, she will have 100(1.1 to the x power) dollars after x years.

MN 8.2.3 - Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.MN 8.2.3.1 - Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables. Example: Evaluate pi r²h when r = 3 and h = 0.5, and then use an approximation of pi, to obtain an approximate answer.

Topic 2 - Algebra Obj. 31 - Evaluate a 2-variable expression with two or three operations substituting fractions or decimals

Obj. 32 - Evaluate an algebraic expression involving negative integer exponents

MN 8.2.3.2 - Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.


081309Page 87 of 198



MN 8.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.

MN 8.2.4.1 - Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. Example: For a cylinder with fixed radius of length 5, the surface area A = 2 pi(5)h + 2 pi(5)² = 10 pi h + 50 pi, is a linear function of the height h, but it is not proportional to the height.

Topic 2 - Algebra Obj. 39 - WP: Use a 1-variable equation with rational coefficients to represent a situation involving two operations

Obj. 40 - WP: Use a 2-variable equation with rational coefficients to represent a situation

MN 8.2.4.2 - Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. Example 1: The equation 10x + 17 = 3x can be changed to 7x + 17 = 0, and then to 7x = -17 by adding/subtracting the same quantities to both sides. These changes do not change the solution of the equation. Example 2: Express the radius of a circle in terms of its circumference.

Topic 2 - Algebra Obj. 38 - Solve a 2-step equation involving rational numbers

MN 8.2.4.3 - Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. Example: Determine an equation of the line through the points (-1,6) and (2/3, -3/4).


081309Page 88 of 198



MN 8.2.4.4 - Use linear inequalities to represent relationships in various contexts. Example: A gas station charges $0.10 less per gallon of gasoline if a customer also gets a car wash. Without the car wash, gas costs $2.79 per gallon. The car wash is $8.95. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $35?

MN 8.2.4.5 - Solve linear inequalities using properties of inequalities. Graph the solutions on a number line. Example: The inequality -3x < 6 is equivalent to x > -2 , which can be represented on the number line by shading in the interval to the right of -2.

Topic 2 - Algebra Obj. 52 - Solve a 2-step linear inequality in one variable

Obj. 54 - WP: Solve a problem involving a 2-step linear inequality in one variableObj. 55 - Determine the graph of the solutions to a 2-step linear inequality in one variable

MN 8.2.4.6 - Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line. Example: A cylindrical machine part is manufactured with a radius of 2.1 cm, with a tolerance of 1/100 cm. The radius r satisfies the inequality |r - 2.1| is less than or equal to .01.


081309Page 89 of 198



MN 8.2.4.7 - Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. Example: Marty's cell phone company charges $15 per month plus $0.04 per minute for each call. Jeannine's company charges $0.25 per minute. Use a system of equations to determine the advantages of each plan based on the number of minutes used.

MN 8.2.4.8 - Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.MN 8.2.4.9 - Use the relationship between square roots and squares of a number to solve problems. Example: If pi x² = 5, then |x| = the square root of (5/pi), or equivalently, x = the square root of (5/pi) or x = - the square root of (5/pi). If x is understood as the radius of a circle in this example, then the negative solution should be discarded and x = the square root of (5/pi).


MN 8.3.1 - Solve problems involving right triangles using the Pythagorean Theorem and its converse.

MN 8.3.1.1 - Use the Pythagorean Theorem to solve problems involving right triangles. Example 1: Determine the perimeter of a right triangle, given the lengths of two of its sides. Example 2: Show that a triangle with side lengths 4, 5 and 6 is not a right triangle.


Obj. 71 - Determine the length of the hypotenuse of a right triangle using the Pythagorean theorem


081309Page 90 of 198



Obj. 72 - Determine the length of a leg of a right triangle using the Pythagorean theoremObj. 73 - WP: Use the Pythagorean theorem to find a length or a distance

Obj. 75 - Determine if a triangle is a right triangle by using the Pythagorean theorem

MN 8.3.1.2 - Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.


Obj. 74 - Determine a distance on the Cartesian plane using the Pythagorean theorem

MN 8.3.1.3 - Informally justify the Pythagorean Theorem by using measurements, diagrams and computer software.MN 8.3.2 - Solve problems involving parallel and perpendicular lines on a coordinate system.MN 8.3.2.1 - Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine the relationships between lines and their equations.

MN 8.3.2.2 - Analyze polygons on a coordinate system by determining the slopes of their sides. Example: Given the coordinates of four points, determine whether the corresponding quadrilateral is a parallelogram.

MN 8.3.2.3 - Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically.MN 8.4 - Data Analysis & Probability

MN 8.4.1 - Interpret data using scatterplots and approximate lines of best fit. Use lines of best fit to draw conclusions about data.


081309Page 91 of 198



MN 8.4.1.1 - Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.


Obj. 77 - Use a scatter plot to organize data

Obj. 79 - Approximate a trend line for a scatter plotObj. 80 - Answer a question using information from a scatter plot

MN 8.4.1.2 - Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set. Example: Given a scatterplot relating student heights to shoe sizes, predict the shoe size of a 5'4" student, even if the data does not contain information for a student of that height.


Obj. 80 - Answer a question using information from a scatter plot

MN 8.4.1.3 - Assess the reasonableness of predictions using scatterplots by interpreting them in the original context. Example: A set of data may show that the number of women in the U.S. Senate is growing at a certain rate each election cycle. Is it reasonable to use this trend to predict the year in which the Senate will eventually include 1000 female Senators?


081309Page 92 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grade 8, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 8.1 - Number & OperationMN 8.1.1 - Read, write, compare, classify and represent real numbers, and use them to solve problems in various contexts.MN 8.1.1.1 - Classify real numbers as rational or irrational. Know that when a square root of a positive integer is not an integer, then it is irrational. Know that the sum of a rational number and an irrational number is irrational, and the product of a non-zero rational number and an irrational number is irrational. Example: Classify the following numbers as whole numbers, integers, rational numbers, irrational numbers, recognizing that some numbers belong in more than one category: 6/3, 3/6, 3.6 repeating, pi/2, - the square root of 4, the square root of 10, -6.7.

MN 8.1.1.2 - Compare real numbers; locate real numbers on a number line. Identify the square root of a positive integer as an integer, or if it is not an integer, locate it as a real number between two consecutive positive integers. Example 1: Put the following numbers in order from smallest to largest: 2, square root of 3, -4, -6.8, - the square root of 37. Example 2: The square root of 68 is an irrational number between 8 and 9.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Algebra 1


081309Page 93 of 198



MN 8.1.1.3 - Determine rational approximations for solutions to problems involving real numbers. Example 1: A calculator can be used to determine that the square root of 7 is approximately 2.65. Example 2: To check that 1 5/12 is slightly bigger than the square root of 2, do the calculation (1 5/12)² = (17/12)² = 289/144 = 2 1/144. Example 3: Knowing that the square root of 10 is between 3 and 4, try squaring numbers like 3.5, 3.3, 3.1 to determine that 3.1 is a reasonable rational approximation of the square root of 10.MN 8.1.1.4 - Know and apply the properties of positive and negative integer exponents to generate equivalent numerical expressions. Example: 3² x 3 to the -5 power = 3 to the -3 power (1/3)³ = 1/27.


Obj. 4 - Evaluate a fraction raised to an integer power

Topic 5 - Properties of Powers Obj. 58 - Apply the product of powers property to a monomial numerical expressionObj. 60 - Apply the power of a power property to a monomial numerical expressionObj. 63 - Apply the quotient of powers property to monomial numerical expressions

MN 8.1.1.5 - Express approximations of very large and very small numbers using scientific notation; understand how calculators display numbers in scientific notation. Multiply and divide numbers expressed in scientific notation, express the answer in scientific notation, using the correct number of significant digits when physical measurements are involved. Example: (4.2 x 10 to the 4th power) x (8.25 x 10³)= 3.465 x 10 to the 8th power, but if these numbers represent physical measurements, the answer should be expressed as 3.5 x 10 to the 8th power because the first factor, 4.2 x 10 to the 4th power, only has two significant digits.


081309Page 94 of 198



MN 8.2 - AlgebraMN 8.2.1 - Understand the concept of function in real-world and mathematical situations, and distinguish between linear and non-linear functions.MN 8.2.1.1 - Understand that a function is a relationship between an independent variable and a dependent variable in which the value of the independent variable determines the value of the dependent variable. Use functional notation, such as f(x), to represent such relationships. Example: The relationship between the area of a square and the side length can be expressed as f(x)=x². In this case, f(5)=25 , which represents the fact that a square of side length 5 units has area 25 units squared.

Topic 2 - Relations and Functions

Obj. 7 - Determine the independent or dependent variable in a given situation

MN 8.2.1.2 - Use linear functions to represent relationships in which changing the input variable by some amount leads to a change in the output variable that is a constant times that amount. Example: Uncle Jim gave Emily $50 on the day she was born and $25 on each birthday after that. The function f(x)=50+25x represents the amount of money Jim has given after x years. The rate of change is $25 per year.

MN 8.2.1.3 - Understand that a function is linear if it can be expressed in the form f(x)=mx+b or if its graph is a straight line. Example: The function f(x)=x² is not a linear function because its graph contains the points (1,1), (-1,1) and (0,0), which are not on a straight line.


