6th to 8th Grade - Gateway 3

The materials reviewed for Amplify Desmos Math Grades 6 through 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 in order to guide their mathematical development.

Materials provide comprehensive guidance that assists teachers in presenting the student and ancillary materials. Each unit contains a Unit Overview landing page that lists the sub-units, a vocabulary list, and the Common Core State Standards and Standards for Mathematical Practice addressed throughout the unit. Each Unit Overview also includes resources, such as the Unit Teacher Edition, Unit Glossary, Routine Facilitation Guide, and Unit Math Language Development Resources, to support teachers. The Unit Teacher Edition provides guidance on the Math of the Unit, Unit at a Glance, Lesson Material and Prep, Assessments, Differentiation, Accessibility, Math Identity and Community, Language Development, Technology, Professional Learning, Connections to Future Learning, and Assess and Respond. This comprehensive document also outlines each sub-unit and lesson.

A Grade 7 example includes:

• Unit 1: Scale Drawings, Unit Overview states, “Students examine and create scaled copies of figures, then explore scale drawings of real-life objects. Sub-Unit 1: Use scale factors to create and compare scaled copies. Describe how scaling affects lengths, angles, and areas in scaled copies. Sub-Unit 2: Represent distances in the real world using scales and scale drawings. Analyze strategies for creating a scale drawing to represent actual distances and areas.“

Materials include sufficient and useful annotations and suggestions that are presented within the context of specific learning objectives. The Course Overview, Navigating This Program, describes support for facilitation throughout the program. Materials state, “Throughout this Teacher Edition, lesson guidance for teachers is organized clearly and consistently so that they have all of the information they need at their fingertips.” In the Lesson at a Glance section, materials explain, “The Lesson at a Glance page describes the purpose of the Warm-Up, Activities, Synthesis, and Show What You Know. Teachers will find suggested timing for each part of the lesson, as well as guidance on whether students should work individually, in pairs, in small groups, or with the whole class.” In the Teacher Edition, each activity includes a Purpose statement: “The Purpose of each activity is highlighted here, as well as suggestions for the student grouping, time frame, and screen pacing for the activity.” Each lesson contains one, two, or three activities, described as “the heart of each lesson.” Materials explain, “Students notice, wonder, explore, calculate, predict, measure, explain their thinking, settle disputes, create challenges for their classmates, and more. Guidance is provided to help teachers Launch, Monitor, and Connect students’ thinking over the course of each activity. Teachers will also find suggestions for pacing, facilitation moves, discussion questions, examples of early student thinking, ideas for students who may enjoy a challenge, ways to increase access to the language and content, as well as opportunities to build and develop the math community in your classroom. The suggestions for facilitation provide comprehensive support for teachers as they prepare for and teach lessons.”

Amplify Desmos Math PD Library, Getting Started Grades 6–A1, Program Guide, page 44, Student Activity Screens states, “To make planning and teaching seamless, tips for instruction are available in both the print Teacher Edition and digitally at point of use. At the bottom of Activity Screens, the teacher will see suggestions for facilitation to support great classroom conversations:

• Teacher Moves: Suggestions for pacing, facilitation moves, discussion questions, examples of early student thinking, and ideas for early finishers, as well as opportunities to build and develop the math community in your classroom.

• Sample Responses: One or more examples of a possible student response to the problem.

• Student Supports: Facilitation suggestions to support students with disabilities and multilingual students.” 

The Teacher Edition also offers facilitation notes with Launch, Monitor, and Connect suggestions.

Grade 6 examples include:

• Unit 2: Introducing Rations, Lesson 4, Teacher Edition, Activity 1, the materials state, “Purpose: Students analyze and generate equivalent ratios. Launch: Use the Notice and Wonder routine to promote curiosity and help students make sense of the table. Create a record of observations students noticed and wondered along with the names of those who shared them. (MP1) Monitor: Select and sequence a variety of student responses. Note: Some students may use additive strategies to obtain ratios that are not equivalent to 6:4 (e.g, 7:5, 8:6, etc.), representing combinations of fruit that do not balance the scale. Invite these students to try their guess on the scale. Consider asking, ‘Why do you think the scale didn’t balance?’ It is okay if students are unsure at this stage; they will see an example of this reasoning in Activity 2. Connect:  Invite students to share and explain their thinking. To surface the Key Takeaway, consider asking: ‘What patterns did you notice in the table? How did that help us create new rows?’ ‘How might Victor have started with the ratio 15:10 and then gotten 3:2?’ ‘How did organizing the information in a table help us understand Victor’s thinking?’ (MP7)”

• Unit 6: Expressions and Equations, Lesson 8, Screen 4, Not Equivalent, the materials state, “How would you convince someone that 2(3x+4) is not equivalent to 6x+4?” Teacher Moves, “Monitor: Look for a variety of explanations, including ones similar to the sample responses. Connect: Consider asking: ‘Why might someone think these two expressions are equivalent? Why are they not equivalent?’ (MP3) ‘What could you change about 6x+4to make it equivalent to 2(3x+4)?’”

