Blank UbD Planning Template - Glassboro Public Schools

GLASSBORO PUBLIC SCHOOLS

Glassboro, New Jersey

Sixth Grade Math Curriculum

August, 2011

Mission Statement

The mission of the Glassboro School District, in partnership

with its families and community, is to ensure that all students

achieve the New Jersey Core Curriculum Content Standards

(NJ CCCS) at all grade levels; to prepare each of our students

with the knowledge, skills, attitudes and values necessary to

succeed as life-long learners; and to be competent, responsible,

well-rounded individuals ready to attain productive and self-

fulfilling roles in an ever changing global society.

Vision Statement

We see a partnership of the Board of Education, staff, all

students, parents and community that provides optimum

opportunities for access, learning and high achievement.

This partnership is responsible for the execution of our

Mission Statement.

GLASSBORO PUBLIC SCHOOLS

Glassboro, New Jersey

Philosophy Statement

UBD UNIT 1- 6th Grade

Title: Everyday Math Subject/Course: Math

Topic: Collection, Display, and

Interpretation of Data

Grade: 6 Designer: Brandi Sheridan

Stage 1- Desired Results

Established Goals:

Standards of Mathematical Practices (SMP) 1-8

6.SP.1. Recognize a statistical question as one that anticipates variability in the data

related to the question and accounts for it in the answers. For example, “How old am

I?” is not a statistical question, but “How old are the students in my school?” is a

statistical question because one anticipates variability in students’ ages.

6.SP.2. Understand that a set of data collected to answer a statistical question has a

distribution which can be described by its center, spread, and overall shape.

6.SP.3. Recognize that a measure of center for a numerical data set summarizes all

of its values with a single number, while a measure of variation describes how its

values vary with a single number.

6.SP.4. Display numerical data in plots on a number line, including dot plots,

histograms, and box plots.

6.SP.5. Summarize numerical data sets in relation to their context, such as by:

a. Reporting the number of observations.

b. Describing the nature of the attribute under investigation, including how it was

measured and its units of measurement.

c. Giving quantitative measures of center (median and/or mean) and

variability (interquartile range and/or mean absolute deviation), as well as describing

any overall pattern and any striking deviations from the overall pattern with reference

to the context in which the data were gathered.

d. Relating the choice of measures of center and variability to the shape of the data

distribution and the context in which the data were gathered.

6.NS.5. Understand that positive and negative numbers are used together to describe

quantities having opposite directions or values (e.g., temperature above/below zero,

elevation above/below sea level, credits/debits, positive/negative electric charge); use

positive and negative numbers to represent quantities in real-world contexts,

explaining the meaning of 0 in each situation.

6.NS.6. Understand a rational number as a point on the number line. Extend number

line diagrams and coordinate axes familiar from previous grades to represent points

on the line and in the plane with negative number coordinates.

a. Recognize opposite signs of numbers as indicating locations on opposite sides of 0

on the number line; recognize that the opposite of the opposite of a number is the

number itself, e.g., –(–3) = 3, and that 0 is its own opposite.

b. Understand signs of numbers in ordered pairs as indicating locations in quadrants

of the coordinate plane; recognize that when two ordered pairs differ only by signs,

the locations of the points are related by reflections across one or both axes.

c. Find and position integers and other rational numbers on a horizontal or vertical

number line diagram; find and position pairs of integers and other rational numbers

on a coordinate plane.

6.NS.7. Understand ordering and absolute value of rational numbers.

a. Interpret statements of inequality as statements about the relative position of two

numbers on a number line diagram. For example, interpret –3 > –7 as a statement that

–3 is located to the right of –7 on a number line oriented from left to right.

b. Write, interpret, and explain statements of order for rational numbers in real-world

contexts. For example, write –3˚C > –7˚C to express the fact that –3˚C is warmer

than –7˚C.

c. Understand the absolute value of a rational number as its distance from 0 on the

number line; interpret absolute value as magnitude for a positive or negative quantity

in a real-world situation. For example, for an account balance of –30 dollars, write

|–30| = 30 to describe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For

example, recognize that an account balance less than –30 dollars represents a debt

greater than 30 dollars.

6.NS.8. Solve real-world and mathematical problems by graphing points in all four

quadrants of the coordinate plane. Include use of coordinates and absolute value to

find distances between points with the same first coordinate or the same second

coordinate.

6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers.

6.EE.9. Use variables to represent two quantities in a real-world problem that change

in relationship to one another; write an equation to express one quantity, thought of

as the dependent variable, in terms of the other quantity, thought of as the

independent variable. Analyze the relationship between the dependent and

independent variables using graphs and tables, and relate these to the equation. For

example, in a problem involving motion at constant speed, list and graph ordered

pairs of distances and times, and write the equation d = 65t to represent the

relationship between distance.

