3rd-5th Grade - Gateway 3

The materials reviewed for Experience Math Grades 3 through 5 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 3, Topic 1: Measuring Area with Non-Standard Units, Lesson 2, Action Task, Differentiation, What Could You Do If…, “Students struggle to justify why the area of each creature is about the same as the area of the given square without counting. You could…Ask students to look at their creatures for rows that are close to the same length of the square. Have them count to check that they can make about 5 rows of 5. Alternatively, students might build their creatures using square tiles and then rearrange the squares.”

• In Grade 4, Topic 2: Representing, Comparing, and Ordering Fractions, Lesson 1, Minds On Activity, Teacher Guidance, Connecting Ideas and Experiences, “To encourage students to share their own unique perspectives, you might: Ask students to consider what makes two fractions easy to compare. Have students think of different scenarios where a whole is divided into equal shares, such as pizza slices or sharing a granola bar.”

• In Grade 5, Topic 3: Representing Multiplication and Division of Fractions, Lesson 3, Action Task, Teacher Guidance, Conversations Starters, “Could Lucas have spent more time than Arlo on his project? Could Mason have spent more time than Arlo on his project? Could you predict if the missing fraction for Amanda is closer to 0 or 1?”

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 3 through 5 meet expectations for containing explanations and examples of grade-level concepts and/or standards and how the concepts and/or standards align to other grade 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 3, Topic 2: Representing Multiplication and Division, seven videos can be viewed to improve a teacher’s knowledge in math, including an Overview: Representing Multiplication and Division, Connecting to Concepts Beyond the Grade: Multiplication and Division, Reasoning in This Task, Recognizing Multiplication Situations, Developing a Sense of Size, Creating Groups of a Given Size, and Writing a Division Equation.

  • In Grade 4, Topic 6: Patterns, six videos can be viewed to improve a teacher’s knowledge in math, including an Overview: Patterns, Connecting to Concepts Beyond the Grade: Patterns, Exploring Repeating Patterns, Exploring Growing Patterns, Multiplication Patterns, Addition Patterns, and Tables of Value, and Using Manipulatives to Visualize Pattern Rules.

  • In Grade 5, Topic 10: Representing Decimals, six videos can be viewed to improve a teacher’s knowledge in math, including an Overview: Representing Decimals, Connecting to Concepts Beyond the Grade: Decimals, Decomposing Decimals to Thousandths, The Thousands Column, Decimal Representations, and Fraction-Decimal Relationships.

• 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 3, Topic 13: Mass states, “Students do not do any formal work with mass in Grade 2, but they have worked with the notion of using units to measure when working with length. In Grade 4, students use customary units for weight as well as metric units for mass.”

  • In Grade 4, Topic 3: Representing Four-Digit Whole Numbers states, “In Grade 3, students focus on place-value relationships and rounding whole numbers. This will help prepare them for extensive work in Grade 4 with greater numbers. In moving from Grade 4 to Grade 5, students extend what they learn about four-, five-, and six-digit whole numbers to work with greater whole numbers.”

  • In Grade 5, Topic 6: Representing Whole Numbers states, “In Grade 4, students examine the structure of the place-value system through one million, and this is extended to greater numbers in Grade 5. In Grade 5, students are introduced to exponents as a way to represent powers of 10. In Grade 6, students extend their understanding of exponents to evaluate algebraic expressions that have exponents in them.”

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

  • In Grade 3, Topic 1: Measuring Area with Non-Standard Units, Lesson 2 states, “Students had experience using a variety of different area units in the previous lesson. In this lesson, students use inch grids to estimate and measure the areas of irregular shapes. This lays the foundation for the introduction of the unit square inches in a later topic. Estimating is important for several reasons: The process of estimating helps students develop spatial reasoning skills. In many cases, an estimate is all that’s needed. Sometimes it is necessary to estimate when finding the area of an irregular shape. Students have worked with ideas related to this lesson before: Grade 2 or earlier - identifying halves, thirds and fourths of 2-D shapes; measuring length using nonstandard units and standard units. Grade 3 - Measuring area using nonstandard units.”

