8th Grade - Gateway 3

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students to guide their mathematical development.

Examples of where and how the materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials include:

• Key instructional support through resources designed to enhance teacher effectiveness. The Unit Planning & Assessment pages offer access to both general course and unit-specific instructional information, ensuring teachers have the necessary materials for lesson execution. The PD Library includes written and video-based professional development on implementing Teacher Gems, Communication Breaks, Fluency Boards & Routines, and the 5E Instructional Model, equipping teachers with techniques for effective instruction. Additionally, the ELL Supports Guide provides strategies for ELL Proficiency Levels, Instructional Design, Mathematical Language Routines (MLRs), and Scaffolding Techniques. This guide includes resources such as a Word Problem Graphic Organizer, Target Trackers, Math Practice Trackers, a Math Self-Assessment Rubric, and a Vocabulary Journal Format, ensuring multilingual learners receive appropriate language supports.

• Lesson planning guidance is structured through unit resources that outline daily instructional expectations. The Unit Launch Guide provides a two-day lesson plan for introducing each unit, detailing required and optional components with class time allocations and facilitation instructions. These components include the Target Tracker Launch, Storyboard Launch, Fluency Board Launch, Readiness Check, and Unit Launch Teacher Gem, all designed to establish foundational knowledge. The Unit Finale Guide supports teachers in unit review, differentiation, and assessment through a three-day lesson plan incorporating the Unit Review, Unit Finale Teacher Gem, Fluency Board Finale, Storyboard Finale, and Assessments, along with explanations of assessment options.

• Lesson implementation support is embedded within the Teacher Guides, which contain detailed two-day lesson plans with structured guidance on instruction and differentiation. The At a Glance section provides a one-page lesson summary covering Standards, Materials, Starter Choice Board, Lesson Planning Overview, and Learning Outcomes. The Deep Dive section offers explicit lesson planning guidance, outlining both required and optional components with recommended class time. Day 1 lessons include the Starter Choice Board, Explore! Activity, Lesson Presentation, and Independent Practice, while Day 2 includes the Starter Choice Board, Teacher Gem options, Exit Card & Target Tracker, and additional Independent Practice. The Deep Dive also incorporates formative assessments, Focus Math Practices, Math Practices: Teacher and Student Moves, and Supports for Students with Learning and Language Differences, ensuring teachers have clear implementation strategies for diverse learners.

Materials include sufficient and useful annotations and suggestions that are embedded within specific learning objectives to support effective lesson implementation. Preparation materials, lesson narratives, and instructional supports provide teachers with structured lesson planning guidance, differentiation strategies, formative assessment recommendations, and opportunities for student engagement. These supports are found in resources such as the Unit Launch Guides, Unit Finale Guides, Lesson Planning Guidance, Teacher Guides, Deep Dive sections, Starter Choice Boards, and Small Group Instruction recommendations.

• Unit 3, Planning & Assessment, Unit Finale Guide, Lesson Planning Guidance: Day 3, “Assessments (40-45 minutes) Four summative assessment options are available, providing teachers with flexibility to select an assessment type that meets their needs. When selecting an assessment, teachers can consider whether they (a) desire a print-ready assessment versus a digital option, (b) prefer a traditional test versus a work sample and (c) if students require particular accommodations. Unit Assessment: The Unit Assessment is a print-ready traditional test which assesses all of the Focus Standards covered in the unit. This assessment offers constructed response items that range from Depth of Knowledge Levels 1 to 3 (Recall + Reproduce, Basic Skills + Concepts and Strategic Thinking). A ‘Form A’ and ‘Form B’ are provided, in which the questions are nearly identical but with different numbers. Tiered Unit Assessment: Like the Unit Assessment, the Tiered Assessment is a print-ready traditional test which assesses all of the Focus Standards covered in the unit using a constructed response format. This version of the assessment includes items that are nearly identical to the Unit Assessment, while providing common accommodations for students with special needs, such as fewer items, a lower reading level, friendlier numbers and more space to work. A ‘Form AT’ and ‘Form BT’ are provided, in which the questions are nearly identical but with different numbers. Online Unit Assessment: Like the Unit Assessment, the Online Unit Assessment assesses all of the Focus Standards covered in the unit at a variety of Depth of Knowledge levels. Unlike the Unit Assessment, which includes constructed response items, the Online Unit Assessment includes selected response items, such as multiple choice, select all that apply, true/false and yes/no. Teachers have the option to provide a print version of the Online Unit Assessment, found in the Editable Resources spreadsheet, to encourage students to show their work before submitting their answers digitally. A ‘Form A’ and ‘Form B’ are available, in which the questions are nearly identical but with different numbers. Performance Assessment: The Performance Assessment is a print-ready assessment in the style of a work sample, providing a Depth of Knowledge Level 4 (Extended Thinking) experience to demonstrate mastery of the unit’s standards. In the Unit 3 Performance Assessment, Students will attend to precision (SMP6) as they explore changing quantities using functions, proportional relationships and slope (8.F.A.1, 8.EE.B.5-6) to consider the impact of unit prices when designing fruit baskets. A grading rubric is also included.”