6.G.1. Find the area of right triangles, other triangles, special quadrilaterals, and

polygons by composing into rectangles or decomposing into triangles and other

shapes; apply these techniques in the context of solving real-world and mathematical

problems.

6.G.3. Draw polygons in the coordinate plane given coordinates for the vertices; use

coordinates to find the length of a side joining points with the same first coordinate

or the same second coordinate. Apply these techniques in the context of solving real-

world and mathematical problems.

6.RP.3. Use ratio and rate reasoning to solve real-world and mathematical problems,

e.g., by reasoning about tables of equivalent ratios, tape diagrams, double number

line diagrams, or equations.

d. Use ratio reasoning to convert measurement units; manipulate and transform units

appropriately when multiplying or dividing quantities.

Understandings:

1. The message conveyed by the data

depends on how the data is collected,

represented, and summarized.

2. The results of a statistical

investigation can be used to support or

refute an argument.

3. One representation may sometimes be

more helpful than another; and, used

together, multiple representations give a

fuller understanding of a problem.

Essential Questions: 1. How can the collection, organization,

interpretation, and display of data be used

to answer questions?

2. How can visual tools be used to answer

questions?

Students will know and be able to …

1. Read, write, and represent whole and decimal numbers.

2. Create and use numerical expressions involving order of operations.

3. Solve number stories.

4. Create and interpret all types of graphs.

5. Find, compare, and use data landmarks.

6. Estimate and measure circle graph sectors.

7. Apply formulas to calculate area and perimeter.

Stage 2- Assessment Evidence

Performance Tasks:

Students will find, compare, and use

data landmarks to answer questions,

draw conclusions, and make predictions.

(graded with rubric)

Other Evidence:

1. Everyday Math Games

2. Exit slips

3. Math logs

4. Red star activities

5. Self-assessment

6. Test and quizzes

Stage 3- Learning Plan

UNIT LENGTH: About 16 days

1-1 Examine the content and organization of the journal and reference book by using

stick on notes to tab sections.

1-2 Construct line plots from data collected about themselves. Then students match

mystery line plots to each category of collected data. They also identify landmarks

for each set of data.

1-3 Review the basics for stem-and-leaf plots. Utilize double stems to organize and

display larger sets of data. Determine the median, mode, and range from constructed

stem-and-leaf plots.

1-4 Find and compare the median and the mean of various data sets. Examine how

the mean and median change as data changes.

1-5 Students play the game, Landmark Shark, in which they score points based on the

range, median, mode, and mean of their cards.

1-6 Use broken line graphs to examine variations in precipitation and temperature

data.

1-7 Draw bar graphs. Use side-by-side bar graphs and stacked bar graphs to examine

variations in snowfall and weather conditions for various locations.

1-8 Read and interpret step graphs involving time. Draw step graphs involving

distance.

1-9 Review the markings on the percent circle. Interpret circle graphs and estimate

percents on circle graphs.

1-10 Find the dimensions of the rectangle with the largest area for a given perimeter.

Use a graph to display data and to solve a problem.

1-11 Discuss how statistics can be presented in specific ways meant to astound the

reader. Analyze a pictograph that displays incorrect and misleading information and

compare broken-line graphs to decide which one is most persuasive.

1-12 Identify samples as random or biased. Introduce a recall survey and analyze the

responses and displays of the data gathered by such a survey.

1-13 Review and assess progress of mathematical content of Unit 1 using Oral and

Slate review, Self-Assessment, Written Assessment, and Performance Tasks.

UBD UNIT 2 – Grade 6


Topic: Operations with Whole

Numbers and Decimals


Established Goals:





d. Relating the choice of measures of center and variability to the shape of the data

distribution and the context in which the data were gathered.

6.NS.2. Fluently divide multi-digit numbers using the standard algorithm.

6.NS.3. Fluently add, subtract, multiply, and divide multi-digit decimals using the

standard algorithm for each operation.











6.EE.1. Write and evaluate numerical expressions involving whole-number

exponents.


b. Identify parts of an expression using mathematical terms (sum, term, product,

factor, quotient, coefficient); view one or more parts of an expression as a single

entity. For example, describe the expression 2 (8 + 7) as a product of two factors;

view (8 + 7) as both a single entity and a sum of two terms.

Understandings:

1. Context is critical when using

estimation.

2. The message conveyed by the data

depends on how the data is collected,

represented, and summarized.

3. One representation may sometimes be

more helpful than another; and, used

together, multiple representations give a

fuller understanding of a problem.

Essential Questions: 1. How can we compare and contrast

numbers?

