Unit 1: Integers and Rational Numbers

Unit 1: Integers and Rational NumbersUnit: Mathematics , Grade(s) Grade 7

This unit focuses on applying number sense from 6th grade to perform operations with integers and rational numbers.

Duration: 21 Days

Unit

Essential Questions/Enduring Understandings

Essential Questions

How can the properties of operations be used to solve problems involving integers and rational numbers?

Enduring Understandings

An integer and its opposite are the same distance from zero on a number line and have a sum of zero.Fractions can be written in decimal form.Adding integers/rational numbers requires adding or subtracting the absolute values and identifying the sign of the sum.Subtracting an integer/rational number is the same as adding its additive inverse.The sign of the product of integers/rational numbers depends on the sign of its factors.Dividing integers/rational numbers use the same rules as multiplication.Solving problems with rational numbers requires understanding their value.

Students will be able to...

1-1 Relate Integers and their Opposites1-2 Understand Rational Numbers1-3 Add Integers1-4 Subtract Integers1-5 Add and Subtract Rational Numbers1-6 Multiply Integers1-7 Multiply Rational Numbers1-8 Divide Integers1-9 Divide Rational Numbers1-10 Solve Problems Involving Rational Numbers3-Act Mathematical Modeling

Evidence of Learning/ Assessment

Materials Bank

For additional instructional materials in Classroom, visit https://edconnectnj.schoolnet.com/1690Generated 12/6/2018

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Formative

Teacher ObservationDaily Quick ChecksQuizzesExit Tickets

Summative

Topic TestsBenchmark TestsPerformance TasksProjects

Interdisciplinary Skills and Career Education

ELA:

NJSLSA.R1. Read closely to determine what the text says explicitly and to make logical inferences and relevant connectionsfrom it; cite specific textual evidence when writing or speaking to support conclusions drawn from the text.

Science:

MS-ETS1-1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution,taking into account relevant scientific principles and potential impacts on people and the natural environmentthat may limit possible solutions.

21st Century Skills and Technology

Career Ready Practices

CRP1. Act as a responsible and contributing citizen and employee.

CRP2. Apply appropriate academic and technical skills.

CRP4. Communicate clearly and effectively and with reason.

CRP8. Utilize critical thinking to make sense of problems and persevere in solving them.

CRP11. Use technology to enhance productivity.

CRP12. Work productively in teams while using cultural global competence.

Technology

8.1.8.A.1,2,3,4 (digital tools, document design,simulations, spreadsheets)

8.1.8.F.1 (digital told to analyze data to make informed decisions)

Accommodations/ Differentiation

IEP

Follow IEP Plan which may contain some of the following examples…

In class/pull out support with special ed teacher

Additional time during intervention time

Materials Bank


of 6

Preferred seating

Questions read aloud

Extended time for completing

Graphic organizer

Mnemonic devices

Songs/videos to reinforce concepts

Limit number of questions

Scribe

Manipulatives

Calculators

Leveled homework

Lesson intervention activities

Reteach pages

Build mathematical literacy sheet

Vocabulary support page

Math Diagnosis & Intervention System

504

Follow 504 Plan which may contain some of the following examples…

Preferred seating


Extended time for completing assignments

Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL

Materials Bank


of 6

Translation device/dictionary

In class/pull out with an ESL teacher

Additional time

Preferred seating



Graphic organizer

Mnemonic devices



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented

Independent projects

Enrichment pages

Materials Bank


of 6

Online games

Leveled Homework

Extension Activities

Today’s Challenge

Unit Materials

Core Materials:

enVision Math 2.0

Topic 1: Integers and Rational Numbers

Intervention Lessons

Enrichment activities

Leveled homework

Fluency practice

Supplemental Materials:

ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources

Math Diagnosis and Intervention System Kit

Online Resources

Materials Bank


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https://web.stmath.com/entrance/go/GAL0RS

https://gfletchy.com/3-act-lessons/

http://www.estimation180.com/

https://mtbos.org/desmosbank/

https://nearpod.com/

https://www.brainpop.com/math/

http://gtpsmath.weebly.com/activities.html

Standards Covered

New Jersey Math Student Learning Standards

MA.7.7.NS: The Number System

MA.7.7.NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

MA.7.7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and

subtraction on a horizontal or vertical number line diagram.

