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SADLIER

New York Progress Mathematics

William H. Sadlier, Inc.www.sadlierschool.com800-221-5175

2 Module 1: Ratios and Proportional Relationships

5 Module 2: Rational Numbers

8 Module 3: Expressions and Equations

11 Module 4: Percent and Proportional Relationships

16 Module 5: Statistics and Probability

21 Module 6: Geometry

Contents

Correlated to the

New York State Common CoreMathematics Curriculum

Grade 7

New York Sta te Common Core Mathemat i c s Cur r i cu lum – NYS CC S tanda rds f o r Mathemat i c s – Sad l ie r New York Prog res s Mathemat i c s Cor re la t ion

Lesson Structure Key: P–Problem Set Lesson, M–Modeling Cycle Lesson, E–Explorations Lesson, S–Socratic Lesson Copyright © William H. Sadlier, Inc. All rights reserved. 2

Module 1 • Ratios and Proportional Relationships NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Proportional Relationships

Instructional Days: 6

Lesson 1: An Experience in Relationships as Measuring Rate (P)

Lesson 2: Proportional Relationships (P)

Lessons 3–4: Identifying Proportional and Non‐Proportional Relationships in Tables (P)

Lessons 5–6: Identifying Proportional and Non‐Proportional Relationships in Graphs (E)

7.RP.A.2

Recognize and represent proportional relationships between quantities.

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.

Lesson 2 Identify Proportional Relationships—pp. 18–25

Topic B: Unit Rate and the Constant of

Proportionality


Lesson 7: Unit Rate as the Constant of Proportionality (P)

Lessons 8–9: Representing Proportional Relationships with Equations (P)

Lesson 10: Interpreting Graphs of Proportional Relationships (P)

7.RP.A.2


7.RP.A.2b Identify the constant of proportionality (unit

rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Lesson 3 Identify the Constant of Proportionality—pp.

26–33

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.

Lesson 4 Represent Proportional Relationships with Equations —pp. 34–41

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.

Lesson 5 Interpret Graphs of Proportional

Relationships—pp. 42–49




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.

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?

Lesson 19 Solve Linear Equations—pp. 166–173

Lesson 20 Problem Solving: Linear Equations—pp. 174–181

Mid‐Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days)

Topic C: Ratios and Rates Involving Fractions


Lessons 11–12: Ratios of Fractions and Their Unit Rates (P)

Lesson 13: Finding Equivalent Ratios Given the Total Quantity (P)

Lesson 14: Multi‐Step Ratio Problems (P)

Lesson 15: Equations and Graphs of Proportional Relationships Involving Fractions (P)

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.

Lesson 1 Compute Unit Rates—pp. 10–17

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.

Lesson 6 Problem Solving: Multi‐step Ratio Problems—pp. 50–57

Lesson 7 Problem Solving: Multi‐step Percent Problems—pp. 58–65




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.

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?



Topic D: Ratios of Scale Drawings


Lesson 16: Relating Scale Drawings to Ratios and Rates (E)

Lesson 17: The Unit Rate as the Scale Factor (P)

Lesson 18: Computing Actual Lengths from a Scale Drawing (P)

Lesson 19: Computing Actual Areas from a Scale Drawing (P)

Lesson 20: An Exercise in Creating a Scale Drawing (E)

Lessons 21–22: An Exercise in Changing Scales (E)

7.RP.A.2


7.RP.A.2b

Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships.

Lesson 3 Identify the Constant of Proportionality—pp.

26–33

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.

Lesson 23 Use Scale Drawings to Solve Problems—pp. 204–211

End‐of‐Module Assessment and Rubric Topics A through D (assessment 1 day, return 1 day, remediation or further applications 2 days)



Module 2 • Rational Numbers NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Addition and Subtraction of Integers and Rational Numbers


Lesson 1: Opposite Quantities Combine to Make Zero (P)

Lesson 2: Using the Number Line to Model the Addition of Integers (P)

Lesson 3: Understanding Addition of Integers (P)

Lesson 4: Efficiently Adding Integers and Other Rational Numbers (P)

Lesson 5: Understanding Subtraction of Integers and Other Rational Numbers (S)

Lesson 6: The Distance Between Two Rational Numbers (S)

Lesson 7: Addition and Subtraction of Rational Numbers (P)

Lessons 8–9: Applying the Properties of Operations to Add and Subtract Rational Numbers (P)

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.

7.NS.A.1a

Describe situations in which opposite quantities combine to make 0. For example, a hydrogen atom has 0 charge because its two constituents are oppositely charged.

Lesson 8 Understand Addition of Integers—pp. 72–79

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.

Lesson 8 Understand Addition of Integers—pp. 72–79

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.

