7th grade Math Guide

Instructional Guide 2026-2027

7

th

Math

Grade

Instructional Guide 2026-2027

Introduction

What’s New and Updated in 7 th grade math

What’s New This section contains a listing of pages in the map that are new this year. Page Number Description

9

New scopes and sequences for new Reveal Curriculum.

9

Link to sample calendaring for adding in differentiation days on year at a glance.

various

Links to honors lessons

56

AI use in Math

55

Digital Tools in Math

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

Middle School Assessment Calendar

DWSBA dates

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 2026-2027

Scope and Sequence

Grade 7

YEAR AT A GLANCE

Unit 1 Math Is…

Unit 2 Solve

Unit 3 Proportional Relationships

Unit 4 Solve

Unit 5 Sampling and Statistics

Unit 6 Solve

Unit 7 Work with Linear Expressions

Unit 8 Solve Problems Using Equations and Inequalities

Unit 9 Probability

Unit 10 Math Is…

Problems Involving Geometry

Problems Involving Percentages

Problems Involving Operations with Integers and Rational Numbers

Suggested Pacing

Aug 17 - Aug 31 (11 days)

Sept 1 - Oct 7 (24 days)

Oct 8 - Nov 6 (19 days)

Nov 9 - Dec 8 (19 days)

Dec 9 - Jan 14 (17 days)

Jan 19 - Feb 17 (20 days)

Feb 18 - Mar 12 (16 days)

Mar 15 - Apr 15 (18 days)

Apr 16 - May 7 (16 days)

May 10 - May 27 (14 days)

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

7.SP.1 7.SP.2 7.SP.3 7.SP.4

7.EE.1 7.EE.2

7.G.1 7.G.2 7.G.3 7.G.4 7.G.5 7.G.6

7.RP.3 7.EE.3

7.NS.1 7.NS.2 7.NS.3

7.EE.3 7.EE.4

7.SP.5 7.SP.6 7.SP.7 7.SP.8

Standards

DWSBA & Testing Window

DWSBA #1

DWSBA #2

DWSBA #3

MAP Window

August 18 - September 24

December 2 - January 14

March 30 - May 7

Additional calendaring details with differentiation days

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.

Unit 1

MATH IS…

PACING

KEY LANGUAGE USES

August 17 - August 31 (11 days)

EXPLAIN

STANDARDS Math Practice Standard 1 Make sense of problems and persevere in solving them. Math Practice Standard 3 Construct viable arguments and critique the reasoning of others. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can see myself as a doer of mathematics. Language Supports: ●​ Vocabulary (strategy)

I can build mathematical habits of mind Language Supports: ●​ Vocabulary (analyze)

I can build an understanding of the norms of interaction that allow for a productive math learning environment. Language Supports: ●​ Vocabulary (strategy, norms)

LEARNING INTENTIONS

●​ I can tell my math biography. ●​ I can recognize the ways in which we are all doers of math. ●​ I can explain different ways to think about numbers. ●​ I can make sense of quantities and the relationship among the quantities. ●​ I can represent a real-world situation using mathematics.

●​ I can describe tools I can use to solve a problem. ●​ I can construct an argument to explain my thinking. ●​ I can explain my thinking with clear and appropriate terms. ●​ I can use patterns to develop efficient strategies to solve problems. ●​ I can explain why patterns are useful to solve problems. ●​ I can recognize the behaviors and attitudes that support a productive classroom learning environment. ●​ I can identify the mindsets that help me problem solve.

KEY VOCABULARY

●​ Compare ●​ Revise

●​ Determine ●​ Clarify

●​ Reinforce

●​ Analyze

SOLVE PROBLEMS INVOLVING GEOMETRY

Unit 2

PACING

KEY LANGUAGE USES

September 1 - October 7 (24 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.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.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.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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can understand how scale applies to tasks such as reading a map. Language Supports: ●​ Vocabulary (scale, scale factor)

I can use understanding of area, surface area, and volume to solve real-world problems. Language Supports: ●​ Vocabulary (volume, surface area)

I can find the circumference and area of real-world objects and spaces. Language Supports: ●​ Vocabulary (circumference, area) DIFFERENTIATION IN ACTION Skill Building Lesson 2.1 - Take another look lesson.