Obj. 12 - Determine if a function is linear or nonlinear

Obj. 13 - Determine whether a graph or a table represents a linear or nonlinear function


081309Page 95 of 198



MN 8.2.1.4 - Understand that an arithmetic sequence is a linear function that can be expressed in the form f(x)=mx+b, where x = 0, 1, 2, 3, .... Example: The arithmetic sequence 3, 7, 11, 15, ..., can be expressed as f(x) = 4x + 3.

MN 8.2.1.5 - Understand that a geometric sequence is a non-linear function that can be expressed in the form , fx(x)=ab where x = 0, 1, 2, 3, .... Example: The geometric sequence 6, 12, 24, 48, ... , can be expressed in the form f(x) = 6(2 to the x power).MN 8.2.2 - Recognize linear functions in real-world and mathematical situations; represent linear functions and other functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions and explain results in the original context.

MN 8.2.2.1 - Represent linear functions with tables, verbal descriptions, symbols, equations and graphs; translate from one representation to another.MN 8.2.2.2 - Identify graphical properties of linear functions including slopes and intercepts. Know that the slope equals the rate of change, and that the y-intercept is zero when the function represents a proportional relationship.

MN 8.2.2.3 - Identify how coefficient changes in the equation f(x) = mx + b affect the graphs of linear functions. Know how to use graphing technology to examine these effects.


081309Page 96 of 198



MN 8.2.2.4 - Represent arithmetic sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl starts with $100 in savings and adds $10 at the end of each month, she will have 100 + 10x dollars after x months.

MN 8.2.2.5 - Represent geometric sequences using equations, tables, graphs and verbal descriptions, and use them to solve problems. Example: If a girl invests $100 at 10% annual interest, she will have 100(1.1 to the x power) dollars after x years.

MN 8.2.3 - Generate equivalent numerical and algebraic expressions and use algebraic properties to evaluate expressions.MN 8.2.3.1 - Evaluate algebraic expressions, including expressions containing radicals and absolute values, at specified values of their variables. Example: Evaluate pi r²h when r = 3 and h = 0.5, and then use an approximation of pi, to obtain an approximate answer.MN 8.2.3.2 - Justify steps in generating equivalent expressions by identifying the properties used, including the properties of algebra. Properties include the associative, commutative and distributive laws, and the order of operations, including grouping symbols.MN 8.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear expressions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.


081309Page 97 of 198



MN 8.2.4.1 - Use linear equations to represent situations involving a constant rate of change, including proportional and non-proportional relationships. Example: For a cylinder with fixed radius of length 5, the surface area A = 2 pi(5)h + 2 pi(5)² = 10 pi h + 50 pi, is a linear function of the height h, but it is not proportional to the height.

Topic 3 - Linear Equations and Inequalities

Obj. 16 - WP: Determine a linear equation that can be used to solve a percent problem

MN 8.2.4.2 - Solve multi-step equations in one variable. Solve for one variable in a multi-variable equation in terms of the other variables. Justify the steps by identifying the properties of equalities used. Example 1: The equation 10x + 17 = 3x can be changed to 7x + 17 = 0, and then to 7x = -17 by adding/subtracting the same quantities to both sides. These changes do not change the solution of the equation. Example 2: Express the radius of a circle in terms of its circumference.


Obj. 14 - Solve a 1-variable linear equation that requires simplification and has the variable on one side

Obj. 15 - Solve a 1-variable linear equation with the variable on both sidesObj. 24 - Rewrite an equation to solve for a specified variable

MN 8.2.4.3 - Express linear equations in slope-intercept, point-slope and standard forms, and convert between these forms. Given sufficient information, find an equation of a line. Example: Determine an equation of the line through the points (-1,6) and (2/3, -3/4).


Obj. 25 - Determine the slope-intercept form or the standard form of a linear equation

Obj. 31 - Determine an equation of a line given the slope and y-intercept of the lineObj. 33 - Determine an equation for a line given the slope of the line and a point on the line that is not the y-interceptObj. 34 - Determine an equation of a line given two points on the line


081309Page 98 of 198



MN 8.2.4.4 - Use linear inequalities to represent relationships in various contexts. Example: A gas station charges $0.10 less per gallon of gasoline if a customer also gets a car wash. Without the car wash, gas costs $2.79 per gallon. The car wash is $8.95. What are the possible amounts (in gallons) of gasoline that you can buy if you also get a car wash and can spend at most $35?

MN 8.2.4.5 - Solve linear inequalities using properties of inequalities. Graph the solutions on a number line. Example: The inequality -3x < 6 is equivalent to x > -2 , which can be represented on the number line by shading in the interval to the right of -2.


Obj. 21 - Solve a 1-variable linear inequality with the variable on one side

Obj. 22 - Solve a 1-variable linear inequality with the variable on both sidesObj. 23 - Solve a 1-variable compound inequality

MN 8.2.4.6 - Represent relationships in various contexts with equations and inequalities involving the absolute value of a linear expression. Solve such equations and inequalities and graph the solutions on a number line. Example: A cylindrical machine part is manufactured with a radius of 2.1 cm, with a tolerance of 1/100 cm. The radius r satisfies the inequality |r - 2.1| is less than or equal to .01.


Obj. 20 - Solve a 1-variable absolute value equation

Obj. 43 - Solve a 1-variable absolute value inequalityObj. 44 - Determine the graph of a 1-variable absolute value inequality


081309Page 99 of 198



MN 8.2.4.7 - Represent relationships in various contexts using systems of linear equations. Solve systems of linear equations in two variables symbolically, graphically and numerically. Example: Marty's cell phone company charges $15 per month plus $0.04 per minute for each call. Jeannine's company charges $0.25 per minute. Use a system of equations to determine the advantages of each plan based on the number of minutes used.

Topic 4 - Systems of Linear Equations and Inequalities

Obj. 45 - Solve a system of linear equations in two variables by graphing

Obj. 46 - Solve a system of linear equations in two variables by substitutionObj. 47 - Solve a system of linear equations in two variables by eliminationObj. 49 - Solve a system of linear equations in two variables using any methodObj. 50 - WP: Determine a system of linear equations that represents a given situationObj. 51 - WP: Solve a mixture problem that can be represented by a system of linear equationsObj. 52 - WP: Solve a motion problem that can be represented by a system of linear equationsObj. 53 - Solve a number problem that can be represented by a linear system of equations

MN 8.2.4.8 - Understand that a system of linear equations may have no solution, one solution, or an infinite number of solutions. Relate the number of solutions to pairs of lines that are intersecting, parallel or identical. Check whether a pair of numbers satisfies a system of two linear equations in two unknowns by substituting the numbers into both equations.


Obj. 48 - Determine the number of solutions to a system of linear equations


081309Page 100 of 198



MN 8.2.4.9 - Use the relationship between square roots and squares of a number to solve problems. Example: If pi x² = 5, then |x| = the square root of (5/pi), or equivalently, x = the square root of (5/pi) or x = - the square root of (5/pi). If x is understood as the radius of a circle in this example, then the negative solution should be discarded and x = the square root of (5/pi).

Topic 8 - Quadratic Equations and Functions

Obj. 89 - Solve a quadratic equation by taking the square root


MN 8.3.1 - Solve problems involving right triangles using the Pythagorean Theorem and its converse.

MN 8.3.1.1 - Use the Pythagorean Theorem to solve problems involving right triangles. Example 1: Determine the perimeter of a right triangle, given the lengths of two of its sides. Example 2: Show that a triangle with side lengths 4, 5 and 6 is not a right triangle.MN 8.3.1.2 - Determine the distance between two points on a horizontal or vertical line in a coordinate system. Use the Pythagorean Theorem to find the distance between any two points in a coordinate system.

MN 8.3.1.3 - Informally justify the Pythagorean Theorem by using measurements, diagrams and computer software.MN 8.3.2 - Solve problems involving parallel and perpendicular lines on a coordinate system.MN 8.3.2.1 - Understand and apply the relationships between the slopes of parallel lines and between the slopes of perpendicular lines. Dynamic graphing software may be used to examine the relationships between lines and their equations.


081309Page 101 of 198



MN 8.3.2.2 - Analyze polygons on a coordinate system by determining the slopes of their sides. Example: Given the coordinates of four points, determine whether the corresponding quadrilateral is a parallelogram.

MN 8.3.2.3 - Given a line on a coordinate system and the coordinates of a point not on the line, find lines through that point that are parallel and perpendicular to the given line, symbolically and graphically.MN 8.4 - Data Analysis & Probability

MN 8.4.1 - Interpret data using scatterplots and approximate lines of best fit. Use lines of best fit to draw conclusions about data.MN 8.4.1.1 - Collect, display and interpret data using scatterplots. Use the shape of the scatterplot to informally estimate a line of best fit and determine an equation for the line. Use appropriate titles, labels and units. Know how to use graphing technology to display scatterplots and corresponding lines of best fit.

MN 8.4.1.2 - Use a line of best fit to make statements about approximate rate of change and to make predictions about values not in the original data set. Example: Given a scatterplot relating student heights to shoe sizes, predict the shoe size of a 5'4" student, even if the data does not contain information for a student of that height.


