7th grade Math Guide

Instructional Guide 2025-2026

Math

Grade

Instructional Guide 2025-2026

Introduction

What’s New and Updated in

7th grade math

What’s New

This section contains a listing of pages in the map that are new this year.

Page Number

Description

What’s Updated

This section contains a listing of pages in the page that have received substantial content updates for this year.

Description

Updated dates for all units

Grade 7

Math Overview

ORGANIZATION OF STANDARDS

The Utah Core Standards are organized into strands, which represent significant areas of learning within content areas. Depending on the core area, these strands may be designated by time periods, thematic principles, modes of practice, or other organizing principles. Within each strand are standards. A standard is an articulation of the demonstrated proficiency to be obtained. A standard represents an essential element of learning that is expected. While some standards within a strand may be more comprehensive than others, all standards are essential for mastery.

UNDERSTANDING MATHEMATICS

These standards define what students should understand and be able to do in their study of mathematics. Asking a student to understand something means asking a teacher to assess whether the student has understood it. But what does mathematical understanding look like? One hallmark of mathematical understanding is the ability to justify, in a way appropriate to the student’s mathematical maturity, why a particular mathematical statement is true or where a mathematical rule comes from. Mathematical understanding and procedural skill are equally important, and both are assessable using mathematical tasks of sufficient richness. The standards set grade-specific standards but do not dictate curriculum or teaching methods, nor do they define the intervention methods or materials necessary to support students who are well below or well above grade-level expectations. It is also beyond the scope of the Standards to define the full range of supports appropriate for English language learners and for students with special needs. At the same time, all students must have the opportunity to learn and meet the same high standards if they are to access the knowledge and skills necessary in their post-school lives. The standards should be read as allowing for the widest possible range of students to participate fully from the outset, along with appropriate accommodations to ensure maximum participation of students with special education needs. No set of grade-specific standards can fully reflect the great variety in abilities, needs, learning rates, and achievement levels of students in any given classroom. However, the standards do provide clear signposts along the way to the goal of college and career readiness for all students. What students can learn at any particular grade level depends upon what they have learned before. Ideally then, each standard in this document might have been phrased in the form, "Students who already know… should next come to learn ..." Grade placements for specific topics have been made on the basis of state and international comparisons and the collective experience and collective

professional judgment of educators, researchers and mathematicians. Learning opportunities will continue to vary across schools and school systems, and educators should make every effort to meet the needs of individual students based on their current understanding.

USBE Course Overview Grade 7 The purpose of this document is to provide a brief overview of the most essential content in the grade level along with a progression of how the content was addressed in the prior grade level and will prepare students for content in the future grade level. This is not a comprehensive list of content in the grade level, but rather highlights the major work of the grade level.

Major Work of Grade Band: Grades 6 - 8 ● Apply and use operations with rational numbers ● Understand ratio concepts and apply proportional reasoning ● Simplify expressions and solve equations ● Represent and analyze relationships

Major Work and Vertical Alignment

Major work: Operations with Rational Numbers Grade 7: Apply and extend understanding of operations with rational numbers : Apply previous understanding of operations with rational numbers (7.NS.1-3) to include integers and negative rational numbers. (Operations with all other rational numbers are being practiced in grade 7, with integers being new at this point in the 7th grade). ● Prior grades : Students have performed all four operations with non-negative rational numbers (6.NS.1-3), including dividing fractions by fractions in grade 6. Students are introduced to integers in grade 6 via number line models, absolute value, and opposite signs/value/ direction (6.NS.5-7). ● Future Grades : In grade 8, students will use their understanding of rational numbers (including identifying and converting to different forms) to develop their understanding of irrational numbers (8.NS.1-3). In Secondary Math II, students will expand the number system to include complex numbers (II.N.CN.1,2,7,8,9). Major work: Proportional Reasoning Grade 7: Understand and apply proportional reasoning : Compute unit rates (7.RP.1), recognize and represent proportional relationships between quantities using multiple representations (7.RP.2), use proportional relationships to solve multi-step and percent problems (7.RP.3), and solve problems using scale drawings of geometric figures (7.G.1). ● Prior Grades: Students create equivalent fractions (4.NF, 5.NF). In grade 6, students are introduced to ratio and rate reasoning (6.RP.1-3), understand the concept of unit