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for containing explanations and examples of grade-level/course-level concepts and/or standards and how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject.

Materials contain adult-level explanations and examples of the more complex grade-level concepts so that teachers can improve their own knowledge of the subject. Each Unit Overview includes three teacher-facing pages, Math of the Unit, Professional Learning, and Connections to Future Learning that explain grade-level concepts, standards, and their progression across grade levels. The Math of the Unit page explains how the unit content aligns with standards, coherence across grade levels, and aspects of rigor, while also pointing out connections to both prior and future learning. The Professional Learning page provides explanations of the mathematics in the unit and describes instructional approaches connected to that content. The Connections to Future Learning page identifies how the unit’s mathematical ideas link to concepts that students will encounter in later grades or courses. Each Unit Overview also includes at least one Unit Overview Video that provides an overview of the content and key features of the unit, telling the story of the unit and showing how the sub-units fit together. When possible, the video highlights key interactions, models, and strategies used within the unit. For example, in Grade 8, Unit 2: Dilations, Similarity, and Slope, the video describes what students will be able to do by the end of the unit, identifies what might be tricky for students, and explains the progression of learning in each sub-unit while manipulating online tools to show key mathematical understandings.

Evidence demonstrates that units provide resources to support teachers in understanding the progression of mathematics across the course. For example, the Grade 8 Overview states, “Each unit includes a range of resources designed to support teachers in thinking through the progression of mathematics that students will engage with over the course of the unit. These resources can support teachers in their unit planning, as well as choices they make in response to students’ thinking, strengths, and needs that arise over the course of the unit.”

Materials also provide sub-unit–level explanations and examples to support teacher knowledge. Each sub-unit contains Math That Matters Most and Sub-Unit Summary pages. The Math That Matters Most page outlines how specific strategies, skills, and language develop across the sub-unit, while the Sub-Unit Summary page provides a Student Edition excerpt that presents the key mathematical learning in student-friendly language. These supports help teachers understand both the mathematical development across the sub-unit and how students will engage with the content.

Materials contain adult-level explanations and examples of concepts beyond the current course so that teachers can improve their own knowledge of the subject. The Scope and Sequence in each grade overview shows how concepts are taught across the 6-8 grade span, helping teachers understand the progression of learning across multiple grades. At the lesson level, each Lesson Overview identifies relevant prior knowledge in the Prior Learning section, with “Building On” tags that connect to standards from earlier grades or units, and highlights future concepts in the Future Learning section, with “Building Toward” tags that identify related standards in later grades. For example, in Grade 6: Unit 8: Describing Data, the Math of the Unit, Professional Learning, and Connections to Future Learning pages explain how the unit’s focus on volume formulas builds from prior knowledge and connects to future high school concepts.

The Connections to Future Learning section also provides adult-level explanations that bridge across grade levels. For example, in Grade 7, Unit 7: Angles, Triangles, and Prisms, the Teacher Edition states, “In this unit, students consider whether two triangles are identical or not when they decide how many triangles can be built with a set of conditions. In Grade 8, Unit 1, students will learn to use the term congruent to describe these types of figures.”

Additional examples demonstrate how the materials prepare teachers with knowledge of future standards. In Grade 8, Unit 5: Functions and Volume, the Professional Learning section describes how functions build from students’ understanding of linear relationships and how they support later learning of exponential functions. In the Connections to Future Learning section, function notation is introduced with examples and a solution, aligned to high school standards (HSF.IF.C, HSF.LE.A). The section also explains how students’ work with volume formulas in middle school will connect to solving contextual problems with cross-sections and volumes in high school geometry (HSG.GMD.A.1, HSG.GMD.A.3, HSG.GMD.B.4), including an example problem with a solution.

Professional development resources also support teachers in building adult-level understanding of grade-level and future concepts. The Program Guide states, “The Unit Overview for each unit includes a Professional Development page, which lists opportunities for teachers to deepen their understanding of the math in the unit and how to teach it. In 2025–26, unit-level supports will include a Unit Overview Video, which provides teachers with an overview of the content and key features of the unit. These videos tell the story of the unit and how the subunits fit together to create an aligned experience for students. Key instructions, models, and strategies used within the unit are showcased, when appropriate.”

