6th to 8th Grade - Gateway 3

The materials reviewed for Experience Math Grades 6 through 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.

The materials offer teacher support both in print via the Teacher Experience Guide and digitally on Savvas Realize. The organized landing pages on Realize and the printed teacher guides provide resources for planning, prepping, and teaching. This includes instructional support for each lesson part: Minds On, Action, Consolidate, and Your Turn. The materials provide ancillary materials, including Games and Activities such as Wonder Tasks, Making Connections Tasks, Math Talks, Brain Benders, Academic Vocabulary, and Math Refresh Videos. These are accessible within the Topic Resources and Lesson Resources sections of Savvas Realize, with guidance that suggests how and when to use them. The Program Overview includes a Pacing Guide that suggests how long to spend on each topic and lesson, allowing time for resources such as Math Talks and Mind-Benders. The Program Overview section, Setting up the Experience Math Classroom, provides suggestions about the physical space in the classroom and discusses developing a math community.

The materials provide annotations and suggestions connected to specific learning objectives within lesson and topic planning guides. In each Lesson Planning Guide, the Mathematical Focus lists the Essential Understandings for each lesson, which specify important mathematical ideas. The Essential Understandings document in the Program Overview states, “they are strand-based and occasionally borrow from other strands, helping to make connections within and among strands. They are spiraled when strands are revisited across grades or within a grade.” In each Lesson Planning Guide, “And the Point Is…” explains why the content of the lessons and activities is important and identifies any related prior learning.

Annotations within the lessons provide useful guidance for teachers in engaging students in mathematical development. 

Examples include:

• In Grade 6, Topic 2: Factors and Multiples, Lesson 3, Action Task, Differentiation, What Could You Do If…, “Students focus on the number of different factors, not the total number of factors. For example, they see 2\times2\times3\times5 as only three factors and not four. You could … Clarify by suggesting that when you are counting how many factors are on the list, you are counting how many numbers are being multiplied, whether the numbers are the same or different.”

• In Grade 7, Topic 11: Collecting Data, Lesson 4, Consolidate, Consolidate Questions, Teacher Guidance, And the Point Is…, “Consolidate Question 1 is a reminder to students about the need for representative samples when drawing conclusions (Essential Understanding D2). Question 2 encourages reflection on the value of graphs in helping us draw conclusions (Essential Understanding D3). Question 3 encourages students to make sense of the fact that variability has a big influence on how “representative” a measure of central tendency is (Essential Understanding D5).” 

• In Grade 8, Topic 4: Dilations and Similarity, Lesson 2, Action Task, Teacher Guidance, Conversations Starters, “What is true about all the resulting coordinates? How do these coordinates relate to the original ones? Why would you subtract 6 from only the first coordinate if you change the axes as shown?”

The materials provide additional support to guide instruction and address student needs. In each topic and lesson, teachers can access coaching related to content through “Marion’s Insights” videos, which offer instructional strategies, math contexts, and implementation tips. Guidance in the Action section includes “What Could You Do If…” notes that address common misconceptions, as well as differentiation strategies such as Parallel Tasks and Multilingual Learner Support. Topic Planning and Resources under Planning include “Going Back…Going Forward,” which shows how content connects across grade levels and may assist teachers in differentiating instruction.

The materials reviewed for Experience Math Grades 6 through 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.

The materials provide adult-level explanations and examples of grade-level concepts so that teachers can improve their own knowledge of the subject.

• Every topic includes multiple “Marian’s Insights” videos. These videos feature embedded professional learning that provides point-of-use instructional support directly within the digital platform. In the Program Overview, a document called “Connecting to Concepts Beyond the Grade” lists the main ideas of the grade and makes connections to future work. The coaching videos from Dr. Marian Small are strategically placed throughout each lesson to offer teachers access to her mathematical expertise and pedagogical guidance. Each topic of Experience Math includes a folder titled Marian’s Insights Videos that contains all of the videos for that topic. For example:

• In Grade 6, Topic 13: Rational Numbers, five different videos can be viewed to improve a teacher's knowledge in math, including an Overview: Rational Numbers, and also a video on Connecting to Concepts Beyond the Grade: Rational Numbers. 

• In Grade 7, Topic 5: Circle Measurement, six different videos can be viewed to improve a teacher's knowledge in math, including Overview: Circle Measurement, and also a video on Connecting to Concepts Beyond the Grade: Measuring.

• In Grade 8, Topic 2: Power and Roots, nine different videos can be viewed to improve a teacher's knowledge in math, including Overview: Powers and Roots, and also a video on Connecting to Concepts Beyond the Grade: Representing Numbers.

