3rd-5th Grade - Gateway 3

The materials reviewed for Imagine IM Grade 3 through Grade 5 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement. Examples include:

The Family Support Hub for Imagine IM K–8 provides an overview of the problem-based curriculum and highlights features such as collaboration, critical thinking, and accessible resources intended to support student learning. In the section titled What is Imagine IM?, the Hub explains that “Imagine IM is a problem-based core curriculum designed to address content and practice standards to foster learning for all. Students learn by doing math, solving problems in mathematical and real-world contexts, and constructing arguments using precise language. Teachers can shift their instruction and facilitate student learning with high-leverage routines to guide learners to understand and make connections between concepts and procedures.”

The Family Support Hub includes an About Our Curriculum section featuring videos titled, What is a problem-based curriculum?, How do the materials support all learners?, and Why is the curriculum designed this way? Another section, Imagine IM for Families: A Video Series, is designed to support families and all stakeholders. Videos in this series include What is Problem-Based Instruction?, How Does Imagine IM Prepare Students for Success in the Real World?, What is a Math Community?, The Benefits of Math Practice, and Supporting Math Learning Outside the Classroom.

Accessing Family Support Materials, For Imagine IM Families helps families navigate the available resources. This section provides information on how to access the Family Support Hub, with detailed directions for locating and exploring the curriculum. The directions state, “With a student's username and password: Locate the Family Support Hub by clicking the hamburger menu in the top left corner of the screen when logged in as a student. Select your student's grade, then navigate to the specific lessons they are currently studying. Please see the image below for an example of where to find the Family Support Hub.” Once families reach their student’s lesson, they will find a range of resources, including Unit Launch Family Support Videos that offer background information caregivers can use to support learning throughout a unit. Family Support Materials provide guidance on key concepts and ideas, and include Spanish-language versions. Additional Support Materials in Spanish are also available to further assist Spanish-speaking families.

Each unit includes Family Support Materials, providing a content overview, guiding questions, and practice problems. A narrative outlines student learning goals for each section, and the Try it at home! component offers structured activities and questions for families to reinforce the mathematical concepts. 

An example in Grade 3 includes:

• Unit 4, Relating Multiplication to Division, 3.4 Support, Family Support Material state, “In this unit, students make sense of division and learn to multiply and divide whole numbers within 100. They also use the four operations to represent and solve two-step word problems. Students work toward these end-of-year goals: Fluently multiply and divide within 100. Know from memory all products of two one-digit numbers. Section A: What is Division?, In this section, students think about division in terms of equal-size groups, just as they have done with multiplication. Sections B: Relating Multiplication and Division, In this section, students make connections between the result of a division and the unknown factor in a multiplication equation. Section C: Multiplying Greater Numbers, In this section, students use different strategies to multiply greater numbers. First, they multiply a single-digit number by a multiple of 10, relying on what they know about place value. Section D: Dividing Greater Numbers, In this section, students divide greater numbers. They continue to use the relationship between multiplication and division and their understanding of place value to find quotients. Try it at home!, Near the end of the unit, ask your third grader to find answers to these problems: 6\times 16, 98\div 7. Questions that may be helpful as they work: How did you break up the expression to make it easier to solve? Can you rewrite the division problem as a multiplication problem?” The guide also includes a Spanish language version.

An example in Grade 4 includes:

• Unit 2, Fraction Equivalence and Comparison, 4.2 Support, Family Support Material states, “In this unit, students deepen their knowledge of fractions. They explore the sizes of fractions, write equivalent fractions, and compare and order fractions with the denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100. Section A: Size and Location of Fractions, In this section, students revisit the meaning of ‘fraction.’ They use fraction strips, tape diagrams, and number lines to represent fractions. Students compare fractions that have the same numerator or the same denominator, and recall that equivalent fractions have the same size. Sections B: Equivalent Fractions, Here, students take a closer look at equivalent fractions and reason using number lines. They show that fractions at the same point on the number line are equivalent. Students then learn to tell if two fractions are equivalent, without using number lines. Section C: Fraction Comparison, In this section, students compare fractions that have different numerators and different denominators, using various strategies. For example, they may think of the fractions in terms of the same denominator, how far each fraction is from 0 on a number line, or how each fraction compares to \frac{1}{2} or 1. Students record the results of comparisons with symbols >, <, or =. They then solve problems that involve comparing fractional measurements, such as lengths in fractions of an inch. Try it at home!, Near the end of the unit, ask your fourth grader to compare \frac{3}{5} and \frac{3}{7} . Questions that may be helpful as they work: How are the two fractions alike? How are they different? What strategy did you use to compare? Is there a different strategy that you could use to compare?” The guide also includes a Spanish language version.

