7th Grade - Gateway 3

The materials reviewed for EdGems Math (2024) Grade 7 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 Launch Guide, Lesson Planning Guidance: Day 1, “Fluency Board Launch (20-25 minutes) The Fluency Boards provide students with opportunities to build number sense through discourse and practice. This unit’s Fluency Boards focus on two skills: (1) multiplying decimals and (2) solving proportions. Each Fluency Board also includes a ‘Mix It Up’ skill. To launch the Fluency Board for this unit, complete the following: (1) Fluency Board Pre-Assessment: Have students fold their pre-assessment in half. For this Fluency Pre-Assessment, students should be given two minutes to complete Target Skill 1 and two minutes to complete Target Skill 2. (2) Fluency Board Cover Sheet: Once completed, have students self-correct their pre-assessment. They should record the number of items completed and number correct for each skill on the cover page and then self-assess their current level of understanding. As a class, come up with key understandings for each skill that are needed for procedural fluency and record those in the corresponding box on the cover sheet. (3) If time allows, you may choose to have students start on the Fluency Board in the first lesson of this unit.“

• Unit 3, Planning & Assessment, Unit Finale Guide, Lesson Planning Guidance: Day 1, “Unit Review (20-25 minutes) Two Unit Review options are available. The style of Unit Assessment you choose for Day 3 of the Unit Finale may guide your choice of Unit Review. Unit Review: The Unit Review is a print-ready resource which addresses all of the Focus Standards covered in the unit. This resource offers constructed response items that are similar to the items on the Unit Assessment without moving beyond Depth of Knowledge (DOK) Level 2 (Basic Skills + Concepts) so as to maintain authenticity when assessing students at a DOK Level 3 (Strategic Thinking) during the actual assessment. The Unit Review resource has a built-in reflection component on groups of items that align to the Pathways Teacher Gem activity that can be used after the Unit Review is completed. Online Unit Review: Like the Unit Review, the Online Unit Review addresses all of the Focus Standards covered in the unit. Unlike the Unit Review, which consists of constructed response items, the Online Unit Review consists of 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 Review, found in the Editable Resources spreadsheet, to encourage students to show their work before submitting their answers digitally. The Online Unit Review provides teachers and students with instant data for each item. The correlation of the Online Unit Review items to the Pathways Teacher Gem are below. Unit Review Skills Review Skill 1: I can convert between fractions, decimals and percents. (Items 1, 2) Review Skill 2: I can use percents to find a missing number using proportions and equations. (Items 3, 4, 5) Review Skill 3: I can find the percentage of increase or decrease or the percent error when given a real-world scenario. (Items 6, 7) Review Skill 4: I can solve problems involving mark-ups, discounts, tips and taxes. (Items 8, 9)”

• Unit 6, Lesson 6.2, Teacher Guide, Deep Dive, Lesson Planning Guidance: Day 1, “Explore! Activity: ‘Formula Frenzy’ (10-15 minutes) In this activity, students will evaluate geometric formulas by substituting values for the variables in the formulas. This activity connects to previous work students have done finding area, surface area and volume as well as vocabulary terms learned in previous grades (variable, evaluate and expression). The activity concludes by asking students to reflect on what it means to “substitute” values in an expression or equation. Implementation Option #1: Have students use Step 1 for an individual brainstorming session before joining with a group of three to four students to discuss and then complete Steps 2-4. As a class, discuss Step 5. Implementation Option #2: Discuss Step 1 as a class and then ask students to complete Steps 2-3 individually. Check answers together and then have students join with a partner to complete Steps 4-5.”

