8th grade Math Guide

Instructional Guide 2024-2025

Math

Grade

Instructional Guide 2024-2025

Introduction

What’s New and Updated in 8th grade math

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

Updated dates for all units

Grade8

Math Overview

ORGANIZATION OF STANDARDS The Utah Core Standards are organized into strands, which represent signifcant 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 profciency 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 defne 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 suffcient richness. The standards set grade-specifc standards but do not dictate curriculum or teaching methods, nor do they defne 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 defne 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-specifc standards can fully refect 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 specifc 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 2024-2025

Scope and Sequence

Grade8

YEAR AT A GLANCE

Unit 1 Rigid

Unit 2 Dilations, Similarity, and Introducing Slope (13 Sections)

Unit 3 Linear

Unit 4 Linear Equations and Linear Systems (16 Sections)

Unit 5 Functions and Volume (22 Sections)

Unit 7 Exponents and

Unit 8 Pythagorean Theorem and Irrational Numbers (16 Sections)

Unit 6 Associations in Data (11 Sections)

Unit 9 Putting it All Together

Illustrative Unit

Transformations and Congruence (17 Sections)

Relationships (14 Sections)

Scientifc Notation (16 Sections)

Suggested Pacing

Aug 19 - Sept 20 (24days)

Sept 23 - Oct 16 (17days)

Oct 22 -Nov 26 (26days)

Dec 2 - Jan 10 (20days)

Jan 13 - Feb 21 (27days)

Feb 24 - Mar 21 (19days)

Mar 25 - Apr 25 (19days)

Apr 29 - May 14 (13days)

May 15 -May 30

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

8.G.2 8.G.3 8.G.4 8.G.5 8.EE.6

8.EE.5 8.G.1 8.EE.6 8.EE.8

8.EE.7 8.EE.8

8.F.1 8.F.2 8.F.3 8.F.4 8.F.5 8.G.9

8.EE.1 8.EE.3 8.EE.4

8.NS.1 8.NS.2 8.NS.3* 8.EE.2

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

8.F 8.SP 8.G

Practice Standards

Practice Standards

Practice Standards

8.G.6 8.G.7 8.G.8

Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

Practice Standards

DWSBA Testing Window

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

DWSBA#1

DWSBA#2

DWSBA#3

MAP Window

SALTA Extensions

“Are You Ready for More?”

Accessing the District-Wide Standards-Based Assessment (DWSBA)

The DWSBA’s will be done through Canvas on Derivita Instructions to access the DWSBA can be found here.

RIGID TRANSFORMATIONS AND CONGRUENCE

Unit 1

PACING

KEY LANGUAGE USES

August 19 - September 20 (24days)

EXPLAIN

STANDARDS

Standard 8.G.1 Verify experimentally the properties of rotations, refections, 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 fgure is congruent to another if the second can be obtained from the frst by a sequence of rotations, refections, and translations; given two congruent fgures, describe a sequence that exhibits the congruence between them.

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

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 explain why a fgure is or is not an image of another fgure based on a series of transformations. Language Supports: ● Vocabulary: (transformation, translation, rotation, refection, image, clockwise, counterclockwise, image) I can explain whether two fgures are congruent to each other using a series of transformations. Language Supports: ● Vocabulary: (congruent, transformation, translation, rotation, refection, image, clockwise, counterclockwise) DIFFERENTIATION IN ACTION

Skill Building

From Activity 3.2: MLR 8 Discussion Supports. To help develop students’ meta-awareness and understanding of the task expectations, think aloud as you transform the quadrilateral in the question about rotating quadrilateral ABCD 60° counterclockwise using center B. As you talk, model mathematical language use and highlight the relationship between quadrilateral ABCD , the image (i.e.,

quadrilateral A’B’C’D’ ), and the steps taken to rotate quadrilateral ABCD .

Extension

From lesson 12 “Are You Ready for More?”: A polygon has 8 sides: fve of length 1, two of length 2, and one of length 3. All sides lie on grid lines. (It may be helpful to use graph paper when working on this problem.) 1. Find a polygon with these properties. 2. Is there a second polygon, not congruent to your frst, with these properties?

