## Alignment: Overall Summary

The instructional materials for Carnegie Learning Math Solution (2018) Course 2 meet the expectation for alignment to the CCSS. In Gateway 1, the instructional materials meet the expectations for focus by assessing grade-level content and spending at least 65% of class time on the major clusters of the grade, and they are coherent and consistent with the Standards. In Gateway 2, the instructional materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, and they connect the Standards for Mathematical Content and the Standards for Mathematical Practice.

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## Gateway 1:

### Focus & Coherence

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

## Gateway 2:

### Rigor & Mathematical Practices

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

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## Gateway 3:

### Usability

0
22
31
38
33
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

## The Report

- Collapsed Version + Full Length Version

## Focus & Coherence

#### Meets Expectations

+
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Gateway One Details

The instructional materials for Middle School Math Solution Course 2 meet the expectations for Gateway 1. These materials do not assess above-grade-level content and spend the majority of the time on the major clusters of each grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are consistent with the mathematical progression in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the materials meet the expectations for focusing on the major work of the grade, and the materials also meet the expectations for coherence.

### 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 for Middle School Math Solution Course 2 meet the expectation for not assessing topics before the grade-level in which the topic should be introduced. The materials did not include any assessment questions that were above grade-level.

### 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 Carnegie Learning Middle School Math Solution Course 2 meet expectations that they assess grade-level content.

The assessments are aligned to grade-level standards. The instructional materials reviewed for this indicator were the Post-Tests, which are the same assessments as the Pre-Tests, both Form A and Form B End of Topic Tests, Standardized Practice Test, and the Topic Level Performance Task.

For example:

• Module 1, Topic 3, End of Topic Test-Form B, 7.RP.2b,2c: Students represent a proportional relationship in an equation. Question 6 states, “The number of trees (n) that the average American uses in paper products varies directly with the time (t) in years. Assume that the constant of proportionality is 7. a. Write an equation to represent the proportional relationship between n and t using the information given. b. How many trees does the average American use in 6 years? c. In how many years would an average American use 133 trees?“
• Module 3, Topic 1, End of Topic Post-test Form B, 7.EE.3: Students solve multi-step equations. Question 2 states, “A theater charges a service fee of $4.50 plus a ticket fee based on the section of the theater.” A table is provided with only part of the information given. Students fill in the missing information; “Write an algebraic expression to represent the cost of x number of Orchestra tickets; Can the same algebraic expression be used for tickets in the Mezzanine and tickets in the Second Balcony? Explain your reasoning. If a group buys 4 Mezzanine tickets and 2 Orchestra tickets, what will be the total cost of the tickets? Explain your reasoning.” • Module 4, Topic 1, Standardized Test, 7.SP.5: Students express the likelihood of a random event. Question 3 states, “Ilana drew a marble at random from a bag containing 4 blue, 3 red, 2 yellow, and 5 green marbles. What is the probability that she picked a marble that is not red?” • Module 3, Topic 2, End of Topic Test Form A, 7.EE.4a: Students solve a word problem in the form px+q=r. Question 11 states, “Rachel ordered early learning software for her daughter from an online retailer. Each item costs$6.50, and there is a shipping fee of 8.50 for the entire order. a. What is the cost of Rachel’s order if she buys 7 items? b. Write a sentence to describe how you calculated the cost of Rachel’s order. c. Write an equation to describe this situation. Let s represent the number of software items ordered and c represent the total cost of the order.” • Module 5, Performance Task, 7.G.5: Students use facts about angles to write multi-step problems to solve for unknown angle measures in a figure. In X Marks the Spot, given pairs of intersecting lines, students reason to “Explain how you could determine the measure of each of the marked angles made by the X; Calculate the measures of the marked angles; Show two different ways to determine the unknown values; Write equations and determine the measures of all four angles.” ### 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 + - Criterion Rating Details The instructional materials for Middle School Math Solution Course 2 meet the expectations for having students and teachers using the materials as designed, devoting the large majority of class time to the major work of the grade. Overall, the materials devote at least 65 percent of class time to major work. ### Indicator 1b Instructional material spends the majority of class time on the major cluster of each grade. 4/4 + - Indicator Rating Details The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations for spending a majority of instructional time on major work of the grade. To determine the amount of time spent on major work, the number of topics, the number of lessons, and the number of days were examined. Review and assessment days were also included in the evidence. • The approximate number of topics devoted to major work of the grade (including assessments and supporting work connected to the major work) is eight out of 14, which is approximately 57 percent. • The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 31 out of 56, which is approximately 55 percent. • The number of days devoted to major work (including assessments and supporting work connected to the major work) is 95 out of 139, which is approximately 68 percent. The approximate number of days is most representative of the instructional materials because it most closely reflects the actual amount of time that students are interacting with major work of the grade. As a result, approximately 68 percent 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. 8/8 + - Criterion Rating Details The instructional materials for Middle School Math Solution Course 2 meet the expectations for being coherent and consistent with the standards. Supporting work is connected to the major work of the grade, and the amount of content for one grade level is viable for one school year and fosters coherence between the grades. Content from prior or future grades is clearly identified, and the materials explicitly relate grade-level concepts to prior knowledge from earlier grades. The objectives for the materials are shaped by the CCSSM cluster headings, and they also incorporate natural connections that will prepare a student for upcoming grades. ### Indicator 1c Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. 2/2 + - Indicator Rating Details The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Supporting standards/clusters are connected to the major standards/clusters of the grade. For example: • In Module 1, Topic 1, Lesson 2, Activity 2.3: That’s a Spicy Pizza-Unit Rates and Circle Areas: Students use their knowledge of circles (7.G.4) and unit rates (7.RP.1) to determine which pizza is the better buy. • In Module 1, Topic 4, Lesson 4, Activity 4.4: More Ups and Downs: Students solve problems involving volume and surface area (7.G.6) to apply percent increase and decrease concepts (7.RP.3). • In Module 4, Topic 3, Lesson 4, students use random samples from two populations to draw conclusions (7.SP.1-4) and solve real-world problems involving the four operations with rational numbers (7.NS.3). Students create graphic displays to answer questions regarding means, medians, ranges, mean absolute deviation, and interquartile ranges. • In Module 5, Topic 1, Lesson 2, students investigate special angle relationships, including complementary and supplementary angles (7.G.5) and solve real-world problems involving the four operations with rational numbers (7.NS.3). Practice question 5 states, “Suppose each street in the map shown represents a line. Provide an example of each angle relationship. a. Vertical angles, b. Supplementary angles, c. Linear pair, d. Adjacent angles, e. Vertical angles, f. Congruent angles. Calculate the measure of each unknown angle.” Questions 6-10 continue the task: “6) Angles C and D are complementary. The measure of angle D is 25 degrees greater than the measure of angle C. What is the measure of each angle? 7) If the supplement of an angle is 30 degrees more than the measure of the angle, what is the measure of the angle? 8) If the supplement of an angle is 12 degrees less than twice the measure of the angle, what is the measure of the angle? 9) If two angles form a linear pair and the measure of the first angle is one-fifth the measure of the second angle, what is the measure of each angle? 10) If two angles form a linear pair and the measure of the first angle is three times the measure of the second angle, what is the measure of each angle?” ### Indicator 1d The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades. 2/2 + - Indicator Rating Details Instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the amount of content designated for one grade-level is viable for one year. The suggested amount of time and expectations for teachers and students of the materials are viable for one school year as written and would not require significant modifications. Carnegie Learning provides explicit pacing information in several places: • The most concise is the Content Map on page FM-15 in the Teacher’s Implementation Guide in both Volumes 1 and 2. There are 139 days of instructional material. This document also provides the information that one day is 50 minutes, facilitator notes offer suggestions for changing the pacing if appropriate, and that allowing 25 assessment days would bring the total to 164 days. • The Course 2 Standards Overview on pages FM-18 and 19 in the Teacher Implementation Guide provides a chart of all standards covered in each lesson indicating that students would be able to master all grade-level standards within one school year. All of the standards for each grade-level are taught at least once in the curriculum, and most are addressed more than once. ### 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations for the materials being consistent with the progressions in the Standards. The instructional materials clearly identify content from prior and future grade levels and use it to support the progressions of the grade-level standards. The content is explicitly related to prior knowledge to help students scaffold new concepts. Content from other grade levels is clearly identified in multiple places throughout the materials. Examples include: • A chart in the Overview shows the sequence of concepts taught within the three grade levels of the series (FM-15). • The Family Guide (included in the student book) presents an overview of each Module with sections that look at “Where have we been?" and "Where are we going?” which address the progression of knowledge. • The Teacher Guide provides a detailed Module Overview which includes two sections titled, “How is ____ connected to prior learning?” and “When will students use knowledge from ___ in future learning?” • Module 2 Overview- How is Operating with Signed Numbers connected to prior learning? (M2-1B): “Operating with Signed Numbers builds on students’ experiences with signed numbers in grade 6. Students revisit distance on a number line in terms of magnitude, building on their prior knowledge of absolute value, to model operations on the number line and to connect the model to an algorithm. The module also draws on students’ fluency with adding, subtracting, multiplying, and dividing whole numbers, decimals, and fractions, developed in grades K through 6. Students are expected to be fluent in these operations when operating with signed rational numbers. Finally, Operating with Signed Numbers uses properties of numbers that were informally developed in elementary school and formalized in grade 6.” • Module 3 Overview- When will students use knowledge from Reasoning Algebraically in future learning? (M3-1B): “The underlying purpose of representing expressions on a number line and solving equations using a double number line—physically transforming expressions or equations and noting the corresponding changes in the symbolic representation—is to provide the underpinnings for geometric and algebraic transformations of objects and equations. In grade 8 and in high school, students will transform geometric objects and make conjectures about how the coordinates of geometric figures on the plane change after undergoing the transformation.” • At the beginning of each Topic in a Module, there is a Topic Overview which includes sections entitled “What is the entry point for students?” and “Why is ____ important?” • Module 1, Topic 1- Circles and Ratio (M1-3A) - What is the entry point for students?: “Throughout elementary school, students used and labeled circles and determined the perimeters of shapes formed with straight lines. In grade 6, students worked extensively with ratio and ratio reasoning. To begin Circles and Ratio, students draw on these experiences as they use physical tools to investigate a constant ratio, pi. They form ratios of the distance around circles to the distance across circles. As they engage in this investigation, students review basic ideas of ratios and proportional relationships." • Module 1, Topic 3- Proportionality (M1-87B) - Why is Proportionality important?: “The characteristics of proportional relationships, their graphs, and their equations as developed in Proportionality provide the underpinnings of algebra and the study of functions. In grade 8, students are expected to “understand the connections between proportional relationships, lines, and linear equations” (8.EE.B) and “define, evaluate, and compare functions” (8.F.A), including nonlinear functions. In each domain, students are expected to compare relationships represented in different ways.” • The Topic Overview also contains a table called “Learning Together” that identifies the standards reviewed from previous lessons and grades called “Spaced Review.” • Each “Lesson Resource” has scaffolded practice for the students to utilize with reminders of concepts taught previously. The design of the materials concentrates on the mathematics of the grade. Each lesson has three sections (Engage, Develop, and Demonstrate) which contain grade-level problems. Each topic also includes a performance task. • In the Engage section, students complete activities that will “activate student thinking by tapping into prior knowledge and real-world experiences and provide an introduction that generates curiosity and plants the seeds for deeper learning.” An example of this is Module 1, Topic 4, Lesson 5 (M1-223), where students are given a triangle drawn on triangular pattern block paper and asked to draw a new triangle with side lengths 50% the length of the original. They determine the ratios that describe the relationship between the original and the new triangle in terms of side lengths, perimeters, and areas. (7.G.1) • In the Develop section, students do multiple activities that “build a deep understanding of mathematics through a variety of activities—real-world problems, sorting activities, worked examples, and peer analysis—in an environment where collaboration, conversations, and questioning are routine practices.” For example, Module 2, Topic 2, Lesson 2, Activity 2.2 (M2-107) has students sort signed rational numbers into sets of equivalent rational numbers. The focus on this activity is understanding that if the quotient of two integers is negative, the negative sign can be placed in front of the representative fraction, in the numerator of the fraction, or in the denominator of the fraction. (7.NS.2b,d) • In the Demonstrate section, students “reflect on and evaluate what was learned.” An example of this is Module 3, Topic 1, Lesson 1 (M3-7), where “students describe a strategy for evaluating an algebraic expression.” (7.EE.1-3) The end of each lesson in the student book includes Practice, Stretch, and Review problems. These problems engage students with grade-level content. Practice problems address the lesson goals. Stretch problems expand and deepen student thinking. Review problems connect to specific, previously-learned standards. All problems, especially Practice and Review, are expected be assigned to all students. After the lessons are complete, the students work individually with the MATHia software and/or on Skills Practice that is included. • MATHia - Module 4, Topic 3 (M4-3E): Students spend approximately one day in MATHia software comparing the characteristics of data displays, specifying which numerical characteristics can be determined from each display, then using data displays to compare populations by determining the visual overlap and describing the difference between the measures of centers in terms of measures of variability. • Skills Practice - Module 5, Topic 1 (M5-3E): Students spend approximately one day classifying angles as complementary, supplementary, or vertical. ### 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Materials include learning objectives that are visibly shaped by CCSSM cluster headings, including: 7. EE.A Use properties of operations to generate equivalent expressions. • In Module 3, Topic 1, Lesson 2, the Lesson Overview states, “Students rewrite linear expressions using the Distributive Property. First, they plot related algebraic expressions on a number line by reasoning about magnitude. Students realize that rewriting the expressions reveals structural similarities in the expressions, which allows them to more accurately plot the expressions. They then review the Distributive Property. Students expand algebraic expressions using both the area model and symbolic representations, focusing on the symbolic. They then reverse the process to factor linear expressions. Students factor expressions by factoring out the greatest common factor and by factoring out the coefficient of the linear variable. Finally, students rewrite expressions in multiple ways by factoring the same value from each term of the expression.” 7.NS.A Apply and extend previous understandings of operations with fractions. • In Module 2, Topic 1, Lesson 4, the Lesson Overview states, “Number lines and two-color counters are used to model subtraction of signed numbers. Through a series of activities, students will develop rules for subtracting integers. As in the lesson on adding signed numbers, the number line method is used to model the difference between two integers. Students then learn how to use zero pairs when performing subtraction using the two-color counter method. Students analyze real-world situations that require calculating the distance between two signed numbers. They build on what they already know about absolute value to determine the distance.” 