Extension

Lesson 2.4 STEM Adventure - Students apply knowledge of geometric figures, scale drawings, angles and side lengths of triangles, surface areas, and volumes to design elements of a new urban park. Honors lesson plan

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.G.1

2.1

7.G.2

2.2, 2.3

7.G.3

2.5

7.G.4

2.8, 2.9

7.G.5

2.4

7.G.6

2.5, 2.6, 2.7

LEARNING INTENTIONS

●​ I can use ratio reasoning to find actual lengths and areas of an object from a scale drawing. ●​ I can reproduce a scale drawing at a different scale. ●​ I can draw triangles with given conditions. ●​ I can use repeated reasoning to determine the conditions that form a unique triangle, more than one triangle, or no triangle. ●​ I can explain why four side lengths can form more than one quadrilateral. ●​ I can use reasoning to determine how many quadrilaterals are formed by four side lengths. ●​ I can use the properties of supplementary, complementary, vertical, and adjacent angles to determine unknown angle measures. ●​ I can ask questions about unknown angle measures in order to apply what I know about angle properties. ●​ I can describe the two-dimensional shape that results from the cross section of a three-dimensional figure. ●​ I can represent the shape of a cross section, using words and drawings. ●​ I can find the area of two-dimensional composite figures. ●​ I can find the surface area of three-dimensional composite figures. ●​ I can use precision to identify the faces of a three-dimensional figure, determine the area of each face, and add the areas to determine surface area. ●​ I can find the volume of prisms. ●​ I can find the volume of three-dimensional composite figures composed of prisms. ●​ I can explain how to find the volume of a prism. ●​ I can find the circumference of a circle. ●​ I can explain how the diameter or radius of a circle is related to its circumference. ●​ I can choose the correct tools to represent characteristics of circles in order to understand diameter, radius, and circumference. ●​ I can find the area of a circle ●​ I can use the area formula to represent the area of a circle.

KEY VOCABULARY

●​ Equivalent Ratios ●​ Scale Drawing ●​ Compute ●​ Utilize

●​ Unique ●​ Simulate ●​ Visual

●​ Base ●​ Cross Section ●​ Presume ●​ Visible ●​ Area ●​ Composite Figure ●​ Surface Area ●​ Determine

●​ Differentiate ●​ Estimate ●​ Circumference

●​ Adjacent Angles ●​ Complementary Angles ●​ Supplementary Angles ●​ Vertical Angles ●​ Compare ●​ Complement

●​ Diameter ●​ Perimeter ●​ Pi ●​ Radius ●​ Random ●​ Reveal ●​ Deviate ●​ Display

●​ Triangle ●​ Unique ●​ Clarify ●​ Identical ●​ Quadrilateral

●​ Evaluate ●​ Volume

PROPORTIONAL RELATIONSHIPS

Unit 3

PACING

KEY LANGUAGE USES

October 8 - November 6 (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.

Standard 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can use proportional reasoning to solve single and multi-step problems. Language Supports: ●​ Vocabulary (constant of proportionality) DIFFERENTIATION IN ACTION Skill Building Unit 3 Fluency Practice on operations with decimals.

Extension

Lesson 3.2 STEM Adventure - Wildlife biologists at a state park are trying to control an algae bloom in the points. Students use ratio and graphing skills to investigate why some pounds have responded well to algae bloom treatment and others have not.

Honors lesson plan

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.RP.1

3.1

7.RP.2

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

7.RP.3

3.6

LEARNING INTENTIONS

●​ I can find the unit rate when one or both terms have a fractional value. ●​ I can use repeated reasoning to write a proportion to solve for a missing value. ●​ I can represent equivalent ratios using tables and determine whether those quantities are proportional. ●​ I can make sense of and identify the constant of proportionality from a table. ●​ I can make use of structure to determine whether a relationship is proportional by analyzing its graph. ●​ I can determine proportionality by creating a graph and determining whether the relationship is proportional. ●​ I can identify the constant of proportionality in the graph of a proportional relationship. ●​ I can identify and interpret the constant of proportionality in verbal descriptions of proportional relationships. ●​ I can identify and interpret the constant of proportionality in equations of the form y = kx. ●​ I can model with mathematics to represent and solve proportional relationships with the equation y = kx . ●​ I can represent proportional relationships using tables, graphs, and equations. ●​ I can make use of the structure of the equation y = kx to describe a proportional relationship.

