8th grade Math Guide

Instructional Guide 2026-2027

8 Grade th

Math

Instructional Guide 2026-2027

Introduction

What’s New and Updated in 8 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

33

Secondary 1H Accelerated year at a glance and calendar

99

AI use in Math

100

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

Grade8

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 8

Major Work of Grade Band: Grades 6 - 8 ● Understand the connections between proportional relationships and linear functions and linear equations ● Apply and use operations with rational and irrational numbers

● Simplify expressions and solve equations ● Understand congruence and similarity ● Understand and apply the Pythagorean Theorem

Major Work and Vertical Alignment

Major work: Proportional Relationships, Linear Functions and Equations Grade 8: Understand the connections between proportional relationships, linear functions, and linear equations. Apply previous understanding of proportional relationships (8.EE.5-6, 8.SP.2-3) to identity, define, evaluate, and compare linear functions, linear equations, and systems of linear equations (8.F.1-5). ● Prior grades : Students have computed unit rates and created representations of proportional relationships between quantities using multiple representations. They have used proportional relationships to solve multi-step and percent problems (7.RP.1-3) and have solved problems using scale drawings of geometric figures (7.G.1). ● Future Grades : In SI, students will use their understanding of linear functions and equations to interpret linear functions in different representations and contexts (I.IF.1 - 9, I.F.BF.1-3, I.F.LE.1-5) Major work: Operations with Rational and Irrational Numbers Grade 8: Apply and extend understanding of operations with rational numbers . Apply previous understanding of operations with rational numbers to include an understanding irrational numbers (8.NS.1-2) and operations with radicals (8.NS.3). (Operations with all other rational numbers is being practiced in grade 7, with irrational numbers being new to the Core Standards for grade 8). ● Prior grades : Students have performed all four operations with rational numbers, including integers in grade 7 (7.NS.1-3). ● Future Grades : In SI, students will use their understanding of real numbers to define appropriate quantities, to choose and interpret units and to level of accuracy on measurements (I.N.Q.1-3)

Major work: Simplify Expressions and Solve Equations Grade 8: Simplify expressions and solve equations : Solve linear equations and inequalities in one variable (8.EE.7). Analyze and solve, by graphing, pairs of simultaneous linear equations (8.EE.8). ● Prior Grades: In grade 7, students have learned to apply properties of operations to factor, expand (7.EE.1), and convert between forms and assess the reasonableness of an answer (7.EE.2-3). They have used variables to represent quantities to construct and solve simple equations and inequalities (7.EE.4). ● Future Grades: In SI, students will interpret linear and exponential expressions with integer exponents (I.A.SSE.1). They will solve systems of equations exactly and approximately (numerically, algebraically, and graphically) (I.A.REI.6). Major work: Congruence and Similarity Grade 8: Understand congruence and similarity using physical models, transparencies, or geometry software. Explore properties of rotations, reflections, and translations that maintain congruent figures and properties of dilations that maintain similar figures (8.G.1-4). (Congruent and similar shapes are new to the Core Standards for grade 8) ● Prior Grades: Students have solved problems involving scale drawings of geometric figures (7.G.1). ● Future Grades: In grade SI, students will extend their understanding of rigid transformations in coordinate geometry. Students will use the property of correspondence to determine congruency (I.G.CO.6-8). In grade SII, students will extend their understanding of similar figures (II.G.SRT.1-3). Major work: Pythagorean Theorem Grade 8: Understand and apply the Pythagorean Theorem and its converse in real-world and mathematical problems in two and three dimensions, and to find the distance between two points in a coordinate system (8.G.6-8). Understand how to simplify radicals with emphasis on square roots (8.NS.3) as well as understanding solutions of square roots (8.EE.2) ● Prior Grades: Students have learned to identify and classify right angles (4.G.1). Students have learned to write and evaluate numerical expressions involving whole number exponents (6.EE.1). ● Future Grades: In SI, students will use coordinates to compute perimeters of polygons and areas of triangles and rectangles, and will connect these concepts with the Pythagorean Theorem and the distance formula (I.G.GPE.7).

Instructional Guide 2026-2027

Scope and Sequence

Instructional Guide 2026-2027

8 Grade th

Math

Grade 8

YEAR AT A GLANCE

Unit 1 Math Is…

Unit 2 Congruence & Similarity

Unit 3 Linear Relationships and Equations

Unit 4 Understand & Analyze Functions

Unit 5 Patterns of Association

Unit 6 Angles, Triangles, and the Pythagorean Theorem

Unit 7 Volume

Unit 8 Systems of Linear Equations

Unit 9 Irrational Numbers, Exponents, and Scientific Notation

Unit 10 Math Is…

Suggested Pacing

Aug 17 - Aug 28 (10 days)

Aug 31 - Oct 2 (22 days)