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for including a year-long scope and sequence with standards correlation information.

A Course Overview for each grade level includes a Grade Level Overview with a table of contents listing lesson titles and the standards addressed. A lesson list with standards correlation outlines alignment to grade-level standards and the Standards for Mathematical Practice. From the landing page, teachers can access a Grade Standards and Routines document that identifies which standards are addressed in each lesson. Each unit and lesson includes an overview page, in both digital and print formats, that identifies prior learning, the standards addressed, and the standards students are building toward. The Scope and Sequence outlines instructional and assessment days and shows connections across grade levels. Correlation tables for both Mathematical Content and Practice standards identify where each standard is addressed within units and lessons.

This structure is consistent across Grades 6-8. Examples from Grade 8 include:

• Unit 2: Dilations, Similarity, and Slope, Lesson 5 landing page identifies the standards as Building On 7.G.A.1, Addressing MP6, MP7, and 8.G.A.3, and Building Toward 8.G.A.4.

• Unit 5: Functions and Volume, Unit Overview (Teacher Edition) lists the focus content standards, including “Define, evaluate, and compare functions. (8.F.A MAJOR WORK) … Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres. (8.G.C ADDITIONAL WORK).” The overview also identifies the Standards for Mathematical Practice such as MP2, MP4, MP6, and MP8 with descriptions of how students engage with them. For example, “Students model linear functions and non-linear functions with multiple linear segments. They use precise language to justify whether a table or graph is a function. (MP4, MP6)”

• Grade 8 Overview, Scope and Sequence, Unit 1: Rigid Transformations and Congruence includes 14 instructional days, 2 assessment days, and 2 optional days, for a total of 16 days.

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for explaining the program’s instructional approaches, identify research-based strategies, and explain the role of the standards.

Materials explain the instructional approaches of the program.

• The Program Guide, Our Philosophy, describes four core tenets of the curriculum: Math that Motivates, A Structured Approach to Problem-Based Learning, Student Thinking is Valuable and Can Be Made Evident, and Access to Grade-Level Math for Every Student, Every Day. For example, lessons are “designed to tell a story by posing problems that invite a variety of approaches before guiding students to synthesize their understanding of the learning goals.” Unit Overview Videos further explain how units are organized. The materials state, “These videos tell the story of the unit and how the sub-units fit together to create an aligned experience for students.”

Materials include and reference research-based strategies.

• Program guidance cites frameworks and studies that informed design. For example, lessons embed the 5 Practices for Orchestrating Productive Classroom Discussions (Smith & Stein) to structure discourse. Universal Design for Learning guidelines (Engagement, Representation, Action & Expression) and Mathematical Language Routines (Zwiers et al., 2017) are integrated into lesson supports. NCTM’s Principles to Action (2014) are referenced directly and published research on student engagement, feedback, and differentiation is cited.

Materials include and reference the role of the standards in the program.

• The Grade Overview includes a Standards document that maps content and practice standards by unit and lesson. Lesson pages mark standards as “Building On,” “Addressing,” and “Building Toward,” clarifying how learning progresses across grades. For example, in Grade 7, Unit 2: Introducing Proportional Relationships, coherence connections are identified from Grade 6 ratio work to Grade 8 slope and linear relationships. In Grade 8, Unit 8: The Pythagorean Theorem and Irrational Numbers, Lesson 1 goal is paired with prior learning on area of squares and future learning on square root notation, with standards noted as “Building Toward 8.NS.A.2.”

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Course Overview Year-long Materials List provides the materials needed throughout the year along with the lessons they correspond to. Each Unit Teacher Edition includes a Lesson Materials and Prep section with a list of materials for the lessons in the unit. Additionally, each Lesson at a Glance Prep Checklist lists the materials needed for that specific lesson.

Examples in Grade 6 include the following; however, each grade has its own set of examples.

• Course Overview, Year-Long Materials List, cardstock, calculators, coloring tools, graph paper, index cards, poster paper, rulers, scissors, stopwatches, straightedges, tape.

• Unit 1: Area and Surface Area, Unit Overview, Unit Teacher Edition, Lesson Materials and Prep, lists the following: Lesson 4 – rulers; Lesson 6 – scissors; Lesson 12 – graph paper (as needed), scissors, tape; Lesson 14 – cardstock or blank paper, coloring tools, rulers, sample to-go containers (optional), scissors, tape.

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for providing consistent opportunities to determine student learning throughout the school year. The assessment system provides sufficient teacher guidance for evaluating student performance and determining instructional next steps.

