Alignment: Overall Summary

The instructional materials reviewed for EdGems Math Grade 6 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.

See Rating Scale
Understanding Gateways

Alignment

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Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
17
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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Meets Expectations

Not Rated

Gateway 3:

Usability

0
22
31
38
32
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for EdGems Math Grade 6 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.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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Criterion Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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.

Indicator 1a

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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. 

Examples of grade-level assessments include: 

  • Lesson 2.5, Dividing Decimals, Online Gem Challenge 1, Problem 3: “Use the fact 9 x 324 = 2916.” “Find the exact product of 0.9 x 3.24.” (6.NS.3)
  • Unit 3, Percents, Form B, Part II, Problem 10: “Gonzalez bought a new duffle bag that had a price tag of $28.00. He bought it in California which has an 8% sales tax. How much did Gonzalez pay for the duffle bag, including sales tax?”(6.RP.3c)
  • Unit 5, Expressions, Form B, Part I, Problem 2: “Four friends went to dinner. The taxi ride to the restaurant cost $15. Each person ordered a hamburger for $6. Which of the following expressions would calculate the total cost of the outing? Circle all that apply. A. 4×6+15, B. 4(15+6), C. 15+6+6+6+6, D. 4+6+15, E. 4×6×15 ” (6.EE.3)
  • Unit 7, Rational Numbers & the Coordinate Plane, Performance Task, Errand Run, “Lucy ran errands on Saturday. She wanted to create a map on a coordinate plane to illustrate the path she followed. She started at her home which was located at (2, −7). First, she went to the library to return some books. The library was located exactly 6 units north of her home on the map. She then went to the store to buy some milk. The store was located at (−5, −1). Before returning home, she went to the gas station to fill up her tank. The gas station was 6 units south of the store. Then she returned home.” Question 1. “Create a map for Lucy showing the path she traveled.” (6.NS.8) Question 2. “What shape best describes the shape that was formed by her path? Explain your answer.” (6.G.3) Question 3. “If each unit on the grid represents 0.5 miles, how many miles did she travel in all? Use words and/or numbers to show how you determined your answer.” (6.NS.8)
  • Unit 6, One-Variable Equations, Form A, Part II, Problem 1: “Determine if the number given is the solution of the equation. y + 11 = 17; Is 6 the solution? Explain how you know.” (6.EE.5)

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 8, Form A, Part I, Problem 6: “Which of the graphs below show the equation ???? = 2x + 3?” Students find an equation in the form of y = mx + b from a line on a coordinate grid. (8.F.1,3)
  • Unit 8, Form A, Part II, Problems 7 and 8: “Graph each equation. 7. y = 1 + 3x and 8. y = = 12 − 2x.” (8.F.1,3)
  • Unit 3, Form A, Part II, Problems 12: “A scooter was originally priced $300. It went on sale for 20% off. It was still not selling so it was discounted an additional 20% off the sale price. Jules bought the scooter. How much did Jules pay for the scooter?” (7.RP.3)
  • Unit 3, Tiered Assessment, Problem 10: “A purse costs $100. It went on sale for 40% off. Since it was still not selling, the store marked it down an additional 10% off the sale price. How much will the purse cost after the additional mark-down?” (7.RP.3)

Criterion 1b

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.
4/4
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Criterion Rating Details

The instructional materials reviewed for EdGems Math Grade 6 meet expectations for devoting the large majority of class time to the major work of the grade. The instructional materials spend approximately 69% of class time on the major work of the grade.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 6 out of 10, which is 60%.
  • The number of lessons devoted to major work of the grade (including supporting work connected to the major work) is 30.5 out of 49, which is approximately 62%.
  • The approximate number of days devoted to major work (including assessments and supporting work connected to the major work) is 103 out of 150, which is approximately 69%. 

A day-level analysis is most representative of the instructional materials because this perspective includes all connections to major work and follows the recommended pacing suggestions for addressing major work. As a result, approximately 69% of the instructional materials focus on major work of the grade.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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Criterion Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 6.NS.3 with 6.RP.3 as students divide decimals to compare unit rates. For example, “The Rodriguez family filled their car with gas while on vacation. They spent $45.60 and put 16 gallons in their car on Monday. On Friday, they spent $33.48 for 12 gallons of gas. On which day did they spend more per gallon? How much more?”
  • Lesson 5.6 connects 6.NS.4 with 6.EE.3 as students find and use the greatest common factor or least common multiple to factor expressions. For example, “Factor each expression using the greatest common factor. a. 48 + 60  b. 6x − 9.”
  • Lesson 9.1 connects 6.G.1 and 6.RP.3 as students find the area of rectangles and triangles and apply understanding of ratios to solve problems. For example, “Square A has side lengths of 8 inches. The ratio of Square A’s side lengths to Square B’s side lengths is 2:3. What is the area of Square B? Students must apply understanding of ratios to find the missing side length of Square B.”
  • Lesson 9.2 connects 6.EE.2c and 6.G.1 as students substitute a value for a variable in order to determine the dimensions to find the area of a triangle. For example, “The base of a triangle is represented by 2y + 6 and the height represented by 2y + 3. When the value of y is 10, what is the area of the triangle?”

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
1/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 121-160 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 49 lessons. Lessons range in length from one to four days. Each unit includes lessons, assessments, and targeted interventions.

  • The Pacing Guide designates four lessons as 1-2 days, 27 lessons as 2-3 days, one lesson as 3-4 days, one lesson as 2-4 days, 13 lessons as 2 days, and three lessons as 3 days leading to a total of 98 - 132 lesson days.
    • 4 lessons = 4 to 8 days.
    • 27 lessons = 54 to 81 days.
    • 1 lesson = 3 to 4 days.
    • 1 lesson = 2 to 4 days.
    • 13 lessons = 26 days.
    • 3 lessons = 9 days
  • Lesson length is 45-60 minutes.
  • The Pacing Guide designates 23-28 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.