Oct 5 - Nov 10 (24 days)

Nov 11 - Dec 8 (17 days)

Dec 9 - Jan 14 (17 days)

Jan 19 - Feb 17 (21 days)

Feb 18 - Mar 12 (16 days)

Mar 15 - Apr 2 (14 days)

Apr 12 - May 7 (20 days)

May 10 - May 27 (14 days)

8.EE.5 8.EE.6 8.EE.7

8.SP.1 8.SP.2 8.SP.3 8.SP.4

8.EE.2 8.G.9

8.G.1 8.G.2 8.G.3 8.G.4 8.G.5

8.F.1 8.F.2 8.F.3 8.F.4 8.F.5

8.G.5 8.G.6 8.G.7 8.G.8 8.EE.2

8.EE.8

8.NS.1 8.NS.2 8.NS.3 8.EE.1 8.EE.3 8.EE.4

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…

KEY LANGUAGE USES

PACING

August 17 - August 28 (10 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 describe the ways in which we are all doers of math. ●​ I can compare and contrast my math biography with those of my classmates. ●​ I can make sense of a problem and represent it in different ways.

●​ I can explain different ways to think about numbers. ●​ 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

●​ Foundation ●​ Visible

●​ Analyze ●​ Determine

●​ Accurate ●​ Evaluate

●​ Visual

Unit 2

CONGRUENCE & SIMILARITY

PACING

KEY LANGUAGE USES

August 31 - October 2 (22 days)

EXPLAIN

STANDARDS S tandard 8.G.1 Verify experimentally the properties of rotations, reflections, and translations : a. ​ Lines are taken to lines, and line segments to line segments of the same length. b. ​ Angles are taken to angles of the same measure. c. ​ Parallel lines are taken to parallel lines.

Standard 8.G.2 Understand that a two-dimensional figure is congruent to another if the second can be obtained from the first by a sequence of rotations, reflections, and translations; given two congruent figures, describe a sequence that exhibits the congruence between them.

Standard 8.G.3 Describe the effect of dilations, translations, rotations, and reflections on two-dimensional figures using coordinates.

Standard 8.G.4 Understand that a two-dimensional figure is similar to another if the second can be obtained from the first by a sequence of rotations, reflections, translations, and dilations; given two similar two-dimensional figures, describe a sequence that exhibits the similarity between them. Standard 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so . END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can draw transformations using a coordinate plane. Language Supports: ●​ Vocabulary (transformation)

I can describe a sequence that exhibits the congruence between two congruent figures. Language Supports: ●​ Vocabulary (congruent) I can describe a sequence of transformations that exhibits the similarity of two figures. Language Supports: ●​ Vocabulary (similarity) DIFFERENTIATION IN ACTION Skill Building

Unit 2 Fluency Practice on adding, subtracting, factoring and expanding expressions.

Extension

Lesson 2.3 STEM Adventure - Game designers are creating a video game to help students learn about renewable energy types. Students use their knowledge of transformations to complete the building design for the game city.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.G.1

2.1, 2.2, 2.3

8.G.2

2.4

8.G.3

2.1, 2.2, 2.3, 2.5

8.G.4

2.5, 2.6

8.G.5

2.7, 2.8

LEARNING INTENTIONS

●​ I can translate figures on the coordinate plane. ●​ I can use coordinate notation to describe a translation (include direction and distance). ●​ I can use precision to explain why a translated figure preserves the same size and shape of the original figure. ●​ I can reflect figures on the coordinate plane. ●​ I can use coordinate notation to describe a reflection and identify the line of reflection. ●​ I can use repeated reasoning to explain why a reflected figure preserves the size and shape of the original figure. ●​ I can rotate figures on the coordinate plane. ●​ I can use coordinate notation to describe a rotation and angle of rotation. ●​ I can use repeated reasoning to explain why a rotated figure preserves the size and shape of the original figure. ●​ I can determine a sequence of transformations that maps one figure to another figure. ●​ I can use mathematical modeling to show that two figures are congruent using a sequence of transformations. ●​ I can dilate figures on the coordinate plane. ●​ I can use coordinate notation to describe dilations on the coordinate plane and determine the scale factor used in a dilation. ●​ I can perform a sequence of rigid motions and dilations to map one figure onto another figure. ●​ I can use coordinate notation to describe the sequence of rigid motions and dilations.

●​ I can determine whether a pair of triangles is similar using Angle-Angle Similarity. ●​ I can reason and prove that two triangles are similar using angle-angle criterion. ●​ I can find an unknown length or distance using proportions or similar triangles. ●​ I can describe the relationship between the angles and sides of similar triangles.