7.RP.A Analyze proportional relationships and use them to solve real-world and mathematical problems. • In Module 1, Topic 3, Lesson 1, the Lesson Overview states, “Students explore tables and graphs that illustrate proportional relationships. First, students review equivalent ratios and that the graphs of equivalent ratios form straight lines that pass through the origin. They are then given three sets of scenarios, equations, and graphs to match, using any strategy. Each group illustrates a different type of relationship: linear and proportional, linear and non-proportional, non-linear. Students classify the groups of representations as linear and non-linear and use tables of values to classify the linear relationships as proportional or as non-proportional. They summarize the relationships between the terms linear relationship, proportional relationship, and equivalent ratios.” Materials include problems and activities that 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. For example: • In Module 1, Topic 4, Lesson 5, clusters 7.G.A and 7.RP.A are connected when students analyze scale drawings and determine which scale will produce the largest and smallest drawing of an object when different units of measure are given. • In Module 2, Topic 2, Lesson 3, clusters 7.NS.A and 7.RP.A are connected when students solve multi-step real-world ratio and percent problems involving simplifying numeric expressions using the four operations and signed rational numbers. • In Module 3, Topic 3, Lesson 3, clusters 7.NS.A and 7.EE.B are connected when students use rational numbers to write and analyze equations and inequalities. • In Module 4, Topic 1, Lesson 1, clusters 7.SP.B and 7.NS.A are connected when students utilize knowledge of rational numbers to represent probability as a value between zero and one. ### Gateway Two ## Rigor & Mathematical Practices #### Meets Expectations + - Gateway Two Details The instructional materials for Middle School Math Solution Course 2 meet the expectation for aligning with the CCSS expectations for rigor and mathematical practices. The instructional materials attend to each of the three aspects of rigor individually, and they also attend to the balance among the three aspects. The instructional materials emphasize mathematical reasoning, identify the Mathematical Practices (MPs), and attend to the full meaning of each practice standard. ### 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 + - Criterion Rating Details The instructional materials for Middle School Math Solution Course 2 meet the expectations for rigor and balance. The materials meet the expectations for rigor as they help students develop conceptual understanding, procedural skill and fluency, and application with a balance of all 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings. Materials include problems and questions that develop conceptual understanding throughout the grade level. Students develop understanding throughout “Engage” and “Develop” activities, which typically activate prior knowledge and use manipulatives to introduce and build understanding of a concept. Students also have the opportunity to independently demonstrate their understanding in the “Demonstrate” questions at the end of each lesson where they attempt to synthesize their learning. • In Module 2, Topic 1, Lesson 1, students show their understanding of adding and subtracting rational numbers using a visual representation. In Talk the Talk, Mixing Up the Sums, students create addition problems from a given sum using number lines to explain and demonstrate their understanding. (7.NS.A) • In Module 2, Topic 1, Lesson 2, students show their understanding of adding and subtracting rational numbers using a visual representation. In Activity 2.1 Walking the Number Line, students walk along a number line to develop a conceptual understanding using physical and visual representations. (7.NS.1b) • In Module 3, Topic 1 Lesson 2, In Activity 2.2 Mathematics Gymnastics - Applying the Distributive Property, students develop their understanding of the distributive property by drawing area models to represent expressions. (7.EE.A) • In Module 5, Topic 2, Lesson 1, students are introduced to and explore the concept of a cross-section when they create different shapes by slicing a three-dimensional figure. In Activity 1.3 Slicing and Dicing - Slicing a Right Rectangular Prism, building from a previous cube activity, students build a right rectangular prism in clay that is not a cube and again slice their clay prisms to create six cross-sectional shapes (a square, a rectangle that is not a square, a triangle, a pentagon, a hexagon, and a parallelogram that is not a rectangle). They discuss with other students where and how they sliced the prism to make the cross-sections. (7.G.3) Materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. • In Module 2, Topic 2, Lesson 1, students interpret models and write explanations to demonstrate an understanding of multiplication of rational numbers. In Activity 1.1 Equal Groups - Modeling the Multiplication of Integers, knowing that multiplication can be represented as repeated addition, students are shown an example of 3 x 4 with both a number line and circles with positives in them. Students explain how these represent the multiplication problem. For each integer problem, students explain their understanding. (7.NS.2, 7.NS.3) • In Module 3 Topic 1, Lesson 1, students demonstrate conceptual understanding of expressions when writing an explanation of their solution. In Talk the Talk - Strategies, students write and describe their strategies for evaluating expressions and explain how tables are helpful. (7.EE.1, 7.EE.2) • In Module 5, Topic 2, Lesson 1, students demonstrate an understanding of a cross-section by categorizing each sliced cross-section. In Activity 1.4 Cross-Sections of Right Rectangular Prism, students create a graphic organizer of cross-sections they sliced in a rectangular prism. They cut out diagram cards and description cards related to the different cross-sections and tape them into the appropriate rows of the organizer. (7.G.3) ### 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that they attend to those standards that set an expectation of procedural skill and fluency. The instructional materials develop procedural skill throughout the grade level. They also provide opportunities to independently demonstrate procedural skill throughout the grade level. This is primarily found in two aspects of the materials: first, in the “Develop” portion of the lesson where students work through activities that help them deepen understanding and practice procedural skill; second, in the MATHia Software, which targets each student’s area of need until they demonstrate proficiency. The instructional materials develop procedural skill and fluency throughout the grade level. • In Module 1, Topic 2, Lesson 1, students develop procedural skill when solving problems involving unit rate. In Getting Started, students complete given tables and include the unit rate of lemon-lime for each cup of punch for each recipe. Students then draw a graph for each recipe on the coordinate plane. Then students label each graph with the person's recipe and the unit rate. (7.RP.1) • In Module 3, Topic 1, Lesson 2, students develop procedural skill when writing expressions using the distributive property. In Mathematics Gymnastics, students rewrite algebraic expressions with rational coefficients using the distributive property. They also expand linear expressions. Students factor linear expressions in a variety of ways, including by factoring out the greatest common factor and the coefficient of the variable. (7.EE.1) The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level. • In Module 2, Topic 2, students demonstrate procedural skill when they make conjectures about the rules for multiplying and dividing integers. In the MATHia Software, students fill in the blanks to show the understanding of multiplying and dividing integers. (7.NS.A) • In Module 3, Topic 2, students demonstrate procedural skill when solving two-step equations through technology. In the MATHia Software, students determine unknown values and enter values into tables to recognize patterns. Students express the patterns in two-step expressions and use the solver tool to solve two-step equations. (7.EE.4a) • In Module 4, Topic 1, students demonstrate procedural skill when determining the probability of an event. In the MATHia Software, students work to build probability models and determine probabilities of simple and disjoint events and use proportions to make predictions based on samples and theoretical probabilities. (7.SP.6 & 7) ### 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the materials are designed so that teachers and students spend sufficient time working with engaging applications of the 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. The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. This is primarily found in two aspects of the materials: first, in the “Demonstrate” portion of the lesson where students apply what they have learned in a variety of activities, often in the “Talk the Talk” section of the lesson; second, in the Topic Performance Tasks where students apply and extend learning in more non-routine situations. 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. • In Module 1, Topic 2, Lesson 1, students engage in the application of mathematical skills when calculating unit rates to solve real-world problems. In Talk the Talk - Getting Unit Rate-ier, students calculate the total amount of smoothie that the recipe makes and then use what they have learned about fractional unit rates to calculate the amount of pumpkin-y ingredients per unit of smoothie. (7.RP.1) • In Module 1, Topic 3, Lesson 1, students engage in the application of mathematical skills when using proportional relationships to solve real-world problems. In Activity 1.3, Proportional or Not?, students explore tables and graphs to discover that graphs of proportional relationships are straight lines and tables have a constant ratio. The paint problem is revisited, building bird houses, growing bamboo, and speed and car rates situations are used. (7.RP.2b) • In Module 3, Topic 3, Lesson 2, students engage in the application of mathematical skills when analyzing and comparing expressions to solve real-world problems. In Getting Started, students examine the cost structures for two different limousine companies in order to create a competitive cost structure for a third company. (7.EE.4) The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. • In Module 1, Topic 4, Lesson 1, students independently demonstrate the use of mathematics when using proportional relationships to solve real-world problems. Percent models, proportions, and the constant of proportionality are revisited to solve percent problems with simple interest, tax, markups and markdowns, gratuities and commissions, fees, percent increase and decrease, and percent error. (7.RP.3) • In Module 2, Topic 1, students independently demonstrate the use of mathematics when addition and subtraction of rational numbers is used to solve real-world problems. In Performance Task, students represent rational numbers as a sum and a difference of two rational numbers, then develop their own real-world problems that model their representations. (7.NS.3) • In Module 4, Topic 3, Lesson 3, students independently demonstrate the use of mathematics when describing how to use a dot plot or stem-and-leaf plot to determine variation of data and the mean. In Talk the Talk, students write one to two paragraphs to summarize the key points in the lesson by explaining how it is possible to determine the mean and the variation of data for two populations from a dot plot or stem-and-leaf plot. They include answers to questions such as: “How can you compare the mean and the spread of data for two populations from a dot plot? If the measures of center for two populations are equivalent, how can the mean absolute variation show the differences in variation for two populations?” (7.SP.B) ### 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 + - Indicator Rating Details The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. Within each topic, students develop conceptual understanding by building upon prior knowledge and completing activities that demonstrate the underlying mathematics. Throughout the series of lessons in the topic, students have ample opportunity to practice new skills in relevant problems, both with teacher guidance and independently. Students also have opportunities to apply their knowledge in a variety of ways that let them show their understanding (graphic organizers, error analysis, real-world application, etc.). In general, the three aspects of rigor are fluidly interwoven. For example: In Module 5, Topic 1, Lesson 1 Overview, “Students are introduced to geometry and geometric constructions. Measuring tools are distinguished from construction tools, and the concepts of sketch, draw, and construct are differentiated. Students sketch and draw the same figure, and then they compare the processes used to create each figure. Point, line, and plane are described as the essential building blocks of geometry. Students learn how to properly draw, sketch, and name each of these essential building blocks. Line segment and endpoints are also defined, and students learn how to name and use symbols to represent them. Finally, they use a compass to construct circles and arcs. The terms arc, congruent, congruent line segments, and intersection are given. Students conclude the lesson by duplicating line segments and angles using only construction tools.” There are areas where an aspect of rigor is treated more independently, such as developing procedural skill and fluency in the MATHia software and Skills Practice or in the Performance Task were students work primarily with Application. ### Criterion 2e - 2g.iii Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice 10/10 + - Criterion Rating Details The instructional materials for Middle School Math Solution Course 2 meet the expectations for practice–content connections. The materials identify and use the MPs to enrich the content, attend to the full meaning of each MP, support the Standards' emphasis on mathematical reasoning, 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 + - Indicator Rating Details The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level. Standards for Mathematical Practice are referred to as Habits of Mind in this program. The Habits of Mind are identified in all lessons in both the teacher and student workbooks using an icon. There are four icons, only one represents a single MP, “attend to precision,” while the other three represent pairs of MPs, though generally one MP is the focus of the lesson. No icon is used for MP1, and it is stated in the Teacher’s Implementation Guide (TIG): “This practice is evident every day in every lesson. No icon used.” Each activity shows the practice or pair of practices being developed. Questions to facilitate the development of Habits of Mind are listed for both students and teachers throughout the program. The Habits are identified in the Overview in the Student and Teacher Editions, but not in the Family Guide that comes with the Topics. The icon appears within each lesson with questions listed in the Teacher Guide to facilitate the learning where they occur. Generally, lessons are developed with activities that require students to make sense of mathematics and to demonstrate their reasoning through problem solving, writing, discussing, and presenting. Overall, the materials clearly identify the MPs and incorporate them into the lessons. All the MPs are represented and attended to multiple times throughout the year. With the inclusion of the “Questions to Ask” in the Teacher Guide and the corresponding Facilitation Notes in each lesson, MPs are used to enrich the content and are not taught as a separate lesson. MP1 - Make sense of problems and persevere in solving them. • In Module 2, Topic 2, Lesson 2, students make sense of problems when classifying numbers. “What types of numbers are the quotients in Question 1? Use the definitions of the different number classifications to explain why this makes sense.” MP2 - Reason abstractly and quantitatively. • In Module 3, Topic 1, Lesson 1, students reason quantitatively when looking at various expressions. “The expressions $$3x^2 + 5$$ and $$-(1/2)xy$$ are examples of expressions that are not linear expressions. Provide a reason why each expression does not represent a linear expression.” • In Module 1, Topic 1, Lesson 1, students reason abstractly when they use a formula to compute circumference. In Activity 1.3, students create a formula for the circumference of any circle and use it to compute unknown values. MP5 - Use appropriate tools strategically. • In Module 5, Topic 1, Lesson 4, students use appropriate tools when constructing triangles with given angles. In Activity 4.1 A Triangle Given Three Angles, students construct various triangles. The lesson specifically states, ”Students should have access to construction tools, measuring tools, and patty paper.” MP6 - Attend to precision. • In Module 1, Topic 3: Lesson 2, students attend to precision when working with proportional relationships. “In a proportional relationship, the ratio of all y-values, or outputs, to their corresponding x-values, or inputs, is constant. This specific ratio, y to x, is called the constant of proportionality. Generally, the variable k is used to represent the constant of proportionality. Suppose you want to determine the actual lengths of your favorite television shows, without commercials, if you know the total program length. Identify the input and output quantities in this scenario.” ### Indicator 2f Materials carefully attend to the full meaning of each practice standard 2/2 + - Indicator Rating Details The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 meet expectations that the instructional materials carefully attend to the full meaning of each practice standard. Each activity asserts that a pair of practices are being developed, so there is some interpretation on the teacher’s part about which is the focus. In addition, what is labeled may not be the best example; i.e., using appropriate tools strategically (MP5) is sometimes weak where it’s labeled, but student choice is evident in Talk the Talk and Performance Tasks, which are not identified as MP5. Over the course of the year, the materials do attend to the full meaning of each mathematical practice. MP1 - Make sense of problems and persevere in solving them. • In Module 1, Topic 4, Lesson 4, students make sense of Percent Increase and Percent Decrease problems such as, “Casey added together all of the increases from 2000 to 2005 and subtracted the decreases. She concluded that there was about a 35 percent increase in gas price from 2000 to 2005. Is Casey correct? Explain why or why not.” MP2 - Reason abstractly and quantitatively. • In Module 1, Topic 4, Lesson 1, students reason about percent problems such as, “Dante has been shopping around for a new mountain bike. He found two bikes that he likes equally, one is sold at Mike’s Bikes for300, and the other is sold at Cycle Center for $275. Dante has a coupon for 25 percent off any bike at Mike’s Bikes. However, the manufacturer of the bike at Cycle Center has included a$40 rebate after the purchase of the bike. Where should Dante purchase his mountain bike? Show all of your work and explain your reasoning.”