The materials reviewed for EdGems Math (2024) Grade 7 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 6, Planning & Assessment, Unit Overview, Content Analysis states, “This unit builds directly upon students’ work in Grade 6 with expressions. The key differences in Grade 7 are the inclusion of negative rational numbers and more complex expressions, including the use of absolute value bars as grouping symbols. Students will spend time in this unit making sense of the inclusion of negative rational numbers, especially as part of the base of a power and as coefficients when distributed to a term inside parentheses. These concepts will be explored in both numerical and algebraic expressions.” Visual student examples of Numerical Expressions and Algebraic Expressions are provided for teachers to review. “Through the practice of generating equivalent expressions, students will apply and develop their understanding of properties of operations, particularly the Associative, Commutative and Distributive Properties, as they work toward fluency in the norms associated with mathematical annotation. For example, given the expression 3 − 2(5x − 6), a student might mistakenly rewrite the expression as 3 − 10x − 12, in which the negative within the parentheses was not taken into account. Alternatively, a student might aim to simplify the expression within the grouping symbols, recalling their work with the order of operations, although the terms within the parentheses are not like terms. Students may choose to organize their work in different manners, such as applying the Commutative Property to group like terms in an expression, or carrying out the Associative Property to multiply the whole numbers in the expression 0.5(−6)(−4) before finding half of the resulting product. The exploration of the properties of operations in this unit will lay the foundation for continued work with algebraic reasoning in this course and beyond.”

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 5, Planning & Assessment, Unit Overview, Content Analysis, Readiness Check & Learning Progression states, “In this unit, students will… Understand that multiplication is extended from fractions to rational numbers through the properties of operations. 7.NS.A.2a Understand integers can be divided as long as the divisor is not zero. 7.NS.A.2b Solve real-world problems involving multiplication and division with rational numbers 7.NS.A.2c, 7.NS.A.3”

• Unit 7, Planning & Assessment, Unit Overview, Content Analysis, Readiness Check & Learning Progression states,  “In the future, students will… Use the formulas for area and circumference of a circle to solve problems. 7.G.B.4 Analyze and solve pairs of simultaneous linear equations. 8.EE.C.8 Create equations and inequalities in one variable and use them to solve problems. HS.A.CED.A.1” 

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 8, Lesson 8.6, Teacher Guide, Supports for Students with Learning and Language Differences, Common Misconceptions states, “The formulas for the area of a circle and the circumference of a circle are often confused by students. Teaching students to memorize these formulas without any understanding of how they relate to a circle increases the chance for confusion. Build the understanding before presenting the formulas. Also, make the connection to area representing square units and the area formula having a value (the radius) squared. Guide a derivation of the relationship between the circumference and area of a circle. Use a circle as a model. Cut the circle into as many equal-sized pie pieces as possible. Lay the pie pieces to form a shape similar to a parallelogram. Have students write an expression for the area of the parallelogram related to the radius (note: the length of the base of the parallelogram is half the circumference, or \pi r, and the height is r, resulting in an area of \pi r^{2}, which is the area of the circle). This derivation is shown at the beginning of the student lesson. For both circumference and area, students may struggle with the idea of the solution being an approximation versus an exact solution. This goes back to their introductory level of understanding of pi being an irrational number. Help students understand this by going back to the idea that they are most likely using an estimate of pi (3.14) or rounding at the end (when using pi on their calculator) so both of these methods lead to approximations rather than exact answers.”

The materials reviewed for EdGems Math (2024) Grade 7 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 2 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 3, Planning and Assessment, Unit Overview, Standards Correlation, Focus Content Standards states, “The Focus Content Standards for this unit conclude the concentration on the Ratios and Proportional Relationships domain within the Grade 7 and the K-12 standards collectively, though these standards will appear as Connecting Standards throughout the rest of the course. In future grades, students will continue to work with proportional relationships, distinguishing these from non-proportional linear relationships within the Functions domain. The 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 4, 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… Added and subtracted fractions with unlike denominators (5.NF.A.1), understood that the opposite of a positive or negative number is the same distance from zero on the opposite side of zero (6.NS.C.5), and ordered rational numbers on a number line (6.NS.C.6-7). In this unit, students will… Describe situations in which opposite quantities combine to make zero and understand absolute value as a distance from zero (7.NS.A.1a, 7.NS.A.1b), understand subtraction of rational numbers as adding the additive inverse (7.NS.A.1c), and solve mathematical problems involving addition and subtraction of rational numbers (7.NS.A.3). In the future, students will… Solve multi-step problems involving positive and negative rational numbers in various forms (7.EE.B.3), use rational approximations of irrational numbers to compare, order, and estimate the value of irrational numbers (8.NS.A.2), and rewrite expressions involving radicals and rational exponents using the properties of exponents (HS.N-RN.2)."

