## EdGems Math

##### v1
###### Usability
Our Review Process

Title ISBN Edition Publisher Year
7th Grade Core Math Annual Online Teacher Subscription 978-1-948860-57-4 EdGems Math, LLC 2018
6th Grade Core Math Annual Online Teacher Subscription 978-1-948860-56-7 EdGems Math, LLC 2018
8th Grade Core Math Annual Online Teacher Subscription 978-1-948860-58-1 EdGems Math, LLC 2018
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### Overall Summary

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for alignment to the CCSSM. In Gateway 1, the instructional materials meet the expectations for focus, and they meet the expectations for coherence. In Gateway 2, the instructional materials meet the expectations for rigor, and they meet the expectations for practice-content connections. Since the materials meet expectations for alignment, they were reviewed for usability in Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for focus and coherence in Gateway 1. The instructional materials meet the expectations for focus by assessing grade-level content and devoting the large majority of class time to major work of the grade. The instructional materials meet expectations for coherence due to being consistent with the progressions in the standards and making connections within the grade.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for not assessing topics before the grade level in which the topic should be introduced. There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials.

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The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for assessing grade-level content.

Each unit includes Form A and Form B Assessments as well as Tiered Assessments Form AT and Form BT, all of which include selected response and constructed response sections. Performance Tasks are also included with each unit. In addition, Gem Challenges are online, standards-based items for use after a standard has been addressed and are located after certain lessons.

• Unit 1, Equations, Online Gem Challenge 1, Problem 1: “Choose the equation that has no solution. 5x - 4 - x = 3x - 4; 5x - (4x+7) = 14x; 12 + 7x = 16 + 11x - 4x; 15 + 5x -4 = 8x + 6 -x
• Unit 2, The Pythagorean Theorem, Form B, Part II, Problem 5: “Kelvin leaves home and walks 5 blocks east and 10 blocks north to the ball park. How far is the ball park from Kelvin’s home if he were to take a direct path? If necessary, round to the nearest tenth.” (8.G.8)
• Unit 5, Systems of Equations, Performance Task: “Jaylee wants to have a mural painted in her bedroom. Two separate artists have given her bids. Artist #1 charges an initial fee of $79.50 plus$1 per square foot. Artist #2 does not have an initial fee and charges $2.50 per square foot. Jaylee wants the mural to cover a wall that is 7 feet by 10 feet. Which artist will be the least expensive for this mural space? Show all work necessary to justify your answer. Which size of mural (in square feet) will be the same cost when painted by either artist? Show all work necessary to justify your answer. Jaylee decides she only wants to spend$120 on the mural from Artist #2. Give one set of dimensions that represent the largest rectangular mural she could get for this price. Use words and/or numbers to show how you determined your answer.” (8.EE.8a, 8.EE.8b, 8.EE.8c)
• Unit 8, Exponent Properties, Form BT, Part II, Problem 4: “Simplify $$(4x^6)^0$$" (8.EE.1)
• Unit 9, Volume, Form A, Part II, Problem 7: “A cylindrical can of soda pop is 12 cm tall and has a diameter of 6 cm. The box for a 12-pack of soda pop has a length of 25 cm, a width of 19 cm and is 12.2 cm tall. The cans are placed in the box in three rows of 4. What is the volume of space that is not used when a 12-pack box of soda pop is full?” (8.G.9)

There are above grade-level assessment items that could be modified or omitted without impact on the underlying structure of the instructional materials. These items include:

• Unit 10, Form A, Part I, Problem 6c and 6d: “For numbers 6a – 6d, use the information in the table below to circle TRUE or FALSE for each statement.” Problems 6c and 6d address conditional frequency. (S-ID.5) “6c. The conditional frequency for carpoolers who own a car is 0.8.” “6d. The conditional frequency for carpoolers who do not own a car is 0.25.”

#### Criterion 1.2: Coherence

Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for devoting the large majority of class time to the major work of the grade. The instructional materials spend approximately 83% of class time on the major work of the grade.

##### Indicator {{'1b' | indicatorName}}
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for spending a majority of instructional time on major work of the grade.

• The number of units devoted to major work of the grade (including assessments and supporting work connected to the major work) is 8 out of 10, which is 80%.
• The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 38 out of 46, which is approximately 83%.
• The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 101 out of 118, which is approximately 86%.

A lesson-level analysis is most representative of the instructional materials because this calculation includes all lessons with connections to major work and is not dependent on pacing suggestions. As a result, approximately 83% of the instructional materials focus on major work of the grade.

#### Criterion 1.3: Coherence

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for being coherent and consistent with the Standards. The instructional materials have supporting work that enhances focus and coherence simultaneously, are consistent with the progressions in the standards, and foster coherence through connections within the grade.

##### Indicator {{'1c' | indicatorName}}
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards and clusters are connected to major standards and clusters of the grade, and lessons address supporting standards while maintaining focus on the major work of the grade. Examples of supporting work being used to support the focus and coherence of the major work of the grade include:

• Lesson 1.4 connects 8.NS.1 and 8.EE.2 as students learn about square root and cube root and apply this knowledge to solve equations with rational exponents. An example is, “The volume of a cube is 512 cubic inches. What is the side length of the cube?”
• Lesson 5.6 connects 8.NS.1 and 8.EE.7 as students convert repeating decimals to rational numbers by solving equations.  Example 3 states, “What is $$0.\overline{83}$$ as a fraction?” The worked out example describes how to set up an equation and solve to convert the repeating decimal into a fraction.”
• Lesson 9.3 connects 8.G.9 and 8.EE.4 as students find the volume of a sphere and must express the volume in scientific notation. An example is, “The equator is an imaginary line on the Earth's surface which divides the Earth into two equal hemispheres. It is approximately 24,901.55 miles long. Assuming the earth is perfectly round, what is the volume of the earth in cubic miles? Write your answer in scientific notation.”
• Lesson 10.3 connects 8.SP.A and 8.EE.B as students create a scatter plot for a given set of data and “a. Find an equation for a line of best fit for the data set. b. Use the equation to predict how many pounds someone will lose if they work out for 40 hours.”
##### Indicator {{'1d' | indicatorName}}
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for EdGems Math Grade 8 partially meet expectations that the amount of content designated for one grade level is viable for one year.

As designed, the instructional materials can be completed in 118-153 days. If teachers followed the pacing guide, and used the minimal amount of days allocated, the materials would not be viable for a full school year. If teachers followed the pacing guide, and used the maximum amount of days allocated, the materials would be viable for a full school year. Considering the variability of instructional days, these materials partially meet expectations that the amount of content designated for one grade level is viable for one year.

The materials include ten units containing 46 lessons. Lessons range in length from one to four days. Each unit includes lessons, assessments, and targeted interventions.

• The Pacing Guide designates 23 lessons as 2-3 days, three lessons as 3-4 days, 19 lessons as 2 days, and one lesson as 3 days leading to a total of 96-122 lesson days.
• 23 lessons = 46 to 69 days
• 3 lessons = 9 to 12 days
• 19 lessons = 38 days
• 1 lesson = 3
• Lesson length is 45-60 minutes.
• The Pacing Guide designates 22-31 days for assessments and targeted review. Each unit has a range of lesson days and a total amount of days including assessments and targeted review. Assessments within each unit include: Exit Cards, Gem Challenges, Performance Tasks, Rich Tasks, Unit Assessments and Tiered Assessments.

Additionally, there is a discrepancy of one day between the number of days the Scope and Sequence suggests and the actual number of days suggested within the materials.

##### Indicator {{'1e' | indicatorName}}
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials for EdGems Math Grade 8 meet expectations for being consistent with the progressions in the Standards. In general, the instructional materials clearly identify content from prior and future grade-levels and use it to support the progressions of the grade-level standards. In addition, the instructional materials give all students extensive work with grade-level problems.