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rate (6.RP.2), and use multiple representations to solve ratio/rate problems (tables of equivalent ratios, equations, and plot values on a coordinate plane) (6.RP.3). ● Future Grades: Students extend their understanding of proportional relationships and connect proportionality to linear equations (recognizing slope as a proportional relationship between quantities (8.EE.5) and that non-proportional linear functions have a vertical shift of b units (8.EE.5-6, 8th grade function standards). Proportional relationships are the foundation for developing an understanding of rates of change (all functions in high school) and the connection between proportional relationships and a function who grows at a rate proportionate to the amount present. Major work: Simplify Expressions and Solve Equations Grade 7: Simplify expressions and solve equations: Apply properties of operations to factor, expand (7.EE.1) and convert between forms of an expression (7.EE.2). Assess reasonableness of solutions( (7.EE.3). Use variables to represent quantities to construct and solve real-world equations and inequalities. For example: px+q < r. (7.EE.4). ● Prior Grades: Students solve for unknown values starting in the early grades (K.OA.4, 1.OA.1, 2.OA1, etc). Students then use variables to solve simple equations and inequalities in grade 6 F or example: x+q < r (6.EE.5-8). ● Future Grades: Students analyze and solve linear equations, inequalities(8.EE.7), and systems of linear equations (8.EE.8,). Understand the relationship between linear equations in one variable vs linear functions with two variables (8.EE.7-8, 8th grade function standards). . Students continue their progress in solving equations/inequalities and justifying solutions (High School algebra standards). Major work: Represent and Analyze Relationships Grade 7: Represent and analyze relationships: Solve problems using numerical and algebraic equations (7.EE.3, 7.EE4), draw inferences about two populations (7.SP.2-4), and investigate probability models (7.SP.5-8). ● Prior Grades: Students solve simple problems using numerical and algebraic expressions (6.EE.5-9), plot relationships on a coordinate plane (6.NS.8, 6.EE.9), and develop an understanding of statistical variability (6.SP.1-3). ● Future Grades: Students represent two variable relationships, compare quantities, and analyze relationships throughout their mathematics career. Paying attention to how quantities interact and how two quantities compare is ongoing throughout all strands in the standards in grade 8 and throughout high school.

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Instructional Guide 2025-2026

Scope and Sequence

Grade 7

YEAR AT A GLANCE Option 1

Unit 5 Rational Number Arithmetic (17 Sections)

Unit 1 Scale Drawings (13 Sections)

Unit 2 Introducing Proportional Relationships (15 Sections)

Unit 3 Measuring Circles (11 Sections)

Unit 4 Proportional Relationships and Percentages (16 Sections)

Unit 6 Expressions, Equations, and Inequalities (23 Sections)

Unit 7 Angles, Triangles, and Prisms (17 Sections)

Unit 8 Probability and Sampling (20 Sections)

Unit 9 Putting it All Together

Illustrative Unit

Suggested Pacing

Aug 18 - Sept 12 (19 days)

Sept 15 - Oct 8 (16 days)

Oct 9 - Nov 10 (20 days)

Nov 11 - Dec 3 (14 days)

Dec 4 - Jan 12 (18 days)

Jan 13 - Feb 26 (29 days)

Mar 2 - Apr 3 (24 days)

Apr 13 - May 8 (20 days)

May 11 - May 29

7.NS.1 7.NS.2 7.NS.3 7.RP.2 7.EE.3 7.EE.4

7.G.1 7.G.6

7.RP.1 7.RP.2

7.G.2 7.G.4 7.RP.3 7.G.6 7.G.4 7.EE.3

7.RP.1 7.RP.2 7.RP.3

7.EE.1 7.EE.2 7.EE.3 7.EE.4

7.G.5 7.EE.4 7.NS.1

7.SP.1 7.SP.2 7.SP.3 7.SP.4 7.SP.5 7.SP.6 7.SP.7 7.SP.8

7.RP 7.EE 7.G 7.SP

Practice Standards

7.G.2 7.G.3 7.G.5 7.G.6

Practice Standards

Practice Standards

Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

DWSBA & Testing Window

These standards will be assessed along with all other standards on the RISE

DWSBA #1

DWSBA #2

DWSBA #3

Aug 19 - Sept 25

Dec 3 - Jan 15

MAP Window

Apr 1 - May 8

SALTA Extensions

“Are You Ready for More?”

Accessing the District-Wide Standards-Based Assessment (DWSBA) The DWSBA’s will be done through Canvas on Derivita Instructions to access the DWSBA can be found here .

Grade 7

YEAR AT A GLANCE Option 2

Unit 1 Scale Drawings (13 Sections)

Unit 2 Introducing Proportional Relationships (15 Sections)

Unit 3 Measuring Circles (11 Sections)

Unit 4 Proportional Relationships and Percentages (16 Sections)

Unit 5 Rational Number Arithmetic (17 Sections)

Unit 6 Expressions, Equations, and Inequalities (23 Sections)

Unit 7 Angles, Triangles, and Prisms (17 Sections)

Unit 8 Probability and Sampling (20 Sections)

Unit 9 Putting it All Together

Illustrative Unit

Suggested Pacing

Aug 18 - Sept 9 (16 days)

Sept 10 - Oct 9 (20 days)