• Unit 5, Lesson 5.3, Teacher Guide, Deep Dive, Lesson Planning Guidance: Day 1, “Lesson Presentation (15-20 minutes) Have students utilize their interactive textbooks or composition notebooks to participate in guided note taking using the Lesson Presentation. Have students attempt Extra Examples with partners, in small groups or independently. Use ‘Communication Break’ slides as opportunities for meaningful discourse. Communication Break–Think, Ink, Pair, Square: Use the prompt ‘Why do you think this method is called substitution?’ Have students think and write independently before joining with a partner to share. Then have two partner sets join together. Ask one group to start and the other group respond using the sentence stems provided. Communication Break–Heads Together: Using Example 2, have students put pencils down and look at the question. Consider reading it together. Ask partner sets or small groups of students to examine the question and think about how it is similar or different to what they have already done in the lesson/unit and how that will affect solving the problem. Have students use the sentence stems to share out in groups and full class, if desired.”

• Unit 7, Lesson 7.4, Teacher Guide, Deep Dive, Math Practices: Teacher and Student Moves, “SMP1 Make sense of problems and persevere in solving them. Teacher Moves Talk with students about when you need to graph a figure to determine the solution to a question or when you can determine it without graphing. Some students may automatically resort to graphing to determine if the figure is a reduction or enlargement. Student Moves Explain how to determine if a dilation is an enlargement or reduction without graphing. SMP2 Reason abstractly and quantitatively. Teacher Moves Ask students to identify and define all quantities. Ask students to explain how the solution is related to the context. Prompt students to continually ask, “]’Does this make sense? How do you know?’ Consider asking students, ‘How is a dilation similar to and/or different from the other types of transformations in this unit?’ Student Moves For Student Lesson Exercises #13-14, determine the meaning of all quantities and distances in each task and how they relate to the situations. After finding a solution to each exercise, relate the solution back to the original context. SMP3 Construct viable arguments and critique the reasoning of others. Teacher Moves Develop students’ ability to justify methods for completing tasks involving transformations and compare their responses to the responses of the peers using the Teacher Gem Stations. Student Moves Communicate mathematical ideas, vocabulary, and methods effectively by comparing answers with peers and justifying the work of others using the Teacher Gem activity Stations.”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for containing adult-level explanations and examples of the more complex grade/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

Each Unit’s Planning & Assessment page includes a PD Library that provides teachers with access to Achieve the Core open-source publications from Student Achievement Partners. These documents offer adult-level explanations of mathematical content, organized by vertical progression within each domain. Additionally, the Planning & Assessment page contains a Unit Overview with the following information:

The Content Analysis section explains the major mathematical concepts taught in the unit, providing examples and explanations to enhance teachers’ understanding of both the content and its vertical progression within the standards. It also illustrates the types of tasks and procedures students will encounter. For example: 

• Unit 3, Planning & Assessment, Unit Overview, Content Analysis states, “Unit 3, Planning & Assessment, Unit Overview, Content Analysis states, “In this unit, students will build upon their work with two-variable equations, tables and graphs in earlier courses to explore relationships in which one quantity is a function of another. Previously in Unit 1 Equations, students worked exclusively with equations in one variable. This unit begins the exploration of equations in two variables in this course, with a specific focus on determining whether relationships between variables presented in tables or graphs represent functions. Though this unit introduces students to the concept of a function, a formal understanding of domain, range and function notation will not occur in this course.” Visual student examples of Relationships that are Functions and Relationships that are not Functions are provided for teachers to review. “This unit revisits students’ work with proportional relationships from Grade 7 as an introduction to linear functions. Students represent and compare functions of proportional relationships in equations, tables and graphs with a focus on identifying the unit rate (or constant of proportionality). By the end of the unit, students are introduced to the concept of slope, which they will calculate for both proportional and non-proportional linear relationships. The slope of a proportional relationship has a constant rate, whereas the slope of a non-proportional linear relationship has a constant rate of change.” Visual student examples of proportional and nonproportional graphs are provided for teachers to review. “Students learn about the four classifications of slope and make the connection that a linear relationship in the form x = a is a linear equation but not a linear function. They build upon their work with calculating distance on the coordinate plane from Unit 2 Pythagorean Theorem to develop the slope formula.” Visual student examples of finding slope from a table and using the slope formula are provided for teachers to review. “While students are introduced to slopes of non-proportional linear relationships in this unit, they will not specifically work with equations in the form y = mx + b, where b ≠ 0, until Unit 4 Functions.”

The Learning Progression section explains and provides specific examples of the vertical progression of standards within the unit’s targeted domains. These examples include diagrams, models, numerical or algebraic representations, sample problems, and solution pathways. The Learning Progression is structured under the headings: ‘Previously, students have…, ‘In this unit, students will…,’ and ‘In the future, students will…’ with corresponding standards identified. For example:

• Unit 6, Planning & Assessment, Unit Overview, Content Analysis, Readiness Check & Learning Progression states, “In the future, students will… Prove theorems about lines and angles. HS.G-CO-C.9, Prove theorems about triangles. HS.G-CO.C.10, Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems. HS.G-GPE.B.5, Use properties of similarity transformations to establish AA criterion for two triangles to be similar. HS.G-SRT.B.4”

• Unit 9, Planning & Assessment, Unit Overview, Content Analysis, Readiness Check & Learning Progression states, “In this unit, students will… Know the formula for volume of a cone and use it to solve real-world problems. 8.G.C.9, Know the formula for volume of a cylinder and use it to solve real-world problems. 8.G.C.9, Know the formula for volume of a sphere and use it to solve real-world problems. 8.G.C.9”

Each lesson’s Teacher Guide includes a Common Misconceptions section, which identifies common errors and provides explanations and recommendations to help students develop a stronger understanding. For example: 