Each Unit Overview describes how the work of the unit is connected to previous grade level work, for example:

• In the Unit 3 Overview, Proportional Relationships, work from prior grades is explicitly stated. “In this unit, students will be introduced to the concept of a function. They will learn how to determine if a relationship is a function by examining a graph or table. Then students will examine a specific type of function formed by a proportional relationship. In CCSS Grade 7, students worked with proportional relationships using graphs, tables, and equations. In Grade 8 CCSS, the students interpret the constant of proportionality (unit rate) as the slope of the graph. In this unit, students will progress from understanding the slope as the unit rate to calculating slope from a graph, a table or two ordered pairs.”

Each Unit Overview includes Learning Progression, and each Learning Progression includes statements identifying what students have learned in earlier grades and what students will learn in future grades, for example:

Unit 7, Unit Overview, In earlier grades, students have…

• Recognized that when two ordered pairs differ only by signs, the locations of the points are related by reflections across one or both axes. (6.NS.6)
• Used facts about angles and side lengths to determine information about polygons. (7.G.2 and 7.G.5)

• Use geometric descriptions of rigid motions to transform figures and to predict the effect of a given rigid motion on a given figure. (G-CO.6)
• Explain how the criteria for triangle congruence (ASA, SAS, and SSS) follow from the definition of congruence in terms of rigid motions. (G-CO.8)

There are multiple opportunities for students to work with grade-level problems. There are exercises contained within each Student Lesson, Explore activity, Student Gem (online activities to provide practice with the content), Online Practice & Gem Challenge (only in some lessons), Exit Card, and Performance Task. For example:

• In Lesson 4.6, students describe the functional relationship between two points (8.F.5). In Exercise 4, students “Choose the best story for each graph. Explain your reasoning.” Students examine a graph that shows a nonlinear relationship between speed and time and choose from: “A. A bus pulls over at a bus stop.” “B. A runner sprints to finish a race.” or “C. A person walks at a constant rate.” In Exercise 9, students “Sketch a graph for each story. Label the x- and y-axes for each situation.” “A person riding a bike is riding at a constant speed and then slows down to stop at a stop sign. Graph time on the x-axis and speed on the y-axis.”

The materials include one example of off grade-level content that is not identified that distracts students from engaging with the grade-level standards:

• Lesson 10.4, Bivariate Data and Frequency Tables, includes conditional frequency (S-ID.5).  For example, Example 2 states, “Use Marsha’s data about flu shots and sickness to answer the questions. a. Find the relative frequencies for the two-way table in Example 1 showing the possible relationship between those who had a flu shot and those who were sick with the flu. b. Explain one observation from the relative frequencies. c. What is the conditional frequency that someone with a flu shot will not get sick?”

Each unit includes a Parent Guide with Connecting Math Concepts, which includes, “Past math topics your child has learned that will be activated in this unit and Future math this unit prepares your child for.” For example, in Unit 2, Pythagorean Theorem, “Past math topics your child has learned that will be activated in this unit; determining if three side lengths can form a triangle; graphing points on a coordinate plane and determined distance between two horizontal or vertical points.” “Future math this unit prepares your child for; understanding that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles; using trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems; using coordinates to compute perimeters of polygons and areas of triangles and rectangles.”

Each Lesson Guide includes Teaching Tips, which often include connections from prior or future grades, for example:

• Lesson 4.4, Linear Equations in Other Forms, connections to future grades, “In Algebra I, students will learn strategies to graph linear equations that are in standard form and point-slope form without converting to slope-intercept form. At Grade 8, students should focus on converting any linear equation into slope-intercept form in order to graph.”
• Lesson 6.1, Alternate Exterior and Interior Angles, connections to prior grades, “The beginning of the lesson reviews angle pairs students have learned in Grade 7 standards. You may have students look at these pairs and share with a partner what they understand about each pair or you may choose to put the terms on the board at the start of the lesson and have students recall the pairs in a group to see how many they remember.”

In each Lesson Guide, Warm Up includes problems noted with prior grade-level standards. For example:

• Lesson 1.3, Concepts and Procedure (7.NS.3), Question 30, Skill: Operations with rational numbers. Find the value of each rational expression:
• a. 3/4 + (− 1/2)
• b. 1-2/5 − (− 1/10)
• c. – 5/6 (− 3/10)
• d. 3-1/3 ÷ 1/5
• e. – 5/8 + (− 1/4)
• f. (3-1/6 )(2-2/5)
• Lesson 5.6, Converting Repeating Decimals to Fractions, Concepts and Procedure (7.NS.2d), Question 12, Skill: Converting decimals to fractions. Write each decimal as a fraction or mixed number in simplest form:
• a. 0.3
• b. 0.6
• c. 0.5
• d. 0.25
• e. 0.15
• f. 1.25

##### Indicator {{'1f' | indicatorName}}
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials for EdGems Grade 8 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

Examples of learning objectives that are visibly shaped by CCSSM cluster headings include:

• The objective of Lesson 1.3, “I can determine if a linear equation in one variable has no solution, one solution or infinitely many solutions” is shaped by 8.EE.C, Analyze and solve linear equations and pairs of simultaneous linear equations.
• The objective of Lesson 2.1, “I can apply the Pythagorean Theorem to solve problems in two and three dimensions,” is shaped by 8.G.B, Understand and apply the Pythagorean Theorem.
• The objective of Lesson 4.3, “I can write a linear equation in slope-intercept form when given information about the line” is shaped by 8.F.A, Define, evaluate, and compare functions.
• The objective of Lesson 7.2, “I can translate an image on a coordinate plane,” is shaped by 8.G.A, Understand congruence and similarity using physical models, transparencies, or geometry software.
• The objective for Lesson 10.1, “I can read, create and describe the associations in scatter plots,” is shaped by 8.SP.A, Investigate patterns of association in bivariate data.

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important, and examples include:

• Lessons 2.1 and 2.2 connect 8.EE.A and 8.G.A as students write and solve equations with integer exponents to find missing side lengths of right triangles using the Pythagorean Theorem.
• Lesson 4.4 connects 8.F.A and 8.EE.B as students use linear equations and rewrite them in slope intercept form.
• Lesson 6.5 connects 8.EE.C and 8.G.A as students write and solve equations to determine unknown angles.
• Lesson 4.3 connects 8.F.B and 8.F.A as students model real-world problems with functions by interpreting the start value and the slope which connects understanding linear equations by describing linear functions and involves comparing different representations of a function.

### Rigor & Mathematical Practices

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for rigor and practice-content connections in Gateway 2. The instructional materials meet the expectations for rigor, and they meet the expectations for practice-content connections.

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor

Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials for EdGems Math Grade 8 meet expectations for reflecting the balances in the standards and helping students meet the standards’ rigorous expectations. The instructional materials attend to conceptual understanding, procedural skill and fluency, applications, and balance among the three aspects of rigor.