Lesson 9 Understand Subtraction of Integers—pp. 80–87

7.NS.A.1d

Apply properties of operations as strategies to add and subtract rational numbers.

Lesson 10 Add and Subtract Rational Numbers—pp. 88–95




Topic B: Multiplication and Division of Integers and Rational Numbers


Lesson 10: Understanding Multiplication of Integers (P)

Lesson 11: Develop Rules for Multiplying Signed Numbers (P)

Lesson 12: Division of Integers (P)

Lesson 13: Converting Between Fractions and Decimals Using Equivalent Fractions (P)

Lesson 14: Converting Rational Numbers to Decimals Using Long Division (P)

Lesson 15: Multiplication and Division of Rational Numbers (P)

Lesson 16: Applying the Properties of Operations to Multiply and Divide Rational Numbers (S)

7.NS.A.2 Apply and extend previous understandings of

multiplication and division and of fractions to multiply and divide rational numbers.

7.NS.A.2a Understand that multiplication is extended from fractions to rational numbers by requiring that operations continue to satisfy the properties of operations, particularly the distributive property, leading to products such as (–1)(–1) = 1 and the rules for multiplying signed numbers. Interpret products of rational numbers by describing real‐world contexts.

Lesson 11 Understand Multiplication of Integers—pp. 96–103

7.NS.A.2b Understand that integers can be divided, provided that the divisor is not zero, and every quotient of integers (with non‐zero divisor) is a rational number. If p and q are integers, then –(p/q) = (–p)/q = p/(–q). Interpret quotients of rational numbers by describing real‐world contexts.

Lesson 12 Understand Division of Integers—pp. 104–111

7.NS.A.2c Apply properties of operations as strategies to multiply and divide rational numbers.

Lesson 13 Multiply and Divide Rational Numbers—pp. 112–119

7.NS.A.2d Convert a rational number to a decimal using long division; know that the decimal form of a rational number terminates in 0s or eventually repeats.

Lesson 14 Convert Rational Numbers to Decimal Form—pp. 120–127

Mid‐Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 1 day)




Topic C: Applying Operations with Rational Numbers to Expressions and Equations


Lesson 17: Comparing Tape Diagram Solutions to Algebraic Solutions (E)

Lessons 18–19: Writing, Evaluating, and Finding Equivalent Expressions with Rational Numbers (P, P)

Lesson 20: Investments–Performing Operations with Rational Numbers (M)

Lesson 21: If‐Then Moves with Integer Number Cards (E)

Lessons 22–23: Solving Equations Using Algebra (P)

7.NS.A.3

Solve real‐world and mathematical problems involving the four operations with rational numbers.

Lesson 15 Apply Rational‐Number Operations—pp. 128–135

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.”

Lesson 16 Combine Like Terms to Simplify Linear Expressions —pp. 142–149

Lesson 17 Expand and Factor Linear Expressions—pp. 150–157

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.

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?



End‐of‐Module Assessment and Rubric Topics A through C (assessment 1 day, return 1 day, remediation or further applications 2 days)



Module 3 • Expressions and Equations NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Use Properties of Operations to Generate Equivalent Expressions


Lessons 1–2: Generating Equivalent Expressions (P)

Lessons 3–4: Writing Products as Sums and Sums as Products (P)

Lesson 5: Using the Identity and Inverse to Write Equivalent Expressions (P)

Lesson 6: Collecting Rational Number Like Terms (P)

7.EE.A.1

Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.



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.”



Topic B: Solve Problems Using Expressions,

Equations, and Inequalities


Lesson 7: Understanding Equations (P)

Lessons 8–9: Using If‐Then Moves in Solving Equations (P)

Lessons 10–11: Angle Problems and Solving Equations (P)

Lesson 12: Properties of Inequalities (E)

Lesson 13: Inequalities (P)

Lesson 14: Solving Inequalities (P)

Lesson 15: Graphing Solutions to Inequalities (P)

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

– continued on next page –

Lesson 18 Problem Solving: Multi‐step Problems with Rational Numbers —pp. 158–165




– continued from previous page –

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.

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.

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?



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.

Lesson 21 Solve Linear Inequalities—pp. 182–189

Lesson 22 Problem Solving: Linear Inequalities—pp. 190–197

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.

Lesson 28 Use Equations to Find Unknown Angle Measures—pp. 244–251




Mid‐Module Assessment and Rubric Topics A through B (assessment 2 days, return 1 day, remediation or further applications 2 days)

Topic C: Use Equations and Inequalities to

Solve Geometry Problems


Lesson 16: The Most Famous Ratio of All (M)

Lesson 17: The Area of a Circle (E)

Lesson 18: More Problems on Area and Circumference (P)

Lesson 19: Unknown Area Problems on the Coordinate Plane (P)

Lesson 20: Composite Area Problems (P)

Lessons 21–22: Surface Area (P)

Lessons 23–24: The Volume of a Right Prism (E)

Lessons 25–26: Volume and Surface Area (P)

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.