KEY VOCABULARY

●​ Image ●​ Preimage

●​ Reflection ●​ Denote ●​ Determine ●​ Center of Rotation

●​ Congruent ●​ Identical ●​ Manipulate ●​ Center of Dilation ●​ Dilation ●​ Scale Factor ●​ Analyze ●​ Reinforce

●​ Similar ●​ Display ●​ Exhibit ●​ Angle-Angle (AA) Similarity ●​ Confirm

●​ Prime (symbol) ●​ Transformation ●​ Translation ●​ Enhance

●​ Rotation ●​ Compare ●​ Transform ●​ Congruence

●​ Revise ●​ Image ●​ Reflected

●​ Infer ●​ Cite ●​ Utilize

LINEAR RELATIONSHIPS AND EQUATIONS

Unit 3

PACING

KEY LANGUAGE USES

October 5 - November 10 (24 days)

EXPLAIN

STANDARDS Standard 8.EE.5 Graph proportional relationships, interpreting the unit rate as the slope of the graph. Compare two different proportional relationships represented in different ways. For example, compare a distance-time graph to a distance-time equation to determine which of two moving objects has greater speed. Standard 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx for a line through the origin and the equation y = mx + b for a line intercepting the vertical axis at b .

Standard 8.EE.7 Solve linear equations and inequalities in one variable.

a. ​ Give examples of linear equations in one variable with one solution, infinitely many solutions, or no solutions. Show which of these possibilities is the case by successively transforming the given equation into simpler forms, until an equivalent equation of the form x = a, a = a, or a = b results (where a and b are different numbers.) b. ​ Solve linear equations and inequalities with rational number coefficients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms. c. ​ Solve single variable absolute value equations.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can apply slope concepts by comparing proportional relationships in real-world problems. Language Supports: ●​ Vocabulary (slope)

I can apply the concept of slope triangles to a real-world situation. Language Supports: ●​ Vocabulary (slope)

I can apply the concept of the equations y = mx and y = mx + b to real-world situations. Language Supports: ●​ Vocabulary (equations) I can apply the concept of solving equations with variables on both sides of the equal sign to a real-world problem. Language Supports: ●​ Vocabulary (solve)

I can determine the number of solutions to a real-world problem. Language Supports: ●​ Vocabulary (solution) DIFFERENTIATION IN ACTION Skill Building Unit 3 Fluency Practice on solving equations.

Extension

Lesson 3.2 STEM Adventure - Biosystems engineers are exploring erosion control solutions for different project sites. Students use their linear relationship and equation knowledge to test and interpret which erosion control solutions are most efficient.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.EE.5

3.1, 3.2

8.EE.6

3.3, 3.4, 3.5

8.EE.7

3.6, 3.7, Secondary 1 Module 2 Lesson 5

LEARNING INTENTIONS

●​ I can graph a proportional relationship and describe the slope of the line as the constant of proportionality or unit rate. ●​ I can look for and make use of structure to graph a proportional relationship. ●​ I can compare two different proportional relationships by comparing the slopes. ●​ I can use repeated reasoning to compare two different proportional relationships. ●​ I can show that hypotenuses of similar triangles have equal slopes. ●​ I can make use of structure to show that similar triangles have equal slopes. ●​ I can derive the equation y = mx for a line through the origin by using the slope to write the equation. ●​ I can make use of structure to derive the equation y = mx for a line through the origin. ●​ I can derive the equation y = mx + b for a line by using the slope formula to write the equation. ●​ I can reason abstractly and quantitatively to use the slope formula to write the equation of a line. ●​ I can solve an equation with variables on each side. ●​ I can use repeated reasoning to solve equations with variables on each side. ●​ I can determine the number of solutions to linear equations. ●​ I can attend to precision to determine the number of solutions to a linear equation. ●​ I can solve absolute value equations.

KEY VOCABULARY

●​ Rise ●​ Run ●​ Slope

●​ Reveal ●​ Hypotenuse ●​ Similar ●​ Slope Triangles ●​ Determine ●​ Visual ●​ Slope Formula ●​ Input

●​ Precede ●​ Initial Value ●​ Nonproportion al ●​ Slope-Intercept Form ●​ Y-Intercept ●​ Differentiate ●​ Reinforce

●​ Distributive Property ●​ Like Terms ●​ Isolate ●​ Manipulate

●​ Unit Rate ●​ Accurate ●​ Inspect ●​ Proportional ●​ Slope ●​ Compare

●​ Solution ●​ Confirm ●​ Diverse

UNDERSTAND & ANALYZE FUNCTIONS

Unit 4

PACING

KEY LANGUAGE USES

November 11 - December 8 (17 days)