081309Page 102 of 198



MN 8.4.1.3 - Assess the reasonableness of predictions using scatterplots by interpreting them in the original context. Example: A set of data may show that the number of women in the U.S. Senate is growing at a certain rate each election cycle. Is it reasonable to use this trend to predict the year in which the Senate will eventually include 1000 female Senators?


081309Page 103 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grades: 9-11, Academic Standards, State Department of EducationStandard Topic Description Objective DescriptionMN 9.2 - AlgebraMN 9.2.1 - Understand the concept of function, and identify important features of functions and other relations using symbolic and graphical methods where appropriate.MN 9.2.1.1 - Understand the definition of a function. Use functional notation and evaluate a function at a given point in its domain. Example: If f(x) - 1/(x²-3),find f(-4).


Obj. 11 - Evaluate a function written in function notation for a given value

MN 9.2.1.2 - Distinguish between functions and other relations defined symbolically, graphically or in tabular form.


Obj. 8 - Determine if a relation is a function

MN 9.2.1.3 - Find the domain of a function defined symbolically, graphically or in a real-world context. Example: The formula f(x) = pi x² can represent a function whose domain is all real numbers, but in the context of the area of a circle, the domain would be restricted to positive x.


Obj. 9 - Determine the domain or range of a function

Obj. 10 - WP: Determine a reasonable domain or range for a function in a given situation

MN 9.2.1.4 - Obtain information and draw conclusions from graphs of functions and other relations. Example: If a graph shows the relationship between the elapsed flight time of a golf ball at a given moment and its height at that same moment, identify the time interval during which the ball is at least 100 feet above the ground.MN 9.2.1.5 - Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax² + bx + c, in the form f(x) = a(x - h)² + k , or in factored form.MN 9.2.1.6 - Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.



081309Page 104 of 198

Agency Tag Set NameMinnesota, Math, 2007, Grades: 9-11, Academic Standards, State Department of EducationStandard Topic Description Objective Description


MN 9.2.1.7 - Understand the concept of an asymptote and identify asymptotes for exponential functions and reciprocals of linear functions, using symbolic and graphical methods.MN 9.2.1.8 - Make qualitative statements about the rate of change of a function, based on its graph or table of values. Example: The function f(x) = 3 to the x power increases for all x, but it increases faster when x > 2 than it does when x < 2.MN 9.2.1.9 - Determine how translations affect the symbolic and graphical forms of a function. Know how to use graphing technology to examine translations. Example: Determine how the graph of f(x) = |x - h| + k changes as h and k change.

MN 9.2.2 - Recognize linear, quadratic, exponential and other common functions in real-world and mathematical situations; represent these functions with tables, verbal descriptions, symbols and graphs; solve problems involving these functions, and explain results in the original context.

MN 9.2.2.1 - Represent and solve problems in various contexts using linear and quadratic functions. Example: Write a function that represents the area of a rectangular garden that can be surrounded with 32 feet of fencing, and use the function to determine the possible dimensions of such a garden if the area must be at least 50 square feet.


Obj. 87 - WP: Answer a question using the graph of a quadratic function

Obj. 94 - WP: Use a given quadratic equation to solve a problem

MN 9.2.2.2 - Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

Topic 9 - Exponential Equations and Functions

Obj. 96 - WP: Evaluate an exponential growth or an exponential decay function


081309Page 105 of 198



Obj. 97 - Solve a problem involving exponential growth or exponential decay

MN 9.2.2.3 - Sketch graphs of linear, quadratic and exponential functions, and translate between graphs, tables and symbolic representations. Know how to use graphing technology to graph these functions.


Obj. 86 - Determine the graph of a given quadratic function

Topic 9 - Exponential Equations and Functions

Obj. 95 - Determine the graph of an exponential function

MN 9.2.2.4 - Express the terms in a geometric sequence recursively and by giving an explicit (closed form) formula, and express the partial sums of a geometric series recursively. Example 1: A closed form formula for the terms tn in the geometric sequence 3, 6, 12, 24, ... is tn = 3(2) to the (n-1) power, where n = 1, 2, 3, ... , and this sequence can be expressed recursively by writing t1 = 3 and tn = 2t(n-1), for n is greater than or equal to 2. Example 2: the partial sums sn of the series 3 + 6 + 12 + 24 + ... can be expressed recursively by writing s1 = 3 and sn = 3 + 2s(n-1), for n is greater than or equal to 2.

MN 9.2.2.5 - Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.MN 9.2.2.6 - Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x³, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.

Topic 11 - Radical Equations and Functions

Obj. 111 - Determine the graph of a radical function

Topic 13 - Rational Equations and Functions

Obj. 126 - Determine the graph of a rational function


081309Page 106 of 198



MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.MN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

Topic 6 - Polynomial Expressions Obj. 70 - Add polynomial expressions

Obj. 71 - Subtract polynomial expressionsObj. 72 - Multiply a polynomial by a monomialObj. 73 - Multiply two binomials of the form (x +/- a)(x +/- b)Obj. 74 - Multiply two binomials of the form (ax +/- b)(cx +/- d)Obj. 75 - Multiply two binomials of the form (ax +/- by)(cx +/- dy)Obj. 76 - Square a binomialObj. 77 - Multiply two nonlinear binomialsObj. 78 - Multiply a trinomial by a binomial

Topic 12 - Rational Expressions Obj. 117 - Divide a polynomial expression by a monomialObj. 118 - Divide a polynomial expression by a binomial

MN 9.2.3.3 - Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Example: 9x to the 6th power - x to the 4th power = (3x³ - x²)(3x³ + x²).

Topic 7 - Factor Algebraic Expressions

Obj. 79 - Factor the GCF from a polynomial expression

Obj. 80 - Factor trinomials that result in factors of the form (x +/- a)(x +/- b)

Obj. 81 - Factor trinomials that result in factors of the form (ax +/- b)(cx +/- d)Obj. 82 - Factor trinomials that result in factors of the form (ax +/- by)(cx +/- dy)Obj. 83 - Factor the difference of two squares


081309Page 107 of 198



Obj. 84 - Factor a perfect-square trinomialObj. 85 - Factor a polynomial that has a GCF and two linear binomial factors

MN 9.2.3.4 - Add, subtract, multiply, divide and simplify algebraic fractions. Example: 1/(1-x) + x/(1+x) is equivalent to (1+2x-x²)/(1-x²).

Topic 12 - Rational Expressions Obj. 114 - Simplify a rational expression involving polynomial terms

Obj. 115 - Multiply rational expressionsObj. 116 - Divide rational expressions

Obj. 120 - Add or subtract two rational expressions with like denominatorsObj. 121 - Add or subtract two rational expressions with unlike monomial denominatorsObj. 122 - Add or subtract two rational expressions with unlike polynomial denominators

MN 9.2.3.5 - Check whether a given complex number is a solution of a quadratic equation by substituting it for the variable and evaluating the expression, using arithmetic with complex numbers. Example: The complex number (1+i)/2 is a solution of 2x² - 2x² + 1 = 0, since 2((1+i)/2)² - 2((1+i)/2) + 1 = i-(1+i) + 1 = 0.

MN 9.2.3.6 - Apply the properties of positive and negative rational exponents to generate equivalent algebraic expressions, including those involving nth roots. Example: The square root of 2 x the square root of 7 = 2 to the 1/2 power x 7 to the 1/2 power = 14 to the 1/2 power = the square root of 14. Rules for computing directly with radicals may also be used: the square root of 2 x the square root of x= the square root of 2x.

Topic 5 - Properties of Powers Obj. 58 - Apply the product of powers property to a monomial numerical expression

Obj. 59 - Apply the product of powers property to a monomial algebraic expressionObj. 60 - Apply the power of a power property to a monomial numerical expression


081309Page 108 of 198



Obj. 61 - Apply the power of a power property to a monomial algebraic expressionObj. 62 - Apply the power of a product property to a monomial algebraic expressionObj. 63 - Apply the quotient of powers property to monomial numerical expressionsObj. 64 - Apply the quotient of powers property to monomial algebraic expressionsObj. 65 - Apply the power of a quotient property to monomial algebraic expressionsObj. 67 - Apply properties of exponents to monomial algebraic expressions

Topic 10 - Radical Expressions Obj. 98 - Simplify a monomial numerical expression involving the square root of a whole numberObj. 99 - Multiply monomial numerical expressions involving radicalsObj. 100 - Divide monomial numerical expressions involving radicalsObj. 101 - Add and/or subtract numerical radical expressionsObj. 102 - Multiply a binomial numerical radical expression by a numerical radical expressionObj. 103 - Rationalize the denominator of a numerical radical expressionObj. 104 - Simplify a monomial algebraic radical expressionObj. 105 - Rationalize the denominator of an algebraic radical expressionObj. 106 - Add or subtract algebraic radical expressionsObj. 107 - Multiply monomial algebraic radical expressionsObj. 108 - Divide monomial algebraic radical expressions


081309Page 109 of 198



MN 9.2.3.7 - Justify steps in generating equivalent expressions by identifying the properties used. Use substitution to check the equality of expressions for some particular values of the variables; recognize that checking with substitution does not guarantee equality of expressions for all values of the variables.