RESOURCES

Teach rules/routines while starting frst lesson Unit 1 Notes Honor’s can combine lessons/go faster Additional Lessons Additional Practice Problems Information about Practice Problems

Mid-Unit Practice Test End of Unit 1 Practice Test Vocabulary Resources Parallel Lines/Angle Relationships Refections & Rotations with Pattern Blocks

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.G.1

1.1, 1.2, 1.3, 1.4, 1.6, 1.7, 1.8, 1.9, 1.10, 1.11, 1.13, 1.14

8.G.2

1.11, 1.12, 1.13, 1.15

8.G.3

1.5, 1.6, 1.17

8.G.5

1.14, 1.15, 1.16

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

1.1

1.1

4.MD.5

2

1.9

1.3

5.G.1, 6.G.3

3

1.3

1.9, 1.14, 1.17

7.G.5

4

1.9

1.9

4.G.1

5

1.15

1.11

6.G.1

6

1.11

1.15

7.G.2

7

1.12

LEARNING INTENTIONS

● Basic understanding of rotation (about a point), refection (about a line), and translation (in a given direction). ● Verify that congruence of line segments and angles is maintained through rotation, refection, and translation. ● Verify that lines remain lines through rotation, refection, and translation. ● Verify that when parallel lines are rotated, refected, or translated, each in the same way, they remain parallel lines. ● Understand that the congruency of two dimensional fgures is maintained while undergoing rigid transformations. ● Describe the transformation of a fgure as a rotation, refection, translation or a combination of transformations. ● Understand congruence via transformations using physical models, transparencies, or geometry software. ● Observe that orientation of the plane is preserved in rotations and translations, but not with refections. ● Understand characteristics of dilations, translations, rotations, and refections of two-dimensional fgures on the coordinate plane (describing transformations as functions takes place in Secondary Mathematics I). ● Effects of transformations might include: size/shape does not change in translations, refections and rotations; orientation changes with refections. ● Use informal arguments (proofs occur in Secondary Mathematics II) to establish facts about:

1. the angle sum of triangles. 2. exterior angle of triangles. 3. about the angles created when parallel lines are cut by a transversal. 4. the angle-angle criterion for similarity of triangles.

KEY VOCABULARY

● Image ● Corresponding ● Clockwise ● Counterclockwise ● Straight Angle ● Sequence of Transformations

● Refection ● Rotation ● Translation ● Transformation ● Congruent

● Vertical Angles ● Alternate Interior Angles ● Transversal ● Rigid Transformations

DILATIONS, SIMILARITY, AND INTRODUCING SLOPE

Unit 2

PACING

KEY LANGUAGE USES

September 23 - October 16 (17days)

EXPLAIN

STANDARDS

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

Standard 8.G.4 Understand that a two-dimensional fgure is similar to another if the second can be obtained from the frst by a sequence of rotations, refections, translations, and dilations; given two similar two-dimensional fgures, 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 . 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 .

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain why two shapes are similar using the concept of dilations. Language Supports: ● Vocabulary (similar, dilation, scale factor) I can fnd the slope of a line using similar triangles and explain how I found it. Language Supports: ● Vocabulary (slope, similar triangle) DIFFERENTIATION IN ACTION

Skill Building

From Lesson 6: Consider using a Venn diagram to compare the similarities and differences between the standard defnition of similarity and the mathematical defnition. From Lesson 8 “Are You Ready for More?”: Quadrilaterals ABCD and EFGH have four angles measuring 240°, 40°, 40°, and 40°. Do ABCD and EFGH have tobe similar?

Extension

RESOURCES

Unit 2 Notes

Ck12 & Desmos

Additional Practice Problems Unit 2 Practice Test Information about Practice Problems