EXPLAIN

STANDARDS Standard 8.F.1 Understand that a function is a rule that assigns to each input exactly one output. The graph of a function is the set of ordered pairs consisting of an input and the corresponding output. Standard 8.F.2 Compare properties of two functions each represented in a different way (algebraically, graphically, numerically in tables, or by verbal descriptions). For example, given a linear function represented by a table of values and a linear function represented by an algebraic expression, determine which function has the greater rate of change. Standard 8.F.3 Interpret the equation y = mx + b as defining a linear function, whose graph is a straight line; give examples of functions that are not linear. For example, the function A = s 2 giving the area of a square as a function of its side length is not linear because its graph contains the points (1,1), (2,4) and (3,9), which are not on a straight line. Standard 8.F.4 Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two ( x, y ) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values. Standard 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can analyze representations for real-world situations modeled by functions. Language Supports: ●​ Vocabulary (function)

I can apply understanding of function properties, such as initial value and rate of change, to compare functions in real-world contexts. Language Supports: ●​ Vocabulary (rate of change)

DIFFERENTIATION IN ACTION Skill Building

Unit 4 Fluency Practice on Similar Figures

Extension

Lesson 4.5 STEM Adventure - Students explore waste management. Their

understanding of functions will help them as they manage a waste management facility.

Honors Lesson

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.F.1

4.2, 4.3

8.F.2

4.6

8.F.3

4.4

8.F.4

4.5

8.F.5

4.1

LEARNING INTENTIONS

●​ I can identify and describe where a relationship is increasing and decreasing. ●​ I can sketch a graph using qualitative features of a relationship. ●​ I can use reasoning to understand how the quantities shown in a graph change in reference to each other. ●​ I can determine if a relation is a function by using a table or mapping diagram. ●​ I can make inferences about the relationship between the inputs and outputs of a function. ●​ I can compare and contrast different representations of functions. ●​ I can represent functions in different forms. ●​ I can use repeated reasoning to determine an equation of a function. ●​ I can explain the parts of a function in relation to a problem. ●​ I can determine whether a function is linear or nonlinear from multiple representations. ●​ I can make use of structure to identify types of functions. ●​ I can explain how to identify linear and nonlinear functions. ●​ I can analyze functions by rate of change and initial value using tables and equations. ●​ I model with mathematics to represent real-world situations. ●​ I can explain how to use linear functions to solve problems and make predictions. ●​ I can compare functions represented in different forms. ●​ I can analyze properties of functions given in different forms. ●​ I can explain how the graphs of functions given in different forms are alike and different. ●​ I can represent a function in a different way to think about its properties.

KEY VOCABULARY

●​ Qualitative Graph ●​ Variable ●​ Display ●​ Interval ●​ Dependent Variable

●​ Function ●​ Independent Variable ●​ Input

●​ Utilize ●​ Initial Value ●​ Linear Function

●​ Differentiate ●​ Explicit ●​ Rate of Change

●​ Determine ●​ Reinforce ●​ Nonlinear Function

●​ Cite ●​ Infer ●​ Compare ●​ Inspect

●​ Output ●​ Analyze

Unit 5

PATTERNS OF ASSOCIATION

PACING

KEY LANGUAGE USES

December 9 - January 14 (17 days)

EXPLAIN

STANDARDS Standard 8.SP.1 Construct and interpret scatter plots for bivariate measurement data to investigate patterns of association between two quantities. Describe patterns such as clustering, outliers, positive or negative association, linear association, and nonlinear association. Standard 8.SP.2 Know that straight lines are widely used to model relationships between two quantitative variables. For scatter plots that suggest a linear association, informally fit a straight line, and informally assess the model fit by judging the closeness of the data points to the line. Standard 8.SP.3 Use the equation of a linear model to solve problems in the context of bivariate measurement data, interpreting the slope and intercept. For example, in a linear model for a biology experiment, interpret a slope of 1.5 cm/hr. as meaning that an additional hour of sunlight each day is associated with an additional 1.5 cm in mature plant height. Standard 8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores ? END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can interpret the data in two-way tables to describe patterns of association between categorical variables in context. Language Supports: ●​ Vocabulary (association) I can use relative frequencies calculated for rows and columns to describe possible associations between two variables. Language Supports: ●​ Vocabulary (frequencies) DIFFERENTIATION IN ACTION Skill Building Unit 5 Fluency Practice on slope and unit rate.

Extension

Lesson 5.1 STEM Adventure - Students explore water sources. Where does drinking water come from? Students’ analytical skills will help you identify patterns in data as they explore water sources.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.SP.1

5.1, 5.2

8.SP.2

5.3

8.SP.3

5.4

8.SP.4

5.5, 5.6

LEARNING INTENTIONS

●​ I can construct scatter plots to show bivariate measurement data. ●​ I can determine the intervals of the axes on a scatter plot. ●​ I can use repeated reasoning to determine the relationship between variables on a scatter plot. ●​ I can interpret scatter plots. ●​ I can determine the association between variables. ●​ I can use repeated reasoning to determine the type of association and how to display it with a scatter plot. ●​ I can use lines of fit in scatter plots to show associations in bivariate data. ●​ I can determine the location of the line of fit. ●​ I can use repeated reasoning to determine the strength of the associations in bivariate data. ●​ I can interpret the slope and y-intercept of linear models in bivariate data and use them to make predictions.