##### Indicator {{'2a' | indicatorName}}
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for EdGems Math Grade 8 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials include problems and questions that develop conceptual understanding throughout the grade level. The instructional materials include Teacher Gems and Student Gems which provide links to activities that build conceptual understanding. Explore! activities provide students the opportunity to develop conceptual understanding at the beginning of each new lesson. In addition, Exercises, Online Practice, and Gem Challenges include problems to allow students to independently demonstrate conceptual understanding. Evidence includes:

• Lesson 3.1, Understanding Functions, the Explore! activity develops understanding of functions by building on student knowledge of proportional relationships. (8.F.1) The activity begins with a description of the following situation, “To find the relative age of a dog, some people use the rule of thumb that every year in a dog’s life is equal to seven years in a human’s life. In Steps 1-3, students have the “opportunity to create an equation for a situation, create a table and then graph the function. This connects to work students have done with proportional relationships in Grade 7. Students are introduced to the term “function” at the end of Step 3 and use this understanding to look at two relationships that are not functions and explain why.”
• Lesson 4.5, Introduction to Non-Linear Functions, Teacher Gems include the activity, “Always, Sometimes, Never” which provides students with a statement and asks them, “Decide if the statement in the box is always true, sometimes true, or never true.” Students demonstrate conceptual understanding by providing evidence of why they chose always, sometimes or never. For example, Statement 4: “Use the remainder of the page to provide mathematical evidence that supports your decision. If a function in the form of y = mx + b has a slope of 0, it is linear.” (8.F.3)
• Lesson 4.6, Interpreting Graphs of Functions, students demonstrate conceptual understanding of graphs of functions. An example is in problem 18, “Sketch a graph that is made up of four connected line segments. The graph should include segments that are increasing and others that are decreasing. Write a story that could be modeled by your sketch.” (8.F.5)
• Lesson 6.1, Student Gems, there is a link for an Illustrative Mathematics Task called “Street Intersections.” In this activity, students “apply facts about angles (including congruence of vertical angles and alternate interior angles for parallel lines cut by a transverse) in order to calculate angle measures in the context of a map.” According to the Commentary from the task, “the goal is not to apply congruence of alternate interior angles for parallel lines cut by a transverse: rather it is to explain why this is true, in this particular setting.” (8.G.5)
• Lesson 5.6, Distributive Property, Online Practice, contains questions that require students to demonstrate conceptual understanding of transformations. The directions state, “Use the point T(4, −3). Write the ordered pair for the final location of the given point after completing the transformations in the order listed.” (8.G.3)

##### Indicator {{'2b' | indicatorName}}
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for EdGems Math Grade 8 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The materials include problems and questions that develop procedural skill and fluency and provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. The materials develop procedural skills and fluencies in Student Gems, Lesson Examples, Student Exercises, and Teacher Gems. The materials provide opportunities for students to independently demonstrate procedural skills and fluencies in Proficient, Tiered, and Challenge Practice, Online Practice, Gem Challenges, and Exit Cards. Each unit provides additional practice with procedural skills in the Student Gems. Additional practice activities are specific to the standard(s) in each lesson. Included in each unit are links to: Khan Academy, IXL Practice, and Desmos Practice. Examples of developing procedural skill and fluency include:

• Lesson 5.4, Proficient Practice, students solve systems of equations using elimination, “Solve each system of equations using the elimination method. Check the solution. 1) 3x − 2y = 10 and 7x + 2y = 30” (8.EE.8b)
• Lesson 1.3, students solve linear equations, “Solve each equation. Describe the number of solutions (one, none or infinitely many). 2(x + 7) = 2x + 7” (8.EE.7)
• Lesson 8.3, students practice identifying large numbers by powers of ten in scientific notation with multiple problems. An example is, “Write each number in scientific notation. 0.000058” (8.EE.3)
• Lesson 5.6, Proficient Practice, students practice converting repeating decimals into fractions with multiple problems. An example is, “Convert each repeating decimal into a fraction. 1.5̅” (8.NS.1)
• Lesson 8.1, Multiplication Properties of Exponents, Exit Card, students know and apply properties of exponents, “Simplify. 1. $$5^4 \times 5^3$$, 2. $$(p^3)^2$$, 3. $$(5w)^2$$, 4. $$(4x^5y)(3x^2y^2)$$.” (8.EE.1)

##### Indicator {{'2c' | indicatorName}}
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for EdGems Math Grade 8 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the grade-level mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

The instructional materials include multiple opportunities for students to engage in routine and non-routine application of mathematical skills and knowledge of the grade level. Students engage with materials that support non-routine and routine applications of mathematics in the Explore! activities, Teacher Gems, Performance Tasks, and Rich Tasks. Some of the Student Pages and Proficient, Tiered, and Challenge Practice allow students to engage with problems including real-world contexts and present multiple opportunities for students to independently demonstrate application of grade-level mathematics. Examples include:

• Lesson 4.2, Writing Linear Equations for Graphs, the Explore! activity engages students in real-world application of constructing a function to model a linear relationship between two quantities (8.F.4). “Stacey and Mario like to go to the coffee shop before school. They decided to conduct an experiment to study the rate at which their coffees cool when left untouched on the table. The graph below and right shows the information they gathered.” A graph that models the situation is given.
• Lesson 5.2, Solving Systems by Graphing, Exercises, students solve systems of linear equations by graphing. (8.EE.8) An example in , Exercise 18, “Sarah begins the year with $100 in her savings account. Each week, she spends$8. Martin begins the year with no money saved, but each week he puts $12 into an account. Let x represent the number of weeks since the beginning of the year and y represent the total money in the account.” Students respond to a series of questions and prompts to determine Sarah’s total money, Martin’s total money, graph both equations, determine intersection, and identify real-world meaning. • Unit 8, Exponent Properties, Performance Task, Ribbon for Sale, students independently demonstrate applying operations with numbers expressed in scientific notation (8.EE.4). The task provides the situation, “A fabric store has $$5.5 \times 10^6$$ inches of ribbon in stock.” Multiple situations are provided, for example, “1. How many spools of ribbon are in stock if each spool holds $$1.1 \times 10^2$$ inches of ribbon? Show all work necessary to justify your answer.” • Unit 7, Transformations, Rich Task, Fractals: A Project Resource for 8th Grade Teachers, students apply transformations to create fractal patterns (8.G.A). Students are given images of several fractals and choose one to recreate. Students must answer a series of questions and tasks related to the image recreated. • Unit 2, The Pythagorean Theorem, Rich Task, students apply the Pythagorean Theorem to solve problems (8.G.7). Students determine how far a golfer is away from the hole based on a statement that the announcer in Act 1 makes, along with an aerial image of the golf course with measurements of three different holes that appear at the end of the Act 1 video. ##### Indicator {{'2d' | indicatorName}} Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade. The instructional materials for EdGems Math Grade 8 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present independently throughout the program materials. Examples include: • In Lesson 5.2, Student Lesson, page 118, students develop procedural skill by solving multiple problems involving systems of equations, “Solve each system of equations using the substitution method. 9) x = y − 3 and 5x + 3y = 1” (8.EE.8b) • In Lesson 7.2, Translations, students develop conceptual understanding of translations through visual representations and representing translations on a graph from context. An example is, “Describe the translation from the pre-image to the image.” “Graph the pre-image and the image under the given translation. Label the vertices correctly.” (8.G.3) • In Lesson 5.5, Applications of Linear Systems, Student Lesson Examples, students engage in routine real-world applications of solving linear systems (8.EE.8c). Example 1, “Nai is trying to decide between two different cell phone plans. Plan A charges a flat fee of$22 per month plus $0.10 per minute of phone usage. Plan B charges$0.18 per minute with no flat fee. How many minutes would Nai have to use each month for the cell phone plans to cost the same amount? How much would it cost?”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the materials. Examples include:

• In Lesson 2.2, Applying the Pythagorean Theorem, Teacher Gems, “Climb the Ladder”, students develop procedural skill within an application problem while using the Pythagorean Theorem (8.G.7). The instructions for the Climb the Ladder Activity state, “Climb the Ladder is an activity where students work through four ladders that increase in complexity and depth of knowledge levels for a given standard. A Climb the Ladder works best for standards that reach a variety of depths of knowledge. The first ladder focuses on the basic skills and concepts of the standard. Each ladder is more challenging, reaching higher depths of knowledge than the previous ladders.” In Ladder 1, students must use the Pythagorean Theorem to find the length of a missing side in each right triangle. In Ladder 4, students are applying the Pythagorean Theorem to solve problems: For example, problem 1, “ The diagonal of a square is 12 centimeters. How long is each side of the square? Round to the nearest tenth of a centimeter.”
• In Lesson 7.1, Reflections, students develop conceptual understanding and procedural skills in understanding and describing the effect of reflections on two dimensional figures. (8.G.3) In the Explore! activity, “Mirror, Mirror,” students create reflections using tracing paper (or patty paper) as well as on a grid. This activity allows for students to use prior knowledge about reflections from everyday life and scaffolds into using a coordinate plane.
• In Lesson 5.3, Solving Systems Using Substitution, Student Gems, MARS Activity, students develop procedural skills within an application problem as they create a system of linear equations to represent the cost of two different baseball jerseys. Then students determine the price of a third jersey that has a cost that is between that of the original two jerseys. (8.EE.8c)

#### Criterion 2.2: Math Practices

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials identify the Standards for Mathematical Practice and use them to enrich mathematics content, prompt students to construct viable arguments and analyze the arguments of others, assist teachers in engaging students to construct viable arguments and analyze the arguments of others, and attend to the specialized language of mathematics.