• Unit 4, Lesson 4.2, Teacher Guide, Supports for Students with Learning and Language Differences, Common Misconceptions states, “One of the most common errors students make when graphing lines from slope-intercept form is confusing the rise and run in the ratio for slope. This mistake is easily observed as students calculate slope. Vocabulary foldables using the terms rise and run may help students remember the differences. Some students may graph the y-intercept as the x-intercept. Have students circle the slope and y-intercept in the linear equation and then label each as such to reinforce the slope being the coefficient of x and the constant representing the y-intercept (not the x-intercept). If a linear equation is written in the form y = b + mx, students may be confused by the order. Reinforce the use of the Commutative Property of Addition with students and help them see how they can rewrite the equation (if desired) to be in y = mx + b form. Students may forget that not every linear function is a proportional relationship (going through the origin). Explain that proportional relationships belong to the linear function family and are a special case of linear functions.”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Standards correlation information is included to support teachers in making connections from grade-level content to prior and future content. Standards can be found in multiple places throughout the course, including the Course Level, Unit Level, and Lesson Level of the program. Examples include:

• Each Unit’s Planning and Assessment section includes a Pacing Guide & Correlations, where the EdGems Math Course 3 Content Standards Alignment lists all grade-level standards along with the specific lessons where they are addressed. The program provides a structured approach to standards alignment through its Focus and Connecting Standards framework. A correlation chart is included, organizing standards into columns that indicate where each standard is taught as a Focus Standard in specific lessons and as a Connecting Standard across different units. This structure helps ensure that concepts are reinforced and revisited throughout the course.

  • “EdGems Math supports students’ proficiency in the Common Core State Standards through a program-design which supports the interconnectivity of mathematical ideas while providing clear learning objectives. This is achieved by designating Focus Standards in each lesson and Connecting Standards in each unit. The qualifiers of Focus and Connecting Standards were developed by the EdGems Math authoring team to design a scope and sequence in which mathematical ideas build upon each other and are revisited throughout the course. Each EdGems Math lesson identifies one or more standards as a Focus Standard to provide a focal point for the lesson objectives. The unit then provides opportunities for further connections to other standards across clusters and domains. These Connecting Standards offer opportunities for students to draw up and apply many mathematical ideas throughout the unit. The following chart shows when each standard is aligned as a Focus Standard or Connecting Standard throughout the course. Further explanations of the Focus and Connecting Standards are available within each Unit Overview.”

• Unit 4, Planning and Assessment, Unit Overview, Standards Correlation, Focus Content Standards states, “This unit incorporates Focus Standards across two domains and three major clusters. Standard 8.EE.B.6 was previously a Focus Standard in Unit 3 Proportional Relationships and Slope and will reappear again as a Focus Standard in Unit 6 Angle Relationships. 8.F.A.2 was also previously targeted in Unit 3. It reappears in this unit alongside 8.F.A.3 to conclude instruction on the cluster. The other major cluster in the Functions domain is also targeted in this unit, completing the concentration on the Functions domain for the remainder of the course. All standards in this unit are formatively assessed throughout the unit and summatively assessed in the unit’s Test Prep, Performance Assessment and Unit Assessments.”

• Each Unit's Planning & Assessment section includes a PD Library with resources from Achieve the Core to support professional learning and instructional planning. These resources offer in-depth explanations of mathematical progressions aligned with the Common Core State Standards.

  • “CCSS Math Learning Progressions: Student Achievement Partners, a nonprofit organization, developed Achieve The Core to provide free professional learning and planning resources to teachers and districts across the country. The narrative documents below provide adult-level descriptions of the progression of mathematical ideas within domains or topics within the Common Core State standards for Mathematics.”

The Planning & Assessment sections within each unit provide coherence by summarizing content connections across grades. These sections highlight how mathematical concepts build upon prior knowledge and prepare students for future learning. Examples of where explanations of the role of specific grade-level mathematics appear in the context of the series include:

• Unit 2, Planning & Assessment, Unit Overview, Connecting Content Standards states, “As students develop their understanding of the Pythagorean Theorem, they will have ample opportunities to solve multi-step linear equations (8.EE.C.7) and equations involving exponents (8.EE.A.2). The Pythagorean Theorem offers students natural connections to irrational numbers (8.NS.A.1-2), and the concept of Pythagorean triples is a building block towards future work with proportions and similar triangles. Students will also make connections to similarity (8.G.A.4-5) when multiplying common Pythagorean triples by a constant to identify other sets of side lengths that form right triangles.”

• Unit 2, Planning and Assessment, Unit Overview, Readiness Check & Learning Progression includes a structured progression of learning, outlining prior knowledge, current instructional goals, and future learning connections to reinforce coherence across grades. It states, "Previously, students have… Graphed polygons in the coordinate plane and determined their side lengths (5.G.A.1-2, 6.G.A.3), solved problems involving area, volume, and surface area (6.G.A.1-2, 7.G.B.6), solved equations involving square or cube roots (8.EE.A.2), and understood the concept of irrational numbers and compared their sizes (8.NS.A.1-2). In this unit, students will… Understand and explain the Pythagorean Theorem (8.G.B.6), apply the Pythagorean Theorem to determine side lengths in right triangles (8.G.B.7), and use the Pythagorean Theorem in the coordinate plane (8.G.B.8). In the future, students will… Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to an understanding of trigonometric ratios (HS.G-SRT.C.6), use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied problems (HS.G.SRT.C.8), and use coordinates to compute the perimeters of polygons using the distance formula (HS.B-GPE.B.7)."