●​ I can analyze a set of data points to look for patterns when I draw a line of fit. ●​ I can describe patterns in two-way tables by analyzing rows and columns. ●​ I can interpret the data in two-way tables to recognize patterns. ●​ I can use two-way tables to help reason about meanings of data. ●​ I can summarize data in two-way tables to solve real-world problems. ●​ I can use relative frequencies of the data to describe relationships. ●​ I can use patterns to construct and interpret two-way relative frequency tables.

KEY VOCABULARY

●​ Bivariate Data ●​ Scatter Plot ●​ Variable ●​ Determine ●​ Display ●​ Association

●​ Deviate ●​ Reinforce ●​ Line of fit ●​ Reinforce ●​ Clarify

●​ Estimate ●​ Revise ●​ Frequencies ●​ Two-Way Table ●​ Infer ●​ Inspect

●​ Two-Way Relative Frequency Table ●​ Two-Way Table ●​ Analyze ●​ Compare

ANGLES, TRIANGLES, AND THE PYTHAGOREAN THEOREM

Unit 6

PACING

KEY LANGUAGE USES

EXPLAIN

January 19 - February 18 (21 days)

STANDARDS Standard 8.G.5 Use informal arguments to establish facts about the angle sum and exterior angle of triangles, about the angles created when parallel lines are cut by a transversal, and the angle-angle criterion for similarity of triangles. For example, arrange three copies of the same triangle so that the sum of the three angles appears to form a line, and give an argument in terms of transversals why this is so .

Standard 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.

Standard 8.G.7 Apply the Pythagorean Theorem to determine unknown side lengths in right triangles in real-world and mathematical problems in two and three dimensions.

Standard 8.G.8 Apply the Pythagorean Theorem to find the distance between two points in a coordinate system.

Standard 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can solve real-world problems using the Pythagorean Theorem. Language Supports: ●​ Vocabulary (Pythagorean Theorem)

I can use the Pythagorean Theorem to determine the length of a diagonal line on the coordinate plane. Language Supports: ●​ Vocabulary (Distance)

I can demonstrate how to use the Pythagorean Theorem in real-world scenarios. Language Supports: ●​ Vocabulary (Hypotenuse)

DIFFERENTIATION IN ACTION Skill Building

Unit 6 Fluency Practice on Tables, Graphs, & Equations

Extension

Lesson 6.6 STEM Adventure - Students apply understanding of triangles and angles to explore what elements are in the air we breathe.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.G.5

6.1, 6.2

8.G.6

6.4, 6.5

8.G.7

6.4, 6.5

8.G.8

6.6

8.EE.2

6.3

LEARNING INTENTIONS

●​ I can use the relationship to find the measures of missing angles when two parallel lines are cut by a transversal. ●​ I can identify angles created when a parallel line is cut by a transversal. ●​ I can explain why angle pairs have equal measures when two parallel lines are cut by a transversal. ●​ I can find the measure of interior and exterior angles in a triangle by using relationships among these angles. ●​ I can justify that the sum of the interior angles equals 180. ●​ I can use square root symbols to represent solutions to equations of the form x 2 = p, where p is a positive rational number. ●​ I can evaluate the square root of small perfect squares. ●​ I can explain a proof of the Pythagorean Theorem. ●​ I can find the measures of the sides of a right triangle using the Pythagorean Theorem. ●​ I can explain a proof of the converse of the Pythagorean Theorem. ●​ I can look for and make use of structure when determining if a triangle is a right triangle by using the converse of the Pythagorean Theorem. ●​ I can use the Pythagorean Theorem to find the distance between two points on the coordinate plane. ●​ I can understand and apply the relationships among the sides of a right triangle as stated in the Pythagorean Theorem. ●​ I can solve real-world problems using the Pythagorean Theorem in two and three dimensions. ●​ I can use the converse of the Pythagorean Theorem. ●​ I can use repeated reasoning to apply the Pythagorean Theorem.