##### Indicator {{'2e' | indicatorName}}
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level.

All 8 MPs are identified throughout the materials. Each lesson includes a Lesson Guide with a section titled, Mathematical Practices - A Closer Look that explains a few of the MPs that will be used within that lesson. The MP is identified and an explanation of how to address the MP within the lesson is provided. At times, the identification is targeted, and gives a specific problem where the MP is included, but often it is broad and provides a general statement of how to include the MP within the lesson.

Examples of MPs that are identified and enrich the mathematical content include:

• Lesson 3.1, Understand Functions, “MP4: Students create or examine a variety of common models (equations, graphs, tables, verbal contexts) in this lesson. Stress the importance of moving between the models as each highlights different information about the relationship.”
• Lesson 5.2, Solving Systems by Graphing, “MP6: Graphing systems of equations to find the point of intersection is not always the most accurate method (other methods will be introduced later in this unit) since the solution may not always be a “nice” number. Explain to students how this makes it important to check their answer by substituting the x- and y-values into the original system.”
• Lesson 9.1, Volume of Cylinders, “MP7: Students should recognize that each single unit of height adds a layer of volume to a cylinder. The area of the base is the first layer and each unit of height is stacked upon the base. Stacks of Petri dishes or coins make good visuals.”
• Lesson 8.3, Scientific Notation, “MP8: Prior to teaching the lesson, give students a variety of numbers (on station cards around the room or small cards in individual packets) that may or may not be in scientific notation. Have them sort the cards into numbers that are in scientific notation and numbers that are not. Have them explain their thinking to a partner and come up with a definition of scientific notation.”
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Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for EdGems Math Grade 8 partially meet expectations for carefully attending to the full meaning of each practice standard.

The materials do not attend to the full meaning of MP5. Throughout the materials students use tools, however, specific tools are selected for the students to use without an opportunity to choose appropriate tools strategically. Examples include:

• MP5: In Lesson 2.2, Applying the Pythagorean Theorem, the Lesson Guide instructs teachers to, “show students how to draw a diagram from a word problem.” This is an example of not attending to the full practice as students are shown how to draw the model. Students do not choose the appropriate tool to solve the problem.
• MP5: Lesson 7.2, Translations, describes MP5 as “Students should be encouraged to use graph paper to verify their thinking as often as necessary. Some students find it easy to determine where a point will end up following a translation where others will need to “see” it happen on graph paper by counting out the movement. Do not discourage the latter.” This description has the teacher providing a specific tool for the students to use.
• MP5: Lesson 8.2, Division Properties of Exponents, describe MP5 as “While students can use calculators to simplify expressions with only numerical values, they must conceptually understand the properties to simplify expressions with variables. Pencil and paper then becomes the most appropriate tool.” This description gives a specific tool for students to use when working on the content.

Examples of the instructional materials attending to the full meaning of the MPs include:

• MP2: Lesson 3.3, Calculating Slope from Graphs, Teacher Guide, describes how finding the slope requires students to reason in both an abstract and quantitative way, “Students must reason both quantitatively and abstractly when finding slope. Lines that have a positive or negative slope can be calculated quantitatively. Lines with 0 or an undefined slope are more abstract to students and may require more time and explanation.”
• MP4: Lesson 1.2, Solving Multi-Step Equations, Problem 19, “Ramona has $800 in her bank account and plans to take$40 out each week. Xavier has $310 in his account and plans to add$30 each week. After how many weeks will Ramona and Xavier have the same amount in their accounts? Use numbers, symbols and/or words to show how you determined your answer.” Students use the content to model how it fits into a real-world example.
• MP7: In Lesson 1.4 Square Roots and Cube Roots, Explore! Activity, students use the structure of the area of squares to make generalizations related to perfect squares and perfect cubes.
• MP8: In Lesson 4.5, Introduction to Non-Linear Functions, “Many students extend their reasoning of equations to the conclusion that any equation, when graphed, forms a line. This lesson gives students experiences working with non-linear functions and helps them understand that this conclusion should not have been made.” This description provides the teacher with tips on encouraging students to use repeated reasoning to connect prior content to what is being learned.
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Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
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Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Examples of the student materials prompting students to construct viable arguments and/or analyze the arguments of others include:

• One of the Teacher Gems activities is called “Always, Sometimes, Never.” The instructions for this type of activity state, “Always, Sometimes, Never is best used with concepts that allow for situations that create exceptions to the “rule” or require students to understand subcategories to fully understand the standard. Students are given the opportunity to create evidence to support whether a statement is always true, sometimes true or never true.” For example, in Lesson 1.2, Square Roots and Cube Roots, the student directions for the Always, Sometimes, Never Activity state, “Decide if the statement in the box below is always true, sometimes true, or never true. Use the remainder of the page to provide mathematical evidence that supports your decision. Statement #1: A decimal is a rational number.”
• In Lesson 2.1, The Pythagorean Theorem, Exercise 27, students solve the problem and construct an argument to explain their reasoning. “Julio leaned a ladder against the tree his clubhouse was built around. The ladder was 8.5 feet long. It leaned against the tree 7.5 feet off the ground. Julio placed the base of the ladder 4 feet from the trunk of the tree. Does the tree make a right angle with the ground? Explain your reasoning.”
• The Unit 8, Exponent Properties, Student Gem from Math Assessment Project, students create a viable argument on how to use different strategies to determine how much money will be made, “For this task, students need to calculate, using exponents, how much would be made through an email money-making scheme. They also need to provide one reason why this type of scheme could go wrong.”
• Lesson 1.1, Solving One- and Two-Step Equations, exercise 24: “Jordin solved three problems incorrectly. Describe the error she made in each problem; then find the correct answers.” (There are pictures of three two-step equations and incorrect worked out solutions to accompany the problem). Students analyze the errors of another student and provide correct answers.
• In Lesson 3.3, Calculating Slope from Graphs, Problem 23, students analyze mathematical reasoning of another person and constructing a viable argument of where he made an error and how to fix it. “Owen incorrectly found the slope of the line on the graph at the right. He said the slope of the line is 23. Explain what he did wrong and give the correct slope.”
• In Lesson 5.1, Parallel, Intersecting, or the Same Line, Exercise 19, students must analyze student work, critique it, and fix the mistake to find the correct solution. Exercise 19: “On her Unit 5 Test, Victoria was asked to give an example of two lines that are parallel but not the same line. She answered with the equations, y = 4x + 5 and y = 3x + 5. Did she get the question right? If not, what mistake did she make?”
• In Lesson 5.4, Solving Systems using Elimination, Problem 22, students analyze others reasoning and construct a viable argument on how one strategy may be more efficient than another:  “Nicolette likes to solve systems of equations using substitution rather than elimination. Her teacher gave her the system of equations below. Explain to Nicolette why solving this system using elimination may be easier than using substitution.”
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Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. The Teacher/Lesson Guide and Teacher Gems within most lessons support teachers to engage students in constructing viable arguments and analyzing the reasoning of others. Examples include:

• In Lesson 1.6, Simplifying Roots, Teacher/Lesson Guide, teachers support students to analyze the reasoning of others and justify their thinking. “Exercise 18 can be used as a small group discussion item prior to releasing students to independent work time or a Teacher Gem activity. Have students locate the error and describe her error in thinking.”
• In Lesson 2.3, Distance on the Coordinate Plane, Teacher/Lesson Guide, teachers group students in pairs to work towards a solution and justify their answers. Students exchange papers with another partner pair to critique the reasoning of others.
• In Lesson 3.1, Understanding Functions, Teacher/Lesson Guide, teachers support students to construct a viable argument and critique the reasoning of others. “Use Exercise 11 to give students an opportunity to construct a viable argument to support their response. Have students partner with a peer and critique each other’s reasoning to come up with the best possible argument as a pair."
• In Lesson 6.3, Angle Sum of a Triangle, Teacher/Lesson Guide, teachers engage students in constructing a viable argument using the Explore! Activity. “In the Explore! students work through the steps to make a conjecture in Step 4. In Step 5 students share their conjectures and listen to the reasoning of others to determine if their conjecture is correct.”
• In Lesson 8.2, Division Property of Exponents, Teacher Gem, Categories, teachers support students to conduct viable arguments. “Once sharing has been done informally in groups and through the use of the observers, the teacher may choose to ask students to share out what categories they created and how they knew what went in each category. Choosing a specific card and asking students which of their categories they would put it in and why allows students to construct arguments and attend to precision.”
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Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols. Throughout the materials, precise terminology is used to describe mathematical concepts, and each lesson includes a visual lesson presentation. In most of the lesson presentations, there is at least one slide dedicated to explicit teaching of vocabulary. The Teacher/Lesson Guide, Student Lesson, and Parent Guide all contain information about mathematical language. Examples include:

• In the Student Lessons, the font for vocabulary words is red and a definition is included.
• Each unit includes a Parent Guide which contains “Important Vocabulary” related to the unit.
• In Lesson 1.2, Solving Multi-Step Equations, the Lesson Presentation includes a slide to introduce vocabulary from the lesson and provide mathematical definitions. “Algebraic Expression - An expression that contains numbers, operations and variables. Term - A number or the product of a number and a variable in an algebraic expression; a number in a sequence. Constant - A term that has no variable. Coefficient - The number multiplied by a variable in a term.”
• In Lesson 2.1, The Pythagorean Theorem, the Lesson Presentation includes a slide to introduce vocabulary from the lesson and provide mathematical definitions. “Hypotenuse - The side opposite the right angle in a right triangle. Legs - The two sides of a right triangle that form a right angle. Pythagorean Theorem - In a right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse.”
• Lesson 3.2, Proportional Relationships, Teacher/Lesson Guide, Teaching Tips includes information about mathematical language. “It is important to connect the idea that the rate of a proportional relationship is also called the constant of proportionality or unit rate. This rate will also be called the slope in the next lesson.”
• In Lesson 5.4, Solving Systems Using Elimination, students use precise mathematical terminology. “As students discuss systems of equations, reinforce the use of vocabulary. Have students describe systems using words such as “coefficient”, “equivalent equations” and “solution”. "
• In Lesson 6.2, Corresponding and Same-Side Interior Angles, students use correct names for angle pairs. “Emphasize the names for the angle pairs when working through the examples and listen to be sure students are using the correct names.”
• Lesson 10.1, Scatter Plots and Associations, Teacher/Lesson Guide, Explore! Summary and Suggestions includes opportunities for students to reinforce new vocabulary terms. “Learn Those Terms” is an Explore! activity focused on vocabulary acquisition. Students are given a variety of scatter plots and must use each term from a word bank one time in the activity to correctly fill in the blanks. Students are encouraged in the instructions of the activity to use their textbook, glossary, and online resources to look up the terms with which they are unfamiliar.

### Usability

##### Gateway 3
Meets Expectations

#### Criterion 3.1: Use & Design

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have a design that is intentional and not haphazard, have variety in what students are asked to produce, and have manipulatives that are faithful representations of the mathematical objects they represent.

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The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.

The instructional materials for EdGems Math Grade 8 meet the expectations for distinguishing between problems and exercises. Each Unit presents lessons with a consistent structure. The instructional sections, which vary by day, include: Warm-Up, Introduction to lesson using Lesson Presentation, Explore! Activity, and Focused Assignment or Online Practice.

Within the Teacher/Lesson Guide, the student work is referred to as exercises, activities, and independent student practice. Examples include:

• In Lesson 9.2, Volume of Cones, Teacher/Lesson Guide, the lesson planning suggestion states, “This lesson may take 2-3 class periods (45-60 minutes per period). A suggested order for covering the content in this lesson in two days is below. Additional time may be given to use more Teacher Gem activities or independent student practice. Day 1: Explore! Activity: “Cones in a Cylinder”, Lesson Presentation, Exit Card (use to assign leveled practice), Leveled worksheet assignment Day 2: Focused Assignment or Online Practice, Teacher Gem Activity (8.G.9 Relay).”

Within the Student Lessons throughout the materials, multiple examples are provided to show the steps to take when working with the content. The students then practice the content out of context before working with the content in story problems within context. Examples include:

• In Lesson 5.3, Solving Systems by Substitution, Student Lesson, students learn the content by solving problems without context and apply the content in real-world contexts. “In each pair, identify the equation that has an isolated variable. State which variable is isolated. 1. Equation 1 3x − 5y = 10; Equation 2 x = 4 − 4y.” Near the conclusion of the problems, students evaluate the reasoning of others. “Problem 23. Aiden solved a system of equations using substitution. He stated that his solution was x = 7. Francis said something seemed wrong about the solution because it was not a point on a graph but just an x-value. Do you think Aiden’s solution is complete? If not, what else does he need to do?”
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Design of assignments is not haphazard: exercises are given in intentional sequences.

The instructional materials for EdGems Math Grade 8 meet the expectations that the design of assignments is intentional and not haphazard. Overall, lessons are sequenced so students develop an understanding of mathematical concepts and skills. The structure of the lessons provides students with the opportunity to activate prior learning, build procedural skills, and engage with multiple activities that increase in complexity, utilizing concrete and abstract representations.

In each Teacher/Lesson Guide, there are Lesson Planning Suggestions. These suggestions sequence the content in an order to help students develop understanding. For example, in Lesson 5.2, Solving Systems by Graphing, Lesson Planning Suggestions builds from guided practice to more abstract and contextual work with the content, “This lesson may take two class periods (45-60 minutes per period). A suggested order for covering the content in this lesson is below.”

Day 1:

• Explore! Activity - serves to motivate and set the stage for students to learn new material and persevere through a related mathematical task.
• Lesson Presentation - opportunities for students to learn and practice new mathematics
• Leveled worksheet assignment - support students in developing independent mastery of the current lessons as well as reviewing material from previous lessons.

Day 2:

• Exit Card-formative assessment opportunity after instruction
• Teacher Gem Activity-opportunities for students to learn and practice new mathematics
• Focused Assignment or Online Practice-support students in developing independent mastery of the current lessons as well as reviewing material from previous lessons.
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There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.

The instructional materials for EdGems Math Grade 8 meet the expectations for having a variety in what students are asked to produce. In the practice pages, students develop concepts and skills by answering multiple questions on the content. An example is:

• In Lesson 1.1, Solving One- and Two-Step Equations, Proficient Practice, students solve equations through multiple examples, “Solve each equation. 1. y + 4/5 = 1 2/5, 2. 4x = 28, 3. p − 83 = 129”

Students connect content to real-world situations through the Student Gems, linked resources from Open Educational online sites. An example is:

• In Unit 5, Systems of Equations, Student Gem from PBS LearningMedia, students use the content of systems of equations to work out a problem that has a real-world connection. Summary (from the website): "Use mathematics to determine what is required to beat world champion Usain Bolt in a 200-meter race. This video focuses on systems of equations that are visualized by completing a table of values and looking for a point of intersection in a set of line graphs.”