Lesson 27 Use Formulas for Area and Circumference of Circles—pp. 236–243

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.

Lesson 29 Problem Solving: Area, Volume, and Surface Area—pp. 252–259

End‐of‐Module Assessment and Rubric Topics A through C (assessment 1 day, return 1 day, remediation or further applications 2 days)



Module 4 • Percent and Proportional Relationships NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Finding the Whole


Lesson 1: Percent (P)

Lesson 2: Part of a Whole as a Percent (P)

Lesson 3: Comparing Quantities with Percent (P)

Lesson 4: Percent Increase and Decrease (P)

Lesson 5: Finding One Hundred Percent Given Another Percent (P)

Lesson 6: Fluency with Percents (P)

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.


7.RP.A.2 Recognize and represent proportional relationships between quantities.



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.



Topic B: Percent Problems Including More Than

One Whole


Lesson 7: Markup and Markdown Problems (P)

Lesson 8: Percent Error Problems (S)

Lesson 9: Problem Solving When the Percent Changes (P)

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






Lesson 10: Simple Interest (P)

Lesson 11: Tax, Commissions, Fees, and Other Real‐World Percent Problems (P)


each 1/4 hour, compute the unit rate as the complex fraction 1/2/1/4 miles per hour, equivalently 2 miles per hour.


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.

Lesson 2 Identify Proportional Relationships—pp. 18–25



Lesson 3 Identify the Constant of Proportionality—pp. 26–33



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.

Lesson 5 Interpret Graphs of Proportional Relationships—pp. 42–49




7.EE.B.3 Solve multi‐step real‐life and mathematical

problems posed with positive and negative – continued on next page –






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.

Mid‐Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 1 day)

Topic C: Scale Drawings


Lesson 12: The Scale Factor as a Percent for a Scale Drawing (P)

Lesson 13: Changing Scales (S)

Lesson 14: Computing Actual Lengths from a Scale Drawing (P)




Lesson 3 Identify the Constant of Proportionality—pp. 26–33




Lesson 15: Solving Area Problems Using Scale Drawings (P)

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.

Lesson 23 Use Scale Drawings to Solve Problems—pp. 204–211

Topic D: Population, Mixture, and Counting

Problems Involving Percents


Lesson 16: Population Problems (P)

Lesson 17: Mixture Problems (P)

Lesson 18: Counting Problems (P)







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.

End‐of‐Module Assessment and Rubric Topics A through D (assessment 2 days, return 1 day, remediation or further applications 1 day)



Module 5 • Statistics and Probability NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Calculating and Interpreting Probabilities


Lesson 1: Chance Experiments (P)

Lesson 2: Estimating Probabilities by Collecting Data (P)

Lesson 3: Chance Experiments with Equally Likely Outcomes (P)

Lesson 4: Calculating Probabilities for Chance Experiments with Equally Likely Outcomes (P)

Lesson 5: Chance Experiments with Outcomes that Are Not Equally Likely (P)

Lesson 6: Using Tree Diagrams to Represent a Sample Space and to Calculate Probabilities (E)

Lesson 7: Calculating Probabilities of Compound Events (P)

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.

Lesson 34 Understand Probability of a Chance Event—pp. 298–305

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.

Lesson 35 Relate Relative Frequency and Probability—pp. 306–313

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.

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.

Lesson 36 Develop a Uniform Probability Model—pp. 314–321




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?

Lesson 37 Use a Chance Process to Develop a Probability Model—pp. 322–329

7.SP.C.8 Find probabilities of compound events using

organized lists, tables, tree diagrams, and simulation.

7.SP.C.8a Understand that, just as with simple events, the

probability of a compound event is the fraction of outcomes in the sample space for which the compound event occurs.

Lesson 38 Find Probabilities of Compound Events—pp. 330–337

7.SP.C.8b Represent sample spaces for compound events using methods such as organized lists, tables and tree diagrams. For an event described in everyday language (e.g., “rolling double sixes”), identify the outcomes in the sample space which compose the event.

Lesson 39 Represent Sample Spaces for Compound Events—pp. 338–345

Topic B: Estimating Probabilities


Lesson 8: The Difference Between Theoretical Probabilities and Estimated Probabilities (P)

Lesson 9: Comparing Estimated Probabilities to Probabilities Predicted by a Model (E)

Lessons 10–11: Using Simulation to Estimate a Probability (P,P)

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.