KEY VOCABULARY

●​ Alternate Exterior Angles ●​ Alternate Interior Angles ●​ Corresponding Angles

●​ Transversal ●​ Confirm

●​ Square root ●​ Estimate ●​ Reinforce ●​ Congruent ●​ Pythagorean Theorem

●​ Converse ●​ Analyze ●​ Compare ●​ Accurate ●​ Reveal ●​ Convert ●​ Determine

●​ Manipulate ●​ Contradict ●​ Determine ●​ Integer ●​ Square number

●​ Parallel Lines ●​ Perpendicular

●​ Clarify ●​ Revise

Unit 7

VOLUME

PACING

KEY LANGUAGE USES

EXPLAIN

February 18 - March 12 (16 days)

STANDARDS Standard 8.G.9 Know the formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and mathematical problems. Standard 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 = p and x 3 = p, where p is a positive rational number. Evaluate square roots of small perfect squares and cube roots of small perfect cubes. Know that √2 is irrational. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can find volumes of cylinders in real-world situations and use volumes to answer questions. Language Supports: ●​ Vocabulary (cylinder, volume) I can solve real-world problems by using the volume formula for cones or spheres. Language Supports: ●​ Vocabulary (cone, sphere)

I can evaluate cube roots of small perfect cubes. Language Supports: ●​ Vocabulary: (cube root) DIFFERENTIATION IN ACTION Skill Building

Unit 7 Fluency practice on determining initial value and rate of change of a function.

Extension

Lesson 7.4 STEM Adventure - Students explore green construction where they use their understanding of volume to explore green buildings.

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.G.9

7.2, 7.3, 7.4, 7.5

8.EE.2

7.1

LEARNING INTENTIONS ●​ I can use cube root symbols to represent solutions to equations of the form x 3 = p,where p is a positive rational number. ●​ I can evaluate the cube root of a small perfect cube. ●​ I can use repeated reasoning to estimate the side length of a cube, given its volume, with precision. ●​ I can determine the volume of a cylinder. ●​ I can explain how finding the volume of a cylinder is like finding the volume of a prism. ●​ I can precisely describe the measurements of a cylinder. ●​ I can determine the volume of a cone. ●​ I can use precision to calculate the volume of a cone. ●​ I can determine the volume of a sphere. ●​ I can explain how to find the volume of a sphere. ●​ I can solve real-world problems using volume formulas. ●​ I can describe real-world scenarios in which volume formulas will be needed.

KEY VOCABULARY

●​ Cube Root ●​ Inverse ●​ Perfect Cube ●​ Volume ●​ Foundation

●​ Highlight ●​ Cylinder ●​ Determine ●​ Estimate ●​ Cone

●​ Compute ●​ Differentiate ●​ Sphere ●​ Compare ●​ Reveal

●​ Composite Figure ●​ Denote ●​ Reinforce

SYSTEMS OF LINEAR FUNCTIONS

Unit 8

PACING

KEY LANGUAGE USES

EXPLAIN

March 15 - Apr 2 (14 days)

STANDARDS Standard 8.EE.8 Analyze and solve pairs of simultaneous linear equations.

a. ​ Understand that solutions to a system of two linear equations in two variables correspond to points of intersection of their graphs, because points of intersection satisfy both equations simultaneously. b. ​ Solve systems of two linear equations in two variables graphically, approximating when solutions are not integers. Solve simple cases by inspection. For example, 3x + 2y = 5 and 3x + 2y = 6 have no solution because 3x + 2y cannot simultaneously be 5 and 6. c. ​ Solve real-world and mathematical problems leading to two linear equations in two variables. For example, given coordinates for two pairs of points, determine whether the line through the first pair of points intersects the line through the second pair.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can graph a system of linear equations and find their point of intersection. Language Supports: ●​ Vocabulary (system of linear equations)

I can estimate the solution to a system of equations. Language Supports: ●​ Vocabulary (estimate)

I can use the graph of a system of equations to determine whether there is one, no, or an infinite number of solutions. Language Supports: ●​ Vocabulary (infinite) 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.

Honors Lesson 1 Honors Lesson 2

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.EE.8

8.1, 8.2, 8.3

LEARNING INTENTIONS

●​ I can explain what a system of equations is. ●​ I can graph equations to solve a system of equations. ●​ I can use repeated reasoning to determine a point of intersection in a system of equations. ●​ I can estimate the solution to a system of equations by graphing. ●​ I can use precision to graph a system of equations and estimate the solution to the system. ●​ I can identify whether a system of equations has no, one, or an infinite number of solutions by inspection in simple cases. ●​ I can explain why a system of equations has no, on, or an infinite number of solutions.

KEY VOCABULARY

●​ Point of

●​ Demonstrate ●​ Determine ●​ Reinforce

●​ Slope-Intercept Form ●​ System of Equations ●​ Display

●​ Presume ●​ Slope ●​ Y-Intercept ●​ Inspect

Intersection

●​ System of Equations

IRRATIONAL NUMBERS, EXPONENTS, AND SCIENTIFIC NOTATION

Unit 9

PACING

KEY LANGUAGE USES

EXPLAIN

April 12 - May 7 (20 days)

STANDARD Standard 8.NS.1 Know that numbers that are not rational are called irrational. Understand informally that every number has a decimal expansion; for rational numbers show that the decimal expansion repeats eventually, and convert a decimal expansion which repeats eventually into a rational number.