Indicator 1e

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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:

  • The introductory paragraph of the Unit 7 Overview, Rational Numbers and the Coordinate Plane, states, “In this unit, students will be introduced to the rational number system, which includes negative numbers. They will describe situations using positive and negative integers. They will find absolute values and compare rational numbers. Students will graph inequalities on a number line and write inequalities that model real world situations. Students will also be introduced to all four quadrants in the coordinate plane (as they have only graphed in the first quadrant previously). Vertices of quadrilaterals will be graphed on the coordinate plane. Students will use previous knowledge about different types of quadrilaterals to name figures on the coordinate plane and find the ordered pair for a missing vertex.”

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 1: Ratios and Rates, In earlier grades, students have…

  • Interpreted a fraction as a division problem (5.NF.3)
  • Multiplied fractions (5.NF.4-6)
  • Converted measurements (4.MD.1)

In future grades, students will…

  • Compute unit rates with ratios of fractions (7.RP.1)
  • Recognize and represent proportional relationships (7.RP.2/8.EE.5)

In some units, the Unit Overview references connections to current, grade-level work that was addressed in prior units. Examples include:

  • Unit 6, One-Variable Equations, the introductory paragraph includes, “Students will connect their understanding of percents from Unit 3 with the percent equation to find the whole when given the percent and a part.” 
  • Unit 8, Two-Variable Equations, the introductory paragraph includes, “Connections will be made to ratios from Unit 1 and graphing ordered pairs in Unit 7.”

The instructional materials present opportunities for students to engage with grade-level problems 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. There are also additional worksheets in each lesson for Proficient Practice, Tiered Practice, and Challenge Practice. For example:

  • In Lesson 7.5, students have multiple opportunities in the lesson to attend to each part of 6.NS.8. “Plot each set of points on a coordinate plane. Connect the points in the order given and connect the last point to the first point. Name the shape with all terms that apply (parallelogram, rectangle, rhombus, square and/or trapezoid). Exercise 6. (0, 4), (0, 0), (4, 0), and (4, 4).” Exercise 25. “Explain in words how to find the distance between (−4, 5) and (2, 5).”
  • In Lesson 5.2, students, “Find the value of $$7 \times (8 - 5)^2 + 2$$.” During Tiered Practice, Problems 1 - 4, students “Number the operations in the order they should be performed:  _____ Grouping Symbols; _____ ; Addition & Subtraction _____; Multiplication & Division _____ Powers.” Proficient Practice, Problem 9, “Three friends go to the movies. Each ticket costs $7. They also buy popcorn for $6, candy for $4 and a drink for $2. The friends want to split the total cost evenly. Write a numerical expression to represent this situation and determine how much each friend owes.” Challenge Practice: “Insert the operations (×, ÷, +, -) in each box of the numerical expressions to make it equal to the stated amount.” Problem 8, “$$(10^2 \Box 2 \Box 1) \Box (3 \Box 4) = 7$$.” (6.EE.1)

The materials include two examples of off grade-level content that are not identified:

  • In Lesson 3.4, Problem 20, students use proportional relationships to solve multistep ratio and percent problems (7.RP.3). “Elli wants a pair of jeans that were originally priced $44. They were marked down 25% and then an additional 10% of the sale price. How much do the jeans cost now?”
  • In Lesson 8.3, students graph two-variable equations that are above grade level. In Exercise 17, “Graph the equation $$y = 2 + x^2$$” (8.F.3), and in Exercise 19, “Write the linear equation of a line that goes through the points (2, 5) and (4, 13).” (8.F.4)

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 4, Fraction Operations, Parent Guide, “Past math topics your child has learned that will be activated in this unit include finding and interpreting quotients of whole numbers less than 100 and multiplying fractions by whole numbers and fractions by fractions.” “Future math this unit prepares your child for includes applying and extending previous understandings of multiplication and division of fractions to multiply and divide rational numbers and solving equations with rational coefficients.”

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

  • Lesson 1.2, Ratio Tables and Graphs, Teaching Tips section, “Students have graphed points in Grade 5 in the Common Core State Standards but they may need to review how to graph in the first Quadrant of the coordinate plane.” 
  • Lesson 3.2, Percents, Decimals, and Fractions, Teaching Tips section, “In Grade 4 of the Common Core State Standards, students worked with decimal fractions to help them see the connections between the decimal name and the fraction. Use this knowledge to help students see decimals as a ratio compared to a power of ten, with the goal of having the denominator equal 100.”
  • Lesson 7.4, The Coordinate Plane, connections to future grades are stated. “In Grade 6 Common Core State Standards, students are asked to find distances between points that have the same x-coordinate or the same y-coordinate. In Grade 8 standards, students find distances between points that do not fall on the same horizontal or vertical line using the Pythagorean Theorem.”

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

  • Lesson 3.1, Introducing Percents, Concepts and Procedure (4.NF.1), Question 27, Skill: Simplify each fraction.
    • a. 25/100 
    • b. 60/100
    • c. 84/100
    • d. 28/100
    • e. 54/100
    • f. 76/100
  • Lesson 8.1, Input-Output Tables, Concepts and Procedure (3.OA.9), Question 26, Skill: Describe the operation used to calculate the next term in each list of numbers. Give the next two numbers in the list.
    • a. 1, 4, 7, 10, _____, _____ 
    • b. 40, 35, 30, 25, _____, _____
    • c. 4-2/5 , 4, 3-3/5 , 3-1/5, ______, _____
    • d. 2.4, 4, 5.6, 7.2, _____, _____

Indicator 1f

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Grade 6 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 2.5, “I can find quotients of expressions involving decimals,” is shaped by 6.NS.B, Compute fluently with multi-digit numbers and find common factors and multiples.
  • The objective of Lesson 4.3, “I can find quotients of expressions involving two fractions,” is shaped by 6.NS.A, Apply and extend previous understandings of multiplication and division to divide fractions by fractions.
  • The objective of Lesson 9.5, “I can find the volume of rectangular prisms,” is shaped by 6.G.A, Solve real-world and mathematical problems involving area, surface area, and volume.