Lesson 35 Relate Relative Frequency and Probability—pp. 306–313




Lesson 12: Using Probability to Make Decisions (P)

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.

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.

Lesson 36 Develop a Uniform Probability Model—pp. 314–321

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?

Lesson 37 Use a Chance Process to Develop a Probability Model—pp. 322–329

7.SP.C.8 Find probabilities of compound events using

organized lists, tables, tree diagrams, and simulation.

7.SP.C.8c Design and use a simulation to generate frequencies for compound events. For example, use random digits as a simulation tool to approximate the answer to the question: If 40% of donors have type A blood, what is the probability that it will take at least 4 donors to find one with type A blood?

Lesson 40 Simulate Compound Events—pp. 346–353

Mid‐Module Assessment and Rubric Topics A through B (assessment 1 day)




Topic C: Random Sampling and Estimating Population Characteristics


Lesson 13: Populations, Samples, and Generalizing from a Sample to a Population (P)

Lesson 14: Selecting a Sample (P)

Lesson 15: Random Sampling (P)

Lesson 16: Methods for Selecting a Random Sample (P)

Lesson 17: Sampling Variability (P)

Lesson 18: Estimating a Population Mean (P)

Lesson 19: Understanding Variability when Estimating a Population Proportion (P)

Lesson 20: Estimating a Population Proportion (P)

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.

Lesson 30 Understand Sampling—pp. 266–273

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.

Lesson 31 Use Sampling to Draw Inferences—pp. 274–281

Topic D: Comparing Populations


Lesson 21: Why Worry About Sampling Variability? (E)

Lessons 22–23: Using Sample Data to Decide if Two Population Means Are Different (P,P)

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


Lesson 32 Use Visual Overlap to Compare Distributions—pp. 282–289





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.

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.

Lesson 33 Use Sample Statistics to Compare Populations—pp. 290–297

End‐of‐Module Assessment and Rubric Topics A through D (assessment 1 day)



Module 6 • Geometry NYS COMMON CORE MATHEMATICS CURRICULUM, GRADE 7 NYS COMMON CORE STANDARDS FOR MATHEMATICS, GRADE 7 SADLIER NEW YORK PROGRESS MATHEMATICS, GRADE 7

Topic A: Unknown Angles


Lesson 1: Complementary and Supplementary Angles (P)

Lessons 2–4: Solve for Unknown Angles using Equations (P, P, P)

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.

Lesson 28 Use Equations to Find Unknown Angle Measures—pp. 244–251

Topic B: Constructing Triangles


Lesson 5: Unique Triangles (S)

Lesson 6: Drawing Geometric Shapes (E)

Lesson 7: Drawing Parallelograms (P)

Lesson 8: Drawing Triangles (E)

Lesson 9: Conditions for a Unique Triangle—Three Sides and Two Sides and the Included Angle (E)

Lesson 10: Conditions for a Unique Triangle—Two Angles and a Given Side (E)

Lesson 11: Conditions on Measurements that Determine a Triangle (E)

Lesson 12: Unique Triangles—Two Sides and a Non‐Included Angle (E)

Lessons 13–14: Checking for Identical Triangles (P, P)

Lesson 15: Using Unique Triangles to Solve Real‐World and Mathematical Problems (P)

7.G.A.2

Draw (freehand, with ruler and protractor, and with technology) 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.

Lesson 24 Draw Shapes that Meet Given Conditions—pp. 212–219

Lesson 25 Construct Triangles Using Both Side Lengths and Angle Measures—pp. 220–227




Mid‐Module Assessment and Rubric Topics A through B (assessment 1 day, return 1 day, remediation or further applications 2 days)

Topic C: Slicing Solids


Lesson 16: Slicing a Right Rectangular Prism with a Plane (E)

Lesson 17: Slicing a Right Rectangular Pyramid with a Plane (E)

Lesson 18: Slicing on an Angle (E)

Lesson 19: Understanding Three‐Dimensional Figures (P)

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.

Lesson 26 Slice Three‐Dimensional Figures—pp. 228–235

Topic D: Problems Involving Area and Surface

Area


Lesson 20: Real‐World Area Problems (P)

Lesson 21: Mathematical Area Problems (P)

Lesson 22: Area Problems with Circular Regions (P)

Lesson 23–24: Surface Area (P)

7.G.B.6






Topic E: Problems Involving Volume


Lesson 25: Volume of Right Prisms (P)

Lesson 26: Volume of Composite Three‐Dimensional Objects (P)

Lesson 27: Real‐World Volume Problems (P)

7.G.B.6



End‐of‐Module Assessment and Rubric Topics C through E (assessment 1 day, return 1 day, remediation or further applications 2 days)

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