MN 9.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.MN 9.2.4.1 - Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. Example: A diver jumps from a 20 meter platform with an upward velocity of 3 meters per second. In finding the time at which the diver hits the surface of the water, the resulting quadratic equation has a positive and a negative solution. The negative solution should be discarded because of the context.


Obj. 88 - Solve a quadratic equation by graphing the associated quadratic function

Obj. 89 - Solve a quadratic equation by taking the square rootObj. 90 - Determine the solution(s) of an equation given in factored form

Obj. 91 - Solve a quadratic equation by factoring


081309Page 110 of 198



Obj. 92 - Solve a quadratic equation using the quadratic formula

MN 9.2.4.2 - Represent relationships in various contexts using equations involving exponential functions; solve these equations graphically or numerically. Know how to use calculators, graphing utilities or other technology to solve these equations.

MN 9.2.4.3 - Recognize that to solve certain equations, number systems need to be extended from whole numbers to integers, from integers to rational numbers, from rational numbers to real numbers, and from real numbers to complex numbers. In particular, non-real complex numbers are needed to solve some quadratic equations with real coefficients.

MN 9.2.4.4 - Represent relationships in various contexts using systems of linear inequalities; solve them graphically. Indicate which parts of the boundary are included in and excluded from the solution set using solid and dotted lines.


Obj. 55 - Determine the graph of the solution set of a system of linear inequalities in two variables

Obj. 56 - WP: Determine a system of linear inequalities that represents a given situationObj. 57 - WP: Determine possible solutions to a problem that can be represented by a system of linear inequalities

MN 9.2.4.5 - Solve linear programming problems in two variables using graphical methods.MN 9.2.4.6 - Represent relationships in various contexts using absolute value inequalities in two variables; solve them graphically. Example: If a pipe is to be cut to a length of 5 meters accurate to within a tenth of its diameter, the relationship between the length x of the pipe and its diameter y satisfies the inequality |x - 5| is less than or equal to 0.1y.


081309Page 111 of 198



MN 9.2.4.7 - Solve equations that contain radical expressions. Recognize that extraneous solutions may arise when using symbolic methods. Example 1: The equation the square root of x-9 = 9 the square root of x may be solved by squaring both sides to obtain x - 9 = 81x, which has the solution x = -9/80. However, this is not a solution of the original equation, so it is an extraneous solution that should be discarded. The original equation has no solution in this case. Example 2: Solve the cubed root of (-x+1) = -5.

Topic 11 - Radical Equations and Functions

Obj. 109 - Solve a radical equation that leads to a linear equation

Obj. 110 - Solve a radical equation that leads to a quadratic equation

MN 9.2.4.8 - Assess the reasonableness of a solution in its given context and compare the solution to appropriate graphical or numerical estimates; interpret a solution in the original context.MN 9.3 - Geometry & Measurement

MN 9.3.1 - Calculate measurements of plane and solid geometric figures; know that physical measurements depend on the choice of a unit and that they are approximations.

MN 9.3.1.1 - Determine the surface area and volume of pyramids, cones and spheres. Use measuring devices or formulas as appropriate. Example: Measure the height and radius of a cone and then use a formula to find its volume.

MN 9.3.1.2 - Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. Example: Find the volume of a regular hexagonal prism by decomposing it into six equal triangular prisms.


081309Page 112 of 198



MN 9.3.1.3 - Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. Example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.

MN 9.3.1.4 - Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.MN 9.3.1.5 - Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements. Example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual area of the rectangle could be smaller than 25 cm² or larger than 26 cm², even though 2.6 × 9.8 = 25.48.

MN 9.3.2 - Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.MN 9.3.2.1 - Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.


081309Page 113 of 198



MN 9.3.2.2 - Accurately interpret and use words and phrases in geometric proofs such as "if...then," "if and only if," "all," and "not." Recognize the logical relationships between an "if...then" statement and its inverse, converse and contrapositive. Example: The statement "If you don't do your homework, you can't go to the dance" is not logically equivalent to its inverse "If you do your homework, you can go to the dance.".

MN 9.3.2.3 - Assess the validity of a logical argument and give counterexamples to disprove a statement.MN 9.3.2.4 - Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. Example: Prove that the sum of the interior angles of a pentagon is 540° using the fact that the sum of the interior angles of a triangle is 180°.MN 9.3.2.5 - Use technology tools to examine theorems, test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.

MN 9.3.3 - Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.


081309Page 114 of 198



MN 9.3.3.1 - Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. Example: Prove that the perpendicular bisector of a line segment is the set of all points equidistant from the two endpoints, and use this fact to solve problems and justify other results.

MN 9.3.3.2 - Know and apply properties of angles, including corresponding, exterior, interior, vertical, complementary and supplementary angles, to solve problems and logically justify results. Example: Prove that two triangles formed by a pair of intersecting lines and a pair of parallel lines (an "X" trapped between two parallel lines) are similar.

MN 9.3.3.3 - Know and apply properties of equilateral, isosceles and scalene triangles to solve problems and logically justify results. Example: Use the triangle inequality to prove that the perimeter of a quadrilateral is larger than the sum of the lengths of its diagonals.

MN 9.3.3.4 - Apply the Pythagorean Theorem and its converse to solve problems and logically justify results. Example: When building a wooden frame that is supposed to have a square corner, ensure that the corner is square by measuring lengths near the corner and applying the Pythagorean Theorem.


081309Page 115 of 198



MN 9.3.3.5 - Know and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems and logically justify results. Example 1: Use 30-60-90 triangles to analyze geometric figures involving equilateral triangles and hexagons. Example 2: Determine exact values of the trigonometric ratios in these special triangles using relationships among the side lengths.

MN 9.3.3.6 - Know and apply properties of congruent and similar figures to solve problems and logically justify results. Example 1: Analyze lengths and areas in a figure formed by drawing a line segment from one side of a triangle to a second side, parallel to the third side. Example 2: Determine the height of a pine tree by comparing the length of its shadow to the length of the shadow of a person of known height. Example 3: When attempting to build two identical 4-sided frames, a person measured the lengths of corresponding sides and found that they matched. Can the person conclude that the shapes of the frames are congruent?

MN 9.3.3.7 - Use properties of polygons-including quadrilaterals and regular polygons-to define them, classify them, solve problems and logically justify results. Example 1: Recognize that a rectangle is a special case of a trapezoid. Example 2: Give a concise and clear definition of a kite.

MN 9.3.3.8 - Know and apply properties of a circle to solve problems and logically justify results. Example: Show that opposite angles of a quadrilateral inscribed in a circle are supplementary.


081309Page 116 of 198



MN 9.3.4 - Solve real-world and mathematical geometric problems using algebraic methods.MN 9.3.4.1 - Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.MN 9.3.4.2 - Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. Example: Find the area of a triangle, given the measure of one of its acute angles and the lengths of the two sides that form that angle.

MN 9.3.4.3 - Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.MN 9.3.4.4 - Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.


Obj. 26 - Determine the slope of a line given two points on the line

MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).


081309Page 117 of 198



MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.MN 9.4 - Data Analysis & Probability

MN 9.4.1 - Display and analyze data; use various measures associated with data to draw conclusions, identify trends and describe relationships.

MN 9.4.1.1 - Describe a data set using data displays, such as box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.MN 9.4.1.2 - Analyze the effects on summary statistics of changes in data sets. Example 1: Understand how inserting or deleting a data point may affect the mean and standard deviation. Example 2: Understand how the median and interquartile range are affected when the entire data set is transformed by adding a constant to each data value or multiplying each data value by a constant.MN 9.4.1.3 - Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.


081309Page 118 of 198



MN 9.4.1.4 - Use the mean and standard deviation of a data set to fit it to a normal distribution (bell-shaped curve) and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets and tables to estimate areas under the normal curve. Example 1: After performing several measurements of some attribute of an irregular physical object, it is appropriate to fit the data to a normal distribution and draw conclusions about measurement error. Example 2: When data involving two very different populations is combined, the resulting histogram may show two distinct peaks, and fitting the data to a normal distribution is not appropriate.

MN 9.4.2 - Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusionsMN 9.4.2.1 - Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays. Example: Shifting data on the vertical axis can make relative changes appear deceptively large.

MN 9.4.2.2 - Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.MN 9.4.2.3 - Explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.


081309Page 119 of 198



MN 9.4.3 - Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.MN 9.4.3.1 - Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Example: If one girl and one boy are picked at random from a class with 20 girls and 15 boys, there are 20 × 15 = 300 different possibilities, so the probability that a particular girl is chosen together with a particular boy is 1/300.

MN 9.4.3.2 - Calculate experimental probabilities by performing simulations or experiments involving a probability model and using relative frequencies of outcomes.

MN 9.4.3.3 - Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.MN 9.4.3.4 - Use random numbers generated by a calculator or a spreadsheet, or taken from a table, to perform probability simulations and to introduce fairness into decision making. Example: If a group of students needs to fairly select one of its members to lead a discussion, they can use a random number to determine the selection.