Oct 10 - Nov 4 (15 days)

Nov 5 - Dec 3 (18 days)

Dec 4 - Jan 12 (18 days)

Jan 13 - Feb 26 (29 days)

Mar 2 - Apr 3 (24 days)

Apr 13 - May 8 (20 days)

May 11 - May 29

7.G.1 7.G.6

7.RP.1 7.RP.2

7.G.2 7.G.4 7.RP.3 7.G.6 7.G.4 7.EE.3

7.RP.1 7.RP.2 7.RP.3

7.NS.1 7.NS.2 7.NS.3 7.RP.2 7.EE.3 7.EE.4

7.EE.1 7.EE.2 7.EE.3 7.EE.4

7.G.5 7.EE.4 7.NS.1

7.SP.1 7.SP.2 7.SP.3 7.SP.4 7.SP.5 7.SP.6 7.SP.7 7.SP.8

7.RP 7.EE 7.G 7.SP

Practice Standards

7.G.2 7.G.3 7.G.5 7.G.6

Practice Standards

Practice Standards

Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

DWSBA & Testing Window

These standards will be assessed along with all other standards on the RISE

DWSBA #1

DWSBA #2

DWSBA #3

Aug 19 - Sept 25

Dec 3 - Jan 15

MAP Window

Apr 1 - May 8

SALTA Extensions

“Are You Ready for More?”

Accessing the District-Wide Standards-Based Assessment (DWSBA) The DWSBA’s will be done through Canvas on Derivita Instructions to access the DWSBA can be found here .

RATIONAL NUMBER ARITHMETIC

Unit 5

PACING

KEY LANGUAGE USES

Option 1: August 18 - September 12 (19 days) Option 2: December 5 - January 12 (18 days)

EXPLAIN

STANDARDS Standard 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a vertical number line diagram. a. ​ Describe situations in which opposite quantities combine to make 0. b. ​ Understand p + q as a the number located a distance 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 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. ​ 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. d. ​ Apply properties of operations as strategies to add and subtract rational numbers. Standard 7.NS.2 Apply and extend previous understandings of multiplication and division and of fractions to multiple and divide rational numbers. a. ​ 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. b. ​ 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) . Interpret quotients of rational numbers by describing real-world contexts. c. ​ Apply properties of operations as strategies to multiply and divide rational numbers. d. ​ 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. Standard 7.NS.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.

Standard 7.RP.2 Recognize and represent proportional relationship between quantities.

a. ​ Decide whether two quantities are in a proportional relationship, e.g. by testing for equivalent rations in a table or graphing on a coordinate plane and observing whether the graph is a straight line through the origin. b. ​ Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. ​ Represent proportional relationships by equations. d. ​ 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. Standard 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, 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.

Standard 7.EE.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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explain what a negative or positive number means in a real world context. Language Supports: ●​ Vocabulary (negative, positive, integer, rational number)

I can solve a real-world problem using all four operations on positive and negative rational numbers and explain what my answer means in terms of the problem itself. Language Supports: ●​ Vocabulary (negative, positive, integer, rational number) DIFFERENTIATION IN ACTION Skill Building From Activity 6.1: MLR 8 Discussion Supports. Display sentence frames for students to use as a support when they explain their strategy. For example, "I noticed that ______." or "First, I ________ because ________." When students share their answers with a partner, prompt them to rehearse what they will say when they share with the whole class. Rehearsing provides students with additional opportunities to clarify their thinking, and to consider how they will communicate their reasoning.

Extension

From Lesson 3 “Are You Ready for More?”: Find the sum without a calculator. 10+21+32+43+54+(-54)+(-43)+(-32)+(-21)+(-10)

RESOURCES Unit 5 Vocabulary

Combine Lessons 1 & 2

Information about Practice Problems Practice Problems that need to be removed with moving unit 5 to beginning of the year

Combine Lessons 3 & 4 Combine Lessons 6 & 7 Combine Lessons 13 & 14 Combine Lessons 15 & 16

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.NS.1

5.1, 5.2, 5.3, 5.4, 5.5, 5.6, 5.7, 5.13

7.NS.2

5.1, 5.8, 5.9, 5.10, 5.11

7.NS.3

5.7, 5.12, 5.14, 5.15, 5.16, 5.17

7.RP.2

5.9, 5.12

7.EE.3

5.12, 5.17

7.EE.4

5.15, 5.16

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

5.3

5.1

6.NS.5

2

5.5

5.2

6.NS.7

3

5.2

5.5

1.OA.4 , 6.NS.6

4

5.1

5.8

6.NS.8

5

5.1

5.9

6.RP.3b

6

5.8

5.10

6.EE.2b

5.14

6.EE.7

5.15

6.EE.5

LEARNING INTENTIONS

●​ Understand, apply, and explain the additive inverse property, including using situations with context. ●​ Model addition and subtraction of rational numbers, including integers, decimals, and fractions, on a number line.