MP3 - Construct viable arguments and critique the reasoning of others.

• In Module 1, Topic 1, Lesson 3, students use different strategies to determine the area of shaded regions inside geometric figures. They compare strategies from other students, explain the one they prefer, and use it to solve additional problems.

MP4 - Model with mathematics.

• In Module 4, Topic 1, Lesson 4, Talk the Talk, students develop a simulation to model different situations and describe one trial. They then conduct the simulations and answer related questions. Supplies such as coins, number cubes, spinners, and note cards for the experiments are provided for students to decide how they will simulate the situation to answer the questions.

MP5 - Use appropriate tools strategically.

• In Module 1, Topic 1, Talk the Talk, students are asked to use what they have learned during previous activities to now draw two circles, one with a radius length of 3 centimeters and one with a diameter length of 3 centimeters and compare their characteristics. No guidance is given on what tools are to be used when doing this.

MP6 - Attend to precision.

• In Module 5, Topic 1, Lesson 1, students are introduced to basic geometry vocabulary. New terms are defined by building on the understanding of the initial terms. Students use the mathematical notation, language, and definitions accurately. They also use tools to create constructions and draw conclusions from those constructions. In Talk the Talk, the problems state: “Use the given sides and angles to complete each construction. 1. Construct and label a segment twice the length of segment PQ. 2. Construct and label an angle twice the measure of angle P. 3. Identify all the points, lines, line segments, rays, and angles that you can in the two figures in Questions 1 and 2.”