KEY VOCABULARY

●​ Equivalent Ratios ●​ Proportion ●​ Unit Rate ●​ Adapt

●​ Transform ●​ Constant of

●​ Display ●​ Identical ●​ Accurate ●​ Inspection

●​ Denote ●​ Explicit ●​ Compute ●​ Reinforce

Proportionality

●​ Proportional

SOLVE PROBLEMS INVOLVING PERCENTAGES

Unit 4

PACING

KEY LANGUAGE USES

November 9 - December 8 (19 days)

EXPLAIN

STANDARDS Standard 7.RP.3 Use proportional relationships to solve multi-step ratio and percent problems. 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 calculate with percentages to understand tips, taxes, and fees in real-world situations. Language Supports: ●​ Vocabulary (tax, tip) I can recognize the effects of percent increase and percent decrease in real-world situations. Language Supports: ●​ Vocabulary (increase, decrease) I can understand how markup and markdown are calculated in purchases and sales, how simple interest is calculated, and how interest affects savings and debt amounts. ●​ Vocabulary (interest) I can understand accuracy and inaccuracy in real-world values by determining the percent error. ●​ Vocabulary (accurate, inaccurate, error) DIFFERENTIATION IN ACTION Skill Building Unit 4 Fluency Practice on finding unit rates.

Extension

Lesson 4.6 STEM Adventure - Students make choices about where and on what to spend their money as they track and analyze their expenses. They explore the effects of reusable packaging on personal spending, business costs, and waste ratios.

Honors Lesson Plan

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.RP.3

4.1, 4.2, 4.3, 4.4, 4.5, 4.6

7.EE.3

4.2, 4.3, 4.4, 4.5, 4.6

LEARNING INTENTIONS

●​ I can solve multistep percent problems using proportional reasoning. ●​ I can make connections between proportions and percentages. ●​ I can solve multistep percent problems using the percent equation for any unknown (part, percent, or whole). ●​ I can use percent vocabulary for the elements of percent problems. ●​ I can analyze problems involving percent change. ●​ I can solve problems involving percent increase and percent decrease. ●​ I can solve problems involving markups and markdowns. ●​ I can think about structure to understand markup and markdown. ●​ I can solve problems involving simple interest. ●​ I can represent interest problems by using the percent equation. ●​ I can solve problems involving percent error ●​ I can plan how to solve problems involving percent error by analyzing the problem and using the percent equation.

KEY VOCABULARY

●​ Percent ●​ Proportion ●​ Foundation ●​ Theme ●​ Proportion ●​ Percent Equation ●​ Initiate

●​ Manipulate ●​ Percent Change ●​ Percent Decrease ●​ Percent Increase ●​ Confirm ●​ Fee ●​ Markdown

●​ Markup ●​ Discriminate ●​ Reverse ●​ Interest ●​ Interest Rate ●​ Principal ●​ Simple Interest

●​ Analyze ●​ Isolate ●​ Error ●​ Percent Error ●​ Deviate ●​ Minimize

Unit 5

SAMPLING AND STATISTICS

PACING

KEY LANGUAGE USES

December 9 - January 14 (17 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.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can describe real-world populations by making inferences based on samples. Language Supports: ●​ Vocabulary (inference, population) I can analyze real-world situations by comparing multiple samples and assessing accuracy of inferences about the population. Language Supports: ●​ Vocabulary (sample) 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.

I can compare real-world populations by analyzing overlap. Language Supports: ●​ Vocabulary (analyze)

DIFFERENTIATION IN ACTION Skill Building

Unit 5 Fluency Practice on percent change.

Extension

Lesson 5.5 STEM Adventures - Students explore the benefits and potential drawbacks of using pesticides to protect our crops.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.SP.1

5.1, 5.2

7.SP.2

5.3, 5.4

7.SP.3

5.5

7.SP.4

5.5

LEARNING INTENTIONS

●​ I can determine whether to use a statistic to describe a population. ●​ I can make sense of statistics for a sample and use the statistics to estimate parameters for a population. ●​ I can determine whether a sample is likely to produce valid or invalid statistics about a population. ●​ I can make valid inferences from valid statistics.

●​ I can construct an argument to critique a sampling method for bias. ●​ I can use a statistic to describe and make inferences about a population.