●​ Add and subtract rational numbers, including integers, decimals, and fractions. ●​ Use strategies such as making zero pairs. For example, 6 + (-8) is the same as 6 + (-6) + (-2). ●​ Multiply and divide rational numbers and use properties of arithmetic to model multiplication and division of rational numbers. ●​ Understand the rules for multiplying and dividing signed numbers. ●​ Understand that every quotient of integers is a rational number (given the divisor is not zero). ●​ Use long division to change a fraction into a terminating or repeating decimal. ●​ Interpret products and quotients of rational numbers in real-world contexts. ●​ Model and solve real world problems involving the four operations with rational numbers. ●​ Model and solve real world problems involving complex fractions. ●​ Solve multi-step real-life and mathematical problems involving calculations with rational numbers in any form. ●​ Utilize various forms of rational numbers to solve and make sense of problems. ●​ Choose between forms of a rational number to simplify calculations or communicate solutions meaningfully.

KEY VOCABULARY

●​ Withdrawal ●​ Deposit

Unit 1

SCALE DRAWINGS

PACING

KEY LANGUAGE USES

Option 1: September 15 - October 8 (16 days) Option 2: August 18 - September 9 (16 days)

EXPLAIN

STANDARDS ●​ Standard 7.G.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. ●​ Standard 7.G.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. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can find the actual distance between two points on a map and explain how I got the distance. Language Supports: ●​ Vocabulary (scale, distance)

I can make a scale drawing of a bedroom. Language Supports: ●​

Vocabulary (scale factor, dimension, etc.)

DIFFERENTIATION IN ACTION Skill Building

From Activity 4.2: MLR 7 Compare and Connect. Use this routine to call attention to the different ways students may identify scale factors. Display the following statements: “The scale factor from EFGH to IJKL is 3,” and “The scale factor from EFGH to IJKL is 1/3.” Give students 2 minutes of quiet think time to read and consider whether either or both of the statements are correct. Invite students to share their initial thinking with a partner before selecting 2–3 students to share with the class. In this discussion, listen for and amplify any comments that refer to the order of the original figure and its scaled copy, as well as those who identify corresponding vertices and distances. Draw students’ attention to the different ways to describe the relationships between scaled copies and the original figure.

Extension

From Lesson 7 “Are You Ready For More?”: The tallest mountain in the

United States, Mount Denali in Alaska, is about 6,190 m tall. If this mountain were shown on the scale drawing, how would its height compare to the heights of the structures? Explain or show your reasoning.

RESOURCES Unit 1 lesson notes Vocabulary resources Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.G.1

1.1, 1.2, 1.3, 1.4, 1.5, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.12, 1.13

7.G.6

1.6

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

1.1

1.1

4.MD.1

2

1.2

1.2

5.NBT.7 , 5.NF.4

3

1.5

1.3

5.MD.1 , 6.RP.3a

4

1.6

1.4

6.NS.3

5

1.7

1.5

5.NBT.6 , 5.NF.5 , 6.NS.1

6

1.3

1.6, 1.10

6.G.1

7

1.8

1.7

6.EE.2c

1.8

6.NS.2 , 6.RP.3b

1.9

3.NF.3 , 5.NBT.3

1.12

6.RP.3d

LEARNING INTENTIONS

●​ Use a scale or scale factor to find a measurement. ●​ Find actual lengths and areas from a scale drawing, using a scale factor. ●​ Create multiple scale drawings from the original model or drawing, using different scales.

KEY VOCABULARY

●​ Scaled Copy ●​ Scale Factor ●​ Corresponding

●​ Scale ●​ Scale Drawing

INTRODUCING PROPORTIONAL RELATIONSHIPS

Unit 2

PACING

KEY LANGUAGE USES

Option 1: October 9 - November 10 (20 days) Option 2: September 10 - October 9 (20 days)

EXPLAIN

STANDARDS Standard 7.RP.1 Compute unit rates associated with ratios of fraction, including ratios of lengths, areas, and other quantities measured in like or different units.