081309Page 120 of 198



MN 9.4.3.5 - Apply probability concepts such as intersections, unions and complements of events, and conditional probability and independence, to calculate probabilities and solve problems. Example: The probability of tossing at least one head when flipping a fair coin three times can be calculated by looking at the complement of this event (flipping three tails in a row).

MN 9.4.3.6 - Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.MN 9.4.3.7 - Understand and use simple probability formulas involving intersections, unions and complements of events. Example 1: If the probability of an event is p, then the probability of the complement of an event is 1 - p; the probability of the intersection of two independent events is the product of their probabilities. Example 2: The probability of the union of two events equals the sum of the probabilities of the two individual events minus the probability of the intersection of the events.

MN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.


081309Page 121 of 198



MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.


081309Page 122 of 198


MN 9.2.1.2 - Distinguish between functions and other relations defined symbolically, graphically or in tabular form.MN 9.2.1.3 - Find the domain of a function defined symbolically, graphically or in a real-world context. Example: The formula f(x) = pi x² can represent a function whose domain is all real numbers, but in the context of the area of a circle, the domain would be restricted to positive x.


Standards List with Aligned Product SkillsProduct NameAccelerated Math Second Edition Geometry

Accelerated Math Grades 9 - 11

081309Page 123 of 198








081309Page 124 of 198






MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.


081309Page 125 of 198



MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.MN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.MN 9.2.3.3 - Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Example: 9x to the 6th power - x to the 4th power = (3x³ - x²)(3x³ + x²).





081309Page 126 of 198







081309Page 127 of 198








081309Page 128 of 198






Topic 10 - Surface Area and Volume

Obj. 88 - Solve a problem involving the surface area of a cone or a pyramid that has a rectangle or right triangle as a base

Obj. 91 - Determine the volume of a right pyramid or a right coneObj. 92 - Solve a problem involving the volume of a right pyramid or a right coneObj. 93 - Determine the volume of an oblique pyramid or an oblique cone

Obj. 94 - Determine the surface area of a sphereObj. 99 - Determine the volume of a sphere or hemisphereObj. 100 - WP: Determine the volume of a sphere or hemisphere

MN 9.3.1.2 - Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. Example: Find the volume of a regular hexagonal prism by decomposing it into six equal triangular prisms.

Topic 9 - Area Obj. 74 - Determine the area of a regular polygon

Obj. 79 - WP: Solve a problem involving the area of a complex shape formed by circles and polygons


Obj. 97 - Determine the surface area of a complex solid figure


081309Page 129 of 198



Obj. 98 - Solve a problem involving the surface area of a complex solid figureObj. 101 - Determine the volume of a complex solid figureObj. 102 - WP: Solve a problem involving the volume of a complex solid figure

MN 9.3.1.3 - Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. Example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.

MN 9.3.1.4 - Understand and apply the fact that the effect of a scale factor k on length, area and volume is to multiply each by k, k² and k³, respectively.


Obj. 103 - Solve a problem involving the surface areas of similar solid figures

Obj. 104 - Solve a problem involving the volumes of similar solid figures

MN 9.3.1.5 - Make reasonable estimates and judgments about the accuracy of values resulting from calculations involving measurements. Example: Suppose the sides of a rectangle are measured to the nearest tenth of a centimeter at 2.6 cm and 9.8 cm. Because of measurement errors, the width could be as small as 2.55 cm or as large as 2.65 cm, with similar errors for the height. These errors affect calculations. For instance, the actual area of the rectangle could be smaller than 25 cm² or larger than 26 cm², even though 2.6 × 9.8 = 25.48.

MN 9.3.2 - Construct logical arguments, based on axioms, definitions and theorems, to prove theorems and other results in geometry.


081309Page 130 of 198



MN 9.3.2.1 - Understand the roles of axioms, definitions, undefined terms and theorems in logical arguments.


MN 9.3.2.3 - Assess the validity of a logical argument and give counterexamples to disprove a statement.MN 9.3.2.4 - Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. Example: Prove that the sum of the interior angles of a pentagon is 540° using the fact that the sum of the interior angles of a triangle is 180°.MN 9.3.2.5 - Use technology tools to examine theorems, test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.

MN 9.3.3 - Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.


081309Page 131 of 198



MN 9.3.3.1 - Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. Example: Prove that the perpendicular bisector of a line segment is the set of all points equidistant from the two endpoints, and use this fact to solve problems and justify other results.

Topic 2 - Parallel and Perpendicular lines

Obj. 10 - Determine the measure of an angle formed by parallel lines and one or more transversals

Obj. 11 - Identify parallel lines using angle relationshipsObj. 12 - Determine the measure of an angle in a figure involving parallel and/or perpendicular linesObj. 13 - Determine if lines through points with given coordinates are parallel or perpendicularObj. 14 - Determine the coordinates of a point through which a line must pass in order to be parallel or perpendicular to a given line


Topic 2 - Parallel and Perpendicular lines

Obj. 9 - Identify angle relationships formed by multiple lines and transversals

Obj. 10 - Determine the measure of an angle formed by parallel lines and one or more transversalsObj. 12 - Determine the measure of an angle in a figure involving parallel and/or perpendicular lines

Topic 3 - Relationships Within Triangles

Obj. 16 - Determine the measure of an angle using angle relationships and the sum of the interior angles in a triangle


081309Page 132 of 198





Obj. 19 - Solve a problem using inequalities in a triangle

Obj. 20 - Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationships



Obj. 18 - Solve for the length of a side of a triangle using the Pythagorean theorem

Topic 7 - Right Triangles and Trigonometry

Obj. 44 - Determine a length in a complex figure using the Pythagorean theoremObj. 48 - WP: Solve a problem involving a complex figure using the Pythagorean theorem



Obj. 45 - Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle

Obj. 46 - Solve a problem using multiple non-trigonometric right-triangle relationshipsObj. 47 - WP: Determine a length using the properties of a 45-45-90 degree triangle or a 30-60-90 degree triangle


081309Page 133 of 198




Topic 4 - Congruent Triangles Obj. 22 - Determine the length of a side or the measure of an angle in congruent triangles

Obj. 23 - Identify a triangle congruence postulate that justifies a congruence statementObj. 24 - Identify congruent triangles using triangle congruence postulates or theoremsObj. 25 - Solve a problem involving a point on the bisector of an angle

Topic 6 - Similarity Obj. 34 - Determine the length of a side in one of two similar polygonsObj. 35 - Determine the length of a side or the measure of an angle in similar trianglesObj. 36 - Determine a length given the perimeters of similar triangles or the lengths of corresponding interior line segmentsObj. 37 - Identify a triangle similarity postulate that justifies a similarity statementObj. 38 - Identify similar triangles using triangle similarity postulates or theoremsObj. 39 - Determine a length in a triangle using a midsegmentObj. 40 - Determine a length using parallel lines and proportional partsObj. 42 - Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle


081309Page 134 of 198



Obj. 43 - WP: Determine a length using similarity


Topic 5 - Quadrilaterals and Other Polygons

Obj. 26 - Determine the measure of an angle or the sum of the angles in a polygon

Obj. 27 - Determine a length or an angle measure using general properties of parallelogramsObj. 28 - Determine a length or an angle measure using properties of squares, rectangles, or rhombiObj. 29 - Determine a length or an angle measure using properties of kitesObj. 30 - Determine a length or an angle measure using properties of trapezoidsObj. 31 - Determine a length or an angle measure in a complex figure using properties of polygonsObj. 32 - WP: Solve a problem using the properties of angles and/or sides of polygons

Topic 9 - Area Obj. 70 - Determine the area of a quadrilateralObj. 71 - Determine a length given the area of a quadrilateralObj. 72 - WP: Solve a problem involving the area of a quadrilateralObj. 75 - Determine a length given the area of a regular polygon


Topic 8 - Circles Obj. 54 - Determine the measure of an arc or a central angle using the relationship between the arc and the central angle

Obj. 55 - Solve a problem involving the length of an arcObj. 56 - Determine the length of a line segment, the measure of an angle, or the measure of an arc using a tangent to a circle


081309Page 135 of 198



Obj. 57 - Determine a length using a line segment tangent to a circle and the radius that intersects the tangent

Obj. 58 - Determine a length using two intersecting tangents to a circle

Obj. 59 - Determine a length or an arc measure using the properties of congruent chordsObj. 60 - Determine a length using a perpendicular bisector of a chordObj. 61 - Determine the measure of an arc or an angle using the relationship between an inscribed angle and its intercepted arcObj. 62 - Determine the measure of an arc or an angle using properties of an inscribed triangle or quadrilateral

Obj. 63 - Determine the measure of an arc or an angle formed by intersecting chords or a chord that intersects a tangent to a circleObj. 64 - Determine the measure of an arc or an angle formed by two tangents, two secants, or a tangent and a secant that intersect outside a circleObj. 65 - Determine a length using intersecting chords, two secants that intersect outside a circle, or a tangent and a secant that intersect outside a circleObj. 66 - Solve a problem involving intersecting chords, tangents, and/or secants of a circle

Topic 9 - Area Obj. 80 - Determine the area of a sector of a circleObj. 81 - Determine the area of a segment of a circleObj. 82 - Determine the length of the radius or the diameter of a circle given the area of a sectorObj. 83 - WP: Determine a length or an area involving a sector of a circle

MN 9.3.4 - Solve real-world and mathematical geometric problems using algebraic methods.