Standard 8.NS.2 Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of expressions (e.g. π 2 ).

Standard 8.NS.3 Understand how to perform operations and simplify radicals with emphasis on square roots.

Standard 8.EE.1 Know and apply the properties of integer exponents to generate equivalent numerical expressions. For example, 3 2 × 3 –5 = 3 –3 = 1/3 3 = 1/27

Standard 8.EE.3 Use numbers expressed in the form of a single digit times an integer power of 10 to estimate very large or very small quantities, and to express how many times as much one is than the other.

Standard 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities (e.g., use millimeters per year for seafloor spreading). Interpret scientific notation that has been generated by technology. END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS I can write fractions as repeating decimals and repeating decimals as fractions. Language Supports: ●​ Vocabulary (repeating)

I can compare and order rational and irrational numbers using a number line.. Language Supports: ●​ Vocabulary (rational, irrational)

I can apply the properties of integer exponents to generate equivalent numerical expressions. Language Supports: ●​ Vocabulary (exponent)

I can use scientific notation to compare very large or very small quantities. Language Supports: ●​ Vocabulary (scientific notation)

I can simplify radicals. Language Supports:

●​ Vocabulary (radical)

DIFFERENTIATION IN ACTION Skill Building

Unit 9 Fluency Practice on Solving Systems of Equations by inspection

Extension

Lesson 9.2 STEM Adventure - Students use their understanding of real numbers to explore harnessing the natural power of the wind to generate electricity.

Honors Lesson 1 Honors Lesson 2

REVEAL MATH AND CORE ALIGNMENT

Standard

Section(s)

8.NS.1

9.1, 9.2

8.NS.2

9.2, 9.3

8.NS.3

Simplifying Radical numbers folder

8.EE.1

9.4, 9.5, 9.6

8.EE.3

9.7

8.EE.4

9.8

LEARNING INTENTIONS

●​ I can use repeated reasoning to show that rational numbers repeat in decimal form. ●​ I can convert a repeating decimal into a rational number. ●​ I can identify if a number is irrational. ●​ I can approximate irrational numbers on the number line. ●​ I can use repeated reasoning to estimate the value of an irrational number. ●​ I can use rational approximations to compare and order real numbers. ●​ I can simplify expressions that include zero and negative exponents. ●​ I can use repeated reasoning to determine the patterns that occur when negative exponents are applied to a variety of bases. ●​ I can attend to precision while using products and quotients to simplify integer exponents. ●​ I can use power of a power and power of a product to simplify integer exponents. ●​ I can reason about the structure of a power expression to rewrite it in different ways. ●​ I can estimate and compare very large or very small quantities using powers of 10. ●​ I can make use of structure to write very large or very small quantities using powers of 10. ●​ I can perform computations with numbers written in scientific notation to solve real-world problems. ●​ I can use repeated reasoning to rewrite numbers in scientific notation with the same place value. ●​ I can simplify square and cube roots. ●​ I can add and subtract radical expressions. ●​ I can multiply radical expressions.

KEY VOCABULARY

●​ Bar Notation ●​ Exhibit ●​ Rational ●​ Irrational Number

●​ Interval ●​ Visual ●​ Exponent ●​ Confirm ●​ Convert ●​ Evaluate ●​ Utilize

●​ Compute ●​ Transform ●​ Scientific Notation ●​ Compare ●​ Display ●​ Denote ●​ Determine

●​ Radical

Expression ●​ Square Root ●​ Perfect Square ●​ Principal Square Root ●​ Cube Root ●​ Perfect Cube

●​ Accurate ●​ Estimate

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 bilateral symmetry 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 boundless. ●​ I can use patterns and symmetry 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 ●​ Display ●​ Unique ●​ The Golden Ratio

●​ Highlight ●​ Abstract ●​ Infer

●​ Adapt ●​ Exceed ●​ Fractal ●​ Iteration

●​ Initiate ●​ Phenomenon

●​ Display ●​ Reveal

Instructional Guide 2026-2027

Secondary Math 1H Accelerated

Secondary 1H Accelerated

SEMESTER 1 AT A GLANCE

Pre-Unit 1

Unit 1

Unit 2

Unit 3

Unit 4

Unit 5

Unit 6

Unit 7

Unit 8

Aug 17 - Aug 21 (5 days)

Aug 24 - Sept 1 (7 days)

Sept 2 - Sept 15 (9 days)

Sept 16 - Oct 2 (12 days)

Oct 23 - Nov 5 (10 days)

Nov 20 - Dec 11 (13 days)

Dec 14 - Jan 14 (14 days)

Suggested Pacing

Oct 5 - Oct 22 (11 days)

Nov 6 - Nov 19 (10 days)