• Unit 5, Lesson 5.3, Teacher Guide, Standards Overview states,“Focus Content Standard(s): 7.NS.A.2b,c (Major), 7.NS.A.3 (Major)” Starter Choice Board Overview “Storyboard: Multiply rational numbers (7.NS.A.2, 7.NS.A.3) Building Blocks: Divide positive decimal numbers and fractions (6.NS.A.1, 6.NS.B.3) Blast from the Past: Solve a percent problem (6.RP.A.3) Fluency Board Skills: Add and subtract integers, add and subtract decimals, simplify using the distributive property.” 

• Unit 9, Planning & Assessment, Unit Overview, Connecting Content Standards states, “In this unit, students will use rational number operations (7.NS.A.1-3) and work with expressions and equations (7.EE.A.1, 7.EE.B.3-4) to solve problems involving surface area and volume of prisms and pyramids. Prism nets and cross sections will offer students more opportunities to practice the two-dimensional geometry skills from the previous unit. Students will also apply proportional reasoning as they consider how areas of figures compare after increasing or decreasing the dimensions by applying a scale factor (7.RP.A.3, 7.G.A.1).” 

The materials reviewed for EdGems Math (2024) Grade 7 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 7 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 3, Lesson 3.4, Teacher Guide, Materials states, “Required: Take-out restaurant menu (for the Explore! activity) Optional: Calculators”

• Unit 4, Lesson 4.1, Teacher Guide, Materials states, “Required: Integer chips or tiles (for the Explore! activity) Optional: Blank number lines, horizontal number lines, vertical number lines, grid paper”

• Unit 8, Lesson 8.5, Teacher Guide, Materials states, “Required: Collection of circular objects (such as lids, cups, cans, Frisbee, etc.), tape measures (for the Explore! activity)”

The materials reviewed for EdGems Math (2024) Grade 7 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, Tiered Assessments, Exercise 4 states, “Jim ran 10 laps in 5 minutes. How many laps will Jim run in 12 minutes?” The assessment information identifies the standard alignment as 7.RP.A.3.

• Unit 7, Planning & Assessment, Unit Overview, Performance Task states, “In ‘Cargo Elevator,’ students solve equations and inequalities to determine how many boxes can be loaded onto an elevator and in how many trips. Students will make use of structure (SMP7) as they explore changing quantities using one- and two-step equations and inequalities (6.EE.B.7, 7.EE.A.3-4) to predict which method of moving boxes will take less time.”

• Unit 7, Planning & Assessment, Unit Overview, Performance Assessment states, “In this Performance Assessment, students will write and solve equations and inequalities involving the dimensions, area and perimeter of various rectangles. Students will reason abstractly and quantitatively (SMP2) as they discover shape and space using one- and two-step equations and inequalities (6.EE.B.7, 7.EE.A.3-4) to understand how changing dimensions affect the area and perimeter of a rectangle.”

• Unit 10, Materials, Online Review & Assessments, Online Unit Review, Item 3 states, “Scott polled 30 seventh graders. Twelve students said they would vote for Pedro in the upcoming election. There are 250 students who will vote in the election. How many votes do you predict Pedro will get?” The assessment information identifies the standard alignment as 7.SP.C.6/7.SP.C.7/7.RP.A.3.

The materials reviewed for EdGems Math (2024) Grade 7 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 2, 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. SMP4 I can represent everyday situations using models and other representations. I represented an everyday situation using a picture or model. I represented an everyday situation using algebraic expressions or equations. I represented an everyday situation using data sets and displays.” 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.”

• Unit 9, Planning & Assessment, includes Form A and Form B of the Unit 9 Assessment, along with an Answer Key and Assessment Scoring Guidelines for each question. The materials state, “3-point Items: #1, 2, 3, 11, 12 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: 27 Not Yet Met 0-16, Nearly Meets 17-18, Meets 19-24, Exceeds 25-27” Similar guidance is provided for 1 and 2 point assessment items.