MP7 - Look for and make use of structure.

• In Module 3, Topic 1, Lesson 2, students analyze an expression in order to write equivalent expressions using the distributive property. This lesson states, “Often, writing an expression in a different form reveals the structure of the expression. Meaghan saw that each expression could be rewritten as a product of two factors.”
• In Module 5, Topic 2, Lesson 5, students develop a strategy for calculating the areas of regular polygons, generalize it by decomposing regular polygons, and determine that they can calculate the area of one of the n congruent triangles in the n-gon and multiply the area by n to calculate the area of the regular polygon. They transfer their work to pentagons and any regular polygonal base of a prism or pyramid.

### 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 Carnegie Learning Middle School Math Solution Course 2 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

Students are consistently asked to verify their work, find mistakes, and look for patterns or similarities. The materials use a thumbs up and thumbs down icon on their “Who’s Correct” activities, where students question the strategy or determine if the solution is correct or incorrect and explain why. These situations have students critique work or answers that are presented to them.

Examples of students constructing viable arguments and/or analyzing the arguments of others include:

• In Module 1, Topic 3, Lesson 1, problems include: “Dontrell claims that the number of bird feeders Bob builds is proportional to the number of bird feeders Jake builds. Do you agree with Dontrell’s claim? Explain your reasoning.” and “Vanessa thinks that there are only two: one with a width of two inches and a length of six inches, and another with a width of three inches and a length of four inches. Is she correct? Explain your reasoning.”
• In Module 2, Topic 2, Lesson 3, “Vernice is told that the DC to Boston flight took 10 minutes longer than estimated. She calculated the percent error and got 10.3 percent. She later learns that she had been given the wrong information. The flight took 10 minutes less than estimated. Vernice thinks that the percent error should just be -10.3 percent. Is she correct? Explain why or why not.”
• In Module 4, Topic 1, Lesson 3, students construct viable arguments when evaluating the probability of the landing position for a cup in a game two friends are designing called Toss the Cup. “1. Predict the probability for each position in which the cup can land. 2. List the sample space for the game. 3. Can you use the sample space to determine the probability that the cup lands on its top, bottom, or side? Explain why or why not. 4) Do you think all the outcomes are equally likely? Explain your reasoning.”
• In Module 5, Topic 1, Lesson 3, “Sarah claims that even though two segment lengths would form many different triangles, she could use any three segment lengths as the three sides of a triangle. Sam does not agree. He thinks some combinations will not work. Who is correct? Remember, you need one counterexample to disprove a statement.”

### 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 Carnegie Learning Middle School Math Solution Course 2 meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. Throughout the teacher materials, there is extensive guidance with question prompts, especially for constructing viable arguments.

• In Module 1, Topic 2, Lesson 3, teachers are prompted to ask, “How are John David’s and Parker’s methods different? How did you verify Natalie’s method? Does using all three methods to solve this proportion always give you the same answer? Is one method easier to use than the other methods? How are the three methods similar to each other? How are the three methods different from each other? What method did you use to solve each proportion? Did the position of the unknown quantity factor into your method for solving the proportion? How can you check your solution to make sure it is correct?”
• In Module 1, Topic 4, Lesson 4, Activity 4.1, teachers are prompted to ask, “Does it matter which number is divided by which number? Will you get the same answer? What is the difference between computing the percent increase and the percent decrease? How do you know when to compute the percent increase or the percent decrease in a problem situation?”
• In Module 2, Topic 2, Lesson 3, Activity 3.2, teachers are prompted to ask, “How is calculating sums with two-color counters similar to calculating sums with a number line? What pattern(s) are you noticing?”
• In Module 3, Topic 1, Lesson 3, Combining Like Terms, teachers are prompted to ask, “Why is x+5 located to the left of x+10? Why is x+10 located to the right of x+5? What is an example of an expression that is located between x+5 and x+10? Is the value of x always a positive number in this situation? Can the value of x be a negative number? Can the variable x represent any number?”

### 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 Carnegie Learning Middle School Math Solution Course 2 meet expectations that materials attend to the specialized language of mathematics.

Each Topic has a “Topic Summary” with vocabulary given with both definitions and examples (problems, pictures, etc.) for each lesson. There is consistency with meaning, examples, and accuracy of the terms.

The materials provide explicit instruction in how to communicate mathematical thinking using words, diagrams, and symbols.

• In Module 5, Topic 1, Lesson 1.3, The terms angle, sides of an angle, vertex, and ray are defined for students. “An angle is formed by two rays that share a common endpoint. The angle symbol is ∠. The sides of an angle are the two rays. The vertex of an angle is the common endpoint the two rays share.” Students copy an angle using a compass and a straightedge. They then identify the angles and vertices of angles in their constructions.

The materials use precise and accurate terminology and definitions when describing mathematics and include support for students to use them.

• In Module 3, Topic 1, Lesson 1, the teacher guide provides detailed definitions to help with explanations. “Variables are used to represent unknown quantities and each quantity corresponds to a specific location on a number line. Values are substituted for the variable to validate the correct placement of the variables on the number lines.” The student book condenses this definition to a more student-friendly version. “In algebra, a variable is a letter or symbol that is used to represent an unknown quantity.”
• In Module 4, Topic 1, Lesson 3, students explain the difference between experimental and theoretical probability in their own words.

## Usability

### 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 for Middle School Math Solution Course 2 meet the expectations for being well designed and taking into account effective lesson structure and pacing. The instructional materials distinguish between problems and exercises, have exercises that are given in intentional sequences, have a variety in what students are asked to produce, and include 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that the underlying design of the materials distinguishes between problems and exercises.

The course has five modules with each module broken into topics. Each topic has a set of three to six lessons/activities. Each lesson consists of several sections, which may include Warm Up, Getting Started, Activities, Talk the Talk, and an Assignment. The Warm Up and Getting Started sections activate students’ prior knowledge and engage students in non-routine problem solving. The Activities develop students' understanding of concepts by exploring problems through both individual and whole group instruction. The students demonstrate their understanding of concepts by applying their knowledge to real-world problems in the Talk the Talk section. The Assignment includes five mini-sections that reinforce understanding of the new mathematical concept. Each lesson has a coordinating practice set called Skills Practice with exercises for students to solve using their new learning. MATHia (online) provides additional personalized exercises for students to show their understanding of the activity/lesson.

### 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that the design of assignments is not haphazard; exercises are given in intentional sequences.

Lessons follow a consistent format that intentionally sequences assignments:

• “Warm Up” - exercises that activate students’ prior knowledge.
• “Getting Started/Engage” - students solve/think/share and notice other’s work/thinking, usually for a non-routine problem.
• “Develop/Activities” - new learning takes place; students explore 5-10 problems that engage them with examples and explanations of the targeted skill. These are typically problems to solve together as a class with instructor guidance. Each Activity includes verbiage describing how the new knowledge relates to previous understanding.
• “Demonstrate/Talk the Talk” - students reflect on and connect what was learned.
• “Assignment” - five sections that review the lesson: Write - reviewing rules or vocabulary, Remember - summary of one to two key points, Practice - problems related to the activities, Stretch - an extension, and Review - looping in previous skills.

Students practice with “Learn Individually” lessons using the MATHia software or, if technology is not accessible, students use the Skills Practice workbooks.

Overall, each topic is sequenced to begin with prior knowledge and build upon that knowledge to develop conceptual understanding and procedural skill.

### 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that there is a variety in what students are asked to produce. Students are asked to produce a variety of products in digital and written form.