With the Teacher Gems, students create arguments and justify their answers. An example is:

• In Lesson 8.2, Division Property of Exponents, Teacher Gem: Partner Math, students solve problems involving the Division Property of Exponents, they justify their answers to others to compare work, “4. Once the students have a new partner, they need to compare answers from the previous two tasks. If they agree, they sign their initials in the circle connecting the two task boxes. If students disagree, they work to determine who is correct prior to signing. Once students compare, the teacher should have posted what the next two tasks are and they work with this partner to complete the next two tasks.”
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Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.

The instructional materials reviewed for EdGems Math Grade 8 meet expectations for having manipulatives that are faithful representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

• The series does not often incorporate the use of manipulatives, but when they are included, manipulatives are consistently aligned to the content in the standards. An example is located in , In Lesson 1.1, Solving One and Two-step Equations: “‘Algebra Tile Modeling’ is an activity that uses algebra tiles to help students create conceptual understanding of the equation solving process. Algebra tiles can be purchased or made from card stock. In this activity, students use the concept of zero pairs to remove positive or negative tiles, and students work in partner sets with one equation mat between them. One student can be responsible for manipulating the tiles on the board while the other records on the Explore! activity sheet. Student pairs share out Step 6 with the class to wrap up the activity.”
• Examples of manipulatives include: Algebra tiles, grid paper, rulers, patty paper/tracing paper, cylinders and cones, protractor, and x-y tables.
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The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

The instructional materials for EdGems Math Grade 8 are not distracting or chaotic and support students in engaging thoughtfully with the subject. The entire series, both print and digital, follows a consistent format, which promotes familiarity with the materials and makes finding specific sections more efficient. The page layout in the materials is user-friendly.

The interface for each digital lesson is the same for the teacher. It includes the “Teacher/Lesson Guide, Student Lesson, Explore!, Teacher Gems, Student Gems, Online Practice & Gem Challenges, Online Class Results, Exit Card, Proficient Practice, Tiered Practice, Challenge Practice, Answer Keys, eBook, Student Lesson in Spanish and Power-Point Lessons”.

The Student Lesson is organized the same for each lesson. It includes an introduction of the concept, Examples with Solutions, Exercises, and Review.  An example is:

• In Lesson 4.2, Writing Linear Equations for Graphs, the Student Lesson begins with, “A linear equation can be written for a specific line if you know the slope and y-intercept. The y-intercept can be determined by locating the point (0, b) where the graph crosses the y-axis. The slope must be calculated using a slope triangle or the slope formula. When dealing with graphs representing real-world situations, the y-intercept represents the initial value and the slope is the rate of change.” Then there are three examples with solutions, 21 Exercise items, and three Review items.

#### Criterion 3.2: Teacher Planning

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.

The instructional materials for EdGems Math Grade 8 partially meet expectations for supporting teacher learning and understanding of the standards. The instructional materials provide quality questions to help guide students’ mathematical development, contain ample and useful annotations and suggestions on how to present the content, and explain the role of the grade-level mathematics in the context of the overall mathematics curriculum. The instructional materials do not contain adult-level explanations so that teachers can improve their own knowledge of the subject.

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Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing quality questions to help guide students’ mathematical development. There is a Communication Prompt in every lesson that provides questions to help guide students’ mathematical development. Examples include:

• In Lesson 2.3, Distance on the Coordinate Plane, Communication Prompt, “What process would you use to find the distance between (2, 7) and (4, 10)?”
• In Lesson 9.3, Volume of Spheres, Communication Prompt, “Why are volumes that use 3.14 for $$\pi$$  approximations? How could a solution be more exact?”

Questions are also located in the Mathematical Practice section, but these questions are not located in every lesson. Examples include:

• In Lesson 1.3, Solutions to Linear Equations, Mathematical Practices - A Closer Look, “MP1: After the Explore! activity, have students look at three equations written on the board (i.e., x = 2, 4 = 4 and 5 = 7). Ask students which statement is never true, always true or sometimes true. This will reinforce making sense of the types of solutions that arise from different situations.”
• In Lesson 4.2, Writing Linear Equations for Graphs, Mathematical Practices - A Closer Look, “MP2: Each time students find the slope or y-intercept of a graph for a real-world scenario, ask “What is the real-world meaning of ____?”
##### Indicator {{'3g' | indicatorName}}
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.

The instructional materials for EdGems Math Grade 8 meet the expectations for containing ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials.  Examples include:

• In the Unit Overview, there is information provided to help teachers understand the materials in order to present the content. The Unit Overview provides a brief overview of the content contained within the unit. It also includes standards, learning progression, pacing, and assessments contained within the unit.
• The Student Gems contain links to outside technology-enhanced activities. These contain instructions for students, but there is no guidance for the teacher as to when to use these activities to enhance student learning.
• Explore! Summary and Suggestions provides details about the Explore! Activity and suggestions for how it can be implemented. For example, in Lesson 2.1, The Pythagorean Theorem, “A Rule for Right Triangles” is made up of two parts. In Part I, students draw right triangles and measure side lengths. Students then use these triangles to look for a relationship between the squares of the side lengths and the square of the length of the hypotenuse. Students work in partners or small groups and then share out as a full class what they observe about the relationship of the side lengths (as prompted in Steps 6-7).
• Mathematical Practices - A Closer Look, contains information related to each Mathematical Practice contained in the lesson and suggestions for teachers. An example in Lesson 3.3 Calculating Slope from Graphs states, “MP4: In this lesson, students learn a method to create a model (graph) of a table of values or two points. They then use this model to find the slope using a slope triangle. Students should be encouraged to fall back on this visual method of finding slope even after they learn to use the slope formula in Lesson 3.4.”
• There are Extra Examples found in each of the lessons for teachers to present if needed.
• Teaching Tips provide teachers with suggestions for teaching the content within the lesson. For example, in Lesson 5.5, Applications of Systems of Equations, Teaching Tip states, “This lesson may be difficult for many students. Each system is different than the last which means that students will not have the repetition that many are used to with many mathematics topics.”
##### Indicator {{'3h' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

The instructional materials for EdGems Math Grade 8 do not meet the expectations for containing adult-level explanations so that teachers can improve their own knowledge of the subject. The materials do not include explanations and examples of the mathematics that are not designed to be used with students, explanations and examples that build teacher understanding of content, or explanations and examples for teachers of mathematical concepts that extend beyond the course.

##### Indicator {{'3i' | indicatorName}}
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.

The instructional materials for EdGems Math Grade 8 meet the expectations for explaining the role of the grade-level mathematics in the context of the overall mathematics curriculum.

The materials provide information that explains the progression of the content across multiple grades and within the series itself. Each Unit Overview includes Learning Progression which includes concepts and skills that students have experienced in the past and ones that they will experience in the future. For example in Unit 8, Angle Relationships, the Learning Progressions contain:

• Solved problems involving scale drawings of geometric figures. (7.G.1)
• Drawn geometric shapes with given conditions with a focus on constructing triangles from three measures of angles or sides, noticing when the conditions determine a unique triangle, more than one triangle, or no triangle. (7.G.2)
• Used facts about supplementary, complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations for an unknown angle in a figure. (7.G.5)

• Prove theorems about lines and angles. (G-CO.9)
• Prove theorems about triangles. (G-CO.10)
• Use the properties of similarity transformations to establish the AA criterion for two triangles to be similar. (G-SRT.3)”
##### Indicator {{'3j' | indicatorName}}
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).

The instructional materials for EdGems Math Grade 8 provide a list of lessons in the Teacher  Edition, cross-­referencing the standards addressed, and a pacing guide.