Standard 7.RP.2 Recognize and represent proportional relationship between quantities.

a. ​ 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. b. ​ Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. ​ Represent proportional relationships by equations. d. ​ 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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explain if two variables make a proportional relationship. Language Supports: ●​ Vocabulary (proportional relationship, variable)

I can explain the meaning of a point (1, x ) on a graph of a proportional relationship. Language Supports: ●​ Vocabulary (graph, point) DIFFERENTIATION IN ACTION Skill Building

From Activity 6.2: MLR 1 Stronger and Clearer Each Time. Use this with successive pair shares to give students a structured opportunity to revise and refine their responses to “How are the solutions different and the same?” and “What are the advantages and disadvantages of each method?” Ask each student to meet with 2–3 other partners in a row for feedback. Provide students with prompts for feedback that will help them strengthen their ideas individually and clarify their language (e.g., "What do

you mean by _____," "You should expand on _____," “Can you clarify _____,” etc.). Listen for phrases such as “constant of proportionality,” “The price of one ticket,” “I believe this to be true because _____,” “This strategy is more efficient because _____,” etc. Students can borrow ideas and language from each partner to strengthen the final product. From lesson 11 “Are You Ready For More?”: If Tyler wanted to get to the bumper cars in half the time, how would the graph representing his walk change? How would the table change? What about the constant of proportionality?

Extension

RESOURCES This is a foundational unit, but it is reinforced in Unit 4 Unit 2 lesson notes Vocabulary Resources Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.RP.1

2.8

7.RP.2

2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.8, 2.9, 2.10, 2.11, 2.12, 2.13, 2.14, 2.15

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

2.2

2.2, 2.7

6.RP.3

5.MD.1 , 6.RP.2 , 6.RP.3b

2

2.3

2.3

3

2.4

2.4

5.NBT.7 , 6.RP.1

4

2.4

2.6

5.NBT.7 , 6.RP.2

5

2.5

2.8

4.OA.5 , 6.EE.2

6

2.10

2.10

6.NS.8

7

2.9

LEARNING INTENTIONS

●​ Extend the concept of a unit rate to include ratios of fractions. ●​ Compute a unit rate, involving quantities measured in like or different units.

●​ Determine if two quantities are in a proportional relationship by testing equivalent ratios ●​ Determine if two quantities are in a proportional relationship by graphing and checking for a straight line through the origin, (0, 0). ●​ Find the constant of proportionality from tables, graphs, equations, diagrams, or verbal descriptions. ●​ Write an equation for a proportional relationship in the form y = kx ●​ Explain the meaning of a point (x, y) in terms of the situation, especially (0, 0) and (1, r) where r is the unit rate.

KEY VOCABULARY

●​ Equivalent Ratios ●​ Proportional Relationship

●​ Constant of Proportionality ●​ Origin

Unit 3

MEASURING CIRCLES

PACING

KEY LANGUAGE USES

Option 1: November 11 - December 3 ( 14 days) Option 2: October 10 - November 4 (15 days)

EXPLAIN

STANDARDS Standard 7.G.2 Draw 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. Standard 7.G.4 Know the formulas for the area and circumference of a circle and use them to solve problems; given an informal derivation of the relationship between circumference and area of a circle. THIS IS THE FIRST TIME STUDENTS WORK WITH CIRCLES Standard 7.G.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. Standard 7.EE.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. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can find the area or circumference of a figure made up of a circle and another shape and explain my reasoning and how I found the area or circumference. Language Supports: ●​ Vocabulary (area, circumference, pi) Standard 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.

DIFFERENTIATION IN ACTION Skill Building

From Activity 9.2: MLR 1 Stronger and Clearer Each Time. After students have determined which figure has the largest shaded region, ask students to show their work and provide a brief explanation of their reasoning. Ask each student to meet with 2–3 other partners for feedback. Provide students with prompts for feedback that will help them strengthen their

ideas and clarify their language (e.g., “How did you find the radius of each circle in the figure?”, “Why did you . . . ?”, etc.). Students can borrow ideas and language from each partner to refine and clarify their original explanation. This will help students refine their own explanation and learn about different strategies to find area. From Lesson 7 “Are You Ready For More?”: 1. ​ How many circles of radius 1 unit can you fit inside a circle of radius 2 units so that they do not overlap? 2. ​ How many circles of radius 1 unit can you fit inside a circle of radius 3 units so that they do not overlap? 3. ​ How many circles of radius 1 unit can you fit inside a circle of radius 4 units so that they do not overlap?

Extension

RESOURCES 3.5 stays it’s optional, but it is necessary

3.6 took 2 days 3.8 took 2 days

3.11 stays optional Unit 3 Lesson Notes Vocabulary Resources Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.G.2