●​ I can use repeated reasoning to analyze and describe statistics in order to make inferences. ●​ I can understand how collecting multiple samples can help me determine how predictions about a population might vary. ●​ I can analyze variability among samples to gauge the accuracy of statistics. ●​ I can use measures of variability to describe the difference between the centers of two populations and assess the amount of overlap in their distributions. ●​ I can reason about data and construct an argument to explain differences between data sets.

KEY VOCABULARY

●​ Mean ●​ Parameter ●​ Population ●​ Proportion

●​ Clarify ●​ Diverse ●​ Biased ●​ Invalid Inference ●​ Unbiased ●​ Widespread

●​ Valid Inference ●​ Determine ●​ Inspect ●​ Infer ●​ Interquartile Range

●​ Mean Absolute Deviation ●​ Median ●​ Cite

●​ Sample ●​ Statistic ●​ Reveal

●​ Visual ●​ Topic

SOLVE PROBLEMS INVOLVING OPERATIONS WITH INTEGERS AND RATIONAL NUMBERS

Unit 6

PACING

KEY LANGUAGE USES

EXPLAIN

January 19 - February 17 (20 days)

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 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. 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.2 Apply and extend previous understandings of multiplication and division and of fractions to multiple and divide rational numbers.

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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can solve real-world problems in contexts related to the addition of rational numbers. Language Supports: ●​ Vocabulary (rational number)

I can solve real-world problems in contexts related to additive inverses. Language Supports: ●​ Vocabulary (additive inverse)

I can interpret the quotients of rational numbers in real-world contexts. Language Supports: ●​ Vocabulary (quotient)

DIFFERENTIATION IN ACTION Skill Building

Unit 6 Fluency Practice on equations and proportional relationships.

Extension

Lesson 6.4 STEM Adventure - Students gather and synthesize data on drought resistant plants. They learn about drought and its effect on food production and how plants adapt to be drought resistant.

Honors Lesson

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.NS.1

6.2, 6.3, 6.4, 6.7

7.NS.2

6.1, 6.5, 6.6, 6.7

7.NS.3

6.7

LEARNING INTENTIONS

●​ I can write a fraction as either a terminating or nonterminating decimal. ●​ I can describe the difference between a terminating and a nonterminating decimal. ●​ I can use precision when writing a fraction as a decimal.

●​ I can look for and make use of structure when determining the sign of the sum of an addition expression. ●​ I can look for and express regularity in repeated reasoning when finding the sum of positive and negative rational numbers. ●​ I can use a number line and other appropriate tools strategically to represent addition. ●​ I can look for and express regularity in repeated reasoning by recognizing that the sum of any number and its opposite is 0. ●​ I can use additive inverse to make sense of problems and persevere in solving them. ●​ I can construct viable arguments and critique the reasoning of others when describing situations in which opposite quantities have a sum of zero.

●​ I can determine the sign of the difference of a subtraction expression. ●​ I can use a number line to find the distance between two rational numbers. ●​ I can model subtracting rational numbers using a number line. ●​ I can determine the sign of the product of a multiplication expression. ●​ I can interpret products of rational numbers by describing real-world contexts. ●​ I can find the quotient of two rational numbers. ●​ I can interpret quotients of rational numbers by describing real-world contexts. ●​ I can use repeated reasoning to find the quotient of two rational numbers.

KEY VOCABULARY

●​ Bar Notation ●​ Quotient ●​ Repeating Decimal ●​ Terminating Decimal

●​ Convert ●​ Determine ●​ Absolute Value ●​ Differentiate ●​ Maximum ●​ Additive Inverse

●​ Additive Inverse Property ●​ Integers ●​ Exhibit

●​ Estimate ●​ Visual ●​ Denominator ●​ Numerator

●​ Identical ●​ Compare ●​ Integer

●​ Compute ●​ Evaluate

WORK WITH LINEAR EXPRESSIONS

Unit 7

PACING

KEY LANGUAGE USES

EXPLAIN

February 18 - March 12 (16 days)

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. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can demonstrate understanding of combining like terms. Language Supports: ●​ Vocabulary (like terms) I can simplify expressions by combining like terms. Language Supports: ●​ Vocabulary (simplify) I can use the Distributive Property to expand linear expressions. Language Supports: ●​ Vocabulary (distributive property) DIFFERENTIATION IN ACTION Skill Building

Unit 7 Fluency Practice on adding & subtracting rational numbers.

Extension

Lesson 6.2 STEM Adventure - Students apply understanding of linear expressions to navigate the process of buying and driving electric vehicles.