MA.7.7.NS.A.1a: Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20

points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?

MA.7.7.NS.A.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is

positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing

real-world contexts.

MA.7.7.NS.A.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two

rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

MA.7.7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

MA.7.7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MA.7.7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers

extend the rules for manipulating fractions to complex fractions.

Additional Properties

Author: Napoli, Betty

Cost/Fee: No

Restricted Use: No

Rights:

Keywords:

Created by: Napoli, Betty (8/10/2018 7:07 PM)

Last modified by: Napoli, Betty (8/10/2018 7:23 PM)

Materials Bank


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Unit 2: Analyze and Use Proportional RelationshipsUnit: Mathematics , Grade(s) Grade 7

This unit focuses on recognizing and representing proportional relationships in verbal descriptions, tables, equations, and graphs.

Duration: 18 Days

Unit


Essential Questions

How can you recognize and represent proportional relationships and use them to solve problems?


Equivalent ratios and unit rates can be used to compare ratios and solve problems.Unit rates can make it easier to solve multi-step problems.Quantities in a proportional relationship can be described by equivalent ratios.Equations that contain the constant of proportionality in the form of y=kx can be used to solve problems.The graph o a proportional relationship is a straight line through the origin.Proportional reasoning can help you solve problems.


2-1 Connect Ratios, Rates, and Unit Rates2-2 Determine Unit Rates with Ratios of Fractions2-3 Understand Proportional Relationships: Equivalent Ratios2-4 Describe Proportional Relationships: Constant of Proportionality3-Act Mathematical Modeling2-5 Graph Proportional Relationships2-6 Apply Proportional Reasoning to Solve Problems


Formative


Summative

Topic TestsBenchmark TestsAlternative Assessments: Performance Tasks & Projects


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ELA:


Science:










Technology




IEP




Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Materials Bank


Page 2 of 6

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL



Additional time

Preferred seating



Graphic organizer

Mnemonic devices


Materials Bank


Page 3 of 6


Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Materials Bank


Page 4 of 6

Core Materials:

enVision Math 2.0

Topic 2: Analyze and Use Proportional Relationships



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Standards Covered


MA.7.7.RP: Ratios and Proportional Relationships

MA.7.7.RP.A: Analyze proportional relationships and use them to solve real-world and mathematical problems.

MA.7.7.RP.A.1: Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different

units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles

per hour.

MA.7.7.RP.A.2: Recognize and represent proportional relationships between quantities.

MA.7.7.RP.A.2a: Decide whether two quantities are in a proportional relationship, e.g., by testing for equivalent ratios in a table or graphing on a

coordinate plane and observing whether the graph is a straight line through the origin.

MA.7.7.RP.A.2b: Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional

relationships.

MA.7.7.RP.A.2c: Represent proportional relationships by equations. For example, if total cost t is proportional to the number n of items purchased at

a constant price p, the relationship between the total cost and the number of items can be expressed as t = pn.

MA.7.7.RP.A.2d: Explain what a point (x, y) on the graph of a proportional relationship means in terms of the situation, with special attention to the

points (0, 0) and (1, r) where r is the unit rate.

MA.7.7.RP.A.3: Use proportional relationships to solve multistep ratio and percent problems. Examples: simple interest, tax, markups and markdowns,

gratuities and commissions, fees, percent increase and decrease, percent error.

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Restricted Use: No

Rights:

Keywords:


Last modified by: Napoli, Betty (12/6/2018 8:28 AM)

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Unit 3: Analyze and Solve Percent ProblemsUnit: Mathematics , Grade(s) Grade 7

This unit focuses on solving problems involving percents.

Duration: 16 Days

Unit


Essential Questions

How can percents show proportional relationships and be used to solve real-world problems?


Equivalent ratios can be used to find the percent of a number.Percent is a ratio out of 100 that relates the ratio of two quantities.The part divided and the percent divided by 100 are equivalent ratios.Proportional reasoning can be used to develop the percent equation which can be used to find the percent, part or whole.The percent equation can be used to solve percent change and percent error problems.Markup is the same as percent increase; markdown is the same as percent decrease, Percent change can be used to solve these types ofproblems.Simple interest is an application of percent problems. The whole is the principal, the part is the interest, and the percent is the interest rate.