081309Page 136 of 198



MN 9.3.4.1 - Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.


Obj. 49 - Determine a sine, cosine, or tangent ratio in a right triangle

MN 9.3.4.2 - Apply the trigonometric ratios sine, cosine and tangent to solve problems, such as determining lengths and areas in right triangles and in figures that can be decomposed into right triangles. Know how to use calculators, tables or other technology to evaluate trigonometric ratios. Example: Find the area of a triangle, given the measure of one of its acute angles and the lengths of the two sides that form that angle.


Obj. 50 - Determine a length using a sine, cosine, or tangent ratio in a right triangle

Obj. 52 - WP: Determine a length in a right triangle using a sine, cosine, or tangent ratioObj. 53 - WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio

Topic 9 - Area Obj. 76 - Approximate the area of a right triangle using trigonometryObj. 77 - Approximate the area of a regular polygon using trigonometry

MN 9.3.4.3 - Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.


Obj. 51 - Determine the measure of an angle using a sine, cosine, or tangent ratio in a right triangle

Obj. 53 - WP: Determine the measure of an angle in a right triangle using a sine, cosine, or tangent ratio

MN 9.3.4.4 - Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.

Topic 1 - Basic Concepts of Geometry

Obj. 4 - Determine the distance between two points

Obj. 5 - Solve a problem involving the distance formulaObj. 6 - Determine the midpoint of a line segment given the coordinates of the endpoints


081309Page 137 of 198



Obj. 7 - Determine the area of a right triangle or a rectangle given the coordinates of the vertices of the figureObj. 8 - Solve a problem involving the midpoint formula

MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.

Topic 8 - Circles Obj. 67 - Determine an equation of a circle

MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).

Topic 11 - Transformations in the coordinate plane

Obj. 107 - Relate the coordinates of a preimage or an image to a translation described using mapping notation

Obj. 108 - Determine the coordinates of a preimage or an image given a reflection across a horizontal line, a vertical line, the line y = x, or the line y = -xObj. 109 - Relate the coordinates of a preimage or an image to a dilation centered at the originObj. 110 - Determine the angle of rotational symmetry of a figureObj. 111 - Determine the coordinates of the image of a figure after two transformations of the same type

Obj. 112 - Determine the coordinates of the image of a figure after two transformations of different types

MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.


Obj. 15 - Determine the measure of an angle using the sum of the interior angles in a triangle

Obj. 17 - Determine a length in a triangle using a median


081309Page 138 of 198



Obj. 18 - Solve for the length of a side of a triangle using the Pythagorean theoremObj. 19 - Solve a problem using inequalities in a triangleObj. 20 - Solve a problem involving two triangles by using the hinge theorem and other triangle inequality relationships

Topic 4 - Congruent Triangles Obj. 22 - Determine the length of a side or the measure of an angle in congruent triangles

Topic 5 - Quadrilaterals and Other Polygons

Obj. 27 - Determine a length or an angle measure using general properties of parallelogramsObj. 28 - Determine a length or an angle measure using properties of squares, rectangles, or rhombiObj. 29 - Determine a length or an angle measure using properties of kitesObj. 30 - Determine a length or an angle measure using properties of trapezoids

Topic 6 - Similarity Obj. 35 - Determine the length of a side or the measure of an angle in similar trianglesObj. 39 - Determine a length in a triangle using a midsegmentObj. 42 - Determine a length using similar triangles formed by the altitude to the hypotenuse of a right triangle




081309Page 139 of 198





081309Page 140 of 198







081309Page 141 of 198







081309Page 142 of 198




Topic 9 - Area Obj. 86 - Determine a probability using an area model


MN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.


081309Page 143 of 198



MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.


081309Page 144 of 198


Topic 3 - Relations, Functions, and Graphs

Obj. 31 - Evaluate functions for given values

Obj. 37 - WP: Function problemsMN 9.2.1.2 - Distinguish between functions and other relations defined symbolically, graphically or in tabular form.


Obj. 29 - Determine if relations are functions

MN 9.2.1.3 - Find the domain of a function defined symbolically, graphically or in a real-world context. Example: The formula f(x) = pi x² can represent a function whose domain is all real numbers, but in the context of the area of a circle, the domain would be restricted to positive x.


Obj. 27 - Domain and range, functions

Topic 10 - Rational Expressions and Equations

Obj. 143 - Rational expressions, domains

MN 9.2.1.4 - Obtain information and draw conclusions from graphs of functions and other relations. Example: If a graph shows the relationship between the elapsed flight time of a golf ball at a given moment and its height at that same moment, identify the time interval during which the ball is at least 100 feet above the ground.MN 9.2.1.5 - Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax² + bx + c, in the form f(x) = a(x - h)² + k , or in factored form.

Topic 11 - Conics and Second-Degree Equations

Obj. 170 - Parabolas, find vertex from equation

MN 9.2.1.6 - Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Algebra 2


081309Page 145 of 198







Obj. 12 - WP: Solve linear equations


Obj. 40 - WP: Linear equations

Topic 7 - Quadratic Obj. 97 - WP: Graph quadratic functionsObj. 99 - WP: Variation problemsObj. 101 - WP: Number problems using quadratic equationsObj. 102 - WP: Area and perimeter


081309Page 146 of 198



Obj. 103 - WP: Other problems using quadratic equations


Obj. 173 - WP: Production and profit problems


Topic 9 - Exponents and Logarithms

Obj. 138 - WP: Interest problems

Obj. 139 - WP: Growth and decay problems



Obj. 34 - Graph linear equations, ax + by = c

Obj. 35 - Graph linear equations, y = ax + b

Topic 7 - Quadratic Obj. 96 - Graph quadratic functions

Obj. 97 - WP: Graph quadratic functions


Obj. 141 - Graph exponential functions


Obj. 171 - Graph parabolas (y = x^2)


Topic 12 - Sequences and Series Obj. 189 - Find general terms of geo seq given first 4 terms


081309Page 147 of 198



MN 9.2.2.5 - Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

Topic 12 - Sequences and Series Obj. 190 - WP: Geometric sequences

Obj. 195 - WP: Geometric seriesMN 9.2.2.6 - Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x³, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.

Topic 6 - Roots, Radicals, and Complex Numbers

Obj. 78 - Graph square roots


Obj. 142 - Graph logarithmic functions


Obj. 147 - Graph rational functions and equations

MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.

Topic 1 - The Real Numbers Obj. 8 - Evaluate expressions for given values

Obj. 9 - WP: Evaluate expressionsTopic 8 - Polynomials Obj. 109 - Evaluate polynomials for

given valuesMN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

Topic 8 - Polynomials Obj. 110 - Add polynomials

Obj. 111 - Subtract polynomialsObj. 112 - Add and subtract polynomialsObj. 113 - Square a binomial, ax + by

Obj. 114 - Multiply 2 binomialsObj. 115 - Multiply monomials by polynomialsObj. 116 - Multiply binomials by trinomialsObj. 117 - Square trinomials


081309Page 148 of 198



Obj. 118 - Simplify polynomial expr using multiplicationObj. 119 - Divide polynomials by monomialsObj. 120 - Divide polynomials


Topic 8 - Polynomials Obj. 122 - Factor trinomials, ax(x + b)(x - c)

Obj. 123 - Factor difference of squares



Obj. 145 - Simplify rational expressions

Obj. 146 - Simplify rational expressions by factoringObj. 148 - Multiply and simplify rational expressionsObj. 149 - Divide and simplify rational expressionsObj. 150 - Add rational expressions

Obj. 151 - Subtract rational expressionsObj. 152 - Add and subtract rational expressionsObj. 154 - Simplify complex rational expressions



081309Page 149 of 198





Obj. 69 - Write square roots as exponential expressions

Obj. 70 - Simplify expressions with fractional exponentsObj. 71 - Simplify nth rootsObj. 73 - Simplify expressions with rational exponentsObj. 74 - Add and subtract radical expressionsObj. 75 - Rationalize denominators


MN 9.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.


081309Page 150 of 198



MN 9.2.4.1 - Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. Example: A diver jumps from a 20 meter platform with an upward velocity of 3 meters per second. In finding the time at which the diver hits the surface of the water, the resulting quadratic equation has a positive and a negative solution. The negative solution should be discarded because of the context.

Topic 7 - Quadratic Obj. 87 - Solve quad eqns, square root rule (real roots)

Obj. 88 - Solve quad eqns, square root rule (complex roots)Obj. 89 - Factor quadratics, real roots

Obj. 90 - Factor quadratics, roots with radicalsObj. 91 - Quadratic formula, 2 real rootsObj. 92 - Quadratic formula, complex rootsObj. 101 - WP: Number problems using quadratic equationsObj. 102 - WP: Area and perimeterObj. 105 - Solve quadratic inequalities



Obj. 136 - Solve exponential equations


081309Page 151 of 198





Topic 4 - Systems of Equations and Inequalities

Obj. 56 - Solve systems of linear inequalities by graphing




Obj. 76 - Solve equations containing radicals

Topic 7 - Quadratic Obj. 90 - Factor quadratics, roots with radicals


081309Page 152 of 198






MN 9.3.1.2 - Compose and decompose two- and three-dimensional figures; use decomposition to determine the perimeter, area, surface area and volume of various figures. Example: Find the volume of a regular hexagonal prism by decomposing it into six equal triangular prisms.MN 9.3.1.3 - Understand that quantities associated with physical measurements must be assigned units; apply such units correctly in expressions, equations and problem solutions that involve measurements; and convert between measurement systems. Example: 60 miles/hour = 60 miles/hour × 5280 feet/mile × 1 hour/3600 seconds = 88 feet/second.