Some of these products include:

• Multiple representations through writing equations and expressions, drawing models, creating arrays, drawing and placing numbers on number lines, etc.
• In Module 1, Topic 2, Lesson 2, students complete a ratio table, explain how rate problems are solved, use the area of a small, shaded section to find the area of the larger section, and solve true and false questions.
• Justification of their thinking and others', critiquing others’ work, explaining why answers given are correct.
• Writing, reviewing, practicing, and stretching activities in each assignment given at the end of each lesson, such as sketching a model to make an estimate, then determining the actual solution and writing an equation. (Module 2, Topic 1, Lesson 5)

Finally, each module includes a real-world connection where students produce solutions in a variety of ways to demonstrate their knowledge, such as determining the cost of an item in various locations with different sales tax or analyzing patrons' visits to a museum to identify trends.

### 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 for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that manipulatives are faithful representations of the mathematical objects they represent and are appropriately connected to written methods.

Manipulatives are embedded in activities and the MATHia Independent Digital Lessons. Number lines, patty paper, equivalency cards, etc. are used throughout the year in connection to the mathematics being presented and are faithful representations. For example, to introduce adding integers, students use number cubes, two-color counters, number lines, and thermometers. (Module 2, Topic 1, Lesson 1)

### 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that the visual design is not distracting or chaotic and supports students in engaging thoughtfully with the subject.

The student materials are clear and consistent between modules within a grade level as well as across grade levels. The black and white design of the program is not distracting or chaotic. The text is supported by graphic elements that enhance the lesson, such as a highlighted worked example or various visual models to help with conceptual understanding. Both the textual and graphic elements complement each other and do not crowd the page or overwhelm the student with too much information.

Side bars complement the lesson and highlight important information. The informational side bars can include reminders of procedural steps, hints as to what strategies may need to be used to solve a problem, new vocabulary definitions, as well as reflective questions to students about their thinking. The program is logically organized with appropriate readability levels. Lesson numbers and activities are labeled in a consistent and orderly fashion. Each question in the student book is followed with a large open space for the student to write in, making the appearance uncluttered and easy to read and write.

### 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 Middle School Math Solution Course 2 partially meet the expectations for supporting teacher learning and understanding of the Standards. The instructional materials support: planning and providing learning experiences with quality questions; contain ample and useful notations and suggestions on how to present the content; and contain explanations of the grade-level mathematics in the context of the overall mathematics curriculum. However, the materials do not contain full, adult-level explanations and examples of the more advanced mathematics concepts.

### Indicator 3f

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

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that the materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students’ mathematical development.

In the Teacher Edition, facilitator notes for each activity include questions for the teacher to guide students' mathematical development and to elicit students' understanding. The material indicates that questions provided are intended to provoke thinking and provide facilitation through the mathematical practices as well as getting the students to think through their work. The Note provided on page FM-21 of the Teacher’s Implementation Guide Volume 1 reads, “When you are facilitating each lesson, listen carefully and value diversity of thought, redirect students’ questions with guiding questions, provide additional support with those struggling with a task, and hold students accountable for an end product. When students share their work, make your expectations clear, require that students defend and talk about their solutions, and monitor student progress by checking for understanding.”

Each lesson guide in the Teacher Edition provides quality questions to help guide students' mathematical development.

For example:

• “What strategies can you use to compare ratios?”
• “What do you remember about the graphs of equivalent ratios?”
• “Do the graphs of equivalent ratios lie on the same line?”
• “Does the line containing equivalent ratios always pass through the origin?”
• “If you draw a line to model the ratio relationship, does that mean that each point on the line will make sense in the problem situation?”

### 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that the materials contain a teacher 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 such as how to use and read data in the MATHia software.

In the Lesson Resources, the teacher guide provides information including a lesson overview, lesson structure and pacing facilitation notes, questions to ask, connections to standards, a materials list, essential ideas, facilitation notes, what to look for when students are working, and a summary of the lesson.

As part of the blended learning approach, there is Learning Individually with MATHia software. There is ample support for students and teachers to engage with this software such as the Getting Started guide, a table of contents, an RTI table of contents, and MATHia system requirements.

### 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 Carnegie Learning Middle School Math Solution Course 2 do not meet the expectation that materials contain a teacher edition (in print or clearly distinguished/accessible as a teacher edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematical concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.

• There are no adult-level explanations or examples for teachers to enhance their own knowledge of the content.
• Teachers are not provided any content beyond what the student sees in the student resources.
• The materials provide extensive information about how the content fits into the curriculum, but do not provide adult-level explanations or examples for teachers to understand the mathematics.

### 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 Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials contain a teacher edition (in print or clearly distinguished/accessible as a teacher 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 12.

• The Module Overview includes information for the teacher with explanations that build the teacher’s understanding of how the lesson content fits into the curriculum. It tells why the module is named, what mathematics is in the module, and how the module connects to prior and future learning.
• Each Topic Overview provides information on the mathematical content in the lessons as well as where it fits in the scope of mathematics from Kindergarten through Grade 12. Knowledge required from prior chapters and/or grades is explicitly called out in this section.
• The Topic Overview also has Spaced Reviews listed which links each lesson to standards from a previous grade. These reviews are embedded into each lesson.
• The Topic Overview describes the entry point or prior experience with the mathematical concept for students, why what is being learned is important, and how the activities in the topic promote student expertise in the MPs.

### 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 Carnegie Learning Middle School Math Solution Course 2 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).

• Each course in this series contains a Scope and Sequence/Table of Contents categorized by Module, Topic, and Lesson and includes the standard, pacing, summary, and the essential ideas of the mathematics.

### 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.
0/0
+
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.

• The Family Guide for each topic is available in PDF file that can be downloaded. The manual contains general topic information, what the students have learned in the past, what they will be learning, talking points, myths about math, keys for student success, vocabulary, content explanations, examples, and practice problems with answers aligned by topic and chapter.
• Families are also provided with generic tips about how to facilitate success:
• “To further nurture your child’s mathematical growth, attend to the learning environment. You can think of it as providing a nutritious mathematical diet that includes: discussing math in the real world, offering encouragement, being available to answer questions, allowing your student to struggle with difficult concepts, and providing space for plenty of practice.”
• “You can further support your student’s learning by asking questions about the work they do in class or at home.”
• How does this problem look like something you did in class?
• Can you show me the strategy you used to solve this problem?
• Do you know another way to solve it?
• Is there anything you don’t understand?
• How can you use today’s lesson to help?

### Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 contain explanations of the instructional approaches of the program and identification of the research-based strategies.

The Middle School Math Solution Teacher’s Implementation Guide contains both the research based strategies and the instructional approaches for the program.

• The instructional approach to learning is described as: “Carnegie Learning’s instructional approach is based upon the collective knowledge of our researchers, instructional designers, cognitive learning scientists, and master practitioners. It is based on a scientific understanding of how people learn and a real-world understanding of how to apply that science to mathematics instructional materials. At its core, our instructional approach is based on three simple yet critical components: Engage, Develop, and Demonstrate.” Each of these components is provided in detail. (FM-11,12)
• The components of the blended learning program are described in detail as well as giving a website to learn more about the approach. (FM-12)

### Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
8/10
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Criterion Rating Details

The instructional materials for Middle School Math Solution Course 2 partially meet the expectations for offering teachers resources and tools to collect ongoing data about student progress on the Standards. The instructional materials provide opportunities to collect information about students’ prior knowledge but lack strategies for about how to utilize the information in the classroom. The materials provide opportunities for identifying and addressing common student errors and misconceptions, ongoing review and practice with feedback, and assessments with standards clearly noted in most cases. The assessments contain detailed rubrics and answer keys, but there is no guidance for interpreting student performance or suggestions for follow-up.

### Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials provide strategies for gathering information about students’ prior knowledge within and across grade levels.