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. Examples include:

  • Lessons 5.3, 5.4, 5.5, and 5.6 connect 6.EE.A and 6.EE.B as students translate mathematical statements to write expressions using variables.
  • Lesson 6.3 connects 6.EE.B with 6.NS.A as students write and solve equations using rational numbers requiring a fraction divided by a fraction. 
  • Lesson 7.3 connects 6.NS.C and 6.EE.B as students write and graph inequalities.
  • Lesson 7.5 connects 6.G.A with 6.NS.B as students use properties of quadrilaterals to find missing points in figures on a coordinate plane. For example, “Three of the four vertices of a square are at (4, 6), (2, 6) and (2, 4). What are the coordinates of the missing vertex?”
  • Lesson 9.1 connects 6.G.A with 6.NS.B as students find the area of rectangles and triangles by multiplying multi-digit decimals.
  • Lesson 10.7 connects 6.SP.B and 6.NS.B as students find absolute mean deviation involving decimal numbers.

Gateway Two

Rigor & Mathematical Practices

Meets Expectations

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Gateway Two Details

The instructional materials reviewed for EdGems Math Grade 6 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.

Criterion 2a - 2d

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.
8/8
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Criterion Rating Details

The instructional materials for EdGems Math Grade 6 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

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 1.2, Ratio Tables and Graphs, Teacher Gems includes the activity, Always, Sometimes, Never. “Decide if the statement in the box is always true, sometimes true, or never true.” Students provide conceptual evidence to support statements about ratio relationships, ratio tables, equivalent ratios, and graphing ratios. (6.RP.3a,d)
  • Lesson 3.1, Introducing Percents, the Explore! activity develops conceptual understanding of percents through the use of a 10 x 10 grid. Students shade the grid to represent decimals, fractions, and percents. (6.RP.3c)
  • Lesson 4.2, Dividing Fractions with Models, the Explore! activity develops conceptual understanding of fraction division by having students make connections between arithmetic expressions and multiple different visual representations. Students use these connections to solve fractional division problems. (6.NS.1)
  • Lesson 8.1, Input-Output Tables, the Explore! activity builds conceptual understanding of independent and dependent variables by having students read a description, underline the quantity that is independent of the other quantity, choose one of the descriptions, and create a table of values. This provides the student with the opportunity to analyze and test values within tables to determine output with a given input. (6.EE.9)

Indicator 2b

Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 2.1, Exit Card, students build fluency in adding and subtracting decimals with multiple examples; “Find the value of: 1. 3.4 – 1.9 , 2. 52.93 + 31.4” (6.NS.3).
  • Lesson 2.4, Gem Challenge 1, students find the exact quotient for several problems (6.NS.2). For example, Question 1, “Divide 19,008 ÷ 32. Find the exact quotient.” Online Practice, Question 4 states, “What is the remainder on the quotient of 1,743 divided by 11?”
  • In Lesson 2.4, Dividing by Multi-Digit Numbers, students develop the procedural skill of dividing multi-digit numbers with multiple problems. For example, Proficient Practice, Problem 12, “Charlie had 150 feet of wire. If he cut the wire into 12 equal pieces, how long was each piece of wire?” (6.NS.2)
  • In Lesson 5.3, Variables and Expressions, Student Gems link to Khan Academy Quiz: "Write an expression to represent: The sum of ten and the quotient of a number x and 6”. Students are provided multiple practice problems to develop procedural skills. (6.EE.2a)
  • Lesson 5.1, Teacher Gems, the activity, “Matho” includes nine numerical expressions that include exponents. The students evaluate the expressions to determine if their expressions match the numbers called in a bingo-like activity. (6.EE.1)

Indicator 2c

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
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 1.4, Comparing Rates, the Explore! Activity, students apply ratio and rate reasoning in real-world problems. (6.RP.3) “Kimiko has two summer job options. She has a daily babysitting job she could do where she gets paid the same hourly rate for each hour she babysits. For a 3 hour babysitting job, she earns $21. She also has the option of helping in her mother’s laundromat. Her mom pays her $64 for every 8 hours she works.” Students complete ratio tables for each job and solve problems about the situation.
  • Lesson 4.3, Dividing Fractions, Student Lesson, students apply dividing fractions in real-world examples (6.NS.1). “Shiloh drives 3/4 mile to school each day. There is a stop sign every 3/8 mile. How many stop signs will she pass on her way to school?” 
  • Lesson 9.3, Area of Composite Figures, Explore! activity, students apply finding area of special polygons in real-world situations. (6.G.1) “Kienan worked for a landscaping company. He was assigned to determine how much bark was needed to put in the kids’ play area at a new park. He was given the blueprint of the polygonal play area. Some dimensions were given on the drawing and others were not. Step 1: Determine the area of the entire play area. Show your method for calculating the area and show all needed dimensions, if not given.” 
  • In Lesson 6.2, Solving Addition and Subtraction Equations, Proficient Practice, students independently apply solving equations with rational numbers in a real-world example, “At the market, Sydni puts a few pears in a bag then weighs the bag on a produce scale. The bag of pears weighs 4.75 pounds. She adds more pears to the bag. The new weight of the bag is 5.6 pounds. Write and solve an addition equation to find the weight of the pears added to the bag.” (6.EE.7)