• Unit 6, Lesson 6.2, Teacher Guide, Standards Overview states, “Focus Content Standard(s): 8.G.A.5 (Major)” Starter Choice Board Overview, “Storyboard: Describe alternate interior and alternate exterior angles (8.G.A.5) Building Blocks: Solve equations (8.EE.C.7) Blast from the Past: Blast from the Past: Determine solutions for inequalities Fluency Board Skills: Plot approximations on a number line, graph linear equations in slope-intercept form, multiply and divide fractions.” 

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Instructional approaches of the program and identification of the research-based strategies can be found throughout the materials, but particularly within each unit’s Planning & Assessment, About EdGems Math, Research Guide. 

Research Guide states, “Middle school is a critical stage for math instruction. Students form conclusions about their mathematical abilities, interests, and motivation.^1-10 Middle school students in the United States are falling behind compared to other countries in their math performance.² Studies have shown that struggles with math are particularly acute in middle school grades. The transition from elementary to middle school can lead to students falling behind with accumulated learning gaps.^3-5 Research shows that the mathematical achievement of middle schoolers has a direct impact on the likelihood that they will persist through the challenging material in pathways that can prepare them for the broadest range of options in high school and beyond.^6-7 Within this crucial time frame, a principal goal for middle school math teachers is to create a learning environment in which students are encouraged to see themselves as capable thinkers and doers of mathematics. Research demonstrates that to do this successfully, instructional materials must provide teachers with opportunities to 1) build upon and expand students’ cultural knowledge bases, identities, and experiences, 2) actively support students’ conceptual understanding, engagement, and motivation, 3) provide relevant, problem-oriented tasks that enables them to combine explicit instruction about key ideas with well-designed inquiry opportunities, and 4) spark student peer-to-peer discussion, perseverance and curiosity as they think and reason mathematically to solve problems in mathematical and real-world contexts.⁸ EdGems Math has been intentionally designed to support the diverse mathematical journeys of middle school students as they grow in their learning, critical thinking, and reasoning abilities. To reach the goal of higher order thinking for all, the EdGems Math curriculum connects each grade’s foundational math concepts to authentic, real-world contexts taught in multi-dimensional ways that meet a variety of learning needs. EdGems Math empowers teachers to adjust the content and instructional strategy and tailor outcomes of how learning is assessed.^9-10 EdGems Math curriculum is comprehensive, rigorous, and focused. It draws on decades of research exploring the best methods for teaching and learning math.”

The Unit Planning & Assessment, About EdGems Math, Research Guide incorporates multiple research-based strategies to support student learning:

• “Explore! Activities: The lesson-based Explore! Activities engage students in scaffolded tasks, guiding students as they begin grappling with the big ideas of the lesson and discovering new concepts (Small, M. and Lin, A.). The steps of the Explore! Activities move students through ‘Comprehension Checkpoints’ (National Council of Teachers of Mathematics) to guide information processing, ensure prior knowledge is activated, and discover patterns, big ideas, and relationships. Utilizing a student-centered approach, Explore! Activities engage students in the Standards of Mathematical Practice, which allows teachers to better facilitate learning using effective mathematical teaching practices (McCullum, W.). Every Explore! Activity provides students with ways to connect to key concepts through investigative, discovery-based tasks, culminating in an opportunity to generalize or transfer learning and move toward procedural and strategic proficiencies (California Department of Education).”

• “Lesson Presentation Communication Breaks: Communication Breaks are integrated into each Lesson Presentation as an opportunity for students to make sense of their learning. Each Lesson Presentation features two of seven structures to support students in the communication of their ideas or questions directly with their peers. The use of sentence stems in each Communication Break increases accessibility, enabling students to develop both social and academic language as they reflect on their learning (Smith et al.). The structures of Communication Breaks allow teachers to elicit student thinking, provide multiple entry points, focus students’ attention on structure, and facilitate student discourse (Chapin, S.H., O’Connor, C., Anderson, N.). As a result, students engage in the Standards of Mathematical Practice and gradually become more secure in their understanding and abilities to develop their knowledge (Bay-Williams, J.M., & Livers, S.).”

• “Mathematical Language Routines: Within every Teacher Lesson Guide are instructional supports and practices called Mathematical Language Routines to help teachers recognize and support students’ language development in the context of mathematical sense-making when planning and delivering lessons (Aguirre, J. M. & Bunch, G. C.). While Mathematical Language Routines can support all students when reading, writing, listening, conversing, and representing in math, they are particularly well-suited to meet the needs of linguistically and culturally diverse students. When students use language in ways that are purposeful and meaningful for themselves, they are motivated to attend to ways in which language can be both clarified and clarifying (Mondada, L. & Pekarek Doehler, S.). These routines help teachers ‘amplify, assess, and develop students’ language in math class’ (Zwiers, J. et al).”

• “Lesson Presentation: The editable Lesson Presentation enables teachers to shape lessons of balanced instruction on mathematical content and practice as they guide students through productive perseverance, small group instruction, and growth mindset activities. Components of the Lesson Presentation include Fluency Routines to develop number sense, vocabulary terms with definitions, examples with solution pathways, extra examples, the Explore! activity, Communication Breaks, and a formative assessment Exit Card. Teaching tips provide guidance on independent, group, and whole-class instruction. Studies identify explicit attention to concepts and students’ opportunity to struggle (as during the Explore! activity and Communication Breaks) as key teaching features that foster conceptual understanding (Hiebert, J., & Grouws, D. A.).”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities. 

