## Carnegie Learning Middle School Math Solution

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###### Usability
Our Review Process

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### Overall Summary

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

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

### Focus & Coherence

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 meet expectations for focus and coherence. For focus, the materials assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 meet expectations for focus as they assess grade-level content and provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

##### Indicator {{'1a' | indicatorName}}

Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

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. Examples include:

• Module 1, Topic 1, Standardized Test Practice, 8.G.2: Students use understanding of congruence in translations to determine the length of a side in an image. Question 2 states, “Blake drew square ABCD. Then, he drew the image of it, square A’B’C’D’, 2 centimeters to the right of the original figure. Line segment BC is 3 centimeters. How long is B’C’?”

• Module 3, Topic 2, Performance Task, 8.SP.1-4: Student create scatter plots and lines of best fit to investigate relationships between age and height. For example, in Patterns in Bivariate Data: Growing Tall: “The average height of girls from age 8 to 15 is plotted below. The second plot shows the heights of professional players on a WNBA team. Two graphs are displayed with data. Describe the pattern of each data set. What do the patterns indicate about the connection between the age and height? Explain. Estimate lines of best fit and use them to make predictions if possible. What would you expect to be the average height of an 18 year old? A 40 year old? Your work should include: Description of patterns of data and an explanation of the connections; Equations for approximate lines of best fit; A description of the slope and y-intercept for each line; Use of the lines of best fit to predict a future value.”

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning. The materials provide language support for students to learn math in English but there is no evidence of promoting home language knowledge as an asset to engage students in the content material or purposefully utilizing student home language in context with the materials.

The following general language supports are provided in the Front Matter across the series:

• “The write-in-nature of MATHbook allows students to highlight, annotate, and even write words in their native language.”

• MATHia includes a Glossary in English and Spanish to help students understand math specific vocabulary; however, the MATHbook Glossary is only available in English.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 partially provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning. The materials provide some guidance to encourage teachers to draw upon student cultural and social backgrounds, but the learning goals, instructional activities, and text are not presented in a context designed to leverage diverse cultural and social backgrounds of students.

The Front Matter in the Teacher’s Implementation Guide provides general guidance to encourage teachers to draw upon student cultural and social background to facilitate learning. The Front Matter states the following:

• “THINK ABOUT…How can you connect to students’ cultural, social, and geographic backgrounds and encourage them to share experiences from their lives?”

• “Student Look Fors…Appreciating the perspective of others and empathizing with their ideas are key elements of social awareness. Continually encourage students to appreciate diversity in perspectives, backgrounds, and culture as they work together during the years.”

Examples of guidance for teachers to draw upon student cultural and social backgrounds to facilitate learning throughout lessons includes:

• In Module 1, Topic 3, Lesson 1, Activity 1, the materials provide a note stating,“All situations provide opportunities for students to learn something new. Consider connecting to students’ cultural, social, and geographic backgrounds by encouraging them to share experiences from their lives related to the mathematical content similar to the given real-world situation.”

• In Module 3, Topic 2, Lesson 1, Activity 3, the materials provide a Student Look-Fors stating, “A classroom environment where students are mindful of classmates’ perspectives, cultures, and experiences.”

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 provide supports for different reading levels to ensure accessibility for students.

The following are examples where materials provide supports for different reading levels to ensure accessibility to students:

• The Teacher’s Implementation Guide for the series includes Language Links providing, “suggestions to support language acquisition for a broader range of academic and contextual terms.”

• Throughout the series, students can enable a text-to-speech feature in MATHia.

• IIn the digital material’s Help Center, under Math, Teaching Strategies, an article titled, “Reading Strategies to Engage All Students” can be used as a resource for teachers to support implementing materials with struggling readers. The following are a few recommendations from each section provided by the article:

• General Classroom Environment

• “Create word walls that include vocabulary from the software and the textbook.”

• “Provide highlighters and a coding structure for students to use when working in the consumable Carnegie Learning textbook.”

• “Maintain high expectations for all learners.”

• “Read or have a fluent student read the problem situation that begins each lesson.”

• “Avoid overt corrections when a student is reading; repeat with correct pronunciation.”

• “Provide students individual time to process the problem situation before engaging in the next part of the lesson.”

• “Group struggling readers, including English language learners, with strong, fluent readers.”

• “Create a structure within the student groups to ensure that each step of the problem is read aloud by a strong reader.”

• “Allow students to first write their answers in their native language before translation into English; stress the importance of communicating the mathematical concepts over getting the English grammar correct.”

• Assessing Mathematical Progress

• “Allow students to present solutions for the first time in their native language. As they become more comfortable with English, transition them into presenting in English.”

• “Ensure that all students are responsible for communicating the mathematics that they’ve learned.”

• “Explicitly review the directions for homework assignment; ensure that all students understand the tasks.”

• Software Interaction

• “Encourage student collaboration.”

• “Give explicit instructions on how to use the self-help tools of the Tutor.”

• “Provide students an opportunity to talk about what they are reading.”

The material uses, “MetaMetrics to conduct Lexile evaluations” of all their solutions to ensure that readability is appropriate. An email is provided so that users can be provided with additional details.

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Example of how Mathbooks manipulatives are accurate representations of mathematical objects and are connected to written methods:

• In Module 1, Topic 3, Lesson 1, Getting Started, students are instructed to, “Draw any triangle on a piece of patty paper. Tear off the triangle’s three angles. Arrange the angles so they are adjacent.” Students use the visual to, “Write a conjecture about the sum of the three angles in a triangle.”