The assessment system includes multiple components across the school year. The mCLASS Beginning-of-Year Screener is a digital, norm-referenced assessment that uncovers students’ mathematical thinking and provides insight into their knowledge, strengths, and areas for support. At the start of each unit, Pre-Unit Checks help teachers identify key concepts and skills from previous grades that may need reinforcement. Each includes an Assess and Respond document with item-level details and follow-up recommendations. At the lesson level, a Show What You Know is included at the end of every lesson, with Beyond the Lesson Differentiation Tables providing suggestions for future learning.

Sub-Unit Quizzes and End-of-Unit Assessments include digital and paper answer keys, rubrics on a four-point scale (Meeting, Approaching, Developing, Beginning), and Assess and Respond documents. These resources provide correct answers, sample responses, item analyses aligned to standards and lessons, DOK levels, and differentiated guidance. End-of-Unit Assessments also include Form A and Form B versions to allow for reassessment opportunities.

Examples from Grade 7 include:

• Unit 1: Scale Drawings, End-of-Unit Assessment: Form A, Problem 6a states, “A runner gets a new map of her favorite running trail. Her old map has a scale of 1 cm to 100 m. Her new map has a scale of 1 cm to 500 m. If the maps represent the same area, are the distances on the new map longer, shorter, or the same size as the old map? A. Longer. B. Shorter. C. The same size. Explain your thinking.” The accompanying rubric aligns the problem to standards 7.G.A.1 and MP6 and provides scoring guidance on a four-point scale (Meeting, Approaching, Developing, Beginning). For example, a “Meeting” response includes the correct choice (shorter) and a complete explanation showing that each centimeter on the new map represents five times the length on the old map. “Approaching” responses may include the correct choice with minor flaws in reasoning or an incorrect choice with a logical explanation. “Developing” and “Beginning” levels show incomplete explanations or misconceptions, such as thinking the new map is longer because 100\\cdot5=500. Assess and Respond guidance directs teachers to revisit Unit 1, Lesson 9 and Lesson 10 to support students who need additional help with this concept.

• Unit 8: Probability and Sampling, Sub-Unit Quiz, Screen 5, Problem 3b states, “Esi does an experiment where she picks a block out of a bag without looking 50 times, putting it back each time. She picks a green block 32 times. If the bag has 8 blocks, how many are likely to be green?” The Assess and Respond resource identifies the concept as making predictions about the sample space and repeated experiments (Lesson 3, DOK 2) and aligns the problem to standards 7.RP.A, 7.SP.C.6, and 7.SP.C.7.B. Differentiation guidance connects the problem to Sub-Unit goals, such as comparing probabilities to repeated experiments and determining probability through sample spaces or simulations. To respond to student thinking, teachers are directed to use the Calculating Probability Using Proportional Relationships mini-lesson or revisit Lesson 3 (Mystery Bag).

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for providing strategies and support for students in special populations to work with grade-level content and meet or exceed grade-level standards, which support their regular and active participation in learning.

The Program Guide within the Grades 6–A1 Math PD Library states the following about the materials: “An excellent mathematics program requires that all students have access to a high-quality mathematics curriculum, effective teaching and learning, high expectations,

and the support and resources needed to maximize their learning potential. This

commitment reflects a broader push within the educational community to foster a

culture of equity, ensuring that every student has the opportunity to thrive as a learner

and practitioner of mathematics. The differentiation of Amplify Desmos Math extends beyond academic differences to encompass variations in student motivation, interests, and identity. Understanding and addressing these aspects are essential for creating inclusive learning environments where all students feel valued and empowered to succeed. We incorporated Universal Design for Learning guidelines (Engagement, Representation, Action & Expression) into each lesson and developed a platform that is intuitive and easy-to-use for all learners. Amplify Desmos Math incorporates research-based Mathematical Language Routines (MLRs) by providing language modality strategies like sentence frames where appropriate, both in the teacher language provided for each task and in the differentiation support section found throughout the program.”

Each grade’s Course Overview, Accessibility, describes ways to support all students in accessing and participating in meaningful and challenging tasks. The materials state, “Lesson Facilitation Supports: Every lesson includes at least one specific suggestion that teachers can use to increase access to the lesson without reducing the mathematical demand of the tasks. These suggestions address the following areas: conceptual processing, visual-spatial processing, executive functioning, memory and attention, fine motor skills, and affective functioning.” Throughout the Teacher Edition, accessibility is identified by a small circle with an “A.” “Accessibility Tools: Students have the ability to control accessibility tools so that each learning experience is customized to their individual needs. In many instances, these tools can be turned on or off at any point of instruction.” These tools include text-to-speech, enlarged font, braille mode, and language selection.