The materials reviewed for EdGems Math (2024) Grade 7 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, Item 8 demonstrates the full intent of 7.RP.2c. Item 8 states, “Which equations represent proportional relationships? Select all that apply. a. y=\frac{x}{7} b. y=5x c. y=0.2x d. y=\frac{9}{x} e. y=4x^{2} f. y=\frac{3}{2}x”

• Unit 6, Planning & Assessment, Assessments, Form B, includes three items that demonstrate the full intent of 7.EE.1, Exercise 15. The materials state, "2(3x-7)+10" Exercise 17 states, “Factor each expression using the greatest common factor. a. 5𝑚 + 20 b. 9𝑥 − 21.” Exercise 20 states, “Explain two different ways to simplify 2(3.5x-10+1.6x). Show that both ways lead to the same simplified expression. Method #1 Method #2”

• Unit 7, Planning & Assessment, Performance Assessment, includes four items that demonstrate the full intent of 7.EE. 4 and SMP2. The materials state, “Ricardo and Emilia are solving problems about a rectangle. The area of the rectangle is twenty-three more than one-half its perimeter. The area of the rectangle is 50 square inches. 1. What is the perimeter of the rectangle? Show all work necessary to justify your answer. 2. What are the dimensions of the rectangle? Show all work necessary to justify your answer. 3. The length and width of the rectangle were cut in half. Karly stated, “The perimeter and area of the rectangle are now half as big as they were originally.” Is she correct? Justify your answer using words and mathematics. 4. Jaime has a rectangle that he is comparing to Ricardo’s and Emilia’s rectangle. Half of Jaime’s rectangle perimeter is at least 10 inches more than three times the perimeter of Ricardo and Emilia’s rectangle. a. Write an inequality to represent the situation. b. Solve the inequality you wrote for part a. Show the work that leads to your answer. c. Explain your solution to part b in the context of the problem. Justify your answer using words and mathematics. d. Give an example of dimensions that could describe Jaime’s rectangle. Show work that supports your answer. e. Give an example of dimensions that could not describe Jaime’s rectangle. Show work that supports your answer.”

The materials reviewed for EdGems Math (2024) Grade 7 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 4, Lesson 4.2, Lesson Presentation, Slide 21, Communication Break, Think, Ink, Pair, Square states, “How would you add two rational numbers if one was written as a decimal and the other as a fraction? Think by yourself. Write down an idea. Share with a partner. Join with another partner set. We think… Do you agree or disagree? I respectfully agree/disagree because…” 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–Think, Ink, Pair, Square: Use the prompt ‘How would you add two rational numbers if one was written as a decimal and the other as a fraction?’ 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.”

• Unit 7, Lesson 7.2, Teacher Gem, Climb the Ladder, Climb the Ladder Instructions states, “NOTE: It is helpful to use four different colors of paper for the four different ladders. One way this is useful is in assessing the progress of each partner set. During the activity, you can quickly scan the room and be able to tell which sets of students are falling behind or are almost finished. Also, you can use colored paper for the expert tents to match the colors of the ladders so students are able to find the appropriate experts quickly. Another way the colored papers are helpful is to allow students who are struggling to be called to a huddle. This is where the teacher can call all of the partner sets with a certain color of paper to huddle with experts around the room. The expert’s job is to stop what they are doing and help these students complete this ladder. The teacher may choose to allow the students who have huddled with an expert to take cuts in line at the scoring table. At the end of the activity, students who finish early can be asked to join groups as a third person. The teacher can direct them to partner sets with a certain color of ladder that is the earliest in the progression.”

The materials reviewed for EdGems Math (2024) Grade 7 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 3, Lesson 3.3, Teacher Gem, Relay, Directions state, “Print the two sets of relay cards. The first set, numbered 1 through 8, provides 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 2, “Identify the percent of change as an increase or a decrease. Find the percent of change. Round to the nearest whole percent if necessary. 40 to 44.” Relay B, “Office Supply Depot buys notebooks at a bulk price of $0.25 each. They sell them to students for $0.75 each. What is the percent of increase?”

• Unit 7, Lesson 7.3, Online Practice and Exit Card, Challenge A, Item 4 states, “Nolan went to the same store three days this week to buy groceries. This store charges the same rate for milk per gallon, even when bought in containers smaller than one gallon in size. The first day he bought two gallons of milk. On the second day he bought a loaf of bread for $2.50 and \frac{1}{2} a gallon of milk. The third day he bought just one gallon of milk. Nolan spent a total of $17.20 on groceries this week. How much did Nolan spend on his first trip to the grocery store?”