• In the Program Overview, additional professional learning videos explain each key element of the program. These include a set of videos that describe the Essential Understandings for each key mathematical concept and a set of videos that describe each Mathematical Practice with examples from the content.

Materials contain explanations and examples of how the concepts and/or standards align to other grade/course levels so that teachers can improve their own knowledge of the subject. For example:

• In Topic Planning and Resources under Planning, “Going Back…Going Forward” shows how content connects across grade levels and provides brief explanations that link learning from the previous grade to the following grade.

  • In Grade 6, Topic 3: Ratios states, “In moving from Grade 5 to Grade 6, students extend their understanding of the use of multiplication and division to compare amounts to more formal discussion of ratios. In Grade 7, students solve more complex ratio problems than in Grade 6. They focus much of their work on ratio on percent ratios.”

  • In Grade 7, Topic 3: Proportionality states, “As students move to Grade 7 from Grade 6, the proportions they consider are more likely to involve fractional quantities and not just whole number quantities. They also begin to describe proportions graphically and algebraically in Grade 7. Grade 8: As students begin to work with linear equations, they start to recognize the relationship between graphing proportions and graphing linear equations; proportion graphs are special cases of linear relations. As well, students see the slopes of lines as unit rates.”

  • In Grade 8, Topic 5: Proportional Relationships and Slope states, “In Grade 7, students think more contextually about graphs of lines as they graph proportional relationships that describe real-life situations. In Grade 8, students move to more abstract thinking about why constant rates of change lead to straight lines. In later grades, students continue to explore other relationships, contrasting proportional relationships and linear relationships with other types of relationships.”

• In Lesson Planning Guides under Planning, “And the Point Is…” provides the rationale for the lesson and makes connections to prior learning.

  • In Grade 6, Topic 3: Ratio, Lesson 1 states, “It is important that students look at ratios as more than just a counting exercise; they need to look at ratios as a multiplicative comparison between two numbers. Students should also realize that many ratios can be used to describe the same situation, for example, part-to-part ratios and part-to-whole ratios. Students have worked with ideas related to this lesson before: Grade 4 or earlier - writing equivalent fractions. Grade 5 - using multiplication or division to compare amounts; familiarity with coins.”

  • In Grade 7, Topic 3: Proportionality, Lesson 3 states, “This lesson provides an opportunity to solve interesting problems that involve proportional relationships and rates. In some of the problems, students determine equivalent unit rates built on existing unit rates with fractional values. Students have worked with ideas related to this lesson before: Grade 6 or Earlier - solving multistep ratio problems using proportional relationships; calculating unit rate. Grade 7 - identifying proportional relationships; identifying the constant of proportionality.”

  • In Grade 8, Topic 5: Proportional Relationships and Slope, Lesson 1 states, “This lesson reminds students that proportional relationships are ones where one quantity is a constant multiple of another; reminds students that the graph of a proportional relationship goes through the origin and the values in the table of values increase in a constant way; and formalizes the use of the term slope as a way of describing the rate of change of a line. Students have worked with ideas related to this lesson before: Grade 6 or Earlier - ratios; unit rates associated with ratios; equivalent ratios and proportions. Grade 7 - graphing proportional relationships.”

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

The Program Overview has multiple documents that can be used by a teacher to guide instruction for the year. For example: 

• The Correlation Document identifies which lessons are aligned with each standard and mathematical practice. 

• The Grade Level Content document lists the progression of content and the standards taught across a school year. Topics are listed with each lesson specifying the aligned standards and mathematical practices. 

• The Pacing Guide outlines the number of lessons with each topic, as well as the number of days necessary to implement them. This is also found in Topic Planning.

• The Scope and Sequence document lists key mathematical ideas K-8 and indicates which topics at which grade levels address the concepts. 

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for explaining the program’s instructional approaches, including reference to research-based strategies, and explaining the role of the standards.

The materials have clear instructional approaches that guide teaching and learning activities. The program is a student-centered curriculum that focuses on enabling students to make sense of mathematics. This is achieved through a framework of Essential Understandings or big ideas. For example:

• In the Program Overview, the document titled “Experience Math Research Base” lists numerous instructional strategies that guide the program’s approach to teaching and learning. These strategies include A Focus on Big Ideas to Help Students Build Connections, Teaching with Intention, Using Backwards Design to Plan More Effective Lessons, Teaching Through Problem Solving Creates Problem Solvers, A Focus on Critical Thinking, Differentiating Instruction to Meet Individual Needs, High-Quality Assessment Enhances Learning, Teacher Metacognition and Professional Learning, and Parental Involvement Influences Student Learning.