3-1 Analyze Percents of Numbers3-2 Connect Percent and Proportion3-3 Represent and Use the Percent Equation3-4 Solve Percent Change and Percent Error Problems3-Act Mathematical Modeling3-5 Solve Markup and Markdown Problems3-6 Solve Simple Interest Problems


Formative


Summative


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Page 1 of 6


ELA:


Science:










Technology




IEP




Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Materials Bank


Page 2 of 6

Manipulatives

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL



Additional time

Preferred seating



Graphic organizer

Mnemonic devices

Materials Bank


Page 3 of 6



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Materials Bank


Page 4 of 6

Core Materials:

enVision Math 2.0

Topic 3: Analyze and Solve Percent Problems



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Standards Covered


MA.7.7.NS: The Number System

MA.7.7.NS.A: Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.

MA.7.7.NS.A.1: Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and

subtraction on a horizontal or vertical number line diagram.

MA.7.7.NS.A.1a: Describe situations in which opposite quantities combine to make 0. For example, in the first round of a game, Maria scored 20

points. In the second round of the same game, she lost 20 points. What is her score at the end of the second round?

MA.7.7.NS.A.1b: Understand p + q as the number located a distance |q| from p, in the positive or negative direction depending on whether q is

positive or negative. Show that a number and its opposite have a sum of 0 (are additive inverses). Interpret sums of rational numbers by describing

real-world contexts.

MA.7.7.NS.A.1c: Understand subtraction of rational numbers as adding the additive inverse, p – q = p + (–q). Show that the distance between two

rational numbers on the number line is the absolute value of their difference, and apply this principle in real-world contexts.

MA.7.7.NS.A.1d: Apply properties of operations as strategies to add and subtract rational numbers.

MA.7.7.NS.A.2: Apply and extend previous understandings of multiplication and division and of fractions to multiply and divide rational numbers.

MA.7.7.NS.A.3: Solve real-world and mathematical problems involving the four operations with rational numbers. Computations with rational numbers

extend the rules for manipulating fractions to complex fractions.

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Restricted Use: No

Rights:

Keywords:



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Unit 4: Generate Equivalent ExpressionsUnit: Mathematics , Grade(s) Grade 7

This unit focuses on extending the use of properties of operations from writing and evaluating algebraic expressions to analyzing equivalent expressions.

Duration: 25 Days

Unit


Essential Questions

How can properties of operations help to generate equivalent expressions that can be used in solving problems?


Algebraic expressions can be used to represent and solve problems in real-world contexts.Re-arranging and combining like terms does not change the value of the expression.All like terms must be combined in order for the expression to be simplified.The distributive property can be used to expand or factor expressions. The expressions remain equivalent to the original.The same rules apply when adding and subtracting coefficients and constants.Equivalent expressions can be used to show how quantities are related in real life situations.


4-1 Write and Evaluate Algebraic Expressions4-2 Understand Linear Expressions4-3 Simplify Linear Expressions4-4 Expand Linear Expressions4-5 Factor Linear Expressions3-Act Mathematical Modeling4-6 Add Linear Expressions4-7 Subtract Linear Expressions4-8 Analyze Equivalent Expressions


Formative


Summative


Materials Bank


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ELA:


Science:










Technology




IEP




Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Materials Bank


Page 2 of 6

Manipulatives

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL



Additional time

Preferred seating



Graphic organizer

Mnemonic devices

Materials Bank


Page 3 of 6



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Materials Bank


Page 4 of 6

Core Materials:

enVision Math 2.0

Topic 4: Generate Equivalent Expressions



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Standards Covered


MA.7.7.EE: Expressions and Equations

MA.7.7.EE.A: Use properties of operations to generate equivalent expressions.

MA.7.7.EE.A.1: Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

MA.7.7.EE.A.2: Understand that rewriting an expression in different forms in a problem context can shed light on the problem and how the quantities in it

are related. For example, a + 0.05a = 1.05a means that "increase by 5%" is the same as "multiply by 1.05."

MA.7.7.EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

MA.7.7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers,

fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as

appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour

gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches

long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on

the exact computation.

MA.7.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve

problems by reasoning about the quantities.