2. How can we decide when to use an

exact answer and when to use an

estimate?

3. How can the collection, organization,




1. Apply place value concepts.

2. Translate between forms of numbers.

3. Compare and order rational numbers.

4. Add and subtract decimals.

5. Multiply by positive and negative powers of 10.

6. Multiply and divide whole and decimal numbers.

7. Construct and interpret a graph.

8. Compare the median and mean of a data set.

9. Estimate differences, products, and quotients of whole numbers and decimals.


Performance Tasks:

Your class is planning the menu for the end-of-

year party for 36 people. Each person will get 2

slices of pizza. You have been assigned to find

the least expensive restaurant from which to

order the pizza. Several local restaurants and

their prices were presented. (Graded by rubric.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



2-1 Read and write numbers to trillions in standard notation, expanded notation, and

number-and-word notation and convert between these notations.

2-2 Read and write numbers to thousandths in standard notation and expanded

notation. Convert between those notations.

2-3 Add and subtract decimals. Round decimals and convert metric units.

2-4 Develop strategies for multiplying by positive and negative powers of ten.

Extend patterns to develop rules for multiplying by powers of ten.

2-5 Find products of decimals and locate the decimal point in an answer by

estimating the product.

2-6 Practice the lattice method of multiplication, including finding products of

decimals. Discuss a traditional method for locating the decimal point in the product.

2-7 Estimate quotients and practice the partial quotients division algorithm for whole

numbers.

2-8 Estimate quotients and use the estimates to insert decimal points into quotients.

Rewrite whole number division problems to obtain quotients to a specified number of

decimal places.

2-9 Discuss how scientific notation is used to represent large and small numbers.

Practice translating between scientific and standard notations.

2-10 Read and write numbers in exponential notation. Convert between exponential

and standard notations, with and without a calculator. Play the game Exponent Ball.

2-11 Interpret scientific notation displays on a calculator. Convert numbers from

standard notation to scientific notation.



Topic: Variables, Formulas, and

Graphs



Established Goals:












problems.





6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠

0, and use rate language in the context of a ratio relationship.




a. Make tables of equivalent ratios relating quantities with whole-number

measurements, find missing values in the tables, and plot the pairs of values on the

coordinate plane. Use tables to compare ratios.

b. Solve unit rate problems including those involving unit pricing and constant speed.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns

could be mowed in 35 hours? At what rate were lawns being mowed?






6.NS.4. Find the greatest common factor of two whole numbers less than or equal to

100 and the least common multiple of two whole numbers less than or equal to 12.

Use the distributive property to express a sum of two whole numbers 1–100 with a

common factor as a multiple of a sum of two whole numbers with no common factor.

For example, express 36 + 8 as 4 (9 + 2).


















than –7˚C.




coordinate.


exponents.


a. Write expressions that record operations with numbers and with letters standing

for numbers. For example, express the calculation “Subtract y from 5” as 5 – y.





c. Evaluate expressions at specific values of their variables. Include expressions that

arise from formulas used in real-world problems. Perform arithmetic operations,

including those involving whole-number exponents, in the conventional order when

there are no parentheses to specify a particular order (Order of Operations). For

example, use the formulas V = s3 and A = 6 s2 to find the volume and surface area of

a cube with sides of length s = 1/2.

6.EE.5. Understand solving an equation or inequality as a process of answering a

question: which values from a specified set, if any, make the equation or inequality

true? Use substitution to determine whether a given number in a specified set makes

an equation or inequality true.

6.EE.6. Use variables to represent numbers and write expressions when solving a

real-world or mathematical problem; understand that a variable can represent an

unknown number, or, depending on the purpose at hand, any number in a specified

set.





independent variables using graphs and tables, and relate these to the equation. For

example, in a problem involving motion at constant speed, list and graph ordered

pairs of distances and times, and write the equation d = 65t to represent the

relationship between distance and time.

Understandings:

1. Algebraic representation can be used

to generalize patterns and relationships.

2. The symbolic language of algebra is

used to communicate and generalize the

patterns in mathematics.

3. Patterns and relationships can be

represented graphically, numerically,

symbolically, or verbally.

Essential Questions: 1. How can patterns, relations, and

functions be used as tools to best describe

and help explain real-life situations?

2. How can change be best represented

mathematically?

3. How are patterns of change related to

the behavior of functions?


1. Find factors and multiples of numbers.

2. Find equivalent names for numbers.

3. Add positive and negative numbers.

4. Multiply and divide whole numbers and decimals.

5. Estimate products and quotients of decimals.

6. Use and interpret data landmarks and data representations.

7. Use formulas.

8. Represent rates with formulas, tables, and graphs. Translate from one

representation to another and use representations to solve problems involving

functions.