Comprehensive lists of materials needed for instruction can be found in the PD Library link on the Unit Planning & Assessments page. The Required & Recommended Materials document provides a lesson-by-lesson breakdown of necessary resources for the course. Additionally, the Teacher Guide for each lesson includes a list of required materials. Examples include:

• Unit 1, Lesson 1.1, Teacher Guide, Materials states, “Required: Equation mats and algebra tiles (for the Explore! activity) Optional: Unifix cubes, base ten blocks, colored pencils, graph paper, and balances”

• Unit 7, Lesson 7.3, Teacher Guide, Materials states, “Required: Patty paper or tracing paper, graph paper (4 quadrants), protractor (for the Explore! activity) Optional: Markers, grid paper, geometric shapes”

• Unit 9, Lesson 9.2, Teacher Guide, Materials states,“Required: Cylinders and cones, rice, beans or popcorn kernels (for the Explore! activity) Optional: Geometric software, sand, measuring tools, grid paper”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Each Unit Overview outlines standards alignment for formal assessments, including the Readiness Check, Performance Assessment, and Fluency Pre- and Post-Assessments. The EdGems website provides grade-level standards alignment for all formal assessments, including Assessments, Tiered Assessments, Performance Assessment, Unit Review (Print and Online), and Review & Assessments, accessible via the information (“i”) button at the bottom right corner of the icon. Each question's assessed standard(s) is listed for teachers, while only the Performance Assessment and Performance Task include practice standards. Examples include:

• Unit 2, Planning & Assessment, Unit Overview, Performance Task states, “In ‘Cross Country Race,’ students will apply the Pythagorean Theorem to determine the distance jogged by a participant before the race. Students will construct viable arguments (SMP3) as they discover shape and space using distance on the coordinate plane and rates (8.G.G.7-8, 7.RP.A.1) to predict if the participant will make it back in time before the race begins."

• Unit 2, Planning & Assessment, Unit Overview, Performance Assessment states, “In this Performance Assessment, students will analyze the map of a lake and plan a family fishing trip. Students will use appropriate tools strategically (SMP5) and discover shape and space as they apply the Pythagorean Theorem and the distance formula (8.G.B.6-8) to make sense of the connections between right triangles and distance on the coordinate plane.”

• Unit 4, Planning & Assessment, Assessments, Exercise 12 states, “Last week, Chet rented a beach bike from Top Notch Bike Rental Company. They charge an initial fee plus $1 for each hour the bike is rented. Chet rented a bike for 6 hours and was charged $10. This week, he wants to try a new bike rental shop, Cruiser Rentals. Cruiser Rentals charges their customers according to the equation y=1.5x, where x represents the number of hours and y represents the total cost of the rental. Which company charges more per hour?” The assessment information identifies the standard alignment as 8.EE.B.6/8.F.A.2/8.F.B.4.

• Unit 10, Materials, Online Review & Assessments, Online Unit Review, Item 4 states, “Michelle sells flowers for weddings. The price she charges (P) can be approximated by the equation for the line of fit: P=40+12d, where d represents how many dozens of flowers are ordered. Ann paid Michelle $400 for the flowers at her wedding. How many dozens of flowers did Ann order?” The assessment information identifies the standard alignment as 8.SP.A.3.

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up. 

Each Lesson At A Glance in the Teacher Guide outlines specific learning goals, ensuring that teachers know the math standards that students should be able to demonstrate by the end of the lesson. Exit Cards serve as formative assessments, providing a real-time snapshot of student understanding, while a related Student Lesson exercise offers another checkpoint to identify students needing additional support. The EdGems website provides rubrics for scoring Exit Cards, ensuring consistency in evaluation.

The Online Class Results page generates automatic proficiency ratings based on student performance in Online Practice, Online Challenge, Test Prep, and Online Unit Reviews. These ratings align with state assessment benchmarks, helping teachers interpret mastery levels. Assessment Scoring Guides for Unit Assessments and Tiered Assessments follow the same ranking system, allowing teachers to track progress across multiple assessment formats.

Teachers receive real-time student performance insights through Teacher Gem activities, which embed informal assessment opportunities. For example, in Relay, teachers track how often a team revises an answer before moving forward, and in Ticket Time, class dot plots allow teachers to identify common errors. The PD Library provides written and video-based facilitation guides to support teachers in implementing these strategies effectively.

The Lesson Guide Deep Dive helps teachers analyze assessment data and adjust instruction accordingly. Exit Card results inform assignments for Leveled Practice and Differentiation Days, while the Differentiation Day guides provide self-assessments and targeted rotations to meet diverse learning needs. The Deep Dive section also identifies common misconceptions, equipping teachers with strategies to proactively address misunderstandings.

Performance assessments include rubrics for teacher grading and student self-reflection prompts, reinforcing the Standards for Mathematical Practice (SMP). The Unit Overview and Lesson Guide At A Glance ensure that all assessments and activities align with content and practice standards, with detailed mapping to Readiness Check skills, Storyboards, Performance Tasks, Fluency Boards, and Tiered Assessments.

To further support follow-up instruction, the Online Class Results tool provides recommended activities based on student proficiency levels, allowing teachers to tailor instructional strategies. By incorporating structured assessments, clear proficiency guidance, real-time monitoring tools, and differentiation strategies, EdGems Math ensures teachers have the necessary resources to assess student learning, interpret performance data, and provide targeted follow-up instruction.