Indicator 2d

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 5.1, Powers & Exponents, students build fluency in writing exponents. For example, Student Lesson, “Write the numerical expression as a power. 3 × 3 × 3 × 3 × 3", students practice this skill with multiple problems including decimal numbers and fractions. (6.EE.1)
  • In Lesson 5.5, Equivalent Expressions, Example 1, students demonstrate conceptual understanding by using a visual representation of a table to compare and test expressions to determine if they are equivalent. Students are instructed to, “Show that 2x + 5 and x + 3 + x + 2 are equivalent expressions. Create a table of values to test different input values.” (6.EE.4) 
  • In Lesson 7.3, Inequalities, Teacher Gems Station activity, students write inequalities to represent real-world situations and work with non-routine problems (6.EE.8). The Stations activity includes tasks that students engage with as they move from station to station. One example included is Station 1: “Write an inequality for the statement: The amount of money Jacob has in his bank account, m, is more than $300.” Station 3: “Write an inequality for the statement: The amount of time Ronnie practices guitar, g, is less than 15 hours a week.” Station A: “Describe a situation modeled by the inequality: x < 15.”

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 1.2, Ratio Tables and Graphs, students develop conceptual understanding within an application problem. In Question 7, students explain how to use a ratio table to find a specific value (6.RP.3a). An example included is “Kyle sells sandwiches at the deli. He sells five turkey sandwiches for every two ham sandwiches. a. Create a ratio table showing the number of turkey sandwiches sold compared to ham sandwiches sold. Include four equivalent ratios. b. Explain how you could use a ratio table to find how many ham sandwiches were sold if 45 turkey sandwiches were sold. Include the number of ham sandwiches sold in your explanation.”
  • In Lesson 1.3, Rates and Unit Rates, Proficient Practice, students develop fluency in finding unit rates as they calculate unit rates in multiple situations. (6.RP.3) Examples included are Problem 13, “Keisha drove 100 miles in 2 hours. At this rate, how far will she drive in 6 hours?” Problem 14, “Jimmy paid $75 for 3 people to attend a play downtown. If it costs the same per ticket, how much will Alan pay for 10 people to attend the play next week?”
  • Lesson 4.4, Multiplying and Dividing Mixed Numbers, Student Gems link to Dan Meyer 3-Act Math tasks, students develop conceptual understanding of multiplying and dividing mixed numbers within an application (6.NS.1). An example is Nana’s Lemonade where students watch a 3 part video, make predictions about the ratio of water to lemon juice, pose questions, answer questions, and compare their thinking with their peers.
  • In Lesson 3.3, Percents of a Number, students develop conceptual understanding simultaneously with procedural skill to find a percent of a quantity (6.RP.3c). The Explore! activity in this lesson provides students with a diagram of a grid representing a room with pieces of furniture and guides students through the process of finding the percent of the room taken up by each object. The directions state: “Kieran used a piece of 4 by 5 grid paper to sketch the floor plan of his room. He colored the location of his bed, dresser and desk.”
    • Step 1: Write the ratio of the parts shaded for each object to the total space as a fraction.
    • Step 2: Convert each fraction in Step 1 to a decimal fraction with a denominator of 100.
    • Step 3: What percentage of the room is taken up by each object?

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
9/10
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Criterion Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 1.2, Ratio Tables and Graphs, “MP1: Students are given the opportunity to make sense of a situation using Exercises 10 through 14. The amount of perseverance needed from students increases throughout this set. Students should ask themselves, “Does my answer make sense?” after reaching an answer for #14.”
  • In Lesson 5.4, Evaluating Expressions, “MP2: Have students substitute a variety of values into an expression representing a real-world scenario (like the taxi in Example 3). Have them discuss what the resulting value represents in terms of the situation.”
  • In Lesson 3.2, Percents, Decimals and Fractions, “MP5: In Example 3, a ratio table is used as a tool to convert a ratio to a percent. Students have many tools they have learned in previous years that they may choose to connect to new content to help it make sense to them. This should be encouraged.”
  • Lesson 7.3, Inequalities, “MP6: When students graph inequalities on a number line, they must pay attention to the inequality sign to determine whether or not the end point is filled in. They must also determine if the arrow should point to numbers greater than or less than the given number. Remind students that each aspect of the graph must be precise to represent the inequality correctly.”

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
1/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 partially meet expectations for carefully attending to the full meaning of each practice standard. 

The materials do not attend to the full meaning of MP4 and MP5. Throughout the materials MP4 is identified, however, most of the examples given for modeling use drawings and tools to solve rather than connect the content to real-world scenarios, thus not attending fully to the practice. Within the materials, students use tools, however, specific tools are given for the students to use without an opportunity to choose appropriate tools strategically. In addition, there are multiple places throughout the materials where MP2 is labeled, however, the description does not always fully attend to the practice, frequently focusing on finding key words in word problems instead of making sense of quantities and their relationships. Examples include:

  • MP2: In Lesson 2.1, Adding and Subtracting Decimals, Lesson Guide, students do not make sense of quantities and relationships as they look for keywords to solve word problems. “Students will need to choose the correct operation for each word problem. Brainstorm keywords they might see that will give clues about whether they should add or subtract when doing the exercises.”
  • MP2: In Lesson 3.3, Percents of a Number, Lesson Guide, “This lesson gives students the skills they will need to solve later word problems as they write equations involving percents and solve them. As such, work with students to understand the words “of ” as multiplying and “is” as equals so they can compute using percents in a decontextualized manner before having the context introduced.” Students look for keywords instead of making sense of quantities and relationships within the problem.
  • MP4: In Lesson 6.3, Solving Multiplication and Division Equations, “Algebra tiles can be used to show the process of solving multiplication equations by grouping. Students need to have a conceptual understanding of multiplication prior to successfully solving equations using this model.” This is a strategy for solving and does not attend to MP4 as students do not work with real-world situations.
  • MP4: In Lesson 1.2, Ratio Tables and Graphs, students visually represent the problem but are not modeling a real-world context. “...students use tape diagrams to model ratio relationships. In this lesson, students are given the opportunity to model ratios using tables and graphs. You may want to have students discuss the strengths and weaknesses of each model.” 
  • MP5: In Lesson 4.1, Multiplying Fractions, Lesson Guide: “Grid paper is an appropriate tool to use to show how to multiply two fractions. Have students create a rectangle with side lengths that correspond to each of the denominators of their fractions and then follow the process shown in the Explore! and Example 1.” Students are instructed on which tool to use.
  • MP5: In Lesson 2.3, Dividing by 1-Digit Numbers, Lesson Guide: “The Explore! has students using base-ten blocks to show division. Students will be trading in tens sticks for ones cubes in order to put a larger number into smaller equal-sized groups.” Students are instructed on which tool to use. 

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

  • MP1: In Lesson 3.4, Percents Application, “Students determine their solution strategy as well as identify whether their answer should be greater than (i.e., tax) or less than (i.e., discount) the original value (if they are not only computing the tax, tip or discount).” Students make sense of given values and use estimation strategies to solve multi-step problems in a real-world situation.
  • MP2: In Lesson 5.1, Powers and Exponents, “Encourage students to reason quantitatively regarding the possible size of powers. If they are raising a fraction less than one to a given exponent, will that make the solution smaller or larger? How about a number greater than one?” This example allows students to reason quantitatively about exponents.
  • MP7: In Lesson 5.2, Order of Operations, “Students make use of structure in this lesson as they put together all the components of the order of operations. Have students verbally share the order of operations structure with another student prior to working independently.” This allows students to engage and use the structure of the order of operations in various problems.
  • MP8: In Lesson 4.3, Dividing Fractions, “Use the Explore! to allow students to use repeated reasoning to discover that dividing by a fraction is the same as multiplying by the reciprocal.” This fits with the practice in that students are repeating a process to understand the concept.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 meet expectations for prompting 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:

  • In Lesson 1.4, Comparing Rates, students construct an argument to explain their work. Exercise 16: “Kent and Aleesha each live 5 miles from school and ride their bikes there every day. They left school at the same time on Thursday. After 5 minutes, Aleesha texted Kent that she had traveled 1 mile. After 15 minutes, Kent texted Aleesha saying he was halfway home. If they each traveled at a constant rate, who got home first? Explain how you know.”
  • 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 4.4 Multiplying and Dividing Mixed Numbers, 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: The quotient of two fractions is the reciprocal of the product of those two fractions.”
  • In Lesson 9.2, Area and Perimeter with Decimals, Exercise 22, Students construct an argument to explain their work. “Two rectangles both have perimeters of 20 cm but have different areas. One of the rectangles has dimensions that are not whole numbers. The other rectangle has a length that is 6 cm longer than its width. Draw a set of two possible rectangles that fit these criteria. Show how your set of rectangles meet each of the criteria.”
  • In Lesson 1.1, Ratios, Problem 26, students analyze someone’s mathematical reasoning. “Dalexis says, “If you multiply a 2-digit number and a 1-digit number, you get a 3-digit number.” Is her statement always true, sometimes true or never true? Support your answer with your reasoning.”
  • In Lesson 2.4, Dividing by Multi-Digit Numbers, Exercise 13, students critique the reasoning of others and justify their thinking. “Vivaan said the answer to #10 above [5240 ÷ 160] should be the same as the answer to 524 ÷ 16. Is he correct? If so, explain why.”
  • Unit 3, Percents Performance Task, “Mack wants to sell his used car. He spends the first month trying to sell it for $5,000, but is unsuccessful. The second month he decides to sell the car at 50% off the original selling price. The car does not sell. The third month he discounts the car by an additional 50%. Now, his friend Jasper says he will buy the car because it is free. Jasper’s thinking is below: 50% + 50% = 100% discount = FREE! 1. Explain what is wrong with Jasper’s thinking. Include the percent of Mack’s original selling price Jasper would pay for the car if he buys it. Use words and/or numbers to show how you determined your answer.” Students critique the reasoning of others and justify their reasoning. 
  • Lesson 3.4, Percent Applications, students analyze a student’s work and provide mathematical reasoning to correct the strategy in Problem 14 of the student lesson, “Mikayla took her friends to lunch. The bill came to $32. She wanted to leave a 15% tip and needed to determine the total cost of the lunch, including the tip. Her work is below. Unfortunately, Mikayla made a mistake. Explain the mistake Mikayla made and then find the correct total for the bill.”