9. Describe general patterns with words and number sentences. Extend and describe

rules for patterns and use them to solve problems.

10. Evaluate expressions.


Performance Tasks:

Since January 1st, you have kept track of the number of

members belonging to 2 school clubs. The math club

currently has 200 members, and it adds 50 new

members per month. The science club currently has 400

members, and it adds 25 new members each month.

Create a table and a graph to represent the data, and to

figure out how many months it will take for the 2 clubs

to have the same number of members if no one quits

either group. (Grade using a rubric.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



3-1 Write special cases for a general pattern.

3-2 Write a general pattern with 2 variables to represent a special case.

3-3 Find decimal solutions to whole number division problems.

3-4 Use algebraic notation to describe general patterns.

3-5 Complete a table from a formula and then graph the data.

3-6 Complete a table from a formula and then graph the data.

3-7 Add positive and negative numbers.

3-8 Solve open number sentences involving signed numbers.

3-9 Analyze the shape of a graph and draw conclusions.

3-10 Name a spreadsheet cell and identify a spreadsheet formula for calculating a

total.



Topic: Rational Number Uses

and Operations



Established Goals:










c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100

times the quantity); solve problems involving finding the whole, given a part and the

percent.





For example, express 36 + 8 as 4 (9 + 2).















Understandings:

1. What we measure affects how

we measure it.

2. A quantity can be represented

numerically in various ways.

Problem solving depends upon

choosing wise ways.

3. Numeric fluency includes both

Essential Questions: 1. How can measurements be used to

solve problems?

2. How can we compare and contrast

numbers?

3. How do exponents and integers

affect the value of expressions?

the understanding of and the

ability to appropriately use

numbers.

Students will know and be able to…

1. Find fractional parts of a region and calculate the percent of a number.

2. Convert between fractions, mixed numbers, decimals, and percents. Express

equivalent fractions in simplest form.

3. Use signs of inequality to compare and order fractions.

4. Divide a decimal by a whole number.

5. Add and subtract fractions and mixed numbers with unlike denominators.

6. Estimate and find products of fractions and mixed numbers.

7. Construct a circle graph from percents.

8. Estimate length with and without tools.

9. Find the perimeter and area of a rectangle.

10. Evaluate expressions involving exponents and integers.


Performance Tasks:

You are designing a wall-mounted wooden rack

for hanging necklaces, belts, and ties. You have

a strip of wood 17.5 inches long and 2.75 inches

wide. You plan to drill 6 peg holes into this strip,

each hole having a diameter of 7/8 inches. You

want the distance between each hole to be the

same. Find the maximum distance between any 2

pegs. Write an explanation of how you found

your answer and complete a detailed diagram as

well. (Grade with a rubric.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



1. Model the multiplication and division rules for finding equivalent fractions.

2. Review how to rename fractions in simplest form.

3. Use and discuss various strategies for comparing fractions.

4. Review methods for finding common denominators and then apply these

methods to add and subtract fractions with like and unlike denominators.

5. Practice adding and subtracting mixed numbers that have fractions with like

denominators.

6. Extend methods to find sums and differences of mixed numbers with unlike

denominators.

7. Use a number line model to review multiplication of fractions. Represent the

standard fraction multiplication algorithm as a general pattern and use the

algorithm to solve fraction-of multiplication problems.

8. Convert between mixed numbers and fractions. Examine 2 methods for

finding the product of mixed numbers and practice multiplying mixed

numbers using the method of their choice.

9. Find equivalent fractions that have denominators of 100 and rename them as

decimals and percents. Convert from percents to decimals and fractions.

10. Develop and apply rules and strategies for converting between decimals and

percents.

11. Convert data, given as counts and measures, to percents. Represent these

percents with circle graphs. Analyze changes is data.

12. Review finding a percent of a number and then solve number stories that

involve finding percents of numbers.



Topic: Geometry: Congruence,

Constructions, and Parallel Lines



Established Goals:

















coordinate.





Understandings:

1. Geometric properties can be

used to construct geometric

figures.

2. Shape and area can be conserved

during mathematical

transformations.

3. Computational fluency includes

understanding the meaning and

the appropriate use of numerical

operations.

Essential Questions: 1. How can spatial relationships be

described by careful use of geometric

language?

2. What situations can be analyzed using

transformations and symmetries?

3. What makes a computational strategy

both effective and efficient?