Honors Lesson

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.EE.1

7.1, 7.2, 7.3, 7.4, 7.5

7.EE.2

7.1, 7.2, 7.3, 7.4, 7.5

LEARNING INTENTIONS

●​ I can combine like terms to simplify expressions. ●​ I can attend to precision as I combine like terms. ●​ I can use the Distributive Property to expand linear expressions. ●​ I can use repeated reasoning to expand linear expressions using the Distributive Property.

●​ I can add linear expressions by combining like terms. ●​ I can attend to precision as I add linear expressions. ●​ I can subtract linear expressions by combining like terms. ●​ I can attend to precision as I subtract linear expressions. ●​ I can write and interpret the factored form of a linear expression. ●​ I can look for and make use of structure to factor linear expressions.

KEY VOCABULARY

●​ Commutative Property of Addition ●​ Simplest Form ●​ Term

●​ Determine ●​ Manipulate ●​ Distributive Property ●​ Linear Expression

●​ Compare ●​ Confirm ●​ Additive Inverse ●​ Like Terms ●​ Infer

●​ Visible ●​ Precede ●​ Reverse ●​ Factoring ●​ Accurate ●​ Clarify

SOLVE PROBLEMS USING EQUATIONS AND INEQUALITIES

Unit 8

PACING

KEY LANGUAGE USES

EXPLAIN

March 15 - April 15 (18 days)

STANDARDS 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. 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 solve multi-step real-life problems and assess the reasonableness of their solution. Language Supports: ●​ Vocabulary (solution) I can apply my knowledge of two-step equations to write and solve two-step equations in real-world situations. Language Supports: ●​ Vocabulary (equation) I can solve real-world problems and consider the reasonableness of the solutions of the inequality in the real-world context of the problems. Language Supports: ●​ Vocabulary (inequality) I can apply my understanding of solving multiplication and division inequalities to real-world contexts. Language Supports: ●​ Vocabulary (inequality) DIFFERENTIATION IN ACTION Skill Building Unit 8 Fluency Practice on Adding and Subtracting rational numbers.

Extension

Lesson 8.2 STEM Adventure - Students apply their understanding of equations and inequalities to explore hiking trails.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.EE.3

8.1, 8.2, 8.3, 8.4, 8.5, 8.6

7.EE.4

8.1, 8.2, 8.3, 8.4, 8.5, 8.6

LEARNING INTENTIONS

●​ I can interpret word problems to solve simple equations in the form px + q = r for real-world and mathematical problems. ●​ I can meaningfully interpret the solution of the equation in the context of the original problem, reasoning about quantities. ●​ I can interpret word problems to solve equations in the form p(x + q) = r for real-world and mathematical problems. ●​ I can write and solve one-step addition and subtraction inequalities to model real-world and mathematical problems. ●​ I can meaningfully interpret the solution of an inequality in the context of the problem, reasoning abstractly and quantitatively. ●​ I can write and solve one-step multiplication and division inequalities with positive and negative coefficients from real-world and mathematical problems. ●​ I can write and solve two-step inequalities from real-world and mathematical problems. ●​ I can use a number line to model solutions of a two-step inequality.

KEY VOCABULARY

●​ Equation ●​ Variable ●​ Abstract ●​ Confirm ●​ Clarify ●​ Revise ●​ Distributive Property

●​ Evaluate ●​ Isolate ●​ Addition Property of Inequality ●​ Inequality ●​ Solution Set

●​ Subtraction Property of Inequality ●​ Compute ●​ Interval ●​ Division Property of Inequality

●​ Multiplication Property of Inequality

●​ Compare ●​ Determine

●​ Denote ●​ Reveal

Unit 9

PROBABILITY

PACING

KEY LANGUAGE USES

April 16 - May 7 (16 days)

EXPLAIN

STANDARD 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 generated from a chance process.