• There is a pretest for every topic in each module that addresses standards that will be taught. The post-test for the topic is the same test.
• The Topic Overview provides a list of Prerequisite Skills needed for the topic, which creates an indirect opportunity for teachers to gather information about students’ prior knowledge although there is no direct guidance provided to the teacher about how to use the information.
• The MATHia software is used as an assessment and progress monitoring tool, providing personalized data about where a student stands on various skills.
• In every assignment in the textbook, there is a Review section. Students practice two questions from the previous lesson, two questions from the previous topic, and two questions that address the fluency standards outlined in the Standards. This provides teachers information about students' learning gaps as they work through the instructional materials.

While there are opportunities to collect information about students’ prior knowledge, the materials do not provide strategies about how to utilize the information in the classroom.

### Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials provide strategies for teachers to identify and address common student errors and misconceptions.

• In the Topic Guide, lessons regularly have a section titled “Misconceptions” with suggestions for teachers to identify and address common student errors and misconceptions.
• Example: “If students decompose a negative mixed number as its whole number value and its fractional part, they may make a sign error by adding the fractional part instead of subtracting it. Help them to use the number line to see why this reasoning is incorrect.” (M2-69G)
• Teachers are encouraged to engage students in mathematical conversations to address student errors and misconceptions with phrases such as, “Remind the students…, Discuss with students…, Point out that….”
• MATHia software provides a solution pathway to common student misconceptions. “Like a human tutor, MATHia re-phrases questions, re-directs the student, and hones in on the parts of the problem that are proving difficult for the student. Hints are customized to address the individual student, understanding that there are often multiple ways to do the math correctly.”

### Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.

The materials provide several opportunities for ongoing review and practice:

• Students practice with “Learn Individually” lessons using the MATHia software or, if technology is not accessible, the Skills Practice workbooks. In the Skills Practice book, odd number answers are provided, so students know if they’re solving problems correctly; and in the MATHia software, feedback is continually given for both correct and incorrect answers.
• The MATHia software includes “Hints” which students can select while reviewing and practicing skills. There are three types of “Hints”:
• Just-in-Time Hints automatically appear when a student makes a common error.
• On-Demand Hints are hints that a student can ask for at any time while working on a problem.
• Step-by-Step demonstrates how to use the tools in a lesson by guiding step-by-step through a sample math problem.
• Each lesson ends with Talk the Talk, a few questions that capture the learning of all of the activities the students have engaged in with the lesson.
• Each lesson also has a short review section that provides a spiral review of previous concepts.
• Standardized Practice Test that the teacher can use at any time to review and practice concepts and skills learned throughout the course.
• Prior to each lesson there is a Warm-Up that reviews previous topics.

### Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

### Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
1/2
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Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 partially meet the expectation for assessments clearly denoting which standards are being emphasized.

• The series provides five options for assessment for every topic: Pretest, Post test, End of Topic test, Standardized Practice test, and a Performance Task. The Performance Task clearly notes which standards are being assessed.
• The other assessment options address the set of standards included in each topic, but there are no standards specifically attached to the questions or the assessments.
• It is stated in the materials that an assessment bank is also available through Edulastic, which is an optional tool that offers technology-enhanced items that can be used as-is or modified. However, reviewers did not evaluate this assessment bank.

### 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.
1/2
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Indicator Rating Details

The instructional materials reviewed for Carnegie Learning Middle School Math Solution Course 2 partially meet the expectation for assessments including aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

• The Performance Task includes a detailed scoring rubric.
• All other assessments provide an answer key, but no guidance about scoring.
• MATHia reports provide teachers with detailed information about student performance in relation to progress on standards.
• None of the assessment options provide guidance for teachers to interpret students performance and suggestions for follow-up.

### Indicator 3q

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

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 encourage students to monitor their own progress.

• MATHia software encourages students to monitor their own progress using strategies such as: Just-in-time hints, On-demand hints, a Progress Bar showing a summary of major skills, and Skill Tracking Behavior.
• There is an review for students at the end of every lesson which includes some spiral review of previous concepts.
• The Family Guide suggests questions for students such as, “Is there anything you don’t understand? How can you use today’s lesson to help?”
• Within the lessons, students do not monitor their own personal learning growth.

### Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
11/12
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Criterion Rating Details

The instructional materials for Middle School Math Solution Course 2 meet the expectations for providing strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners. The instructional materials provide a balanced portrayal of various demographic and personal characteristics. The instructional materials also consistently provide: tasks with multiple entry-points; support, accommodations, and modifications for English Language Learners and other special populations; and opportunities for teachers to use a variety of grouping strategies. There are opportunities for students to investigate mathematics content at greater depth, but they are intended for all students over the course of the school year, and there are very few tips for teachers to expand or deepen lessons.

### Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.

The materials include a detailed Scope and Sequence of the course, including pacing. The lesson summary and the essential ideas provide further information on sequencing of the lessons. There is a chart in the Teacher’s Implementation Guide that includes a table with a column entitled, “Connections to Prior Learning,” which enhances the opportunity to scaffold instruction by identifying prerequisite skills that students should have.

All lessons include instructional notes and classroom strategies that provide teachers with key math concepts, sample questions, differentiation strategies, discussion questions, possible misconceptions, what to look for from students, and summary points providing structure for the teacher in making content accessible to all learners.

### Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations for providing teachers with strategies for meeting the needs of a range of learners.

A primary strategy for meeting the needs of all learners in this program is MATHia software. MATHia differentiates the learning experience for every learner, adapting the amount of support based on the students answers and path through each problem. This level of support is similar to a one-on-one tutored experience, where the software is adapting based on everything the student is doing.

Most lessons provide “Differentiation strategies”, “Questions to ask” and a“Misconception” section. Most of the suggestions and the questions included in the “Questions to ask” section are intended for all students rather than geared toward helping students who struggle or challenging students ready to go deeper. For example, in Module 4, Topic 2, Lesson 3, Talk the Talk, Questions to ask, “What strategies did you use to list the possible outcomes? Do you think you could have used another model to help you organize all the possible outcomes for the game? What would have made the game not fair? Do you think the game would be fair if there were two more equal sections added to the spinner?”

However, in the “Differentiation strategies” section, suggestions are limited but more specific. For example, in Module 3, Topic 3, Lesson 4.3, “For students who struggle with scaling and interpreting graphs, you may want to provide a scaled graph for only the first 5 values in the table. This may help them “see” the unit rate on the graph more easily.”

### Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet the expectation that materials embed tasks with multiple entry­ points that can be solved using a variety of solution strategies or representations.

• Each Topic Overview includes a section called, “What is the entry point for students?” The Compound Probability Overview states: “In the prior topic, Introduction to Probability, students explored simple events. At the start of Compound Probability, students use two simple events—tossing two coins—and create an array of outcomes. Students have used arrays to represent relationships between numbers throughout their academic careers; here, they apply their knowledge of arrays to represent outcomes from conducting two simple events simultaneously. Students then use arrays and organized lists to list sample spaces and calculate probabilities for compound events. Throughout Compound Probability, probability concepts learned in the prior topic (e.g., experimental versus theoretical, making predictions, and simulation) are reinforced and deepened.”
• Some application tasks, particularly the Performance Task, allow for multiple solution strategies or representations. For example, Module 4, Topic 3, “Drawing Inferences” provides examples of box and whisker plots and prompts, “Without actually calculating the mean absolute deviation for the length of the visits, predict which exhibit would have more variation in length of visits. Why?”
• Some assessment questions allow for multiple entry-points. For example, in Module 3, Topic 3, End of Topic Test Form A, students are given a graph that shows the relationship between two quantities and are prompted to write a problem situation that fits the equation.
• Lesson activities provide limited opportunities for students to create their own solution paths since strategies are often provided.

### 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).
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet 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 (e.g., modifying vocabulary words within word problems).