• In the Program Overview, the document titled “Setting Up the Experience Math Classroom” provides ideas for different instructional approaches found within the materials. Topics in this section include Setting Up for Small-Group Discussions, Transitioning to Whole-Class Discussions, Building a Math Community, Focusing Discussions, and Encouraging Student Participation.

• In the Program Overview, the document titled “Making Decisions” acknowledges, “We provide some guidance, but you know your class best.” The author also provides a professional learning video that explains how these decisions relate to instruction.

• In the Program Overview, Additional Activities and Practice sections, such as Wonder Tasks, Math Talks, Math Refresh Videos, etc., include explanations describing what each component is, why it is beneficial, and when it should be used. The same type of explanation is also provided for each Differentiated Instruction strategy and each category within the Assessment System.

• In Professional Learning Videos, there are more than 50 videos from the author explaining the rationale behind various elements of the program. These include topics such as 3-Part Lesson Structure and Essential Understandings, among others. While some content overlaps with the documents in the Program Overview, the videos provide additional detail, explanation, and coverage of several new topics.

Materials include and reference research-based strategies. For example:

• In the Program Overview, the document titled “Experience Math Research Base” includes two pages of references that were used to develop the instructional approaches in the program.

Materials include and reference the role of the standards in the program. For example:

• In the Program Overview, the document titled “Focus, Coherence, and Rigor” explains how the program addresses the major work of the grade and identifies where to find information about standards progressions. It also includes a narrative describing how program elements and additional activities relate to grade-level content. Another document in the Program Overview, the Grade Level Content document, shows which standards each lesson aligns with. In the Topic and Lesson Planning Guides, the related standards are accessible within the Teacher Guidance column on the right-hand side of the page.

A Materials List spreadsheet is found in the Program Overview folder for each grade level and is a comprehensive spreadsheet that categorizes materials. It explicitly indicates whether each item is included in the curated manipulatives kit or requires separate procurement by the school or district. 

For example:

• In the Read Me of the Materials List, Overview, “This spreadsheet contains a comprehensive list of all materials referenced throughout the Experience Math K-8 program. Each grade level has its own tab, and materials are organized to show exactly which topics use each item, making it easy for teachers to plan and prepare for upcoming lessons.” 

• In the Read Me of the Materials List, Column Layout, “Column A (ITEM): Lists the specific material or resource name. Column B (TYPE): Indicates the material category (see Material Types section below.) Columns C and beyond: Show which topics use each material, marked with an ‘X.’”

• In the Read Me of the Materials List, Material Types, “Understanding the material types will help you determine what you need to source:

  • Included in Kit: These materials come with the Experience Math manipulative kit for your grade level. If your district purchased the Manipulative kit, you don’t need to source these separately. 

  • Not included in Kit: These are additional materials you’ll need to gather from your classroom, school, or purchase separately. Examples include everyday items like boxes, plates, classroom books, or access to outdoor spaces.

  • Teacher Resource Page: These are printable resources and worksheets available through the Savvas Realize platform. You can download and print these as needed for specific topics.

  • Picture Book (not included in Kit): Optional literature connections that enhance the mathematical learning experience. While not required, these books can enrich your lessons when available. 

  • Poster (Digital Version Included): Visual resources available digitally through Savvas Realize that you can project for classroom use. All posters are contained within the print Student Experience Book. 

At the Topic level, Teacher Resource Masters are included that also contain Materials List, and in the Planning Guide, every lesson includes a Materials list specific to the lesson. 

The materials reviewed for Experience Math Grades 6 through 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.

Materials provide strategies, supports, and resources for students in special populations to support their regular and active participation in grade-level mathematical tasks and problem-solving activities. 

• In each lesson, the Action Task side panel includes a Differentiation tab that provides guidance and access to a Parallel Task. Parallel Tasks are designed to meet the needs of students who need additional support and those ready for additional challenge. They include suggestions about when it might make sense to differentiate. Although Parallel Tasks and assessments vary in complexity from the Action Task and Topic Assessment, they focus on the same Essential Understandings.

• In each lesson, the Your Turn: What You Learned Teacher Guidance column includes a people icon for Differentiation, which provides access to a reteaching activity. For example:

  • Grade 6, Topic 1, Integers, Lesson 1, Your Turn: What You Learned, Reteaching Activity: “If students are struggling with representing integers, you might use this reteaching activity. Set up a number line starting at 0 and showing counting numbers to 10. Place a mirror vertical to the line at 0 and let students see the dots on the other side. Point out that even though they are seeing the images of the numbers 1 to 10 on the other side, these numbers are actually called −1 to −10 to say they are on the opposite side. Ask students to point out what they notice about −7, what they notice about −10, etc. Now ask them why it might make sense to represent a debt of $7 as −7. Ask them what they think −7 might mean if: it is about a roll in a board game, it is about a sea depth, it is about a temperature.”