Examples include: 

• Unit 4, Planning & Assessment, includes Form A and Form B of the Unit 4 Assessment, along with an Answer Key and Assessment Scoring Guidelines for each question. The materials state, “3-point Items: #12, 13, 17 Items that are each worth three points consist primarily of Depth of Knowledge Level 3 items considered 'Strategic Thinking'. Students may earn partial credit on items when showing progress on a solution pathway that connects to the concept being assessed with one or more errors. Students can earn either 0, 1, 2 or 3 points for items in this category. 0 points: An incorrect solution is given with no work or with work that does not show understanding of the concept. 1 point: Progress is made towards a correct solution, but multiple errors have been made. OR A correct solution is given with no supporting work or explanation. 2 points: Progress is made towards a correct solution, but one small error is made. OR A correct solution is given with partial supporting work provided. 3 points: The correct solution is given and is supported by necessary work or explanation. Total Points Possible: 33 Not Yet Met 0-19, Nearly Meets 20-23, Meets 24-29, Exceeds 30-33” Similar guidance is provided for 1 and 2 point assessment items.

• Unit 10, Planning & Assessment, Performance Assessment, Performance Assessment Rubric ~ Student Reflection states, “Describe at least two ways you demonstrated the Focus Math practice below while completing this performance assessment. SMP7 I can look for and use structure to improve my understanding. I made a connection between different representations. I noticed a structure that helped me understand a concept. I made a rule for when something is always, sometimes or never true.” The Performance Assessment Rubric ~ Teacher Grading Rubric consists of four categories rated on a scale of 4 to 1 and a space for Comments. The four categories are “Making Sense of the Problem: Interpret the concepts of the assessment and translate them into mathematics. Representing and Solving the Problem: Select an effective strategy that uses models, pictures, diagrams, and/or symbols to represent and solve problems. Communicating Reasoning: Effectively communicate mathematical reasoning and clearly use mathematical language. Accuracy: Solutions are correct and supported.”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of the course-level standards and practices across the series.

Assessments align with grade-level content and practice standards through various item types, including multiple-choice, short answer, extended response prompts, graphing, mistake analysis, and constructed response items. They are available as downloadable PDFs for in-class printing and administration or can be completed through the online platform. Examples include:

• Unit 2, Materials, Online Review & Assessments, Unit Assessment, Form A, includes two items that demonstrate the full intent of 8.G.7. The materials state, “1. What is the length of the hypotenuse in the triangle? a. \approx 4.8 b. 17 c. 23 d. 289” An image of a right triangle with legs 8 and 15 is provided. “4. Seth bikes 3 miles south then 2 miles west. If Seth walks directly back to his starting point, how far will he walk? a. \approx 1 mile b. 6 miles c. \approx 5 miles d. \approx 13 miles”

• Unit 5, Planning & Assessment, Performance Assessment includes five items that demonstrate the full intent of 8.EE.8 and SMP3. The materials state, “Olaf wants to build a small rectangular concrete patio in his backyard. Two separate builders have given him bids. Builder #1 charges an initial fee of $50 plus $1.50 per square foot. Builder #2 does not have an initial fee and charges $2.50 per square foot. 1. Olaf wants the patio to form a rectangle measuring 7 feet by 10 feet. Which builder will be the least expensive in this case? Show all work necessary to justify your answer. 2. Olaf believes that if he builds a 64 square foot patio, it will cost $146 no matter who he chooses. Write Olaf’s prediction as an ordered pair. Do you agree or disagree with Olaf? Show all work necessary to justify your answer. 3. Write a system of equations that represents Olaf’s options for the cost of building his patio. Let 𝑥 represent the number of square feet of concrete and 𝑦𝑦 represent the total cost. 4. Solve the system of equations you wrote using either substitution or elimination. Explain your solution in the context of the problem. 5. Graph the system of equations. Does your graph verify your solution?”

• Unit 8, Planning & Assessment, Assessments, Form A, includes two items that demonstrate the full intent of 8.EE.1, Exercise 2. The materials state, “Simplify. \frac{3^{13}}{3^{6}}” Exercise 12, “Esther wrote the equation at the right. a. Give a possible value for a and b that would make the equation true. b. If the value of a is 11, what is the value of b? c. Write an equation relating a, b and 7 that is true for all values in Esther’s equation.” The equation \frac{5^{b}}{5^{a}}=5^{7} is provided.

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

For each lesson, teacher guidance is provided alongside the Teacher Gem activity, which includes strategies to support instruction and student engagement. Printable PDF resources, such as the Student Lesson Textbook and Interactive consumable, include tools like graphic organizers, sentence stems, number lines, and coordinate planes. Lessons are also available as e-books with features including adjustable font sizes, text highlighting, text-to-speech, and note-taking tools.

Resources that support students in special populations to actively participate in learning grade level mathematics include:

• Differentiation Days: Differentiation Days are designed to provide teachers with structured opportunities to work with small groups based on specific learning targets. During these sessions, other students participate in mixed-ability group rotations, including the Teacher Small Group Rotation, Additional Practice Rotation, Application Rotation, and Tech Rotation. 

• Leveled Practice: The program includes three levels of leveled practice to address varying student needs. “Leveled Practice-T” is structured for students with learning and language differences, offering shorter problem sets, additional workspace, and simplified terminology and numbers to align with accessibility needs while maintaining grade-level alignment.