• In Module 2, Topic 2, Lesson 6, Activity 1, students, “Carefully cut out the graphs, tables, contexts, and equations located on pages 299 and 301.” First, students match the equation card with the appropriate table, graph, or scenario. Then, students analyze the graphs.

Example of how MATHia’s manipulatives are accurate representations of mathematical objects and are connected to written methods:

• In Module 1, Topic 1, MATHia Software Workspaces, Rigid Motions on the Coordinate Plane, Translating Plane Figures, students are given a pre-image and image on the coordinate plane and need to select the appropriate transformation (options include reflection, rotation, dilation, horizontal translation, and vertical translation) and how to move the image (i.e. reflect over the x or y-axis, how many degrees to rotate, scale factor for a dilation, or number of units to move horizontally or vertically for a translation). Once students map the pre-image onto the image, students answer the following question, “Does the transformed pre-image match the image target?” and determine whether the pre-image and image are congruent and/or similar.

• In Module 4, Topic 2, MATHia Software Workspaces, The Pythagorean Theorem, Exploring the Pythagorean Theorem, students engage with an “Explore Tool” that provides a right triangle with squares along the edge of each triangle to investigate the Pythagorean Theorem. Students drag the corners to build triangles of certain lengths and see how the squares change, while examining how the areas of the two smaller squares compare to the area of the largest square.

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable. Throughout the series, the Front Matter in the Teacher’s Implementation guide states, “MATHbook + MATHia work in parallel to engage students with various learning experiences they need to understand the mathematics at each grade level.”

In Concept Builder Workspaces, students are exposed to animations, classifications, explore tools, real-world problem solving, and worked examples. In Mastery Workspaces, students are exposed to classification, equation solver, graphing tools, interactive diagrams, and real-world problem solving. Since MATHia is self-paced, students are supported in learning mathematics at the series standard.

Examples of how the materials integrate technology such as interactive tools, virtual manipulative/objects, and/or dynamic mathematics software in ways that engage students in the series standard using MATHia include:

• In Module 1, Topic 3, MATHia Software Workspaces, The Angle-Angle Similarity Theorem, Identifying Similar Triangles, students determine whether triangles are similar or nor similar. Students are given a table with angle pairs. Students use a drop down menu to identify the angle pair as congruent, not congruent, or cannot determine. Students use a second drop down menu to explain why the angles are congruent, not congruent, or cannot determine. Finally, students complete a multiple choice statement identifying the triangles as similar, not similar, or can not be determined.

• In Module 3, Topic 2, MATHia Software Workspaces, Drawing Lines of Best Fit, Estimating Lines of Best Fit, students are provided visual examples and definitions of scatterplots representing a negative linear association, positive linear association, outlier, non-linear pattern, and no clear association. Then they must classify seven scatter plots as a positive linear association, negative linear association, or no linear association in a drag-and-drop workspace, based on those examples and definitions.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 partially includes digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable. The materials include digital technology that provides opportunities for teacher to teacher and student to student collaboration but student to teacher collaboration is not provided.

Teachers are invited to collaborate with other educators through the “LONG + LIVE + MATH” community, “a like-minded community of educators to connect with and learn from”. Once joined, teachers will get invites to meetups, can join the online group,and have access to math-focused content through its blog.

The materials also provide LiveLab, a digital technology facilitating MATHia. LiveLab provides teachers with data, allowing teachers to identify students who need additional support. Although LiveLab offers data to teachers, it is not a form of communication between teachers and students.

The digital materials offer a MATHiaFlex resource that utilizes Flipgrid as a digital tool. Flipgids provides students the opportunity to, “...record videos ranging from 15 seconds to 10 minutes. Flipgrid features allow students to capture widescreen videos, pause while recording, add more after reviewing, trim to perfect their video, and erase and begin an unlimited number of times again. When finished, students take a picture to be displayed along with their responses and are able to add fun stickers and emojis. MATHiaFlex creates a grid community for your classroom so students can reply to each other’s videos.”

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 partially have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic. Although the materials have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, there are discrepancies between the lesson plans, google slides and the questions to support discourse.

Teacher and student materials are consistent in layout and structure across the grade. The general structure of MATHbook is organized by Modules, Topics, Lessons, and Activities. Each Lesson contains a Lesson Overview, Getting Started, Activities, Talk the Talk, and Assignment. Additionally, MATHbook contains an open space after each question for students to write.

Images, graphs, and models are not frequently used in MATHbook. When images, graphics, or models are included, they clearly communicate information supporting student understanding of topics, texts, or concepts.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Carnegie Learning Middle School Math Solution Course 3 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Front Matter in the Teacher’s Implementation Guide provides general information on Implementing MATHia. Each topic provides a chart showing the recommended sequence of MATHbook and MATHia sessions when utilizing the program in a parallel manner.

Teacher’s are also provided support with MATHia digitally through the program’s Help Center. Example of resources/articles supporting MATHia include, but are not limited to:

• Getting Started in MATHia

• MATHia FAQs articles

• Technical Help for MATHia articles

• Unlocking a MATHia Module

• Accessing MATHia Progress Trackers for MATHbook

## Report Overview

### Summary of Alignment & Usability for Carnegie Learning Middle School Math Solution | Math

#### Math 6-8

The materials reviewed for Carnegie Learning Middle School Math Solution meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability.

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

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### Overall Summary

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###### Usability
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