8th Grade Unit 9 Irrational Numbers, Exponents, and

Sec 1 Module 7 Systems of Linear Equations

Sec 1 Module 2 Equations in One Variable

Sec 1 Module 3 Relations and Functions

Sec 1 Module 4 Linear and Nonlinear Functions

Sec 1 Module 5 Creating Linear Functions

Sec 1 Module 6 Linear Inequalities

Sec 1 Module 8 Exponential Functions

Sec 1 Module 1 Expressions

Unit

Scientific Notation

8.F.3 8.F.4

8.EE.5 8.EE.6

8.F.1 8.F.2 8.F.5 N.Q.1

8.SP.1 8.SP.2 8.SP.3

8.F.3 8.F.4 A.REI.10 F.LE.1a

F.LE.1c F.LE.2 F.LE.5 F.IF.3 F.IF.7e F.BF.2 F.BF.3

8.EE.8 A.CED.3 A.REI.5 A.REI.6 A.REI.11 A.REI.12

8.EE.7 A.CED.1 A.CED.3 A.REI.3 A.REI.12

8.NS.1 8.NS.2 8.EE.1

8.EE.7 A.CED.1 A.REI.1 A.REI.3

A.CED.2 A.CED.3 S.ID.7 S.ID.6 S.ID.9 S.ID.8 A.CED.2

Standards/ Performance Expectations

F.IF.1 F.IF.2 F.IF.4 F.IF.5 F.IF.9 A.REI.10

Review

F.LE.2 F.LE.5 F.BF.3 F.BF.1a F.BF.2 F.IF.4 F.IF.7a

Secondary 1H Accelerated

SEMESTER 2 AT A GLANCE

Unit 9

Unit 10

Unit 11

Unit 12

Unit 13

Unit 14

Unit 15

Suggested Pacing

Jan 19 - Feb 2 (11 days)

Feb 3 - Mar 2 (17 days)

Mar 3 - Mar 16 (10 days)

Mar 17 - Apr 2 (11 days)

Apr 12 - Apr 21 (8 days)

Apr 22 - May 5 (10 days)

May 6 - May 20 (10 days)

Sec 1 Module 10 + 8th grade Unit 6 Tools of Geometry & Angles, Triangles, and the Pythagorean Theorem

Sec 1 Module 12 Logical Arguments and Line Relationships

Sec 1 Module 11 Angles and Geometric Figures

Sec 1 Module 13 Transformations and Symmetry

Sec 1 Module 14 Triangles and Congruence

Sec 1 Honors Module Matrix and Vectors

Sec 1 Module 9 Statistics

Unit

N.VM.1 N.VM.2 N.VM.3 N.VM.4 N.VM.5 N.VM.6 N.VM.7 N.VM.8 N.VM.9 N.VM.10 N.VM.11 N.VM.12 N.VM.13

8.G.1 8.G.2 8.G.3 8.G.9 G.CO.1 G.CO.12 G.GPE.7 N.Q.3

8.G.1 8.G.2 8.G.3

8.EE.2 8.G.5 8..G.6

S.ID.1 S.ID.2 S.ID.3 S.ID.5 N.Q.1

G.CO.1 G.CO.9 G.CO.12 G.GPE.5

G.CO.10 G.CO.7 G.CO.8 G.GPE.4

Standards/ Performance Expectations

G.CO.3 G.CO.4 G.CO.5 G.CO.6

8.G.7 8.G.8 G.CO.1 G.CO.12

August 2026

Monday

Tuesday Friday August 17 August 18 August 19 August 20 August 21 Wednesday Thursday

1.5 Expressions

First Day of School Involving Absolute Value August 24 August 25 August 26 August 27 August 28 1.1 Numerical Expressions 1.2 Algebraic Expressions 1.4 Distributive Property

9.5 Use Product and Quotient of Powers Propoerties

9.7 Use Powers of 10 to Estimate Quantities

9.4 Explore Patterns of Exponents

MAP

MAP

August 31

Review

September 2026

Monday

Tuesday Friday September 1 September 2 September 3 September 4 Wednesday Thursday

2.1 Writing and Interpreting Equations 2.2 Solving

Units 9 & 1 Test 2.4 Solving Equations with the Variable on Each Side September 7 September 8 September 9 September 10 September 11 2.3 Solving Multi-Step Equations

2.5 Solving Equations

Involving Absolute Value

No School 2.7 Using Formulas September 14 September 15 September 16 September 17 September 18 2.6 Solving Proportions 2.7 Using Formulas

Review 3.3 Linearity and Continuity of Graphs September 21 September 22 September 23 September 24 September 25 Module 2 Test 3.1 Representing Relations 3.2 Functions

3.4 Intercepts of Graphs

3.4 Intercepts of Graphs

3.5 Shapes of Graphs

Quiz

No School

September 28 September 29 September 30

3.6 Sketching Graphs and Comparing Functions

3.6 Sketching Graphs and Comparing Functions

No School