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Restricted Use: No

Rights:

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Unit 5: Solve Problems Using Equations and InequalitiesUnit: Mathematics , Grade(s) Grade 7

This unit focuses on extending students' understanding of dependent and independent variables, the coefficient and constant to lead students into writing and

solving equations and inequalities.

Duration: 20 Days

Unit


Essential Questions

How can you solve real-world and mathematical problems with numerical and algebraic equations and inequalities?


Equations with more than one operation can be used to represent a situation.One and two step problems are both solved using properties of equality.The distributive property can be used to solve equations in the form of p(x+q)=r.Solving inequalities with addition and subtraction is the same as solving equations. When multiplying or dividing by an inequality, the inequality symbol is reversed.


5-1 Write Two-Step Equations5-2 Solve Two-Step Equations5-3 Solve Equations Using the Distributive Property5-4 Solve Inequalities Using Addition or Subtraction5-5 Solve Inequalities Using Multiplication or Division3-Act Mathematical Modeling5-6 Graph Solutions to Inequalities5-7 Write Two-Step Inequalities5-8 Solve Two-Step Inequalities5-9 Solve Multi-Step Inequalities


Formative


Summative


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ELA:


Science:










Technology




IEP




Preferred seating



Graphic organizer

Mnemonic devices



Materials Bank


Page 2 of 6

Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL



Additional time

Preferred seating



Graphic organizer

Materials Bank


Page 3 of 6

Mnemonic devices



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Materials Bank


Page 4 of 6

Core Materials:

enVision Math 2.0

Topic 5: Solve Problems Using Equations and Inequalities



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Standards Covered


MA.7.7.EE: Expressions and Equations

MA.7.7.EE.B: Solve real-life and mathematical problems using numerical and algebraic expressions and equations.

MA.7.7.EE.B.3: Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form (whole numbers,

fractions, and decimals), using tools strategically. Apply properties of operations to calculate with numbers in any form; convert between forms as

appropriate; and assess the reasonableness of answers using mental computation and estimation strategies. For example: If a woman making $25 an hour

gets a 10% raise, she will make an additional 1/10 of her salary an hour, or $2.50, for a new salary of $27.50. If you want to place a towel bar 9 3/4 inches

long in the center of a door that is 27 1/2 inches wide, you will need to place the bar about 9 inches from each edge; this estimate can be used as a check on

the exact computation.

MA.7.7.EE.B.4: Use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve

problems by reasoning about the quantities.

MA.7.7.EE.B.4a: Solve word problems leading to equations of the form px + q = r and p(x + q) = r, where p, q, and r are specific rational numbers.

Solve equations of these forms fluently. Compare an algebraic solution to an arithmetic solution, identifying the sequence of the operations used

in each approach. For example, the perimeter of a rectangle is 54 cm. Its length is 6 cm. What is its width?

MA.7.7.EE.B.4b: Solve word problems leading to inequalities of the form px + q > r or px + q < r, where p, q, and r are specific rational numbers.

Graph the solution set of the inequality and interpret it in the context of the problem. For example: As a salesperson, you are paid $50 per week

plus $3 per sale. This week you want your pay to be at least $100. Write an inequality for the number of sales you need to make, and describe the

solutions.

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Unit 6: Use Sampling to Draw Inferences about OperationsUnit: Mathematics , Grade(s) Grade 7

This unit focuses on how display, describe, and summarize numerical data by introducing the concepts of populations and samples, making inferences about a

population using a sample, and how to compare two populations.

Duration: 12 Days

Unit


Essential Questions

How can sampling be used to draw inferences about one or more populations?


Representative samples must reflect the entire population. It should be randomly chosen.Data from random samples can be used to make valid inferences about a population by looking at patterns and trends in the distribution ofthe data.Measures of center and variability and using proportions with random samples can help describe the entire population.Data displays, such as box plots, can be used to make informal comparisons between two populations.Data can be compared by using the shapes of the data displays or the measures of center and variability.


6-1 Populations and Samples6-2 Biased and Unbiased Samples6-3 Draw Inferences About Populations6-4 Compare Populations Using Data Displays6-5 Compare Populations Using Statistical Measures3-Act Mathematical Modeling


Formative


Summative



Materials Bank


Page 1 of 6

ELA:


Science:










Technology




IEP




Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Materials Bank


Page 2 of 6

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL



Additional time

Preferred seating



Graphic organizer

Mnemonic devices


Materials Bank


Page 3 of 6


Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Materials Bank


Page 4 of 6

Core Materials:

enVision Math 2.0

Topic 6: Use Sampling to Draw Inferences about Operations



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Standards Covered


MA.7.7.SP: Statistics and Probability

MA.7.7.SP.A: Use random sampling to draw inferences about a population.