Bee Transformation Animation Resources for Lesson 11 Worksheet/Card sort Papers

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.G.3

2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7, 2.12

8.G.4

2.6, 2.7, 2.9

8.G.5

2.8

8.EE.6

2.10, 2.11, 2.12, 2.13*

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

2.9

2.1, 2.4, 2.9

7.G.1

2

2.9

2.2

4.MD.5

3

2.9, 2.10

2.8

6.NS.1, 7.RP.2a

4

2.10

2.9

6.NS.8

5

2.8

2.9, 2.11, 2.13

7.RP.2

6

2.6

2.10

5.NBT.7, 5.NF.3, 7.RP.2

7

2.4

LEARNING INTENTIONS

● Understand that the congruency of two dimensional fgures is maintained while undergoing rigid transformations. ● Describe the transformation of a fgure as a rotation, refection, translation or a combination of transformations. ● Understand congruence via transformations using physical models, transparencies, or geometry software. ● Observe that orientation of the plane is preserved in rotations and translations, but not with refections. ● Understand characteristics of dilations, translations, rotations, and refections of two-dimensional fgures on the coordinate plane (describing transformations as functions takes place in Secondary Mathematics I). ● Effects of transformations might include: size/shape does not change in translations, refections and rotations; orientation changes with refections. ● Understand that any combination of rotations, refections, translations, and dilations will result in a similar fgure. ● Describe the sequence of transformations needed to show how one fgure is similar to another. ● Perform transformations using physical models, transparencies, or geometry software. (Rigid motion transformations will be addressed in Secondary Mathematics I.) ● Understand similarity using physical models, transparencies, or geometry software. (Properties of dilations given by a center and a scale factor will be addressed in Secondary Mathematics II). ● Use informal arguments (proofs occur in Secondary Mathematics II) to establish facts about: 1. the angle sum of triangles. 2. exterior angle of triangles. 3. about the angles created when parallel lines are cut by a transversal. 4. the angle-angle criterion for similarity of triangles. ● Determine the slope of a line as the ratio of the leg lengths of similar right triangles. ● Explain why the slope is the same between any two distinct points on a line using similar right triangles. ● Derive an equation in the form y = mx + b from a graph of a line on the coordinate plane .

KEY VOCABULARY

● Dilation ● Center (of a dilation)

● Similar ● Slope

Unit 3

LINEAR RELATIONSHIPS

PACING

KEY LANGUAGE USES

October 22 - November 26 (26days)

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 . 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 frst pair of points intersects the line through the second pair. Standard 8.EE.8 Analyze and solve pairs of simultaneous linear equations.

Standard 8.G.1 Verify experimentally the properties of rotations, refections, 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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain where the solution to a system of equations is found on a graph and what that solution means. Language Supports: ● Vocabulary (graph, solution, system of equations) I can explain the relationship between unit rate, constant of proportionality, and the slope of a line. Language Supports: ● Vocabulary (unit rate, constant of proportionality, slope, line) DIFFERENTIATION IN ACTION

Skill Building

From Activity 5.1: MLR 8 Discussion Supports. Display sentence frames for students to use as a support when they explain their strategy. For example, "I noticed that ______." or "First, I ________ because ________." When students share their answers with a partner, prompt them to rehearse what they will say when they share with the whole class. Rehearsing provides students with additional opportunities to clarify their thinking, and to consider how they will communicate their reasoning.

. = 5 + 1 2

Extension

From Lesson 7 “Are You Ready for More?” A situation is represented by the equation

1. Invent a story for this situation. 2. Graph the equation. 3. What do the and the 5 represent in your situation? 4. Where do you see the and 5 on the graph?

RESOURCES

Defnitely do 3.1 and emphasize it. CK12 and Desmos Activities Vocabulary Additional Practice Problems Information about Practice Problems