081309Page 153 of 198






MN 9.3.2.3 - Assess the validity of a logical argument and give counterexamples to disprove a statement.


081309Page 154 of 198



MN 9.3.2.4 - Construct logical arguments and write proofs of theorems and other results in geometry, including proofs by contradiction. Express proofs in a form that clearly justifies the reasoning, such as two-column proofs, paragraph proofs, flow charts or illustrations. Example: Prove that the sum of the interior angles of a pentagon is 540° using the fact that the sum of the interior angles of a triangle is 180°.MN 9.3.2.5 - Use technology tools to examine theorems, test conjectures, perform constructions and develop mathematical reasoning skills in multi-step problems. The tools may include compass and straight edge, dynamic geometry software, design software or Internet applets.

MN 9.3.3 - Know and apply properties of geometric figures to solve real-world and mathematical problems and to logically justify results in geometry.MN 9.3.3.1 - Know and apply properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve problems and logically justify results. Example: Prove that the perpendicular bisector of a line segment is the set of all points equidistant from the two endpoints, and use this fact to solve problems and justify other results.



081309Page 155 of 198





Topic 7 - Quadratic Obj. 100 - WP: Pythagorean Theorem



081309Page 156 of 198






MN 9.3.4 - Solve real-world and mathematical geometric problems using algebraic methods.MN 9.3.4.1 - Understand how the properties of similar right triangles allow the trigonometric ratios to be defined, and determine the sine, cosine and tangent of an acute angle in a right triangle.

Topic 15 - Trigonometry Obj. 223 - Find the sine, cosine, or tangent


081309Page 157 of 198




Topic 15 - Trigonometry Obj. 234 - Find a side given side and angle

Obj. 235 - Find unknown sides of right trianglesObj. 236 - WP: Trigonometry



Obj. 39 - Find slopes from 2 points

MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.


Obj. 158 - Graph circles

Obj. 160 - Circles, write equations given centers and radiiObj. 162 - WP: Circles

MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).


081309Page 158 of 198



MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.

Topic 7 - Quadratic Obj. 100 - WP: Pythagorean Theorem



MN 9.4.1.1 - Describe a data set using data displays, such as box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.

Topic 14 - Statistics Obj. 208 - Line and stem-and-leaf plots

Obj. 209 - Box-and-whisker plotsObj. 210 - Interquartile ranges of data setsObj. 211 - Means of data setsObj. 212 - Medians of data setsObj. 213 - Modes of data setsObj. 214 - Means, medians, and modes of data sets

MN 9.4.1.2 - Analyze the effects on summary statistics of changes in data sets. Example 1: Understand how inserting or deleting a data point may affect the mean and standard deviation. Example 2: Understand how the median and interquartile range are affected when the entire data set is transformed by adding a constant to each data value or multiplying each data value by a constant.


081309Page 159 of 198



MN 9.4.1.3 - Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.


MN 9.4.2 - Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions


081309Page 160 of 198



MN 9.4.2.1 - Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays. Example: Shifting data on the vertical axis can make relative changes appear deceptively large.

MN 9.4.2.2 - Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.MN 9.4.2.3 - Explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.MN 9.4.3 - Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.MN 9.4.3.1 - Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Example: If one girl and one boy are picked at random from a class with 20 girls and 15 boys, there are 20 × 15 = 300 different possibilities, so the probability that a particular girl is chosen together with a particular boy is 1/300.

Topic 13 - Probability Obj. 196 - Fundamental Counting Principle

Obj. 202 - Probability of single events



081309Page 161 of 198





Topic 13 - Probability Obj. 204 - Probability of independent events

Obj. 205 - Conditional probabilityMN 9.4.3.6 - Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.


081309Page 162 of 198



MN 9.4.3.7 - Understand and use simple probability formulas involving intersections, unions and complements of events. Example 1: If the probability of an event is p, then the probability of the complement of an event is 1 - p; the probability of the intersection of two independent events is the product of their probabilities. Example 2: The probability of the union of two events equals the sum of the probabilities of the two individual events minus the probability of the intersection of the events.

MN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.

Topic 13 - Probability Obj. 205 - Conditional probability


081309Page 163 of 198


Topic 1 - Review of Fundamental Concepts of Algebra

Obj. 17 - Evaluate functions for given values


MN 9.2.1.4 - Obtain information and draw conclusions from graphs of functions and other relations. Example: If a graph shows the relationship between the elapsed flight time of a golf ball at a given moment and its height at that same moment, identify the time interval during which the ball is at least 100 feet above the ground.MN 9.2.1.5 - Identify the vertex, line of symmetry and intercepts of the parabola corresponding to a quadratic function, using symbolic and graphical methods, when the function is expressed in the form f(x) = ax² + bx + c, in the form f(x) = a(x - h)² + k , or in factored form.

Topic 2 - Polynomials Obj. 35 - Parabolas, find vertex from equation

MN 9.2.1.6 - Identify intercepts, zeros, maxima, minima and intervals of increase and decrease from the graph of a function.

Standards List with Aligned Product SkillsProduct NameAccelerated Math Pre-Calculus


081309Page 164 of 198







Obj. 4 - Solve linear equations

Obj. 5 - WP: Linear EquationsObj. 15 - WP: Quadratic equations

Topic 2 - Polynomials Obj. 37 - WP: Quadratic functionsMN 9.2.2.2 - Represent and solve problems in various contexts using exponential functions, such as investment growth, depreciation and population growth.

Topic 3 - Exponential and Logarithmic Functions

Obj. 57 - WP: Exponential functions


081309Page 165 of 198




Obj. 60 - WP: Compound interestObj. 61 - WP: Radioactive decay



Obj. 2 - Graph lines

Topic 2 - Polynomials Obj. 36 - Graph quadratic functions



Topic 7 - Conic Sections Obj. 91 - Parabolas, graph given equations


Topic 9 - Sequences and Series Obj. 130 - Find terms of geo seq (1st term & common ratio)

Obj. 131 - Find terms of geo seq given first terms

MN 9.2.2.5 - Recognize and solve problems that can be modeled using finite geometric sequences and series, such as home mortgage and other compound interest examples. Know how to use spreadsheets and calculators to explore geometric sequences and series in various contexts.

Topic 9 - Sequences and Series Obj. 132 - WP: Geometric sequences

Obj. 136 - WP: Geometric series


081309Page 166 of 198



MN 9.2.2.6 - Sketch the graphs of common non-linear functions such as f(x)= the square root of x, f(x) = |x|, f(x)= 1/x, f(x) = x³, and translations of these functions, such as f(x) = the square root of (x-2) + 4. Know how to use graphing technology to graph these functions.


Obj. 22 - Use rigid & nonrigid transformations to graph func

Obj. 23 - Graph rational functionsTopic 2 - Polynomials Obj. 36 - Graph quadratic functions



MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.MN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.

Topic 2 - Polynomials Obj. 39 - Synthetic division




Obj. 32 - Simplify, multiply, & divide rational expressions



081309Page 167 of 198





Obj. 27 - Simplify expressions w/ rational exponents

Obj. 28 - Factor expressions w/ rational exponentsObj. 29 - Simplify radical expressions


MN 9.2.4 - Represent real-world and mathematical situations using equations and inequalities involving linear, quadratic, exponential, and nth root functions. Solve equations and inequalities symbolically and graphically. Interpret solutions in the original context.


081309Page 168 of 198



MN 9.2.4.1 - Represent relationships in various contexts using quadratic equations and inequalities. Solve quadratic equations and inequalities by appropriate methods including factoring, completing the square, graphing and the quadratic formula. Find non-real complex roots when they exist. Recognize that a particular solution may not be applicable in the original context. Know how to use calculators, graphing utilities or other technology to solve quadratic equations and inequalities. Example: A diver jumps from a 20 meter platform with an upward velocity of 3 meters per second. In finding the time at which the diver hits the surface of the water, the resulting quadratic equation has a positive and a negative solution. The negative solution should be discarded because of the context.


Obj. 11 - Solve quad eqns, square root rule

Obj. 12 - Solve quad eqns, factor (real roots)Obj. 13 - Solve quad eqns, quadratic formulaObj. 15 - WP: Quadratic equations



Obj. 57 - WP: Exponential functions


Obj. 60 - WP: Compound interestObj. 61 - WP: Radioactive decay


081309Page 169 of 198






Obj. 119 - Solve systems of linear inequalities




Obj. 30 - Solve radical equations


081309Page 170 of 198









081309Page 171 of 198








081309Page 172 of 198







081309Page 173 of 198






Topic 5 - Applications in Trigonometry

Obj. 73 - WP: Right triangles


081309Page 174 of 198








081309Page 175 of 198





Obj. 73 - WP: Right triangles

MN 9.3.4.3 - Use calculators, tables or other technologies in connection with the trigonometric ratios to find angle measures in right triangles in various contexts.