There is clear documentation that provides lesson alignment to the standards and estimated instructional time for lessons. Each Teacher Unit Page includes a Pacing Guide & Correlations which contains a Scope and Sequence that specifies CCSS Alignment, Recommended Lesson Pacing, and Recommended Unit Pacing. It also has a Standards Alignment that lists all the grade-level standards and indicates which lessons address each standard. Also, “Standards Correlation by Lesson” contains a table that lists each lesson with the CCSS Alignment.

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Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

The instructional materials for EdGems Math Grade 8 include strategies for parents or caregivers to support their students' progress and achievement.

The materials include a Parent Guide in each unit that contains information about the content and vocabulary in the unit, as well as a table that contains “Past math topics your child has learned that will be activated in this unit” and “Future math this unit prepares your child for.”

The Parent Guide also has, “How You Can Help at Home,” that provides ways parents can support student achievement. Examples in Unit 1 include:

• Discuss situations where there is an unknown amount and talk about how an equation may be able to be written to represent the situation.
• Check solutions to equations by substituting back into the original equation.
• Continue to work on fluency with integers as well as fraction and decimal operations.
• Make a list of perfect squares and perfect cubes for whole numbers 1 to 12.
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Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials for EdGems Math Grade 8 explain instructional strategies and routines in the Teacher Gems Professional Development (PD) Overview, however, there are no sections that include how any of the materials in the resource are research-based. Examples of  instructional strategies include:

• In Unit 5, Teacher Gems PD Overview, MATHO is an activity that can be used when students need motivation to practice a procedural skill. Students complete a set of problems individually and then participate in a BINGO-type activity with their solutions. MATHO works best with items addressing the “recall and reproduce” level of cognition.
• In Unit 10, Teacher Gem PD Overview, Four Corners is used with standards that ask students to represent their learning flexibly with models, expressions, equations, and/or context situations. Students receive one piece of information and must create three other models for that same information.

#### Criterion 3.3: Assessment

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.

The instructional materials for EdGems Math Grade 8 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the standards. The instructional materials provide strategies for teachers to identify and address common student errors and misconceptions, and they have assessments that clearly denote which standards are being emphasized. The instructional materials partially provide strategies for gathering information about students’ prior knowledge, opportunities for ongoing review and practice, with feedback, and assessments that include aligned rubrics and scoring guidelines.

##### Indicator {{'3m' | indicatorName}}
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.

The instructional materials for EdGems Math Grade 8 partially meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels. Evidence includes:

• The Teacher/Lesson Guide in each unit provides suggested Warm-Up problems from the previous lesson. These are found in the Exercise section of the Student page and are usually the last three, four, or five items given.
• The Unit Overview contains two sections that identify prior learning, Previously Learned and Learning Progression. These sections provide overarching information about the mathematical content but do not provide information that is designed for students’ prior knowledge.
##### Indicator {{'3n' | indicatorName}}
Materials provide strategies for teachers to identify and address common student errors and misconceptions.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing strategies for teachers to identify and address common student errors and misconceptions. Each Unit contains a Common Misconceptions document that discusses the common misconceptions for each lesson. This document also provides mathematically sound strategies for the teacher to address student errors. An example is:

• In Lesson 2.1, The Pythagorean Theorem, Common Misconceptions, “When trying to describe the location of the hypotenuse on a right triangle, some students may find the word “opposite” confusing and may not be able to determine where the hypotenuse is located. Teachers may want to diagram this, using an arrow from the right angle to the longest side, and labeling it as the hypotenuse.”
##### Indicator {{'3o' | indicatorName}}
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The instructional materials for EdGems Math Grade 8 partially meet the expectations for providing opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills. The materials include limited support for teachers to provide feedback. Evidence includes:

• Each lesson ends with 3-4 Review questions for ongoing practice in Exercise of the Student Lesson. The Teacher Guide includes which standard is being addressed and a small description of the skill. An example is, "In Lesson 4.3, I can write a linear equation in slope-intercept form when given information about the line, Concepts and Procedure (8.F.4): Problem 22 Skill: Slope".
• Each lesson contains Online Practice, where a student is given the correct answer, if they choose, but feedback is not provided.
• Each lesson contains Gem Challenges. If students choose Gem Challenge 2, they are able to see the problem completed.
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Materials offer ongoing formative and summative assessments:
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Assessments clearly denote which standards are being emphasized.

The instructional materials for EdGems Math Grade 8  meet the expectations that assessments clearly denote which standards are being emphasized.

Standards for the unit are denoted at the unit level in the Unit Overview in the Standards and Recommended Pacing. The unit standards are also noted on the Pacing Guide for each lesson in the unit. The assessments, tiered assessments, and performance tasks indicate which standards are being assessed at the question level. Standards are provided on the Teacher Unit Page with a blue “i” icon for the assessments, tiered assessments, and performance tasks. Standards are noted using the blue “i” icon for Exit Cards on the Lesson pages. The standards are noted on the Unit Overview in the Assessment section for the Gem Challenges.

##### Indicator {{'3p.ii' | indicatorName}}
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

The instructional materials for EdGems Math Grade 8 partially meet the expectations that assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. Evidence includes:

• The assessments do not provide follow-up steps or suggestions for the teacher.
• The Unit Performance Task Rubrics do not suggest Reteach Lessons, but they do provide solutions and reasoning as to why an answer is incorrect.
##### Indicator {{'3q' | indicatorName}}
Materials encourage students to monitor their own progress.

The instructional materials for EdGems Math Grade 8 encourage students to monitor their own progress. The materials include Target Trackers for each unit for students to monitor their progress. The Target Tracker contains the objective from each lesson within the unit with a picture of a thermometer that students can fill in as they progress toward the objective. It also contains a section where students can list “Skills to Improve.”

#### Criterion 3.4: Differentiation

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.

The instructional materials for EdGems Math Grade 8 meet the expectations for supporting teachers in differentiating instruction for diverse learners within and across grades. The instructional materials provide strategies to help teachers sequence or scaffold lessons, strategies for meeting the needs of a range of learners, tasks with multiple entry-points that can be solved using a variety of solution strategies or representations, opportunities for advanced students to investigate mathematics content at greater depth, and a balanced portrayal of various demographic and personal characteristics.

##### Indicator {{'3r' | indicatorName}}
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. Evidence includes:

• Every lesson in the Teacher/Lesson Guide has Teaching Tips which provide information on strategies to use when teaching the concept, manipulatives that might be useful, questions to focus on, and other tips depending on the lesson.
• At the beginning of each unit, Learning Progressions makes connections to both prior and future skills and standards to scaffold instruction.
• Each lesson provides a Warm-up to activate prior knowledge.
• The materials provide three different levels of practice for each lesson (Tiered, Proficient, and Challenge Practice) as well as tiered assessments; however, there are no strategies or instructions for teachers on how to sequence or scaffold these items.
##### Indicator {{'3s' | indicatorName}}
Materials provide teachers with strategies for meeting the needs of a range of learners.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing teachers with strategies for meeting the needs of a range of learners.

Within the materials there are three levels of practice pages: Proficient (on level), Tiered (more focused development), and Challenge (extension). These pages allow for more development of the content knowledge regardless of the level of the students. The material presents different types of questions all related to the content from the lesson. An example is:

• In Lesson 1.2, Solving Multi-Step Equations, Proficient Practice for on-level students has questions focusing on the content, “Solve each equation and check your solution. 1. 3(2x + 4) = 60 2. 5x + 1 = 8x − 23”. The Challenge practice, focused on extension of the concept, includes solving the equations and taking it to the next step of graphing the solution on a number line: “Solve each inequality. Graph the solution on a number line. Research online for tips on solving and graphing linear inequalities. 2. 2f + 4 < 5f − 11”. The Tiered Practice is geared towards students that need more focused help with the content which is done by providing the steps to solving multi-step equations: “TO SOLVE MULTI-STEP EQUATIONS: 1. Simplify by distributing and combining like terms 2. Move all variables to one side of the equation 3. Solve the one- or two-step equation 1. 4(2x + 3) = 36”.
• Assessments and Tiered Assessments are located in each Unit.
##### Indicator {{'3t' | indicatorName}}
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.