• ELL Supports: ELL supports are provided in the Planning and Assessment menu of each unit. These include explanations of Mathematical Language Routines (MLRs) and specific directions for incorporating these routines into lessons and activities. 

Each lesson includes Spanish translations of the student lesson, Explore! activities, leveled practice, and Exit tickets. Accompanying videos are included to guide students through the lesson content. These resources are structured to support student learning and accessibility.

Examples of the materials providing strategies and support for students in special populations include:

• Unit 3, Lesson 3.3, Lesson Presentation, Slide 15, Communication Break - Heads Together states, “Graph a line with a slope of 2. How is the problem similar or different to other problems we have done? One way the problem is similar is… One way this problem is different is… How do you think this will affect solving the problem? This might affect solving the problem by… To solve this problem, we will need to…” Lesson Guide, Teacher Presentation “Have students utilize their interactive textbooks or composition notebooks to participate in guided note taking using the Lesson Presentation. Have students attempt Extra Examples with partners, in small groups or independently. Use ‘Communication Break’ slides as opportunities for meaningful discourse. Heads Together: Using Example 3, have students put pencils down and look at the question. Consider reading it together. Ask partner sets or small groups of students to examine the question and think about how it is similar or different to what they have already done in the lesson/unit and how that will affect solving the problem. Have students use the sentence stems to share out in groups and full class, if desired. ”

• Unit 6, Lesson 6.3, Teacher Gem, Partner Math, Partner Math Instructions state, “1. Students should be separated into two groups using formative or self-assessment ratings on the standard addressed in the Partner Math activity. Students still struggling with the content should be given one color of the Partner Math template while students who have shown proficiency in the standard should be given a second color of the template. The two groups need to be equal in size. 2. Next, students find a partner with a different color template and sit next to them. Two problems (Task A and B) addressing the standard are projected or written on the board. Students work with their partner to solve the problems. Both students write on their own papers but work together to reach the same solutions.”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

Each unit includes multiple opportunities for students to engage with grade-level mathematics at increasing levels of complexity. These opportunities are embedded within lessons and available to all students, supporting a range of learners in exploring mathematical concepts at higher levels of complexity.

Several resources and features within the program provide opportunities for extended mathematical exploration.

• Performance Task: “The Performance Task provides applications of most or all of the standards addressed in the unit. This task contains Depth of Knowledge Level 3 and 4 strategic and extended thinking questions where students apply multiple standards in a non-routine manner to solve. These tasks provide entry points for all levels of learners and encourage students to explain their thought processes or critique the reasoning of others.”

• Performance Assessment: These non-routine problems require students to engage in higher-level thinking while applying their knowledge of the standards.

• Leveled Practice: The “C” in each lesson is designed for students who have already demonstrated proficiency. It extends their learning by making connections to future standards and incorporating Depth of Knowledge (DOK) Level 3 or 4 exercises.

•  Tic-Tac-Toe Boards: According to the EdGems Math Program Components state, “Each Tic-Tac-Toe Board includes nine activities that extend or look at the content of the unit in different ways. The Tic-Tac-Toe Boards include activities that make use of a variety of multiple intelligences.”

• Teacher Gems: Teacher Gems include problem sets at multiple levels of complexity, allowing for differentiated problem-solving experiences. For example, activities such as Four Corners, Relay, and Stations include multiple levels of complexity within the tasks.

• Online Practice & Exit Card Resource: This resource offers five options for each lesson: Two Online Practice sets (A and B), each containing six items at the proficient level. Two Online Challenge sets (A and B), each containing four challenge questions. Attempt A provides immediate feedback on correctness, while Attempt B includes worked-out solution pathways to help students identify errors in their work.

The materials include structured activities that provide opportunities for students to engage with mathematical concepts at increasing levels of complexity.

• Unit 1, Materials, Performance Task states, “Jaylee owns a coffee shop and wants to have a mural painted on one of the walls. Two separate artists have given her bids: Artist 1. Design Fee: $84. Cost per Square Foot: $1. Artist 2. Design Fee: $0. Cost per Square Foot: $2.50. Part 3: Jaylee decides that she wants to spend around $120 on the mural and thinks that the mural would look best if it were square-shaped. 5. Which artist could create the largest square-shaped mural for $120? 6. Based on your work above, what is the difference in height between the two $120 square shaped murals? Round to the nearest hundredth.”

• Unit 8, Lesson 8.4, Teacher Gem, Relay, Directions state, “Print the two sets of relay cards. The first set, numbered 1 through 8, provide students practice in the standard at a proficiency level. A challenge set of cards, A through H, provide opportunities for students to extend and apply their thinking around the standard. The questions in each set of relay cards increase in difficulty throughout the activity.” Relay 1, “(1.46\times 10^{4})(2\times 10^{4})" Relay H, “The diameter of Jupiter is 1.428\times 10^{5} kilometers. The diameter of Mercury is 4.879 million meters. Which has the larger diameter? Approximately how many times larger is it?”

The materials reviewed for EdGems Math (2024) Grade 8 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

Guidance is consistently provided for teachers to support students who read, write, and/or speak in a language other than English, providing scaffolds for them to meet or exceed grade-level standards. According to the ELL Supports Guide, “We view the background knowledge, experiences, and insights that English Learners bring to the classroom as strengths to be leveraged, and we are committed to ensuring that they receive academic success with rigorous grade-level curriculum. In recognition of the unique needs of learners, including those with diverse levels of mathematical proficiency, our curriculum includes research-based guidance for differentiated English Language Learner (ELL) instruction."