ELL Tips are specifically cited throughout the materials. For example, “ELL Tip: After constructing dot plots, ask advanced English Language Learners to use mathematical vocabulary as they share their observations. Guide the discussion by providing students with vocabulary words that can be used in the discussion. Such words may include skewed right, skewed left, symmetric, clusters, data values, mean data values, and samples.” (M4-185)

Additional differentiation strategies included in the materials are often general, such as providing additional examples, using manipulatives, or using a graphic organizer.

Some suggestions are specific to the lesson, but don’t necessarily further knowledge such as, “Differentiation strategy: Have manipulatives that can be stacked, such as storage containers or styrofoam cups, for a demonstration or individual group use. It is important that the manipulatives have a consistent length that can be easily seen when the objects are stacked.” (M3-139F)

There are differentiation suggestions that do not include a rationale as to how they would provide support. For example, in Module 2, Topic 1, Lesson 5.2: “For students who struggle, explain that zero can be used for a qualifying height in Question 4, even though the qualifying height can’t possibly be zero.” It is unclear how this suggestion would support a student’s understanding, particularly if they are very concrete thinkers.

However, there are numerous examples that do support accommodations for special populations. For example:

• “For students who struggle with this context, explain the role of the concentrate and club soda in the recipe and act out the context by using food coloring and water. “ (M1-51C)
• “For students who struggle, have them label each part of the circle before cutting it out; have them put an “r” next to each radius and “C” on the inside of each curved part to demonstrate that it is part of the circumference. Once the parallelogram is composed, they will have an “r” on two sides to represent the height. They will be able to see that the other two sides are each composed of half of the circumference.” (M1-19D)
• “Provide students with sets of two-color counters to act out the examples. Students may find it helpful to remove pairs of positive and negative two-color counters from their desk model.” (M2-49E)
• “To support students who struggle, have two blank number lines to redo each example after the class discussion. Modifications may be to have students draw the two steps side by side on the number line rather than one above the other. Then as they show 5 and 8, have students show each individual “jump” as they count the spaces.” (M2-17D)
• “Have students interact with the worked example by using colored pencils to mark features of the graphs.” (M3-155F)
• “Compare and contrast these terms as they are encountered in this activity: line and line segment, circle and arc, congruent and equal, symbols.” (M5-7D)

### Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
1/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 partially meet the expectation that the materials provide opportunities for advanced students to investigate mathematics content at greater depth.

The problems provided are grade-level work and are intended for all students over the course of the school year. There are very few tips for teachers to expand or deepen the lesson.

• There are “Stretch” questions at the end of a lesson, but they are also designed for all students.
• Some of the differentiation suggestions are for extension but benefit all students such as: “Differentiation strategy: To extend the activity, have students write inequalities for the time frame when each plan is the less expensive plan, explain what constant in their price structure each company should emphasize when advertising” (M3-139C) It is not clear whether these are generic lesson extensions or geared toward advanced students.

### Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
2/2
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 meet expectations for providing a balanced portrayal of various demographic and personal characteristics.

• No examples of bias were found.
• Pictures, names, and situations present a variety of ethnicities and interests.
• The text is black and white with green as the only color. The people are gray with black hair, but still appear to represent many ethnicities.
• Problems include a wide span of international settings, as well as situations in urban, suburban, and rural settings.
• There is a wide variety of names in the problems, from James, Ben, and Haley to Keirstin, Miguel, and Miko, representing a variety of cultures.

### Indicator 3x

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

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 provide opportunities for teachers to use a variety of grouping strategies. The Blended Learning Model is explained in the Teacher’s Implementation Guide (FM-11). “Carnegie Learning delivers a different brand of blended learning: it combines collaborative group learning with focused individual learning. The two components are Learning Together and Learning Individually. Carnegie believes students “learn together” in a collaborative classroom model where they can think critically, reason mathematically, and learn from each other. Consumable textbooks and manipulatives allow them to engage directly with the mathematics as they learn. “Learning individually” offers two models: with or without technology. With MATHia, students learn independently using powerful 1-to-1 tutoring technology that adapts to give them exactly what they need at any given moment. With Skills Practice, students practice the important concepts of each topic to improve their problem-solving abilities and to gain fluency.”

Throughout the program, the facilitation guide instructs the teacher to, “Have students work individually to answer,” or “Have students work in groups or partners to answer question 2 and 3.” There is no explanation of how to form groups based on a skill or topic and/or why certain questions are given to groups or individuals.

### Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 partially encourage teachers to draw upon home language and culture to facilitate learning.

• There is no evidence of teachers drawing upon home language and culture to facilitate learning.
• There is a Family Guide with each Topic that explains the mathematics and provides tips to support learning, but it does not utilize aspects of language and culture.
• Materials are also available in Spanish.

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0
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Criterion Rating Details

The instructional materials for Middle School Math Solution Course 2 integrate technology in ways that engage students in the Mathematical Practices. The digital materials are web-based and compatible with multiple internet browsers, and they include opportunities to assess students' mathematical understandings and knowledge of procedural skills. The instructional materials include opportunities for teachers to personalize learning for all students, and the materials offer opportunities for customized, local use. However, the instructional materials do not include opportunities for teachers and/or students to collaborate with each other.

### 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.
0/0
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Indicator Rating Details

Online materials for Carnegie Learning Middle School Math Solution Course 2 (MATHia) integrate technology incorporating Mathematical Practices that include:

• Explore Tools to investigate different mathematical concepts, search for patterns, and look for structure
• Animations to watch, pause, and re-watch demonstrations of various mathematical concepts
• Classification Tools to categorize answers based on similarities
• Problem Solving Tools provide students with individualized and self-paced instruction that adapts to their needs
• Worked Examples to allow students to identify their own misconceptions

In MATHia, “Unit goals, based on CCSS and mathematical practices as well as aligned with the print materials, are listed at the beginning of the unit. Students are doing math by being engaged with sample problems and hints (just-in-time and on-demand), system help, a glossary, and a progress bar. Features are included to motivate and engage students like the creation of a personal avatar and tools such as 3D Geometry, Algebra Tiles, Fraction Shapes, and Pattern Blocks.”

### 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.
0/0
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Indicator Rating Details

Carnegie Learning Middle School Math Solution Course 2 claims that MATHia software will run on:

• Windows Computers with operating systems Windows 7 and 10
• Apple Computers with operating systems Mac OS X 10.11 or higher
• Apple iPads with iOS 10 or higher
• Windows Tablets with operating systems Window 8 or higher
• Android Tablets with Android 4.1 and above
• Chromebooks with ChromeOS 52 or higher
• It is not recommended for phones or small devices.

All of these, except Android tablets, were tested, and all access was successful.

### 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 for Carnegie Learning Middle School Math Solution Course 2 include opportunities to assess student mathematical understandings and knowledge of procedural skills using MATHia’s Adaptive Personalized Learning Reports. These reports provide information used for assessing students' learning and adjusting instruction.

### 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.
0/0
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Indicator Rating Details

Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. The MATHia software for Carnegie Learning Middle School Math Solution Course 2 is customizable for individual learners users. Teachers can select specific skills and levels for individuals, and it adapts to the learners' needs as they progress.

Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic. Within the lessons and assessment sections, the teacher chooses which exercises to assign students. Teachers can assign the lessons in any order; however, the lesson must be completed as provided before moving on. Additionally, these exercises cannot be modified for content or wording from the way in which they are given.

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.).
0/0
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Indicator Rating Details

The instructional materials for Carnegie Learning Middle School Math Solution Course 2 do not provide opportunities for teachers and/or students to collaborate with each other online or in any technology-based environment.

Report Published Date: 03/06/2018

Report Edition: 2018

Title ISBN Edition Publisher Year
Course 2: Student Edition 978-1-60972-890-8 Carnegie Learning 2017
Course 2 Blended: Student Edition and MATHia 978-1-60972-894-6 Carnegie Learning 2017
Course 2: Teacher Implementation Guide 978-60972-880-9 Carnegie Learning 2017

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.

• 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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