Unit 3 Notes Stained Glass Project Unit 3 Practice Test Lesson6

Lesson8 Lesson10 Lesson12 Lesson13

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.EE.5

3.1, 3.2, 3.3, 3.4, 3.5, 3.6

8.EE.6

3.7, 3.9, 3.10, 3.11, 3.14

8.EE.8

3.12, 3.13, 3.14

8.G.1

3.8

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

3.1

3.1, 3.5, 3.6 7.RP.2a

2

3.3

3.2

7.RP.2

3

3.7

3.3

6.EE.3, 6.NS.1, 6.NS.3, 7.RP.3

4

3.11

3.6

5.OA.3

5

3.8

3.7

5.MD.3

3.5

6

3.8

7.RP.2c

3.12

6.G.1

LEARNING INTENTIONS

● Graph a proportional relationship given a table, equation or contextual situation. ● Recognize unit rate as slope and interpret the meaning of the slope in context. ● Compare different representations of two proportional relationships represented as contextual situations, graphs, tables, or equations. ● Determine the slope of a line as the ratio of the leg lengths of similar right triangles. ● Explain why the slope is the same between any two distinct points on a line using similar right triangles. ● Derive an equation in the form y = mx + b from a graph of a line on the coordinate plane. ● Understand that solutions to a system of two linear equations is where the lines intersect. ● Solve systems of two linear equations graphically and identify the number of solutions (one solution, infnitely many solutions or no solutions). ● Interpret the solution to graphs of systems of linear equations, estimating when solutions are not integers. ● Basic understanding of rotation (about a point), refection (about a line), and translation (in a given direction). ● Verify that congruence of line segments and angles is maintained through rotation, refection, and translation. ● Verify that lines remain lines through rotation, refection, and translation. ● Verify that when parallel lines are rotated, refected, or translated, each in the same way, they remain parallel lines.

KEY VOCABULARY

● ● ●

● ●

Rate of Change

Vertical Intercept

Slope

Solution to an equation with two variables

Linear Relationships

LINEAR EQUATIONS AND LINEAR SYSTEMS

Unit 4

PACING

KEY LANGUAGE USES

December 2 - January 10 (20days)

EXPLAIN

STANDARDS

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

a. Give examples of linear equations in one variable with one solution, infnitely 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 coeffcients, including equations and inequalities whose solutions require expanding expressions using the distributive property and collecting like terms. c. Solve single variable absolute value 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 frst pair of points intersects the line through the second pair. Standard 8.EE.8 Analyze and solve pairs of simultaneous linear equations.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain what the solution to a system of equations means in terms of the situation it represents. Language Supports: ● Vocabulary (solution, linear equation)

DIFFERENTIATION IN ACTION

Skill Building

From Activity 6.2: MLR 8 Discussion Supports. When partners are comparing their work, provide sentence frames to help students describe reasons for whether an equation has a solution that is positive, negative, or zero. Displaying the following: “I know that equation _____ will have a positive/negative/zero solution because

____.”, “Some features of equations with a positive/negative/zero solution are ____.” and “When I look at structure of this equation I notice that ____.” This will help students practice talking about the structure of equations and the operations within them. From Lesson 6 “Are You Ready for More?”: Mai gave half of her brownies, and then half a brownie more, to Kiran. Then she gave half of what was left, and half a brownie more, to Tyler. That left her with one remaining brownie. How many brownies did she have to start with?

Extension

RESOURCES

DO NOT TEACH 4.14 CK12 and Desmos Activities Vocabulary Unit 4 Notes Information about Practice Problems

Optional Practice Problems Unit 4 Practice Test

Lesson8 Lesson13 Lesson15

Lesson3 Lesson6 Lesson7

Be careful in lesson 15: Practice Problems 1 & 3 require students to solve algebraically.

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.EE.7

4.1, 4.2, 4.3, 4.4, 4.5, 4.5, 4.6, 4.7, 4.8, 4.9, 4.10, **8.EE.7 is not completely covered by Illustrative Mathematics, as the following parts are specifc to Utah: Solving multi-step inequalities and solving absolute value equations.

8.EE.8

4.10, 4.11, 4.12, 4.13, 4.15, 4.16

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

4.1

4.1

7.NS.1

2

4.2

4.2

6.EE.3, 6.EE.7, 7.EE.4a

3

4.3

4.7, 4.13

6.EE.5

4

4.2

4.16

6.EE.9

5

4.7

LEARNING INTENTIONS

● Understand that the simplifed form of an equation ( x=a, a=a, or a=b) indicates the number of solutions (one, zero, or infnitely many solutions).

● Solve multistep linear equations and inequalities with rational coeffcients and variables on both sides. ● Solve absolute value equations (not inequalities) and understand why there are either zero, one, or two solutions. ● Understand that solutions to a system of two linear equations is where the lines intersect. ● Solve systems of two linear equations graphically and identify the number of solutions (one solution, infnitely many solutions or no solutions). ● Interpret the solution to graphs of systems of linear equations, estimating when solutions are not integers.

KEY VOCABULARY

● ●

Constant Term

System of equations

Unit 5 FUNCTIONS AND VOLUME

PACING

KEY LANGUAGE USES

January 13 - February 21 (27days)

ARGUE

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 defning 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.