Indicator 2g.ii

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.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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:

  • Lesson 1.1, Ratios, Teacher/Lesson Guide, Exercise 19b, supports teachers in engaging students in constructing viable arguments. “Exercise 19b could be used as an opener to the lesson as it builds upon previous knowledge. Groups can discuss if the situation is possible and create arguments for or against to share with classmates.” 
  • In Lesson 3.2, Percents, Decimals and Fractions, Teacher/Lesson Guide, Explore!, teachers engage students to construct an argument and justify their thinking. “In Step 5 of the Explore!, students will create differently shaded grids. Have them share their work with one another or as a class using a document reader and discuss whether or not the shaded grids accurately reflect the furniture in Tamika’s room. Have students emphasize their work in Step 4 as justification for their grids.”
  • Lesson 5.1, Powers and Exponents, Teacher/Lesson Guide, supports teachers to help students construct viable arguments. “Show one correct and one incorrect statement (e.g., 3⁴ = 81 and 3⁴ = 12). Ask students to find the correct statement and construct a viable argument as to why it is correct.”
  • Lesson 5.4, Evaluating Expressions, Teacher/Lesson Guide, supports teachers to help students critique the reasoning of others. Teachers are informed of a misconception: “It is very common for students to insert values into expressions using multiplication and lose the operation (i.e., 5y when y = 2 becomes 52).” Teachers are instructed to, “Show this common error on the board and see if anyone can figure out what you did wrong.”
  • In Lesson 6.1, Equations and Solutions, Teachers Gems, Partner, teachers assist students in constructing viable arguments and critiquing the reasoning of others. “After a rotation, if there is a lot of discrepancy in student answers as they compare with their new partner, the teacher can call a FREEZE. With a FREEZE, all students should put their writing utensils down then ask for a partner set where they got different answers on a specific task. These students hand over their templates for the class to examine (under a document camera) and provide feedback on. Having classroom sentence starters for the FREEZE component can be helpful in guiding the conversation such as “I like… I wonder… Your next step could be…”

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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, Ratio Tables and Graphs, the Lesson Presentation includes a slide dedicated to introducing vocabulary from the lesson and provides mathematical definitions. “Equivalent Ratios - A comparison of two quantities with the same value. Ratio Table - A model that shows multiple equivalent ratios."
  • In Lesson 6.1, Equations and Solutions, the Lesson Presentation includes a slide that provides the definitions and terms important to the lesson. “Equation - A mathematical sentence that contains an equals sign (=) between two equivalent expressions. Solution - Any value or values that makes an equation true.”
  • Lesson 5.1, Powers and Exponents, Teacher/Lesson Guide, Teaching Tips includes information about mathematical language, “People often use the word “squared” for power of 2 and “cubed” for power of 3. For example, students should understand that four squared means four to the power of 2, or 4².”
  • Lesson 7.1, Understanding Integers, Teacher/Lesson Guide, Teaching Tips includes information about mathematical language. “Addition and subtraction are inverse operations that “undo” one another. Positive and negative integers are opposites of one another. Be careful not to say addition and subtraction are opposites as this may confuse students.”
  • In Lesson 2.3, Dividing by 1-Digit Numbers, Online Practice, students identify a number based on accurate terminology. “In each expression determine if 4 is the ‘dividend’ or the ‘divisor’.”

Examples of not attending to the specialized language of mathematics include:

  • In Lesson 6.3, Solving Multiplication and Division Equations, Teacher/Lesson Guide, “MP6: In a division equation, students may struggle with seeing how multiplying both sides by the number in the denominator cancels out the value in the denominator. Show students the importance of writing the value they are multiplying by in the numerator, not in the denominator.” “Cancels out the value in the denominator” is not precise mathematical terminology.
  • In Lesson 2.1, Adding and Subtracting Decimals, Teacher/Lesson Guide, Teaching Tips, “Remind students, when adding or subtracting decimals, that once the problem is lined up properly the decimal points are ignored until the end when it is brought straight down and placed in the answer.” This teaching tip is not mathematically sound. Students should be conceptually aware of why a process is occuring versus simply stating a procedure. 
  • In Lesson 5.5, Equivalent Expressions, Teacher/Lesson Guide, “MP6: When combining like terms, help students attend to precision by understanding that the operation preceding each term ‘belongs’ to that term. When a term is being subtracted from a previous term, the subtraction sign should move with that term as a negative sign.” Student Lesson: “In order to simplify an algebraic expression you must combine all like terms. When combining like terms you must remember that the operation in front of the term (addition or subtraction) must stay with the term. Rewrite the expression by grouping like terms together before adding or subtracting the coefficients to simplify.” In both the Lesson Guide and Student Lesson, the explanation for combining like terms and the idea that the operation “belongs” to the term is not mathematically sound. Students should be conceptually aware of why a process is occurring versus simply stating a procedure.

Gateway Three

Usability

Meets Expectations

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
8/8
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Criterion Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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.

Indicator 3a

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 2.1, Adding and Subtracting Decimals, Teacher/Lesson Guide, the lesson planning suggestion states, “This lesson may take 2 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 Tic-Tac-Toe activities or independent student practice. Day 1: Warm-up of choice from above, Lesson Presentation, Teacher Gem Activity (6.NS.3 Relay), Focused Assignment or Online Practice.”

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. For example:

  • In Lesson 4.3, Dividing Fractions, Student Lesson, students learn the content by solving problems without context and apply the content in real-world contexts. “Find each quotient. Write your answer in simplest form. 5. 2/3 ÷ 1/3.” Near the conclusion of the problems, students evaluate the reasoning of others. “Two students solved division expressions. In Exercises 30 and 31, determine if the work shown by each student is correct and solve correctly if an error was made. Explain your reasoning.”

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 3.3, Percents of a Number, Lesson Planning Suggestions builds from guided practice to more abstract and contextual work with the content, “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.”

Day 1: 

  • Explore! Activity: “Double Number Lines” 
  • Lesson Presentation 
  • Teacher Gem Activity (6.RP.3c Relay) 

Day 2: 

  • Exit Card as entrance activity 
  • Focused Assignment or Online Practice 
  • Communication Prompt

Indicator 3c

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 1.3, Rates and Unit Rates, Exercises, students find unit rates through multiple examples, “Find each unit rate. 1. 60 miles/2 hours”

Students connect content to real-world situations and gain extra practice through the Student Gems, linked resources from Open Educational online sites. For example:

  • In Lesson 5.2, Order of Operations, Student Gems from Desmos, students complete extra practice on the order of operations. Summary from the Desmos website, “In this activity, students use sketch to solve "twin puzzles" as a way to practice their order of operations skills. Teachers can use the overlay feature in the teacher dashboard to assess the class at a glance and to facilitate class-wide error analysis discussions, or the response view to identify individual students who need additional support.”