3.1, 3.2, 3.6

7.G.4

3.3, 3.4, 3.5, 3.7, 3.8, 3.9, 3.10, 3.11

7.G.6

3.6

7.RP.3

3.1, 3.5

7.EE.3

3.11

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

3.1

3.1

6.RP.3c , 4.MD.1 , 4.MD.3

2

3.3

3.3

6.SP.5c

3

3.1

3.6

6.G.1, 6.EE.7

4

3.6

5

3.6

6

3.6

LEARNING INTENTIONS

●​ Draw precise geometric figures based on given conditions. ●​ Discover the conditions necessary for a set of angles (sum of 180°) or sides to make a triangle (Triangle Inequality Theorem) by exploring different combinations of sides and angles. ●​ Explore conditions that determine unique triangles, multiple triangles, or no triangles (Foundational for future coursework involving Triangle Congruence Theorem). ●​ Use the formulas for area and circumference of a circle to solve problems. ●​ Know the relationship between diameter, circumference, and pi. ●​ Show and explain how the circumference and area of a circle are related. ●​ Decompose two-dimensional composite shapes into triangles, quadrilaterals, and polygons to find the area. ●​ Decompose three-dimensional composite shapes into cubes, and right prisms to find volume. ●​ Decompose three-dimensional composite shapes whose faces are triangles, quadrilaterals, and polygons, to find the surface area. ●​ Find volumes of cubes, right prisms, and composite polyhedra including those found in real-world contexts. ●​ Use proportional reasoning to solve multistep ratio and multistep percent problems. ●​ Write proportions from various contexts. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error. ●​ Solve multi-step real-life and mathematical problems involving calculations with rational numbers in any form. ●​ Utilize various forms of rational numbers to solve and make sense of problems. ●​ Choose between forms of a rational number to simplify calculations or communicate solutions meaningfully. ●​ Assess the reasonableness of answers using mental computation and estimation.

KEY VOCABULARY

●​ Radius ●​ Diameter ●​ Circumference ●​ Circle

●​ Pi ​ ●​ Area of a Circle

PROPORTIONAL RELATIONSHIPS AND PERCENTAGES

Unit 4

PACING

KEY LANGUAGE USES

Option 1: December 4 - January 12 (18 days) Option 2: November 5 - December 4 (19 days)

EXPLAIN

STANDARDS Standard 7.RP.1 Compute unit rates associated with ratios of fraction, including ratios of lengths, areas, and other quantities measured in like or different units.

Standard 7.RP.2 Recognize and represent proportional relationship between quantities.

a. ​ 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. b. ​ Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships. c. ​ Represent proportional relationships by equations. d. ​ 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. END OF UNIT COMPETENCY WITH LANGUAGE SUPPaORTS I can explain how to find the discount or markup using percents and proportional reasoning. Language Supports: ●​ Vocabulary (percent, proportional reasoning, discount, markup) DIFFERENTIATION IN ACTION Skill Building From Lesson 4.2: MLR 8 Discussion Supports. Use this routine to support whole-class discussion. After selected students share their explanations for who they agree with (Mai or Kiran). Call on students to restate and/or revoice the explanations presented using mathematical language (e.g., distributive property, equivalent equation, etc.). Consider giving students time to practice restating what they heard to a partner, before selecting one or two students to share with the class. This will provide more students with Standard 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.

an opportunity to produce language to explain whether two equations are equivalent. From Lesson 13 “Are You Ready for More?”: Before there were standard units of measurement, people often measured things using their hands or feet. 1. ​ Measure the length of your foot to the nearest centimeter with your shoe on. 2. ​ How many foot-lengths long is your classroom? Try to determine this as precisely as possible by carefully placing your heel next to your toe as you pace off the room. 3. ​ Use this information to estimate the length of your classroom in centimeters. 4. ​ Use a tape measure to measure the length of your classroom. What is the difference between the two measurements? Which one do you think is more accurate?

Extension

RESOURCES 4.13 is a shorter lesson 4.15 is not optional Simple Interest is not found explicitly here. You may want to teach the formula I = prt

Unit 4 Lesson Notes Vocabulary Resources Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.RP.1

4.1, 4.2, 4.3

7.RP.2

4.1, 4.3, 4.4, 4.5

7.RP.3

4.6, 4.7, 4.8, 4.9, 4.10, 4.11, 4.12, 4.13, 4.14, 4.15, 4.16

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

4.2

4.2

6.NS.1

2

4.2

4.3, 4.6, 4.9, 4.12 6.RP.3

3

4.6

4.4

6.EE.2

4

4.7

4.11, 4.14

6.EE.2b , 6.RP.3c

5

4.11

4.13

2.MD.3 , 5.NBT.7

6

4.11

7

4.8

LEARNING INTENTIONS

●​ Extend the concept of a unit rate to include ratios of fractions. ●​ Compute a unit rate, involving quantities measured in like or different units.

●​ Determine if two quantities are in a proportional relationship by testing equivalent ratios ●​ Determine if two quantities are in a proportional relationship by graphing and checking for straight line through (0, 0) ●​ Find the constant of proportionality from tables, graphs, equations, diagram, or verbal descriptions. ●​ Write an equation for a proportional relationship in the form y = kx ●​ Explain the meaning of a point (x, y) in terms of the situation, especially (0, 0) and (1, r) where r is the unit rate. ●​ Use proportional reasoning to solve multistep ratio and multistep percent problems. ●​ Write proportions from various contexts. Examples: simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, percent error

KEY VOCABULARY

●​ Repeating Decimal ●​ Percentage Increase

●​ Percentage Decrease

●​ Measurement Error

●​ Percent Error

EXPRESSIONS, EQUATIONS, AND INEQUALITIES

Unit 6

PACING

KEY LANGUAGE USES

January 13 - February 26 (29 days)

EXPLAIN

STANDARDS Standard 7.EE.1 Apply properties of operations as strategies to add, subtract, factor, and expand linear expressions with rational coefficients.