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.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain whether a relationship is a function, and whether or not it is linear. Language Supports: ● Vocabulary (linear, function, relationship)

DIFFERENTIATION IN ACTION

Skill Building

From Activity 6.3: MLR 2 Collect and Display. As students work in groups, capture

the vocabulary and phrases students use to describe the relationship between the variables they selected over time. Listen for students who refer to the story to justify their decisions as they create the shape of the graph. Record their language on a visual display that can be referenced in future discussions. This will help students to produce and make sense of the language needed to communicate about the relationship between quantities represented by functions graphically and in story contexts. From Lesson 6 “Are You Ready for More?” It is the year 3000. Noah’s descendants are still racing around the park, but thanks to incredible technological advances, now with much more powerful gadgets at their disposal. How might their newfound access to teleportation and time-travel devices alter the graph of stories of their daily adventures? Could they affect whether or not the distance from home is a function of the time elapsed?

Extension

RESOURCES

Preview to Functions Combining Lessons in frst half of unit Mid-Unit Practice Test Information about Practice Problems

Combining Lessons in last half of unit End of Unit Practice Test Practice with Cylinders and Cones Don’t do #3 Practice Problems on Lesson 1. *Could do problem 6 in lesson 11, if they graph it.

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.F.1

5.1, 5.2, 5.3, 5.4, 5.5, 5.17

8.F.2

5.7, 5.8

8.F.3

5.4, 5.7, 5.8, 5.18

8.F.4

5.8, 5.9, 5.10, 5.11

8.F.5

5.6, 5.10

8.G.9

5.11, 5.12, 5.13, 5.14, 5.15, 5.16, 5.17, 5.18, 5.19, 5.20, 5.21, 5.22*

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

5.3

5.1

7.NS.2, 7.NS.1, 6.EE.2c

2

5.9

5.3

7.EE.4

3

5.8

5.8

7.RP.2a, 7.RP.2c

4

5.1

5.11

7.G.6, 3.MD.7, 3.MD.8

5

5.11

5.12

7.G.4

6

5.12

5.13

6.G.2

LEARNING INTENTIONS

● Understand that functions describe relationships where for each input there is exactly one output. ● Recognize a graph of a function as the set of ordered pairs consisting of an input and its corresponding output. ● Identify properties of functions from any given representation (algebraically, graphically, numerically in tables, or by verbal descriptions). ● Compare two linear functions each represented a different way and describe similarities and differences. ● Distinguish between linear and non-linear functions given their algebraic expression, a table, a verbal description, or a graph. ● Recognize functions written in the form y=mx+b are linear and that every linear function can be written in the form y=mx+b . ● Understand the slope of a linear function as a constant rate of change, whose graph is a straight line. ● Determine and interpret the initial value and rate of change given two points, a graph, a table of values, a geometric representation (visual model), or a verbal description of a linear relationship. ● Write the equation of a line given two points, a graph, a table of values, a geometric representation (visual model), or a verbal description of a linear relationship. ● Describe attributes of a function by analyzing a graph. ● Create a graphical representation given the description of the relationship between two quantities.

● Understand when and how to use formulas for volume of cones, cylinders, and spheres. ● Use the Pythagorean Theorem to fnd heights of oblique and right cones and cylinders. ● Apply volume formulas to real-world problems.

KEY VOCABULARY

● Function ● Independent Variable ● Dependent Variable

EXPONENTS AND SCIENTIFIC NOTATION

Unit 7

PACING

KEY LANGUAGE USES

February 24 - March 21 (19 days)

EXPLAIN

STANDARDS

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 seafoor spreading). Interpret scientific notation that has been generated by technology.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can know the properties of exponents and explain the process of simplifying an expression with exponents. Language Supports: ● Vocabulary (exponents) DIFFERENTIATION IN ACTION

Skill Building

From Activity 3.2: MLR 1 Stronger and Clearer Each Time. Use this routine to give students a structured opportunity to revise and refne their explanation of the patterns they noticed in the task. Ask each student to meet with 2–3 other partners in a row for feedback. Provide student with prompts for feedback that will help students strengthen their ideas and clarify their language (e.g., “Can you give an example?”, “Can you say that another way?”, “How do you know…?”, etc.). Students can borrow ideas and language from each partner to strengthen their fnal explanation.