The Teacher Edition lists accessibility supports for every lesson. Each lesson includes a differentiation table with explicit next steps based on student responses to Show What You Know. Each sub-unit provides Support Mini-Lessons that “provide targeted intervention for students by using these resources.” Assess and Respond guidance is also included for each Pre-Unit Check, Sub-Unit Quiz, and End-of-Unit Assessment.

An example from Grade 7 includes:

• Unit 2: Introducing Proportional Relationships, Lesson 5, Screen 4, Equation to Table states, “An equation for this relationship is d=30t. Here are a few moments from the car’s trip. Use the equation to complete the table.” A table with the column headings Time (sec), t and Distance (m), d is provided. The values in the time column are 6, 1, 30, and 3, and the values in the distance column are 180, 30, 900, and 60. Student Supports state, “Accessibility: Conceptual Processing. Invite students to read their equation aloud with variable definitions instead of d and t (e.g., ‘The distance is equal to 30 times the number of seconds.’).”

The materials reviewed for Amplify Desmos Math Grades 6 through Grade 8 meet expectations for regularly providing extensions and/or opportunities for advanced students to engage with grade-level/course-level mathematics at greater depth.

The Program Guide within the Grades 6–A1 Math PD Library describes resources for extending student learning. In Beyond the Lesson, materials state, “The learning goal of each lesson is broken down for teachers into what it looks like for students to need support in the lesson goal, for students to need to keep strengthening their understanding of the lesson goal, and for students to be ready to stretch their learning. Teachers are provided with recommendations for resources to use with each group of students.” Assess and Respond states, “At each Assessment point in a unit, teachers have the opportunity to respond to student understanding…Students who are ready to strengthen or stretch their learning based on the assessment can access any of the strengthen or stretch resources aligned to the content of the assessment.” Within lessons, Differentiation Teacher Moves include “Stretch” suggestions.  The materials state, “Within every lesson activity, teachers can use the Differentiation Teacher Moves suggestions to provide in-the-moment instructional support…Teachers are provided with clear student actions and understanding to look for, each matched with immediately usable suggestions.”

In addition to in-lesson supports, Amplify Desmos Math provides Sub-Unit Extensions. The Intervention and Extension Resources provides Sub-Unit Extensions that allow students to explore mathematical concepts from the sub-unit in greater depth. For example, in Grade 6, Unit 2: Introducing Ratios, Sub-Unit 2, students have opportunities to extend their work with divisibility rules, factors, and multiples.

Challenge Creators also extend student learning. In Grade 7, Unit 4: Proportional Relationships and Percentages, Lesson 5, Screen 9, the student-facing prompt is “Make My Challenge,” where students design mathematical challenges and then solve those created by classmates. Teacher guidance explains, “Students express their creativity by creating their own challenge and also practice calculating the original value given the new value and a percent change.”

Lesson-level Stretch opportunities are consistently embedded. In Grade 8, Unit 5: Functions and Volume, Lesson 6, Activity 1, Differentiation table states, “Consider asking, ‘How would this graph change to represent the height of Tyler’s shoes?’ Differentiation: Explore More (Stretch) Invite students who would like to explore graphing stories further to complete this optional task. Encourage them to discuss their thinking with a partner.”

The materials reviewed for Amplify Desmos Grades 6 through Grade 8 include manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

Virtual and physical manipulatives support students’ understanding throughout the curriculum. Each unit’s Materials and Prep section identifies the manipulatives needed, and lesson-specific materials are listed in the Lesson Prep Checklist on the Lesson at a Glance page. Virtual manipulatives are integrated into many lessons, often embedded within student digital screens that provide Responsive Feedback. 

Examples from Grade 7 include:

• Unit 3: Measuring Circles, Lesson 6, Student Edition, Activity 2, students visualize the relationship between the radius, radius square, and area of a circle. The activity states, “Let’s find out how many radius squares are needed to cover a circle. Your group will get four circles and four sets of radius squares. For each circle, cut on the dashed lines to separate the radius squares and rearrange the pieces to cover the circle.” Teachers provide a supplemental sheet with circles and radius squares, along with tape and scissors, so students can cut and rearrange pieces to determine how many radius squares cover a circle.

• Unit 7: Angles, Triangles, and Prisms, Lesson 7, Screen 6, Reflection, students use virtual segments to build triangles. The materials state, “Malik claims he will always get identical copies if the 25\\degree angle is between the side lengths of 4 and 6. Is Malik’s claim correct?” Students select from the choices “Yes,” “No,” or “I’m not sure.” After explaining their thinking, they share with the class using the “Share With Class” button. The virtual workspace allows students to manipulate two sides around a given angle.