  • Grade 7, Topic 1, Probability of Single Events, Lesson 1, Your Turn: What You Learned, Reteaching Activity, “If students are struggling with listing all possible outcomes, you might use this Reteaching Activity. Propose a situation where someone is choosing a number between 1 and 50, but the number has to be even. Discuss how many possible outcomes there are, for example, 2, 4, 6, …, 50, or 25 outcomes. Then ask for the number of possible outcome if the number has a ones digit of 4, has a tens digit of 4, has digits that add to 6. Help students consider ways to ensure they don’t overlook any possibilities.”

  • Grade 8, Topic 1, The Pythagorean Theorem, Lesson 1, Your Turn: What You Learned, Reteaching Activity, “Provide the reproducible page Demonstrating the Pythagorean Theorem to each student or pair of students. Have them cut out the two smaller squares and try to find a way to fit them (by cutting, when necessary) onto the larger square for the 5–12–13 triangle and the 5–5–2 triangle. Ask why it worked for the right triangle and did not work for the non-right triangle.”

• In each lesson, Open Questions appear throughout the materials and are structured with a low-floor, high-ceiling design to support access for all students and opportunities for extension.

• Most topics include a student-facing Math Refresh video that provides step-by-step guidance related to lesson content.

• A Professional Learning Video for Differentiation explains where in the program teachers can find strategies and supports. These videos reference Parallel Tasks and Open Questions that appear throughout lessons.

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

Materials provide multiple extensions and opportunities for advanced students to engage with grade-level mathematics at greater depth throughout every topic and lesson. The program’s differentiation system provides opportunities for advanced students to engage with grade-level mathematics at greater depth. For example: 

• Most Action Tasks include enriched tasks that address the same essential understandings as the core lesson and include variations that add mathematical sophistication, computational complexity, or conceptual depth.

• In each lesson, Open Questions uses a "low floor, high ceiling" structure that supports access for all students and allows advanced students to extend their reasoning and explore concepts in greater depth.

• In Topic Planning and Resources, Wonder Tasks are three-act, problem-based activities that include multiple solution pathways. The Teacher Guidance column includes a people icon linking to Differentiation support, which contains Extension Questions.

• Brain Benders include open-ended questions in real-world contexts that involve multiple variables and mathematical models and allow for exploration of different solution approaches.

• Making Connections Tasks integrate concepts from multiple mathematical domains and include problems that connect mathematical relationships across domains and require varied problem-solving strategies.

The materials embed extension opportunities within lessons through questions that prompt students to extend their thinking beyond grade-level expectations, rather than through separate assignments.

There are no instances of advanced students doing more assignments than their classmates.

• Enriched tasks within the embedded differentiation framework maintain the same essential understandings as the core lesson and include increased mathematical sophistication, computational complexity, or conceptual depth.

The materials reviewed for Experience Math Grades 6 through 8 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods. 

Examples include:

• Each grade has a physical manipulative kit that varies by grade, and contents are included in a comprehensive chart that is specific to their content, including items such as color tiles, protractors, snap cubes, fraction tiles, etc. 

• Digital manipulatives are accessible via Savvas Realize through Brainingcamp. Examples of items included are fraction tiles, geoboards, and place value disks.

• Manipulatives are routinely incorporated into Minds On Activities, Action Tasks, Your Turn Questions, and Supporting Activities across all grade levels. Examples include:

  • Grade 6, Topic 6: Area, Lesson 3, Action Task, Teacher Guidance, Materials, “Geoboards™ (optional), Rulers, Square tiles (optional), Grid Paper.” And the Point Is … states, “Students are allowed to choose the area measurement they work with so that they can see that the process is the same for any area. If students choose to work with square tiles, note that the units will be in inches, not centimeters. You may offer students to create polygons in a digital format, however, please be aware that the answers will look different than those in the sample responses.”

  • Grade 7, Topic 4: Extending Percent, Lesson 1, Action Task, Teacher Guidance, Materials, “Hundredths Grids, Double Number Lines (optional)."

  • Grade 8, Topic 3: Scientific Notation, Lesson 3, Action Task, Teacher Guidance, Materials, “Calculators (optional), Unit Prefixes.” Using the Action Task states, “Display a chart relating unit prefixes to place value, or provide copies of the reproducible page Unit Prefixes. You could suggest that students use calculators if they find them helpful.”