Obj. 78 - Find values of inverse trig functions

MN 9.3.4.4 - Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints and slopes of line segments.MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.

Topic 7 - Conic Sections Obj. 95 - Circles, write eqns from given information

Obj. 96 - Circle, graph given equations

MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.


081309Page 176 of 198







081309Page 177 of 198







081309Page 178 of 198




Topic 10 - Probability Obj. 137 - Fundamental Counting Principle

Obj. 140 - WP: PermutationsObj. 141 - Find number of distinct arrangements of lettersObj. 143 - WP: CombinationsObj. 144 - Probability of single events

Obj. 145 - Probability of independent eventsObj. 146 - Conditional probabilityObj. 147 - Probability of dependent eventsObj. 148 - Probability of mutually exclusive events


MN 9.4.3.3 - Understand that the Law of Large Numbers expresses a relationship between the probabilities in a probability model and the experimental probabilities found by performing simulations or experiments involving the model.


081309Page 179 of 198



MN 9.4.3.4 - Use random numbers generated by a calculator or a spreadsheet, or taken from a table, to perform probability simulations and to introduce fairness into decision making. Example: If a group of students needs to fairly select one of its members to lead a discussion, they can use a random number to determine the selection.



Obj. 146 - Conditional probabilityObj. 147 - Probability of dependent events



Obj. 147 - Probability of dependent events


081309Page 180 of 198



MN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.

Topic 10 - Probability Obj. 146 - Conditional probability


081309Page 181 of 198




Standards List with Aligned Product SkillsProduct NameAM Probability & Statistics


081309Page 182 of 198








081309Page 183 of 198






MN 9.2.3 - Generate equivalent algebraic expressions involving polynomials and radicals; use algebraic properties to evaluate expressions.


081309Page 184 of 198



MN 9.2.3.1 - Evaluate polynomial and rational expressions and expressions containing radicals and absolute values at specified points in their domains.MN 9.2.3.2 - Add, subtract and multiply polynomials; divide a polynomial by a polynomial of equal or lower degree.MN 9.2.3.3 - Factor common monomial factors from polynomials, factor quadratic polynomials, and factor the difference of two squares. Example: 9x to the 6th power - x to the 4th power = (3x³ - x²)(3x³ + x²).





081309Page 185 of 198







081309Page 186 of 198








081309Page 187 of 198









081309Page 188 of 198








081309Page 189 of 198







081309Page 190 of 198







081309Page 191 of 198








081309Page 192 of 198





Topic 1 - Pre-requisites Obj. 4 - Slope of a line

MN 9.3.4.5 - Know the equation for the graph of a circle with radius r and center (h,k), (x - h)² + (y - k)² = r², and justify this equation using the Pythagorean Theorem and properties of translations.MN 9.3.4.6 - Use numeric, graphic and symbolic representations of transformations in two dimensions, such as reflections, translations, scale changes and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate grid. Example: If the point (3,-2) is rotated 90° counterclockwise about the origin, it becomes the point (2,3).MN 9.3.4.7 - Use algebra to solve geometric problems unrelated to coordinate geometry, such as solving for an unknown length in a figure involving similar triangles, or using the Pythagorean Theorem to obtain a quadratic equation for a length in a geometric figure.MN 9.4 - Data Analysis & Probability


081309Page 193 of 198




MN 9.4.1.1 - Describe a data set using data displays, such as box-and-whisker plots; describe and compare data sets using summary statistics, including measures of center, location and spread. Measures of center and location include mean, median, quartile and percentile. Measures of spread include standard deviation, range and inter-quartile range. Know how to use calculators, spreadsheets or other technology to display data and calculate summary statistics.

Topic 1 - Pre-requisites Obj. 3 - Scatter plots

Topic 3 - Sample spaces Obj. 19 - Circle graphsTopic 4 - Descriptive statistics Obj. 23 - Frequency histograms

Obj. 24 - Relative frequency histogramsObj. 25 - Stem-and-leaf plotsObj. 27 - MeanObj. 28 - MedianObj. 29 - ModeObj. 30 - Choose best measure of central tendencyObj. 31 - RangeObj. 32 - PercentilesObj. 35 - Box-and-whisker plotsObj. 38 - Standard deviation

Topic 8 - Bivariate data Obj. 69 - Stacked bar chartsMN 9.4.1.2 - Analyze the effects on summary statistics of changes in data sets. Example 1: Understand how inserting or deleting a data point may affect the mean and standard deviation. Example 2: Understand how the median and interquartile range are affected when the entire data set is transformed by adding a constant to each data value or multiplying each data value by a constant.


081309Page 194 of 198



MN 9.4.1.3 - Use scatterplots to analyze patterns and describe relationships between two variables. Using technology, determine regression lines (line of best fit) and correlation coefficients; use regression lines to make predictions and correlation coefficients to assess the reliability of those predictions.

Topic 1 - Pre-requisites Obj. 3 - Scatter plots

Topic 8 - Bivariate data Obj. 71 - Calculate correlation coefficient

Topic 11 - Linear regression Obj. 92 - Interpret scatter plotsObj. 94 - Calculate SxxObj. 95 - Calculate the slope of regression lineObj. 96 - Calculate aObj. 97 - Calculate regression line equationObj. 98 - Estimate the predicted value y-hatObj. 99 - Forecasting


Topic 6 - Continuous probability distributions

Obj. 57 - Normal distribution

Topic 9 - Confidence intervals Obj. 75 - Areas in tailsObj. 76 - Areas between tails

MN 9.4.2 - Explain the uses of data and statistical thinking to draw inferences, make predictions and justify conclusions


081309Page 195 of 198



MN 9.4.2.1 - Evaluate reports based on data published in the media by identifying the source of the data, the design of the study, and the way the data are analyzed and displayed. Show how graphs and data can be distorted to support different points of view. Know how to use spreadsheet tables and graphs or graphing technology to recognize and analyze distortions in data displays. Example: Shifting data on the vertical axis can make relative changes appear deceptively large.

MN 9.4.2.2 - Identify and explain misleading uses of data; recognize when arguments based on data confuse correlation and causation.

Topic 4 - Descriptive statistics Obj. 26 - Misleading graphs

MN 9.4.2.3 - Explain the impact of sampling methods, bias and the phrasing of questions asked during data collection.

Topic 7 - Data collection Obj. 62 - Sampling techniques

Obj. 63 - Identify biasMN 9.4.3 - Calculate probabilities and apply probability concepts to solve real-world and mathematical problems.MN 9.4.3.1 - Select and apply counting procedures, such as the multiplication and addition principles and tree diagrams, to determine the size of a sample space (the number of possible outcomes) and to calculate probabilities. Example: If one girl and one boy are picked at random from a class with 20 girls and 15 boys, there are 20 × 15 = 300 different possibilities, so the probability that a particular girl is chosen together with a particular boy is 1/300.

Topic 2 - Counting Obj. 5 - Fundamental counting principle

Obj. 8 - PermutationsObj. 9 - CombinationsObj. 10 - Pascal's triangle

Topic 3 - Sample spaces Obj. 13 - Probability of simple events


081309Page 196 of 198




Topic 7 - Data collection Obj. 64 - Experimental probability - predict using sample results


Topic 2 - Counting Obj. 12 - Random numbers


Topic 3 - Sample spaces Obj. 14 - Probability of compound events

Obj. 15 - Complement of eventsObj. 20 - Bayes' formula for conditional probability

Topic 5 - Discrete probability distributions

Obj. 40 - WP: Discrete uniform distribution

MN 9.4.3.6 - Describe the concepts of intersections, unions and complements using Venn diagrams. Understand the relationships between these concepts and the words AND, OR, NOT, as used in computerized searches and spreadsheets.

Topic 3 - Sample spaces Obj. 17 - Venn diagrams


081309Page 197 of 198



MN 9.4.3.7 - Understand and use simple probability formulas involving intersections, unions and complements of events. Example 1: If the probability of an event is p, then the probability of the complement of an event is 1 - p; the probability of the intersection of two independent events is the product of their probabilities. Example 2: The probability of the union of two events equals the sum of the probabilities of the two individual events minus the probability of the intersection of the events.

Topic 3 - Sample spaces Obj. 14 - Probability of compound events

Obj. 15 - Complement of eventsMN 9.4.3.8 - Apply probability concepts to real-world situations to make informed decisions. Example 1: Explain why a hockey coach might decide near the end of the game to pull the goalie to add another forward position player if the team is behind. Example 2: Consider the role that probabilities play in health care decisions, such as deciding between having eye surgery and wearing glasses.MN 9.4.3.9 - Use the relationship between conditional probabilities and relative frequencies in contingency tables. Example: A table that displays percentages relating gender (male or female) and handedness (right-handed or left-handed) can be used to determine the conditional probability of being left-handed, given that the gender is male.


081309Page 198 of 198

Minnesota State Standards Alignment Grades One through ...

Documents

Transcript of Minnesota State Standards Alignment Grades One through ...