MA.7.7.SP.A.1: Understand that statistics can be used to gain information about a population by examining a sample of the population; generalizations

about a population from a sample are valid only if the sample is representative of that population. Understand that random sampling tends to produce

representative samples and support valid inferences.

MA.7.7.SP.A.2: Use data from a random sample to draw inferences about a population with an unknown characteristic of interest. Generate multiple

samples (or simulated samples) of the same size to gauge the variation in estimates or predictions. For example, estimate the mean word length in a book

by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the

estimate or prediction might be.

MA.7.7.SP.B: Draw informal comparative inferences about two populations.

MA.7.7.SP.B.3: Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference

between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm

greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the

separation between the two distributions of heights is noticeable.

MA.7.7.SP.B.4: Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about

two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a

fourth-grade science book.

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Unit 7: ProbabilityUnit: Mathematics , Grade(s) Grade 7

This unit focuses on determining the probability of an event.

Duration: 14 Days

Unit


Essential Questions

How can How can you investigate chance processes and develop, use, and evaluate probability models?


Probability is the likelihood that an event will occur. Probability can be described using a ratio such as 1 out of 2. The closer a ratio is to zero,the less likely it is to occur. The closer the value is to one, the more likely the event will occur.Theoretical probability of an event is the number of favorable outcomes divided by the number of possible outcomes, when all outcomes areequally likely. Experimental probability consists of the results of an actual experiment. These probabilities are often very close, but are usually not identical.A probability model can be used to evaluate a chance process and its outcomes to develop theoretical or experimental probability.The possible outcomes of a compound event can be represented using a tree diagram, a table, or an organized list.A model such as a table, organized list, or tree diagram can represent the sample space can then be used to determine the probability of afavorable outcome.


7-1 Understand Likelihood and Probability7-2 Connect Relative Frequency and Experimental Probability7-3 Represent Sample Spaces7-4 Find Probabilities of Simple Events3-Act Mathematical Modeling7-5 Determine Outcomes of Compound Events7-6 Find Probabilities of Compound Events7-7 Simulate Compound Events


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Formative


Summative

Topic TestsBenchmark TestsPerformance TasksProjects


ELA:


Science:

MS-ETS1-1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successfulsolution, taking into account relevant scientific principles and potential impacts on people and the natural environment that maylimit possible solutions.









Technology




IEP




Materials Bank


Page 2 of 6

Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL

Materials Bank


Page 3 of 6



Additional time

Preferred seating



Graphic organizer

Mnemonic devices



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

Materials Bank


Page 4 of 6

Online games

Leveled Homework


Today’s Challenge

Unit Materials

Core Materials:

enVision Math 2.0

Topic 7: Probability



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

Materials Bank


Page 5 of 6








Standards Covered


MA.7.7.SP: Statistics and Probability

MA.7.7.SP.C: Investigate chance processes and develop, use, and evaluate probability models.

MA.7.7.SP.C.5: Understand that the probability of a chance event is a number between 0 and 1 that expresses the likelihood of the event occurring. Larger

numbers indicate greater likelihood. A probability near 0 indicates an unlikely event, a probability around 1/2 indicates an event that is neither unlikely

nor likely, and a probability near 1 indicates a likely event.

MA.7.7.SP.C.6: Approximate the probability of a chance event by collecting data on the chance process that produces it and observing its long-‐run relative

frequency, and predict the approximate relative frequency given the probability. For example, when rolling a number cube 600 times, predict that a 3 or 6

would be rolled roughly 200 times, but probably not exactly 200 times.

MA.7.7.SP.C.7: Develop a probability model and use it to find probabilities of events. Compare probabilities from a model to observed frequencies; if the

agreement is not good, explain possible sources of the discrepancy.

MA.7.7.SP.C.7a: Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of

events. For example, if a student is selected at random from a class, find the probability that Jane will be selected and the probability that a girl

will be selected.