1. Rename fractions as decimals and percents. Calculate the percent of a number.

2. Find sums of whole and signed numbers.

3. Estimate and find sums, differences, and products of fractions and mixed numbers.

4. Use a protractor to construct a circle graph.

5. Measure / draw angles to the nearest degree using a protractor.

6. Plot ordered number pairs in four quadrants. Use ordered pairs to name points.

7. Classify angles. Apply properties of supplementary and vertical angles; of angles

formed by 2 parallel lines and a transversal; of sums and angle measures of triangles

and quadrangles.

8. Use a compass and straightedge to construct geometric and congruent figures.

9. Perform isometry transformations on a coordinate grid.

10. Practice estimating and finding the measures of angles by playing Angle Tangle.


Performance Tasks:

You are a scientist who has studied the

solar system extensively. You have

investigated the size, distance, and motion

of each planet. You are ready to offer an

informed opinion in regards to travel to

another planet. (Grade using rubric.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



1. Use full circle and half circle protractors to measure angles, and a half circle

protractor to draw angles.

2. Practice estimating and finding measures of angles by playing Angle Tangle.

3. Solve problems involving supplementary and vertical angles. Determine

angle measures and sums within triangles and quadrangles.

4. Use fractions, decimals, and percents to calculate the degree measure of

sectors in a circle graph. Use protractors to draw each sector.

5. Review how to plot ordered number pairs on a rectangular grid. Plot and

name vertices in polygons.

6. Review and perform isometry transformations, including reflections,

translations, and rotations.

7. Explore the properties of congruent line segments, angles, and other figures.

Use drawing tolls to construct congruent segments, angles, and 2 dimensional

figures.

8. Review 2 basic compass and straight edge constructions. Copy a line segment

and a triangle.

9. Review methods for copying angles and constructing perpendicular bisectors.

Apply these methods to solve construction problems.

10. Explore and apply the special relationship between angles that are formed

when parallel lines are cut by a transversal.

11. Explore the relationships between angles of parallelograms. Construct a

parallelogram using a compass and a straightedge.



Topic: Number Systems and

Algebra Concepts



Established Goals:


6.NS.1. Interpret and compute quotients of fractions, and solve word problems

involving division of fractions by fractions, e.g., by using visual fraction models and

equations to represent the problem.























than –7˚C.

c. Understand the absolute value of a rational number as its distance from 0 on the

number line; interpret absolute value as magnitude for a positive or negative quantity

in a real-world situation. For example, for an account balance of –30 dollars, write |–

30| = 30 to describe the size of the debt in dollars.

d. Distinguish comparisons of absolute value from statements about order. For

example, recognize that an account balance less than –30 dollars represents a debt

greater than 30 dollars.




coordinate.




problems.

6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by

packing it with unit cubes of the appropriate unit fraction edge lengths, and show that

the volume is the same as would be found by multiplying the edge lengths of the

prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular

prisms with fractional edge lengths in the context of solving real-world and

mathematical problems.


exponents.

6.EE.2. Write, read, and evaluate expressions in which letters stand for numbers








there are no parentheses to specify a particular order (Order of Operations).





6.EE.7. Solve real-world and mathematical problems by writing and solving

equations of the form x + p = q and px = q for cases in which p, q and x are all

nonnegative rational numbers.

6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or

condition in a real-world or mathematical problem. Recognize that inequalities of the

form x > c or x < c have infinitely many solutions; represent solutions of such

inequalities on number line diagrams.

Understandings:

1. Computational fluency includes

understanding the meaning and

the appropriate use of numerical

operations.

2. Geometric properties can be

used to construct geometric

figures.

3. Number patterns and

relationships can be represented

using variables.

4. Fractions, decimals, and percents

express a relationship between 2

numbers.

Essential Questions: 1. How do operations affect numbers?

2. How can spatial relationships be

described by careful use of geometric

language?

3. What strategies can be used to solve for

unknowns?

4. How is computation with rational

numbers similar and different to whole

number computation?


1. Compare signed numbers.

2. Add and subtract signed numbers.

3. Multiply and divide whole, decimal, and signed numbers.

4. Divide fractions and mixed numbers.

5. Estimate products and quotients.

6. Apply properties of congruent figures.

7. Represent rates with formulas, tables, and graphs; extend and describe numeric

patterns; describe rules for patterns and use them to solve problems.

8. Determine whether number sentences are true or false. Use strategies to solve

open-number sentences.

9. Apply order of operations to evaluate expressions.

10. Apply basic properties of the four operations of arithmetic.


Performance Tasks:

Some years ago, you planted a 7-foot tree in

your yard. The tree grew 3 feet each year. Now

the tree is 4 times the original height. Determine

how many years ago the tree was planted. Write

an equation you can use to solve the problem.

Show and explain all of your work. (Use a rubric

for grading.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes


UNIT LENGTH: About 15days

1. Review multiplying fractions and mixed numbers. Practice finding the

reciprocal of a number.