Extension

From Lesson 3 “Are You Ready for More?”: 2 12 = 4,096. How many other whole numbers can you raise to a power and get 4,096? Explain or show your reasoning.

RESOURCES

Vocabulary Information about Practice Problems

Practice Test Do not assign # 4 in lesson 10, #2 in lesson 12

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.EE.1

7.1, 7.2, 7.3, 7.4, 7.5, 7.5, 7.6, 7.7, 7.8, 7.11, 7.14

8.EE.3

7.9, 7.10, 7.11, 7.12, 7.14, 7.16*

8.EE.4

7.11, 7.12, 7.13, 7.14, 7.15, 7.16*

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

7.2

7.1

6.EE.1

2

7.4

7.2, 7.9

5.NBT.3a

3

7.1

7.3

6.NS.3

4

7.2

7.4, 7.6

5.NF.5b

5

7.11

7.5, 7.9, 7.13

5.NBT.2

6

7.11

7.4

6.NS.2

7

7.6

7.6

5.NF.5b, 4.NF.1

7.10

6.NS.6

LEARNING INTENTIONS

● Know the properties of integer exponents. (Rational exponents are in Secondary II Mathematics) ● Apply the properties of integer exponents to simplify and evaluate numerical expressions. ● Write very large or very small numbers as the product of a single digit and a power of ten. ● Estimate numbers as a product of a single digit and a power of ten. ● Compare numbers expressed as a product of a single digit and a power of ten by expressing how many times one is bigger or smaller than the other. ● Add, subtract, multiply and divide with numbers expressed in scientifc notation and decimal notation. ● Represent very large and small quantities in scientifc notation and use appropriate units. ● Convert between decimal notation and scientifc notation. ● Interpret numbers expressed in scientifc notation, including numbers generated by technology.

KEY VOCABULARY

● Scientifc Notation

PYTHAGOREAN THEOREM AND IRRATIONAL NUMBERS

Unit 8

PACING

KEY LANGUAGE USES

March 25 - April 25 (19 days)

EXPLAIN

STANDARDS

Standard 8.EE.2 Use square root and cube root symbols to represent solutions to equations of the form x 2 =pand 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. 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.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 fnd the distance between two points in a coordinate system.

END OF UNIT COMPETENCY WITH LANGUAGE SUPPORTS

I can explain whether a number is rational or irrational. Language Supports: ● Vocabulary (rational, irrational) I can explain a proof of the Pythagorean Theorem Language Supports: ● Vocabulary (Proof, Pythagorean Theorem, triangle)

DIFFERENTIATION IN ACTION

Skill Building

From Activity 7.2: MLR 5 Co-Craft Questions. Before revealing the questions in this activity, display the image of the squares with a side length of and invite students to write possible mathematical questions about the diagram. Ask students to compare the questions they generated with a partner before sharing questions

with the whole class. Listen for and amplify questions about the total area for each square or the area of each of the nine smaller regions of the squares. If no student asks about the area of each smaller region, ask students to adapt a question to align with the learning goals of this lesson. Then reveal and ask students to work on the actual questions of the task. This routine will help develop students’ meta-awareness of language as they generate questions about area in preparation for the proof of the Pythagorean Theorem. From lesson 5 “Are You Ready for More?”: Can we do any better than “between 3 and4” for ? Explain a way to fgure out if the value is closer to 3.1 or closer to 12 3.9.

Extension

RESOURCES

Unit 8 Combined Lessons Vocabulary Information about Practice Problems

Do not assign: Lesson3#6 Lesson4#5 Lesson5#7 Lesson7#6 Lesson8#6

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.EE.2

8.2, 8.3, 8.4, 8.5, 8.11, 8.12, 8.13

8.NS.1

8.14, 8.15

8.NS.2

8.1, 8.4, 8.5, 8.12, 8.13

8.NS.3

** 8.NS.3 is not found in Illustrative Mathematics as it is unique to Utah Core. Refer to student learning intentions for example problems