Standard 7.EE.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.

Standard 7.EE.3 Solve multi-step real-life and mathematical problems posed with positive and negative rational numbers in any form, 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.

Standard 7.EE.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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can create and solve an equation from a real world problem and explain what my answer means in terms of the problem itself. Language Supports: ●​ Vocabulary (equation, solution) I can create and solve an inequality from a real world problem and explain what my answer means in terms of the problem itself. Language Supports: ●​ Vocabulary (inequality, solution) DIFFERENTIATION IN ACTION Skill Building From Activity 5.1: Provide sentence frames to support students with

explaining their strategies. For example, “I noticed that ______, so I ______.” or “First, I ________ because ________.” When students share their answers with a partner, prompt them to rehearse what they will say when they share

with the full group. Rehearsing provides opportunities to clarify their thinking. From Lesson 5 “Are You Ready for More?”: Han, his sister, his dad, and his grandmother step onto a crowded bus with only 3 open seats for a 42-minute ride. They decide Han’s grandmother should sit for the entire ride. Han, his sister, and his dad take turns sitting in the remaining two seats, and Han’s dad sits 1.5 times as long as both Han and his sister. How many minutes did each one spend sitting?

Extension

RESOURCES Combine Lessons 1 & 2 Combine Lessons 3 & 4 Combine Lessons 7 & 8 Combine Lessons 10 & 11 Combine Lessons 13 & 14 Combine Lessons 18 & 19 Combine Lessons 20 & 21

Throw in expanding and factoring into lessons throughout the unit

Vocabulary Resources Equation Extra Practice Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.EE.1

6.18, 6.19, 6.20, 6.21, 6.22

7.EE.2

6.12

7.EE.3

6.2, 6.3, 6.4, 6.6, 6.11, 6.12

7.EE.4

6.1, 6.4, 6.5, 6.7, 6.8, 6.9, 6.10, 6.12, 6.13, 6.14, 6.15, 6.16, 6.17

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

1

6.6

6.1, 6.2, 6.4, 6.13

6.EE.5

2

6.1

6.2

6.EE.8

3

6.2

6.3

6.EE.4

4

6.1

6.6

6.EE.7

5

6.10

6.10

6.EE.3

6

6.2

6.3

7

LEARNING INTENTIONS

●​ Generate equivalent expressions by applying properties of operations (associative, commutative, distributive, etc) as strategies to add, subtract, factor, and expand linear expressions with rational coefficients. ●​ Combine like terms with rational coefficients. ●​ Recognize that different forms of an expression can highlight different aspects of the problem. ●​ Recognize and explain the meaning of a given expression and its component parts in terms of a context. ●​ Solve multi-step real-life and mathematical problems involving calculations with rational numbers in any form. ●​ Utilize various forms of rational numbers to solve and make sense of problems. ●​ Choose between forms of a rational number to simplify calculations or communicate solutions meaningfully. ●​ Assess the reasonableness of answers using mental computation and estimation. ●​ Use variables to create and solve equations (px+q=r and p(x+q)=r ) that model word problems. ●​ Connect arithmetic solution processes that do not use variables to algebraic solution processes that use equations. ●​ Use variables to create and solve inequalities (px + q > r or px + q < r ) that model word problems. ●​ Graph and interpret the solution set of an inequality (compare the solution of an equation to that of an inequality). ●​ Distinguish between equations and inequalities

ANGLES, TRIANGLES, AND PRISMS

Unit 7

PACING

KEY LANGUAGE USES

March 2 - April 3 (24 days)

EXPLAIN

STANDARDS Standard 7.G.2 Draw geometric shapes with given conditions. Focus on constructing triangle from three measures of angles or sides noticing when the conditions determine a unique triangle, more than one triangle, or no triangle.

Standard 7.G.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.

Standard 7.G.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.

Standard 7.G.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. Standard 7.NS.1 Apply and extend previous understandings of addition and subtraction to add and subtract rational numbers; represent addition and subtraction on a vertical number line diagram. a. ​ Describe situations in which opposite quantities combine to make 0. b. ​ Understand p + q as the number located a distance 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 0 (are additive inverses). Interpret sums of rational numbers by describing real-world contexts. c. ​ 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. d. ​ Apply properties of operations as strategies to add and subtract rational numbers. Standard 7.EE.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. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explain, given three side measures, if a triangle would exist using those side measurements.