2. Play Fraction / Whole Number Top-It.

3. Learn a division algorithm for fractions and use it to divide fractions and

mixed numbers.

4. Use a number line model to add and subtract signed numbers. Use the

subtraction rule.

5. Play the game Credits/Debits.

6. Study patterns to devise rules for multiplying and dividing positive and

negative numbers.

7. Explore the real number system and properties of various sets of numbers

within it.

8. Evaluate expressions using the order of operations.

9. Play the game Name that Number.

10. Determine of number sentences are true or false.

11. Use the trial-and-error method to solve problems. Learn how to solve

equations using the cover-up method.

12. Use pan-balance models to understand equality and equations. Solve

equations using multiple steps.

13. Use inverse operations and properties of equality to find and solve equivalent

equations. Write equations for group members to solve.

14. Solve equations by transforming them into equivalent equations of the form x

= a.

15. Practice evaluating expressions and solving equations by playing Algebra

Election.

16. Extend work with equations to finding solution sets of inequalities.

17. Practice solving inequalities by playing Solution Search.

UBD UNIT 7- Grade 6


Topic: Probability and Discrete

Mathematics



Established Goals:


6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio

relationship between two quantities.



on the line and in the plane with negative number coordinates







6.EE.6. Use variables to represent numbers and write expressions when solving a

real-world or mathematical problem; understand that a variable can represent an

unknown number, or, depending on the purpose at hand, any number in a specified

set.

6.EE.8. Write an inequality of the form x > c or x < c to represent a constraint or

condition in a real-world or mathematical problem. Recognize that inequalities of the

form x > c or x < c have infinitely many solutions; represent solutions of such

inequalities on number line diagrams.

Understandings:

1. One representation may

sometimes be more helpful than

another; and, used together,

multiple representations give a

fuller understanding of a

problem.

2. Reasoning and/or proof can be

used to verify or refute

conjectures or theorems in

algebra.

3. The results of a statistical

investigation can be used to

support or refute an argument.

Essential Questions: 1. How do mathematical ideas

interconnect and build on one another to

produce a coherent whole?

2. What makes an algebraic algorithm

both effective and efficient?

3. How can the collection, organization,




1. Translate between number-and-word and standard notations.

2. Convert between fractions, decimals, and percents.

3. Calculate the percent of a number. Interpret the remainder and round the quotient

accordingly.

4. Multiply fractions and whole numbers.

5. Interpret Venn diagrams.

6. Calculate probabilities when outcomes are equally likely. Understand and apply

the concept of random numbers to probability situations. Determine expected

outcomes.

7. Understand and use tree diagrams to solve problems. Understand what constitutes

a fair game. Understand how sample size affects results.

8. Determine whether number sentences are true or false. Solve equations.

9. Use formulas to solve problems.


Performance Tasks:

You have the cards 3, 4, 5, 6. You shuffle the cards and

place them facedown. Turn 2 of the cards over and

multiply the numbers on them. Suppose you wish to

invent a solitaire game called Card Products. The

product of the two numbers on the card determines if

you win or lose. Write a set of rules for this game so

that both players have an equal chance of winning or

losing. (Grade with a rubric.)

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes


UNIT LENGTH: Around 12 days

1. Calculate probabilities for various experiments with equally likely outcomes.

2. Practice identifying solutions to inequalities by playing Solution Search.

3. Discover that the more times a number is generated within a given range, the

more likely they are to obtain an equal distribution of possible outcomes.

4. Toss coins to simulate a tournament with equally matched teams. Estimate the

chances of various outcomes of the tournament.

5. Practice renaming fractions as percents by playing the percent version of

Frac-Tac-Toe.

6. Introduce tree diagrams and use them to find expected outcomes.

7. Carry out a series of simulations and compare actual results to expected

outcomes.

8. Practice applying order of operations by playing Name that Number.

9. Use tree diagrams to find expected outcomes and calculate the probabilities of

those outcomes.

10. Use Venn diagrams to analyze situations and solve problems.

11. Play four simple games of chance, estimate the probability of winning each

game, and decide which of the games are fair.

12. Practice probability skills by playing Greedy.

13. Investigate the effects of guessing on multiple-choice tests when they can

eliminate one or two possible answer choices. Calculate expected scores, as

well as the probabilities of improved scores and lowered scores.

UBD UNIT 8- Grade 6


Topic: Rates and Ratios Grade: 6 Designer: Brandi Sheridan


Established Goals:


6.RP.1. Understand the concept of a ratio and use ratio language to describe a ratio

relationship between two quantities.