The materials reviewed for EdGems Math (2024) Grade 7 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 4, Lesson 4.1, 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 – Vocabulary Bank: After the vocabulary is introduced, use the Vocabulary Bank slide to give students a set of vocabulary words and ask them to create their own sentence(s) that connect the words. Select specific students in each group to share their sentence(s) and have others respond using the sentence stems.” Lesson Presentation states, “Communication Break – Vocabulary Bank Integer, Opposites, Absolute Value Write one or two sentences using all the works in a context that makes sense mathematically. Compare your sentence(s) with another group and give them feedback. Your sentence helped me understand. I think the word was used correctly/incorrectly because…”

• Unit 7, Lesson 7.2, Teacher Guide, Supports for Students with Learning and Language Differences, Mathematical Language Routines states, “MLR 1 – Stronger & Clearer Each Time: After groups complete Exercise #5 from the Teacher Gem activity Masterpiece, but before they check with the teacher, groups exchange their work with 2 -3 other groups to get feedback on how to improve their work and their explanations. When students receive their work back with the feedback, they revise their work and explanations. While groups are providing feedback, display the following questions to help them think about what types of feedback will be helpful: Did the group answer the questions? Did the group follow all of the constraints of the problem? Are the group’s calculations accurate? Did the group justify their reasoning, referencing their work? How can the group make their work and explanations stronger?”

• Unit 9, Lesson 9.1, Teacher Guide, Supports for Students with Learning and Language Differences, Common Misconceptions states, “Students may not count attributes of a three-dimensional figure that are not visible in a two-dimensional drawing. Students may also count certain attributes twice within an image of a three-dimensional figure. Provide hands on models (i.e., plastic nets) where possible to support students counting attributes of three-dimensional figures. Teachers will find that it helps to keep showing students shapes in different ways and have them describe what they see. Students have been exposed to many of the vocabulary terms in this unit in previous grades but the amount of terminology introduced in one lesson may cause many students to mix up definitions. Have students create an organizer that shows each term, its definition and/or diagram. It may also be helpful for them to think of real-world objects that connect to each solid. Many students struggle with visualizing slices of solids. It may be helpful to have clay and plastic knives available for students to have hands-on manipulatives to support their understanding.”

The materials reviewed for EdGems Grade 7 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 2, Lesson 2.1, Student Gems, Desmos, Resource Info states, “This activity will help your students understand the definition of a proportional relationship. They'll create a giant and then make sure all of his features are proportional. They'll see the representation of his proportions on a graph and manipulate the graph to see the giant change dynamically.”

• Unit 4, Lesson 4.1, Teacher Guide, Explore! Activity, Integer Chips states, “In ‘Integer Chips,’ students use integer chips or tiles to model the addition of integers. The activity begins by introducing vocabulary terms and the concept of a zero pair. Students then model various expressions using integer chips and learn how to form zero pairs to determine the sum of each expression. The activity culminates in an opportunity for students to generalize their learning and develop their own rules for when a sum will be positive, negative or zero. Implementation Option #1: Facilitate the activity as a whole class without the activity sheet, using the steps from the activity sheets as verbal prompts to guide the activity. Ensure each student has their own set of integer chips to model each expression on their table. Implementation Option #2: Assign partner sets and give each set of partners a bag of integer chips. Work through Steps 1-4 together as a class and then have students complete Steps 5- 10 with their partner. Discuss Step 10 together as a class, allowing a variety of students to share their ideas.”

• Unit 7, Lesson 7.2, Teacher Guide, Math Practices: Teacher and Student Moves, SMP5 Teacher Moves states, “Provide students with unifix cubes, base ten blocks, colored pencils, graph paper, equation mats, balances, algebra tiles and other manipulatives from which to choose. Instruct students to choose one or more tools to help represent and visualize solving two step equations, and explain their choice. After solving the equations, ask students to reflect on their choice of tools and determine if a different tool would be a better choice.”