The instructional materials for EdGems Math Grade 8 meet the expectations for embedding tasks with multiple entry-points that can be solved using a variety of solution strategies or representations. The materials have Performance Tasks embedded into each unit, and teacher guidance on how to help students solve these problems is limited. Evidence includes:

• Each Unit includes Performance Tasks, some of which include multiple entry-points. Within the Unit Overview, Assessment section, the Performance Tasks (Formative or Summative) for each unit are identified. For example, Unit 6, Triangle Puzzle, allows for students find congruent triangles and explain what makes them congruent.
• Each Lesson has an Explore! task which does include instructions on its use. For example: “In “Mirror, Mirror”, students create reflections using tracing paper (or patty paper) as well as on a grid. This activity allows for students to use common sense about reflections from everyday life and scaffold into using a coordinate plane. Step 5 asks students to discuss if the image and pre-image are congruent. If students were working in smaller groups, you may want to bring the full class together for this discussion.”
##### Indicator {{'3u' | indicatorName}}
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).

The instructional materials for EdGems Math Grade 8 partially meet the expectations for suggesting support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics. All supports given are general statements about ELL students and other special populations. Evidence includes:

• Proficient, Tiered, and Challenge Practices are located in each lesson.
• Assessments and Tiered Assessments are located in each unit.
• There is an ELL Guide that includes unit-based and lesson-based general strategies to assist teachers in meeting the needs of all learners.
##### Indicator {{'3v' | indicatorName}}
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing opportunities for advanced students to investigate mathematics content at greater depth. The materials provide some opportunities for advanced students to investigate the course-level mathematics at a greater depth. Each lesson includes Tiered Practice, Proficient Practice, and Challenge Practice sheets. The Challenge Practice sheets include more comlex problems than the Tiered and Proficient Practice sheets, and the number of problems is comparable.

##### Indicator {{'3w' | indicatorName}}
Materials provide a balanced portrayal of various demographic and personal characteristics.

The instructional materials for EdGems Math Grade 8 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics. Lessons contain a variety of demographic and personal characteristics. Evidence includes:

• Names and wording are chosen with diversity in mind. The materials include various names throughout the problems for example: Juan, Seth, Sherry, Mikayla, Julio, Jaylynn, Kobe, Ebizah, Ginger, Gracin, Kitts, Vadek. The names are used in ways that do not stereotype characters by gender, race, or ethnicity.
• Images portrayed in many student lessons are of fair skinned children. For example, in Lessons: 1.4, 1.6, 2.2, 4.2, 4.5, 6.2, 7.3, the same images are used in both the English and Spanish versions of the Student Lessons.
• One image of a person with a disability was observed. In Lesson 2.1, The Pythagorean Theorem, Problem 8, an image of a person in a wheelchair is used. “According to federal guidelines, wheelchair ramps must be built with a 1-foot vertical rise for every 12 feet of horizontal distance.  a. What is the length of a ramp that rises 1 foot? Round to the nearest hundredth.  b. If Max needs to build a ramp to reach a 2-foot porch, what horizontal distance will it cover?  c. How long will the hypotenuse of Max’s ramp be? Round to the nearest hundredth.”
• When multiple characters are involved in a scenario, they are often doing similar tasks or jobs in ways not expressing gender, race, or ethnic bias, and there is no pattern in one character using more/fewer sophisticated strategies.
##### Indicator {{'3x' | indicatorName}}
Materials provide opportunities for teachers to use a variety of grouping strategies.

The instructional materials reviewed for EdGems Math Grade 8 provide opportunities for teachers to use a variety of grouping strategies. Teacher and Student Gems include various strategies for teachers to group students in multiple lessons. Examples include:

• In Lesson 4.4, Linear Equations In Other Forms, the Teacher Gems activity titled “Partner Math” instructs students to work with one partner.
• In Lesson 8.2, Division Property of Exponents, the Teacher Gems activity titled “Categories”, states that students can be grouped with partners or small groups of students.
• The Teacher Gems include multiple activities such as Always, Sometimes, Never and Climb the Ladder that instructs teachers to either assign partners or work in small groups to complete the activities given.
##### Indicator {{'3y' | indicatorName}}
Materials encourage teachers to draw upon home language and culture to facilitate learning.

The instructional materials reviewed for EdGems Math Grade 8 do not consistently encourage teachers to draw upon home language and culture to facilitate learning. The materials include a PDF booklet, “Strategies for English Language Learners Using EdGems Math”. This is located in the Teacher Unit page of each unit. The materials include a multilingual glossary for ELL students, and all lessons are offered in both English and Spanish. A Parent Guide is found in each unit. However, it is only provided in English, and it addresses only the mathematical concepts included in the upcoming unit and does not incorporate student culture.

#### Criterion 3.5: Technology

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.

The instructional materials for EdGems Math Grade 8 integrate technology, including interactive tools, virtual manipulatives, and dynamic software,  are web-based and compatible with multiple internet browsers, include Gem Challenges with online multiple choice items,  include opportunities for teachers to assign specific elements of a lesson to personalize individual student learning. They do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

##### Indicator {{'3aa' | indicatorName}}
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.

The instructional materials reviewed for EdGems Math Grade 8 are web-based and compatible with multiple internet browsers.

• EdGems Math can be accessed through multiple internet browsers. All features are accessible through all web browsers. Clicking on lesson elements opens new tabs which do not have clear labels attached to them across all web browsers.
• Materials can be accessed from multiple platforms with no loss of content. However, if typing in the address bar, the URL needs to be typed www.edgems.com. If the www is not included, an error message occurs. This is consistent across multiple web browsers and across device types.
• Many of the options in the lessons require downloading of documents onto the mobile device such as, in Lesson 6.4, Congruent and Similar Triangles, the Student Lesson requires a PDF download.
##### Indicator {{'3ab' | indicatorName}}
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.

The instructional materials reviewed for EdGems Math Grade 8 include Gem Challenges with online multiple choice items. However, all unit assessments are PDF only and cannot be completed online. There is also no feature that allows teachers to construct their own assessments.

##### Indicator {{'3ac' | indicatorName}}
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.

The instructional materials reviewed for EdGems Math Grade 8 include opportunities for teachers to assign specific elements of a lesson to personalize individual student learning. No online data analytics are provided for a teacher to use for personalizations. However, teachers can personalize student learning in each student account.

While specific tasks can be assigned to specific students from the materials, the content of the materials cannot be modified for local use.

Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).

The instructional materials reviewed for EdGems Math Grade 8 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

##### Indicator {{'3z' | indicatorName}}
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.

The instructional materials reviewed for EdGems Math Grade 8 integrate technology, including interactive tools, virtual manipulatives, and dynamic software in ways that engage students in the Mathematical Practices. Technology integration is located in Student Gems and Online Practice & Gem Challenge. Examples include:

• Lesson 5.4, Solving Systems Using Elimination, Student Gems includes three Desmos Activities, one Khan Academy video lesson, one IXL task, and one Illustrative Mathematics task.
• Lesson 10.4, Bivariate Data and Frequency Tables, Student Gems includes three Desmos Activities, two Khan Academy video lessons, and one Illustrative Mathematics task.
• All lessons have Online Practice and Gem Challenges included for student use.

## Report Overview

### Summary of Alignment & Usability for EdGems Math | Math

#### Math 6-8

The instructional materials reviewed for EdGems Math Grades 6-8 meet the expectations for alignment to the CCSSM. The instructional materials for Grades 6-8 meet the expectations for focus and coherence in Gateway 1, and they also meet the expectations for rigor and practice-content connections in Gateway 2. The instructional materials for Grades 6-8 also meet the expectations for Usability in Gateway 3.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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