• The ELL Supports Guide outlines strategies for students who read, write, and/or speak in a language other than English to engage with grade-level mathematics. Key areas of focus include scaffolding tasks, fostering mathematical discourse, and incorporating instructional strategies informed by research. Tasks include scaffolds and language supports designed to facilitate mathematical understanding. The instructional design integrates opportunities for students to express their mathematical thinking both orally and in writing.

• The ELL Supports Guide contain recommendations related to student assessments. Additional resources in the materials include Target Trackers and Math Practice Trackers, which align with structured conferencing planned three times per unit. A Math Self-Assessment Rubric is included to support student reflection, along with a Sample Vocabulary Journal Format that provides space for root words, home-language translations, definitions, images, and sentence frames.

• Each lesson’s Teacher Guide includes three lesson-specific Mathematical Language Routines (MLRs), with two MLRs suggested for implementation per lesson. Strategies described in the materials include language modeling through think-alouds, the use of visual aids featuring key vocabulary, and a multilingual glossary with online vocabulary available in ten languages. Videos within the ELL Supports Guide provide examples of teachers breaking down tasks, using cognates, and prompting students to explain their thinking. Language functions are also included to structure discussions.

Examples where the materials provide strategies and supports for students who read, write, and/or speak in a language other than English include:

• Unit 3, Lesson 3.2, Teacher Guide, Supports for Students with Learning and Language Differences, Mathematical Language Routines states, “MLR 4 – Information Gap: In partner sets, students use information from Challenge Leveled Practice #4 to work with each other to piece information together about the given situation. Prepare in advance a Question Card and an Info Card for each partner set by breaking the problem apart, as shown below: Question Card: Philip is putting books into boxes. How much does each novel weigh? Does this represent a proportional relationship? Info Card: Philip is putting books into boxes. All of the books are novels, and they each weigh \frac{3}{4} pound. Each box holds two dozen novels. Students bridge the gap between their information orally and visually (on a common recording sheet). Encourage students to focus on using mathematical language while discussing the Question and Info Card provided. Emphasize an environment where students are working together to consider the information they need to know and efficient strategies for solving the given question.”

• Unit 5, Lesson 5-5, Teacher Guide, Lesson Presentation states, “Have students utilize their interactive textbooks or composition notebooks to participate in guided note taking using the Lesson Presentation. Have students attempt Extra Examples with partners, in small groups or independently. Use ‘Communication Break’ slides as opportunities for meaningful discourse.Communication Break–Estimation Pause: Use an ‘Estimation Pause’ for Extra Example 1. Have students work with partners or small groups to complete one of the sentence frames provided on the slide and be ready to share their reasoning. Then work together to solve the task and compare to initial estimates.“ Lesson Presentation, Extra Example 1, “Communication Break–Estimation Pause 1. Examine the Problem. 2. Without writing, estimate the answer or range of answers. I think the answer will be between and because… I think the answer will be more/less than because… I think the answer may be about because….”

• Unit 10, Lesson 10.3, Teacher Guide, Supports for Students with Learning and Language Differences, Common Misconceptions states, “Many students have difficulty finding the ‘best’ equation for a set of graphed points. (i.e., some may not understand the importance of having the same number of points above and below the line of fit; some will provide the wrong sign for the slope). In their journals or notebooks, teachers may want to have students map out each of the steps of finding a linear equation for a line of fit, using a situation that is engaging/interesting to all the students in the class. Have them write down common errors for each step, so that they can refer back to their notebooks when given similar problems. Some students may think that correlation will always imply causation. Ask them for examples of a situation where other factors or a third correlation can contribute to an outcome. Using data sets that are associative but do not imply causal relationships can help clarify this misconception. Students should be exposed to scatter plots with different correlations, no correlations, tight correlations, and loose correlations.”

The materials reviewed for EdGems Grade 8 meet expectations for providing manipulatives, physical but not virtual, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Materials consistently include suggestions and links to manipulatives to support grade-level math concepts. The Teacher and Student Moves for Math Practice 5 and Explore! Activities incorporate physical manipulatives when appropriate, with required materials listed in the full course materials list under the Teacher Guide At A Glance section. Student Gems in each lesson provide virtual manipulatives, such as Desmos and Geogebra, to help students make sense of concepts and procedures. Examples include:

• Unit 5, Lesson 5.2, Student Gems, Desmos states, “What does it mean for a point to be a solution to a system of equations?” Resource Info states, “This activity will help students understand what it means for a point to be a solution to a system of equations–both graphically and algebraically.”

• Unit 7, Lesson 7.1, Teacher Guide, Explore! Activity: Mirror! Mirror! "In ‘Mirror, Mirror,’ students create reflections using tracing paper (or patty paper) as well as on a grid. This activity allows for students to build upon their experiences with reflections from everyday life and progress into representing reflections on a coordinate plane. The activity concludes by asking students to consider if the pre-image and image are congruent after a reflection has occurred.”

• Unit 9, Lesson 9.1, Teacher Guide, Math Practices: Teacher and Student Moves, SMP5 Teacher Moves states, “Provide 3-dimensional shapes, measuring tools, grid paper and other tools. Instruct students to choose one or more tools to explain the reason they chose the tools, and how they will use them prior to solving problems. Then, ask them to reflect on their use of the tools and how they helped in solving a given problem.”