8.G.6

8.7, 8.9, 8.10

8.G.7

8.6, 8.7, 8.8, 8.11

8.G.8

8.11

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

8.1

8.1, 8.3

6.EE.1

2

8.3

8.1

6.G.1

3

8.4

8.2

6.G.3

4

8.14

8.3

5.NF.4

5

8.15

8.4

6.NS.6c

6

8.1

8.14, 8.15

7.NS.2d

8.13

7

8.14

5.NBT.3

LEARNING INTENTIONS

● Know that real numbers that are not rational are irrational. ● Understand that fnite decimal expansions of irrational numbers are approximations. ● Show that rational numbers have decimal expansions that repeat eventually. ● Convert a decimal expansion, which repeats eventually, into a rational number. ● Compare and order irrational numbers. ● Place irrational numbers on a number line. ● Use approximations of irrational numbers to estimate the value of expressions. ● Simplify radicals such as: 1 3 2 , 8, 16, 3 27 ● Perform operations and collect like terms such as: 6( 15+ 6), 27−12, 26+66 ● Evaluate the square roots of small perfect squares and cube roots of small perfect cubes. ● Represent the solutions to equations using square root and cube root symbols. ● Know that in a right triangle a² + b² = c² (the Pythagorean Theorem). ● Explore proofs of the Pythagorean Theorem (for example, by decomposing a square in different ways) and be able to explain a proof of the Pythagorean Theorem. ● Understand and explain a proof of the converse of the Pythagorean Theorem. ● Use the Pythagorean Theorem to solve for a missing side of a right triangle given the other two sides. ● Use the Pythagorean Theorem to solve and model problems in real-world and mathematical problems. ● Use the Pythagorean Theorem to solve and model problems involving three-dimensional contexts (cones, diagonals of rectangular prisms, etc.). ● Recognize that applying the Pythagorean Theorem can result in rational and irrational numbers (this could be the frst time students encounter irrational numbers). ● Calculate the distance between two points in a coordinate system using the Pythagorean Theorem.

KEY VOCABULARY

● Square Root ● Irrational Number ● Rational Number

● Pythagorean Theorem ● Hypotenuse

● CubeRoot ● Legs

Unit 6 ASSOCIATIONS IN DATA

PACING

KEY LANGUAGE USES

April 29 - May 14 (13 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 ft a straight line, and informally assess the model ft 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 fnd a line of best ft for a set of bivariate data and predict what a point on the line means in terms of the situation. Language Supports: ● Vocabulary (line of best ft, statistics, scatter plot, bivariate data) DIFFERENTIATION IN ACTION

Skill Building

From Activity 8.2: MLR 8 Discussion Supports. Use this routine to support whole-class discussion. For each response or observation that is shared, ask students to restate and/or revoice what they heard using mathematical language. Consider providing students time to restate what they hear to a partner, before selecting one or two students to share with the class. Ask the original speaker if their peer was accurately able to restate their thinking. Call students' attention to any words or phrases that helped to clarify the original statement.

Extension

From Lesson 8 “Are You Ready for More?” Use one of the suggestions or fnd another set of data that interested you to look for associations between the variables. ● Number of wins vs number of points per game for your favorite sports team in different seasons ● Amount of money grossed vs critic rating for your favorite movies ● Price of a ticket vs stadium capacity for popular bands on tour

After you have collected the data,

1. Create a scatter plot for the data. 2. Are any of the points very far away from the rest of the data? 3. Would a linear model ft the data in your scatter plot? If so, draw it. If not, explain why a line would be a bad ft. 4. Is there an association between the two variables? Explain your reasoning.

RESOURCES

Combine 6.1-6.2 Combine 6.3-6.4 Combine 6.5-6.6

Vocabulary Unit 6 Practice Test Information about Practice Problems

ILLUSTRATIVE MATHEMATICS AND CORE ALIGNMENT

Standard

Section(s)

8.SP.1

6.1, 6.2, 6.3, 6.4, 6.5, 6.6, 6.7, 6.8

8.SP.2

6.4, 6.5, 6.8

8.SP.3

6.6, 6.8

8.SP.4

6.9. 610, 6.11*

Pre-Assessment

Previous Standards with Example Problems

Number on Pre-Assessment

Section

Section

Unfnished Learning Standard

1

6.5

6.2

6.SP.4

2

6.6

6.3

5.G.2

3

6.9

6.6

6.RP.3b

4

6.9

6.9

6.RP.3c

5

6.10

6.10

2.MD.10, 3.MD.3

6

6.10