  • In Grade 4, Topic 10: Shapes and Lines, Lesson 1 states, “Most students will have an intuitive understanding of line symmetry. This lesson will formalize what lines of symmetry are and provide opportunities for students to identify lines of symmetry and to create shapes with particular numbers of lines of symmetry. Students have met ideas related to this lesson before: Grade 2 or earlier - considering simple attributes of shapes; identifying triangles, quadrilaterals, pentagons, hexagons, and cubes. Grade 3 - recognizing subsets of shapes within larger sets of shapes, e.g., recognizing squares as quadrilaterals; composing and decomposing shapes.” 

  • In Grade 5, Topic 8: Geometry, Lesson 2 states, “This is the introduction to the coordinate plane for students. In this grid system, horizontal and vertical coordinates are used to locate specific points on the grid. This lesson involves only positive coordinates. They indicate how far to move right and up from the point where the axes intersect. Students have worked with ideas related to this lesson before: Grade 3 or earlier - work with numbers lines. Grade 4 - attributes of parallelograms; concepts of parallelism and perpendicularity.”

The materials reviewed for Experience Math Grades 3 through 5 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.

In addition, a discrepancy in the materials that were noted for Grade 3 related to instructional time include, but is not limited to:

• Lessons 1-2 and 1-3 are identified as correlated to 3.MD.6 on each lesson’s planning page tab; however, these lessons are not listed as correlated to 3.MD.6 in the Experience Math Grade 3 Correlation to the Common Core Standards document.

The materials reviewed for Experience Math Grades 3 through 5 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.

The materials reviewed for Experience Math Grades 3 through 5 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

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 Kindergarten through Grade 3 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. For example:

  • Grade 3, Topic 2: Representing Multiplication and Division, Lesson 3, Action Task, Differentiation, Parallel Tasks, “If students are struggling to use a different number of people sharing each time, allow them to duplicate the number if they need to. Encourage students seeking more challenge to find as many number pairs as they can where there is exactly one blueberry left over when sharing. This will allow students the opportunity to deal more explicitly with remainders. Working with remainders is not expected for assessment or for all students.” 

  • Grade 4, Topic 6: Patterns, Lesson 1, Action Task, Differentiation, Parallel Tasks, “If students are struggling to predict, you could direct them to select Patterns A and B, which are somewhat simpler. You might ask about position 20 instead of position 29 and you might omit the part about the 12th, 24th, and 36th terms. Students seeking more of a challenge should probably include Pattern C or Pattern D, both of which are more challenging. They could also be encouraged to develop a pattern with two attributes in Question 2.”

  • Grade 5, Topic 5: Fraction Operations, Lesson 1, Action Task, Differentiation, Parallel Tasks, “If students are struggling because they aren’t given specific fractions to try, suggest these possibilities: \frac{1}{4}+\frac{1}{5}, \frac{3}{4}+\frac{4}{5}, and \frac{2}{4}+\frac{4}{5}. You could ask students seeking more challenge to come up with their own rule for how you could predict the denominator of the sum of two fractions if you know the original denominators. This could replace the specific task assigned to most students.”

• 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.

• 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 3 through 5 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 3 through 5 meet expectations for providing manipulatives, both virtual and physical, 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 the contents are included in a comprehensive chart specific to their content, including items such as base-ten blocks, linking cubes, pattern blocks, and number cubes. 

• Digital manipulatives are accessible via Savvas Realize through Brainingcamp. Examples of items included are base ten blocks, fraction circles, 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 3, Topic 10: Adding and Subtracting Whole Numbers, Lesson 1, Minds On Activity, Teacher Guidance, Materials: “Base-ten blocks (optional), Number Lines (optional).”

  • Grade 4, Topic 2: Representing, Comparing, and Ordering Fractions, Lesson 4, Action Task, Teacher Guidance, Materials, “Fraction towers.” And the Point Is… states, “uses a model to show equivalence.”

  • Grade 5, Topic 2: Representing Addition and Subtraction of Fractions, Lesson 2, Action Task, Teacher Guidance, Materials: “Counters, Rulers, Fraction Strips or Fraction Tower, Inch Grid Paper.” Conversation Starters states, “How could you use fraction strips? How could you use grids? How might you use equivalent fractions? Do you think the difference will be closer to 0 or closer to 1? Why?”