Standard 7.SP.8 Find probabilities of compound events using organized lists, tables, tree diagrams, and simulation.

a. ​ 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. b. ​ 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 composes the event. c. ​ Design and use a simulation to generate frequencies for compound events.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can solve real-world problems by using organized lists, tables, and tree diagrams to determine the probability of

compound events. Language Supports:

●​ Vocabulary (probability)

I can solve real-world problems by using a simulation to estimate the probability of a compound event. Language Supports: ●​ Vocabulary (compound event)

DIFFERENTIATION IN ACTION Skill Building

Unit 9 Fluency Practice on Solving Equations

Extension

Lesson 9.2 STEM Adventure - Students apply their understanding of probability to explore trackers.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

7.SP.5

9.1, 9.3

7.SP.6

9.2, 9.4

7.SP.7

9.2, 9.3, 9.4

7.SP.8

9.5, 9.6

LEARNING INTENTIONS

●​ I can find the probability of a given event. ●​ I can express the probability of an event as a number between 0 and 1. ●​ I can classify the probability of a given event as likely, unlikely, or neither. ●​ I can predict the relative frequency of an event, given the probability. ●​ I can approximate the probability of a chance event by conducting an experiment and collecting data. ●​ I can create a probability model (which may not be uniform) by observing frequencies in the data from a chance process. ●​ I can find the theoretical probability of an event occurring. ●​ I can express the theoretical probability of an event as a number between 0 and 1. ●​ I can recognize and explain theoretical probability. ●​ I can create a probability model (which may not be uniform) and use it to determine probabilities of events. ●​ I can perform probability experiments to compare experimental and theoretical probabilities. ●​ I can compare theoretical and experimental probabilities of simple events. ●​ I can explain how to find the probability of compound events. ●​ I can express the probability of a compound event as a fraction of desirable outcomes to all possible outcomes. ●​ I can use organized lists, tables, and tree diagrams to determine the probability of a compound event. ●​ I can explain how to find the probability of compound events. ●​ I can design and use a simulation to approximate the probability of a compound event.

KEY VOCABULARY

●​ Probability ●​ Event ●​ Differentiate ●​ Reinforce ●​ Experimental Probability ●​ Probability

●​ Relative

●​ Uniform

●​ Compound Events ●​ Display ●​ Compare ●​ Simulation ●​ Compute

Frequency

Probability Model

●​ Confirm ●​ Determine

●​ Denote ●​ Utilize ●​ Accurate ●​ Compare

●​ Sample Space ●​ Simple Event ●​ Theoretical Probability

●​ Estimate ●​ Simulate

Unit 10

MATH IS…

PACING

KEY LANGUAGE USES

May 10 - May 27 (14 days)

EXPLAIN

STANDARDS Math Practice Standard 3 Construct viable arguments and critique the reasoning of others.

Math Practice Standard 4 Model with mathematics.

Math Practice Standard 7 Look for and make use of structure.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can explore different ways to use mathematics to represent and find creative solutions to real-world problems. Language Supports: ●​ Vocabulary (strategy)

I can use generalizations derived from repeated reasoning to solve problems. Language Supports: ●​ Vocabulary (pattern)

LEARNING INTENTIONS

●​ I can see applications of math outside of school. ●​ I can use my math noticings as a tool to solve problems. ●​ I can see the beauty in math. ●​ I can use the Fibonacci sequence to describe structure in nature and in human creations. ●​ I can use patterns or relationships to help me make sense of a puzzle or game and to think logically about solutions. ●​ I can use the playfulness of math to imagine different ways to visualize the problem.

●​ I can use models to come up with creative solutions to everyday problems. ●​ I can apply mathematics that I know to solve problems in everyday life. ●​ I can create and describe designs that are boundaries. ●​ I can use patterns, repetition, and rhythm to create designs with math structure. ●​ I can see how my math biography has changed. ●​ I can recognize ways in which we are all doers of math.