6.RP.2. Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠

0, and use rate language in the context of a ratio relationship. For example, “This

recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for

each cup of sugar.” “We paid $75 for 15 hamburgers, which is a rate of $5 per

hamburger.”




b. Solve unit rate problems including those involving unit pricing and constant speed.

For example, if it took 7 hours to mow 4 lawns, then at that rate, how many lawns

could be mowed in 35 hours? At what rate were lawns being mowed?

c. Find a percent of a quantity as a rate per 100 (e.g., 30% of a quantity means 30/100

times the quantity); solve problems involving finding the whole, given a part and the

percent.










coordinate.








Understandings:

1. Rates and ratios can be used to

represent and compare real life

situations.

2. Proportional relationships

express how quantities change in

relationship to each other.

Essential Questions: 1. How are ratios and rates used in

everyday life?

2. How does comparing quantities

describe the relationship between

them?


1. Solve percent problems. Find a unit whole when a fractional part is given.

2. Estimate equivalent percents for fractions.

3. Apply strategies for comparing ratios.

4. Solve division problems involving decimals.

5. Use proportions to model, summarize, and solve rate and ratio problems. Solve

open proportions.

6. Solve problems involving a size-change factor.

7. Use ratios expressed as words and fractions to solve problems; use scaling to

model multiplication.

8. Solve perimeter and area problems.

9. Solve rate problems using unit rates and rate tables.

10. Use order of operations to evaluate expression. Find multiplicative inverses.


Performance Tasks:

You are designing a banner for school’s Eat

Healthy Campaign. The finished banner should

measure 60 in long by 24 in wide. Although you

are making a rough draft, you want it to be

mathematically similar to the final product. There

are many different sizes of paper you can use to

create the rough draft. Given several choices, which

pieces of paper can be used for the rough draft?

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



1. Review the meaning of rates and rate notation and terminology.

2. Solve rate problems by finding unit rates, completing rate tables, and using

proportions.

3. Use simplified rate tables to write open proportions. Solve simple rate

problems by setting up and solving proportions.

4. Use the cross-products rule to determine whether 2 fractions are equivalent.

Solve rate problems by writing proportions and using cross multiplication.

5. Practice finding and comparing products of fractions and whole numbers by

playing Fraction / Whole Number Top-It.

6. Refer to a calorie use chart to estimate their calorie use in a typical 24-hour

day.

7. Use unit rates to calculate the number and percent of carbohydrate, protein,

and fat calories in food.

8. Review the notations for and meanings of ratios and share real-life examples

or ratios. Use playing cards to model and solve problems involving part-to-

part and part-to-whole ratios.

9. Practice comparing and ordering fractions by playing Built It.

10. Set up and use proportions as an alternative method for solving percent

problems. Use this method to solve problems in which the percent is

unknown, the part is unknown, or the whole is unknown.

11. Practice whole-number division by playing the advanced version of Division

Top-It.

12. Develop estimation and mental computation skills for converting fractions to

percents. Estimate and them calculate the percents of total calories that come

from fat, protein, and carbohydrate.

13. Explore the use of ratios to describe size changes for geometric figures, scale

models, and maps. Practice using notations to show the size-change factor.

14. Practice adding, multiplying, and renaming fractions by playing Spoon

Scramble.

15. Use pattern blocks to explore the properties of similar polygons. Use ratios to

find the lengths of corresponding sides of similar polygons.

16. Rename and compare ratios.

17. Explore the length-to-width ratio, known as the Golden Ratio.

18. Practice evaluating expressions by playing the game First to 100.

UBD UNIT 9 - Grade 6


Topic: More about Variables,

Formulas, and Graphs



Established Goals:



exponents.














6.EE.3. Apply the properties of operations to generate equivalent expressions. For

example, apply the distributive property to the expression 3 (2 + x) to produce the

equivalent expression 6 + 3x; apply the distributive property to the expression 24x +

18y to produce the equivalent expression 6 (4x + 3y); apply properties of operations

to y + y + y to produce the equivalent expression 3y.

6.EE.4. Identify when two expressions are equivalent (i.e., when the two expressions

name the same number regardless of which value is substituted into them). For

example, the expressions y + y + y and 3y are equivalent because they name the same

number regardless of which number y stands for.












independent variables using graphs and tables, and relate these to the equation.




problems.

6.G.2. Find the volume of a right rectangular prism with fractional edge lengths by

packing it with unit cubes of the appropriate unit fraction edge lengths, and show that

the volume is the same as would be found by multiplying the edge lengths of the

prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular

prisms with fractional edge lengths in the context of solving real-world and

mathematical problems.