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

  • In Lesson 9.5, Volume of Rectangular Prisms, Teacher Gem: Partner Math, students solve problems involving the volume of rectangular prisms, 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.”

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
2/2
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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. For example, In Lesson 4.1, Multiplying Fractions, Explore, ‘Fraction Action’ is an activity that uses paper to help students create conceptual understanding of multiplying fractions. “Step A: First he divided a piece of paper horizontally into as many sections as were shown in the denominator of one of the factors. For 3/4 , divided the paper into 4 horizontal sections.”
  • Examples of manipulatives include: Algebra tiles, grid paper, rulers, patty paper/tracing paper, cylinders and cones, protractor, and x-y tables.

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 5.6, The Distributive Property, the Student Lesson begins with, “Some numeric and algebraic expressions include parentheses. The Distributive Property is a property that allows you to simplify computations or algebraic expressions that include parentheses.” Then there are four examples with solutions, thirty-eight Exercise items, and three Review items.

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
6/8
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Criterion Rating Details

The instructional materials for EdGems Math Grade 6 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.

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 3.2, Percents, Decimals, and Fractions, Communication Prompt, “Explain how you would write 2/5 as a percent.”
  • In Lesson 10.3, Dot Plots, Communication Prompt, “Describe the process for creating a dot plot. Include at least 3 steps in your description”

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

  • In Lesson 2.1, Adding and Subtracting Decimals - A Closer Look, “MP2: Students will need to choose the correct operation for each word problem. Brainstorm key words they might see that will give clues about whether they should add or subtract when doing the exercises”
  • In Lesson 8.2, Writing Two-Step Equations - A Closer Look, “MP3: Give students an input-output table and ask them to find the equation. Have students construct a viable argument for why their equation is correct.”

Indicator 3g

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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.

  • 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 6.3, Solving Multiplication and Division Equations, “Students have another opportunity to model with equation mats and algebra tiles in “Multiplication Equations”. Students use the tiles to model multiplication equations and then balance their mats. The Explore! activity ends with students summarizing how to use the mats and tiles to model and solve multiplication equations. You may choose to discuss with students what it might look like to solve a division equation on a mat and what the model’s limitations are for this operation.”
  • Mathematical Practices - A Closer Look, contains information related to each Mathematical Practice contained in the lesson and suggestions for teachers. For example, in Lesson 1.5, Measurement Conversions, “MP6: Physically show students objects that represent different measurements so they understand better how one relates to another. Focus on the meaning of the prefixes used with metric measurements in the table at the beginning of the lesson. Encourage students to think of other words with these prefixes (e.g., decade for deca-).”
  • 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 9.4, Nets and Surface Area, Teaching Tip, “Encourage and point out different nets for the same solid. Having students show different nets for the same solid will reinforce that there are many ways to draw a net. On a wall have students tape up different nets for the same solid.”

Indicator 3h

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.
0/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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

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.
2/2
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 7, Rational Numbers and the Coordinate Plane, the Learning Progressions contains:

“In earlier grades, students have: 

  • Compared whole numbers and positive rational numbers. (K.CC-5.NBT) 
  • Graphed points in the first quadrant of the coordinate plane. (5.G.1-2) 
  • Named shapes based on their properties. (3.G, 4.G and 5.G) 

In future grades, students will:

  • Add, subtract, multiply and divide rational numbers. (7.NS)
  • Graph proportional relationships and functions on a coordinate plane. (7.RP.2 and 8.F)”

Indicator 3j

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).
0/0
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 provide a list of lessons in the teacher's 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.

Indicator 3k

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

The instructional materials for EdGems Math Grade 6 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. For example in Unit 8:

  • Find graphs showing relationships between two variables in the newspaper or online. 
  • Discuss situations at home that may be represented by linear relationships (i.e. allowance paid over time, calories consumed per cup of cereal, etc).
  • Continue working on fluency with graphing ordered pairs.

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
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Indicator Rating Details

The materials for EdGems Math Grade 6 explain instructional strategies and routines in the Teacher Gems PD Overview, however, there are no sections that include how any of the materials in the resource are research-based. Example of an instructional strategy:

  • In Unit 2, 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 9, 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 3m - 3q

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

The instructional materials for EdGems Math Grade 6 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

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 partially meet the expectations for providing strategies for gathering information about students’ prior knowledge within and across grade levels.

  • 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

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 4.2, Dividing Fractions with Models, Common Misconceptions, “ The concepts of dividing by 1/2 and dividing in half may confuse some students. Division by 1/2 equates to finding how many one-halves there are in a quantity; division in half yields two equal parts of the original quantity. When teaching fraction division with models, have students show two similar examples (i.e., one for dividing by half, one for dividing in half).”

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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.

  • 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. For example:
    • In Lesson 5.5,  I can recognize and combine like terms to generate equivalent expressions, Concepts and Procedure (5.NBT.7): Page 102 #28 Skill: Area and conversions.
  • Each lesson contains Online Practice, where a student is given the correct answer, if they choose, but feedback is not provided.

Indicator 3p

Materials offer ongoing formative and summative assessments:
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Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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.