KEY VOCABULARY

●​ Determine ●​ Unique ●​ Enhance

●​ Visible ●​ Highlight ●​ Adapt

●​ Priority ●​ Analyze

●​ Contradict ●​ Foundation ●​ Revise

Instructional Guide 2026-2027

Resources

UTAH CORE STATE STANDARDS for MATHEMATICS

Mathematics | Grade 7 In Grade 7, instructional time should focus on four critical areas: (1) developing understanding of and applying proportional relationships; (2) developing understanding of operations with rational numbers and working with expressions and linear equations; (3) solving problems involving scale drawings and informal geometric constructions, and working with two- and three-dimensional shapes to solve problems involving area, surface area, and volume; and (4) drawing inferences about populations based on samples. (1) Students extend their understanding of ratios and develop understanding of propor tionality to solve single- and multi-step problems. Students use their understanding of ratios and proportionality to solve a wide variety of percent problems, including those involving discounts, interest, taxes, tips, and percent increase or decrease. Students solve problems about scale drawings by relating corresponding lengths between the objects or by using the fact that relationships of lengths within an object are preserved in similar ob jects. Students graph proportional relationships and understand the unit rate informally as a measure of the steepness of the related line, called the slope. They distinguish propor tional relationships from other relationships. (2) Students develop a unified understanding of number, recognizing fractions, decimals (that have a finite or a repeating decimal representation), and percents as different repre sentations of rational numbers. Students extend addition, subtraction, multiplication, and division to all rational numbers, maintaining the properties of operations and the relation ships between addition and subtraction, and between multiplication and division. By ap plying these properties, and by viewing negative numbers in terms of everyday contexts (e.g., amounts owed or temperatures below zero), students explain and interpret the rules for adding, subtracting, multiplying, and dividing with negative numbers. They use the arithmetic of rational numbers as they formulate expressions and equations in one vari able and use these equations to solve problems. (3) Students continue their work with area from Grade 6, solving problems involving the area and circumference of a circle and surface area of three-dimensional objects. In prepa ration for work on congruence and similarity in Grade 8, they reason about relationships among two-dimensional figures using scale drawings and informal geometric construc tions, and they gain familiarity with the relationships between angles formed by intersect ing lines. Students work with three-dimensional figures, relating them to two-dimensional figures by examining cross-sections. They solve real-world and mathematical problems involving area, surface area, and volume of two- and three-dimensional objects composed of triangles, quadrilaterals, polygons, cubes and right prisms. (4) Students build on their previous work with single-data distributions to compare two data distributions and address questions about differences between populations. They begin informal work with random sampling to generate data sets and learn about the im portance of representative samples for drawing inferences.

GRADE 7 | 13

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UTAH CORE STATE STANDARDS for MATHEMATICS

Strand: MATHEMATICAL PRACTICES (7.MP) The Standards for Mathematical Practice in Seventh Grade describe mathematical habits of mind that teachers should seek to develop in their students. Students become mathematical ly proficient in engaging with mathematical content and concepts as they learn, experience, and apply these skills and attitudes (Standards 7.MP.1–8). „ „ Standard 7.MP.1 Make sense of problems and persevere in solving them. Explain the meaning of a problem and look for entry points to its solution. Analyze givens, con straints, relationships, and goals. Make conjectures about the form and meaning of the solution, plan a solution pathway, and continually monitor progress asking, “Does this make sense?” Consider analogous problems, make connections between multiple repre sentations, identify the correspondence between different approaches, look for trends, and transform algebraic expressions to highlight meaningful mathematics. Check an swers to problems using a different method. „ „ Standard 7.MP.2 Reason abstractly and quantitatively. Make sense of the quantities and their relationships in problem situations. Translate between context and algebraic representations by contextualizing and decontextualizing quantitative relationships. This includes the ability to decontextualize a given situation, representing it algebra ically and manipulating symbols fluently as well as the ability to contextualize algebraic representations to make sense of the problem. „ „ Standard 7.MP.3 Construct viable arguments and critique the reasoning of others. Understand and use stated assumptions, definitions, and previously established results in constructing arguments. Make conjectures and build a logical progression of state ments to explore the truth of their conjectures. Justify conclusions and communicate them to others. Respond to the arguments of others by listening, asking clarifying ques tions, and critiquing the reasoning of others. „ „ Standard 7.MP.4 Model with mathematics. Apply mathematics to solve problems aris ing in everyday life, society, and the workplace. Make assumptions and approximations, identifying important quantities to construct a mathematical model. Routinely interpret mathematical results in the context of the situation and reflect on whether the results make sense, possibly improving the model if it has not served its purpose. „ „ Standard 7.MP.5 Use appropriate tools strategically. Consider the available tools and be sufficiently familiar with them to make sound decisions about when each tool might be helpful, recognizing both the insight to be gained as well as the limitations. Identify relevant external mathematical resources and use them to pose or solve problems. Use tools to explore and deepen their understanding of concepts. „ „ Standard 7.MP.6 Attend to precision. Communicate precisely to others. Use explicit definitions in discussion with others and in their own reasoning. They state the meaning of the symbols they choose. Specify units of measure and label axes to clarify the cor respondence with quantities in a problem. Calculate accurately and efficiently, express numerical answers with a degree of precision appropriate for the problem context.

GRADE 7 | 14

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