6.G.4. Represent three-dimensional figures using nets made up of rectangles and

triangles, and use the nets to find the surface area of these figures. Apply these

techniques in the context of solving real-world and mathematical problems.








coordinate.




a. Make tables of equivalent ratios relating quantities with whole-number

measurements, find missing values in the tables, and plot the pairs of values on the

coordinate plane. Use tables to compare ratios.

Understandings:

1. Algebraic expressions and equations

generalize relationships from specific

cases.

2. Geometric properties can be used to

construct geometric figures.

Essential Questions: 1. How do I use algebraic expressions to

analyze or solve problems?

2. How do geometric relationships help us

to solve problems and/or make sense of

phenomena?


1. Identify the unit whole when a fractional part is given.

2. Solve problems involving a size-change factor or part-to-whole ratios.

3. Use and evaluate formulas to solve problems.

4. Determine angle measures by applying properties of orientations of angles.

5. Apply properties of similar figures.

6. Identify algebraic representations of functions.

7. Write and solve equations. Identify equivalent equations. Apply a trial and

error strategy to find approximate solutions to equations.

8. Use order of operations to simplify expressions and equations. Evaluate

expressions involving square roots and exponents with a calculator.

9. Apply distributive strategies.

Stage 2 - Assessment Evidence

Performance Tasks:

Explain how to find the area of a regular

octagon with sides that measure x feet

each. Your explanation should be

detailed, clear, and easy to follow. Be

sure to include formulas in your

explanation and a sketch.

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



1. Write number sentences representing 2 methods for finding the areas of

partitioned rectangles.

2. Apply the distributive property to simplify algebraic expressions and mentally

calculate products.

3. Apply place value concepts and practice a trial and error method by playing

the game Getting to One.

4. Use the distributive property to combine like terms. Simplify expressions

containing like terms.

5. Measure line segments to the nearest sixteenth of an inch and nearest

millimeter.

6. Use the distributive property to remove parentheses. Simplify algebraic

expressions and equations by combining like terms.

7. Practice evaluating expressions by playing First to 100.

8. Solve simplified equations by using the equivalent-equations method

previously learned.

9. Use the distributive property to solve number stories.

10. Explore the mathematics of balanced mobiles. Write and solve equations to

find the weights of suspended objects and their distances from the fulcrum.

11. Practice identifying solutions to inequalities by playing the game Solution

Search.

12. Learn how labels, numbers, and formulas are entered and displayed in a

spreadsheet.

13. Solve spreadsheet problems.

UBD UNIT 10 - Grade 6


Topic: Geometry Topics Grade: 6 Designer: Brandi Sheridan


Established Goals:











coordinate.





Understandings:

1. Geometry and spatial sense offer

ways to interpret and reflect on our

physical environment.

2. Shape and area can be conserved

during mathematical transformation.

3. Patterns provide insights into

potential relationships.

Essential Questions: 1. How do geometric models describe

spatial relationships?

2. What situations can be analyzed using

transformations and symmetries?

3. How can patterns be used to make

predictions?


1. Convert between standard, number-and-word, and scientific notations.

2. Estimate products and quotients of decimal numbers.

3. Use and evaluate formulas to solve problems.

4. Determine angle measures by applying properties of orientations of angles.

5. Describe properties of similar and congruent figures. Recognize objects that

are topologically equivalent.

6. Identify and describe instances of reflections, translations, and rotations.

7. Describe patterns and rules for patterns and use them to solve problems.

Represent situations using algebraic notation.

8. Write and solve equations.

9. Use order of operations to simplify expressions.

Stage 2 - Assessment Evidence

Performance Tasks:

Use your geometry template, draw the assigned number

of polygons for each of the following:

1 polygon that has NO lines of symmetry

3 polygons, each having exactly 1 line of

symmetry

3 polygons, each having at least 3 lines of

symmetry

Draw the lines of symmetry for each polygon.

Categorize the polygons according to the number of

ways each polygon can be rotated around a center point

to exactly match itself. Show or explain your categories

and tell which polygons belong in each category.

Make a true statement about the relationship between a

polygon’s lines of symmetry and the number of ways it

can be rotated to exactly match itself.

Other Evidence:


2. Exit slips

3. Math logs


5. Self-assessment

6. Test and quizzes



1. Review regular tessellations and learn about semi-regular tessellations. Find

all 8 possible semi-regular tessellations.

2. Create non-polygonal, Escher-type translation tessellations.

3. Determine the number of ways a figure can be rotated about a point so the

image exactly matches the pre-image.

4. Use clay and rubber sheets to explore topological transformations.

5. Practice applying order of operations by playing the game Name That

Number.

6. Estimate lengths without tools.

7. Measure line segments to the nearest 0.5 of an inch.

8. Recognize patterns and apply them to solve problems.

9. Practice identifying line and rotation symmetry of various figures.

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