MA.7.7.SP.C.7b: Develop a probability model (which may not be uniform) by observing frequencies in data generated from a chance process. For

example, find the approximate probability that a spinning penny will land heads up or that a tossed paper cup will land open-‐end down. Do the

outcomes for the spinning penny appear to be equally likely based on the observed frequencies?

MA.7.7.SP.C.8: Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.



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Unit 8: Solve Problems Involving GeometryUnit: Mathematics , Grade(s) Grade 7

This unit focuses on representing proportional relationships to solve scale drawing problems. Additionally, the topic includes solving problems involving area and

circumference of circles and surface area and volume of two and three-dimensional figures.

Duration: 21 Days

Unit


Essential Questions

How can geometry be used to solve problems?


Use a scale drawing to calculate measurements and to reproduce proportional scale drawings.Understand that drawing a unique quadrilateral needs a combination of side lengths, angle measures, and side angle relationships.Understand how to construct triangles with given conditions and determine whether it is a unique triangle, more than one triangle, or notriangle.The measure of angles that are formed by intersecting lines and rays can be determined when the relationship between different types ofangles are known.The circumference and diameter of a circle, regardless of size, have a unique and constant ratio that is an irrational number symbolized by The formula for the area of a circle can be used to solve problems by substituting the known values for area (A) and or radius (r) to

solve for the unknown value.A cross section is a 2D figure that is exposed when a 3D figure is sliced by a plane.The surface area of a composite figure is the sum of the area of its surfaces. The surface area of a 3D figure is the combined surface area ofall of the faces of the figure.To find the volume of a prism, find the area of the base and multiply by its height.


8-1 Solve Problems Involving Scale Drawings8-2 Draw Geometric Figures8-3 Draw Triangles with Given Conditions

8-4 Solve Problems Using Angle Relationships8-5 Solve Problems Involving Circumference of a Circle8-6 Solve Problems Involving Area of a Circle3-Act Mathematical Modeling8-7 Describe Cross Sections3-Act Mathematical Modeling8-8 Solve Problems Involving Surface Area8-9 Solve Problems Involving Volume


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Formative


Summative



ELA:


Science:

MS-ETS1-1. Define the criteria and constraints of a design problem with sufficient precision to ensure a successfulsolution, taking into account relevant scientific principles and potential impacts on people and the natural environment that maylimit possible solutions.









Technology




IEP




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Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




504


Preferred seating



Graphic organizer

Mnemonic devices



Scribe

Manipulatives

Calculators

Leveled homework


Reteach pages




ELL

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Additional time

Preferred seating



Graphic organizer

Mnemonic devices



Manipulatives

Leveled homework


Reteach pages




At Risk Students


Preferred seating

Graphic organizer

Mnemonic devices



Manipulatives

Calculators

Leveled homework


Reteach pages




Gifted & Talented


Enrichment pages

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Online games

Leveled Homework


Today’s Challenge

Unit Materials

Core Materials:

enVision Math 2.0

Topic 8: Solve Problems Involving Geometry



Leveled homework

Fluency practice


ST Math

3 Act Lessons

Estimation 180

Desmos Lessons

Nearpod Lessons

BrainPop resources


Online Resources

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Standards Covered


MA.7.7.G: Geometry

MA.7.7.G.A: Draw, construct, and describe geometrical figures and describe the relationships between them.

MA.7.7.G.A.1: Solve problems involving scale drawings of geometric figures, including computing actual lengths and areas from a scale drawing and

reproducing a scale drawing at a different scale.

MA.7.7.G.A.2: Draw (with technology, with ruler and protractor, as well as freehand) geometric shapes with given conditions. Focus on constructing

triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

MA.7.7.G.A.3: Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and

right rectangular pyramids.

MA.7.7.G.B: Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

MA.7.7.G.B.4: Know the formulas for the area and circumference of a circle and use them to solve problems; give an informal derivation of the relationship

between the circumference and area of a circle.

MA.7.7.G.B.5: Use facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for

an unknown angle in a figure.

MA.7.7.G.B.6: Solve real-world and mathematical problems involving area, volume and surface area of two- and three-dimensional objects composed of

triangles, quadrilaterals, polygons, cubes, and right prisms.



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Unit 1: Integers and Rational Numbers

Documents

Transcript of Unit 1: Integers and Rational Numbers