  • 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

Materials encourage students to monitor their own progress.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 3r - 3y

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

The instructional materials for EdGems Math Grade 6 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

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

  • 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

Materials provide teachers with strategies for meeting the needs of a range of learners.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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. For example:

  • In Lesson 6.1, Equations and Solutions, Proficient Practice for on-level students has questions focusing on the content, “Determine if the number given is the solution of the equation. 1. ???? + 5 = 12 Is 7 the solution? ”. The Challenge practice, focused on extension of the concept, includes solving equations and finding the solutions, “Match each equation on the left with its solution on the right. 1. ???? + 5 = 17 ”. The Tiered Practice is geared towards students that need more focused help with the content which is done by providing the steps to determine if a number is a solution, “Determine if the number given is the solution of the equation. Shade in the correct answer. 1. ???? − 2 = 11 Is 9 the solution?”.
  • Assessments and Tiered Assessments are located in each Unit.

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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.

  • 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. 
  • Each Lesson has an Explore! task which does include instructions on its use. For example: Lesson 8.2, Writing two-variable equations, Teacher Guide, “In this Explore! students will write an equation that models the relationship between the number of weeks of school and the number of homework assignments completed. Students work through the development of a linear equation by creating an input-output table of values, looking for the pattern in the table and then writing the equation for the relationship. Students develop the equation by looking for the start value, which corresponds to an input value of 0, and the rate of change, which is the amount the output values increase or decrease by for each increase of 1 in the input column. This Explore! activity helps set the stage for the lesson presentation. You may choose to have students work in partner sets or work through this Explore! activity as a full class.”

Indicator 3u

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).
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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.

  • 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

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 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 complex problems than the Tiered and Proficient Practice sheets, and the number of problems is comparable. 

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
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Indicator Rating Details

The instructional materials for EdGems Math Grade 6 meet the expectations for providing a balanced portrayal of various demographic and personal characteristics. Lessons contain a variety of demographic and personal characteristics.

  • Names and wording are chosen with diversity in mind. The materials include various names throughout the problems for example: Mikayla, Shawna, Juan, Seth, Sherry, Dalexis, 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 of students throughout the lessons show a wide range of students according to gender, race, and ethnicity. 
  • 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

Materials provide opportunities for teachers to use a variety of grouping strategies.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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. For example:

  • In Lesson 2.5, Dividing Decimals, the Teacher Gems activity titled “Partner Math” instructs students to work with one partner. 
  • In Lesson 7.1, Understanding Integers, 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

Materials encourage teachers to draw upon home language and culture to facilitate learning.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 3z - 3ad

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

The instructional materials for EdGems Math Grade 6 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 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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. For example:

  • Lesson 2.6, Common Factors and Multiples, Student Gems includes two Desmos Activities, one Khan Academy video lesson, one IXL task, one Robertkaplinsky.com activity,  and one Illustrative Mathematics task.
  • Lesson 9.2, Area and Perimeter with Decimals, Student Gems includes three Desmos Activities, one Khan Academy video lesson, on Youcubed activity, and one Illustrative Mathematics task.
  • All lessons have Online Practice and Gem Challenges included for student use.

Indicator 3aa

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.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 left off 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 10.4, Histograms, the Student Lesson requires a PDF download.

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 include Gem Challenges with online multiple choice items. However, all unit assessments are PDF or editable Word document and cannot be completed online. While there is no feature that allows teachers to construct their own assessments, teachers can edit the assessments using the included Word documents in the Editable Resources file on each Teacher Unit page. 

Indicator 3ac

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.
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 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 personalization. However, teachers can personalize student learning in each student account.  

The instructional materials reviewed for EdGems Math Grade 6 are easily customized for local use. Specific tasks can be assigned to specific students from the materials. All Explore, Proficient Practice, Tiered Practice, Challenge Practice, Exit Cards, Performance tasks, and assessments can be edited for local use using the linked Word documents in a Google Sheet found in the Editable Resources file on each Teacher Unit page.

Indicator 3ad

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.).
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Indicator Rating Details

The instructional materials reviewed for EdGems Math Grade 6 do not incorporate technology that provides opportunities for multiple students to collaborate with the teacher or one another.

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Additional Publication Details

Report Published Date: 11/07/2019

Report Edition: 2018

Title ISBN Edition Publisher Year
6th Grade Core Math Annual Online Teacher Subscription 978-1-948860-56-7 EdGems Math, LLC 2018

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

Rubric Design

The EdReports.org’s rubric supports a sequential review process through three gateways. These gateways reflect the importance of standards alignment to the fundamental design elements of the materials and considers other attributes of high-quality curriculum as recommended by educators.

Advancing Through Gateways

  • Materials must meet or partially meet expectations for the first set of indicators to move along the process. Gateways 1 and 2 focus on questions of alignment. Are the instructional materials aligned to the standards? Are all standards present and treated with appropriate depth and quality required to support student learning?
  • Gateway 3 focuses on the question of usability. Are the instructional materials user-friendly for students and educators? Materials must be well designed to facilitate student learning and enhance a teacher’s ability to differentiate and build knowledge within the classroom. In order to be reviewed and attain a rating for usability (Gateway 3), the instructional materials must first meet expectations for alignment (Gateways 1 and 2).

Key Terms Used throughout Review Rubric and Reports

  • Indicator Specific item that reviewers look for in materials.
  • Criterion Combination of all of the individual indicators for a single focus area.
  • Gateway Organizing feature of the evaluation rubric that combines criteria and prioritizes order for sequential review.
  • Alignment Rating Degree to which materials meet expectations for alignment, including that all standards are present and treated with the appropriate depth to support students in learning the skills and knowledge that they need to be ready for college and career.
  • Usability Degree to which materials are consistent with effective practices for use and design, teacher planning and learning, assessment, and differentiated instruction.

Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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