Language Supports: I can explain how to make a unique triangle from two side measurements and determine what the length of the third side should be. ●​ Vocabulary (triangle)

I can explain how to find the volume of a prism. Language Supports: ●​ Vocabulary (volume, formula, prism) DIFFERENTIATION IN ACTION Skill Building

From Activity 6.2: MLR 8 Discussion Supports. Use this routine to support whole-class discussion. After a group shares the side lengths they chose for their triangle, ask students to restate or revoice what they heard using mathematical language. Consider providing students time to restate what they heard to a partner, before selecting one or two students to share with the class. Ask the original group if their peer was accurately able to restate their thinking. Encourage students to supplement their explanations multi-modally by using gestures with the polygons. From Lesson 7 “Are You Ready for More?”: Assuming you had access to strips of any length, and you used the 9-inch and 5-inch strips as the first two sides, complete the sentences:

Extension

1. ​ The third side can't be _____ inches or longer. 2. ​ The third side can't be _____ inches or shorter.

RESOURCES Combine Lessons 1 & 2 Combine Lessons 3 & 4 Combine Lessons 6 & 7 Combine Lessons 9 & 10 Combine Lessons 15 & 16 Additional Practice Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

7.G.2

7.6, 7.7, 7.8, 7.9, 7.10, 7.17

7.G.3

7.11

7.G.5

7.1, 7.2, 7.3, 7.4, 7.5

7.G.6

7.12, 7.13, 7.14, 7.15, 7.16

7.NS.1

7.6

7.EE.4

7.5

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfinished Learning Standard

4.MD.6 , 4.MD.7

1

7.1

7.1

3.MD.5 , 3.MD.8

2

7.6

7.4

6.G.4

3

7.1

7.14, 7.17

4

7.1

5

7.12

6

7.12

7.13

7

LEARNING INTENTIONS

●​ Use variables to create and solve equations (px+q=r and p(x+q)=r ) that model word problems. ●​ Connect arithmetic solution processes that do not use variables to algebraic solution processes that use equations. ●​ Use variables to create and solve inequalities (px + q > r or px + q < r ) that model word problems. ●​ Graph and interpret the solution set of an inequality (compare the solution of an equation to that of an inequality). ●​ Distinguish between equations and inequalities. ●​ Draw precise geometric figures based on given conditions. ●​ Discover the conditions necessary for a set of angles (sum of 180°) or sides to make a triangle (Triangle Inequality Theorem) by exploring different combinations of sides and angles. ●​ Explore conditions that determine unique triangles, multiple triangles, or no triangles (Foundational for future coursework involving Triangle Congruence Theorem). ●​ Describe the different ways to slice a 3D figure (i.e. vertical slice, horizontal slice, and angled slice). ●​ Describe the different 2D cross-sections that will result depending on how you slice the 3D figure. ●​ Define and understand properties of supplementary, complementary, vertical and adjacent angles. ●​ Use properties of supplementary, complementary, vertical and adjacent angles to solve for unknown angles in a figure. ●​ Write and solve equations based on a diagram of intersecting lines with some known angle measures. ●​ Decompose two-dimensional composite shapes into triangles, quadrilaterals, and polygons to

find the area. ●​ Decompose three-dimensional composite shapes into cubes, and right prisms to find volume. ●​ Decompose three-dimensional composite shapes whose faces are triangles, quadrilaterals, and polygons, to find the surface area. ●​ Find volumes of cubes, right prisms, and composite polyhedra including those found in real-world contexts. ●​ Understand, apply, and explain the additive inverse property, including using situations with context. ●​ Model addition and subtraction of rational numbers, including integers, decimals, and fractions, on a number line. ●​ Add and subtract rational numbers, including integers, decimals, and fractions.

KEY VOCABULARY

●​ Adjacent Angles ●​ Straight Angle ●​ Right Angle ●​ Cross Section

●​ Complementary ●​ Supplementary ●​ Vertical Angles

PROBABILITY AND SAMPLING

Unit 8

PACING

KEY LANGUAGE USES

April 13 - May 8 (20 days)

EXPLAIN

STANDARDS Standard 7.SP.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 sample and support valid inferences. Standard 7.SP.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. Standard 7.SP.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.

Standard 7.SP.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations.

Standard 7.SP.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 ½ indicates an event that is neither unlikely nor likely, and probability near 1 indicates a likely event.

Standard 7.SP.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 given the probability.

Standard 7.SP.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 possibly sources of discrepancy. a. ​ Develop a uniform probability model by assigning equal probability to all outcomes, and use the model to determine probabilities of events. b. ​ Develop a probability model (which may not be uniform) by observing frequencies in data