An example in Grade 5 includes:

• Unit 2, Fractions as Quotients and Fraction Multiplication, 5.2 Support, Family Support Material states, “In this unit, students solve problems involving division of whole numbers, with answers that are fractions (which could be in the form of mixed numbers). They develop an understanding of fractions as the division of the numerator by the denominator, that is a b = ab. They then solve problems that involve the multiplication of a whole number by a fraction or a mixed number. Section A: Fractions as Quotients, In this section, students learn that fractions are quotients and can be interpreted as division of the numerator by the denominator. Students draw and analyze tape diagrams that represent sharing situations. Through the context of first sharing 1, and then sharing more than 1, then sharing a number of things with increasingly more people, students notice patterns and begin to understand that in general \frac{a}{b}=a\div b. Sections B: Fractions of Whole Numbers, In this section, students make connections between multiplication and division and use visual representations that can show both operations. Section C: Area and Fractional Side Lengths, In this section, students use what they know about the area of a rectangle with whole-number side lengths to find the area of a rectangle that has a pair of whole-number side lengths and a pair of fractional side lengths. Try it at home!, Near the end of the unit, ask your fifth grader the following questions: 1. Write as many expressions as you can that represent this diagram:\frac{3}{5} and 4 is shown in the diagram. 2. What is the area of the following rectangle? Questions that may be helpful as they work: How are the two problems alike? How are they different? How does your expression represent the diagram? How did you break up the rectangle to help you solve for the entire area? What are the side lengths of the rectangle?” The guide also includes a Spanish language version.

The materials reviewed for Imagine IM Grade 3 through Grade 5 provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways within each lesson, which consists of four phases: Warm-Up, Instructional Activities, Lesson Synthesis, and Cool-Down. According to the Teacher Course Guide (Flipbook), What’s in an Imagine IM Lesson, Instructional Activities, “After the Warm-Up, lessons consist of a sequence of 1–3 instructional activities. The activities are the heart of the mathematical experience and make up the majority of the time spent in class. An activity serves one or more purposes: Provide experience with a new context. Introduce a new concept and associated language. Introduce a new representation. Formalize a definition of a term for an idea previously encountered informally. Identify and resolve common mistakes and misconceptions that people make. Practice using mathematical language. Work toward mastery of a concept or a procedure. Offer the opportunity to apply mathematics to an open-ended problem such as modeling. The purpose of each activity is described in its Activity Narrative. Each instructional activity has three phases. Launch: During the Launch, make sure that students understand the context (if there is a context) and what the problem is asking them to do. This is not the same as making sure students know how to do the problem—part of the work that students should do for themselves is to figure out how to solve the problem. The Launch invites students into the lesson and helps them connect to contexts with which they are unfamiliar. Student Work Time: The Launch of an activity frequently includes suggestions for grouping students. At different times, students are given opportunities to work individually, with a partner, and in small groups. Activity Synthesis: During the Activity Synthesis, allow time for students to incorporate and make connections to what they have learned. This time ensures that all students have an opportunity to understand the mathematical punch line of the activity and to situate the new learning within their previous understanding.”

Centers can be used for ongoing review, practice, and self-reflection. Students can work on skills beyond the lesson as well as reinforce current and previous skills. Teacher Course Guide (Flipbook), Key Structures in This Course, Center Overview, “Centers are intended to give students time to practice skills and concepts that are developed across the year. There are two types of centers. Addressing centers address the work of a lesson or a section of a unit. Supporting centers review prior unit or prior grade-level understandings and fluencies. Each center builds across multiple stages that may span several grades.” Structure of Center Time, “In IM Grades 3–5, center time is in addition to regular class time, as desired by the teacher. Occasionally, optional center-day lessons are included in a unit to introduce a center to students, but in general, centers are provided as an extra resource for teachers.” Examples include:

• In Grade 3, Additional Resources, Centers, Number Line Scoot (2-3), Stage 2: Halves, Thirds, and Fourths, students generate numbers and move that interval on a number line. Narrative states, “Students take turns rolling a number cube and using the number as the numerator in a fraction with a denominator of 2, 3, or 4. Students move their centimeter cube to the corresponding interval on one of the shared number lines. A player whose cube lands exactly on the last tick mark of a number line keeps that cube. They then put a new cube at 0 on the same number line. The first player to collect five cubes wins.”

• In Grade 4, Additional Resources, Centers, Compare (1-5), Stage 4: Divide within 100 with One Divisors, Narrative states, “Both students flip over a card that shows a division expression within 100, with one-digit divisors. The student whose card has the greater value takes both cards. If the cards have the same value, students flip over two new cards. The game is over when one student runs out of cards to flip. The partner with the most cards wins.”

• In Grade 5, Additional Resources, Centers, Would You Rather? (2-5), Stage 3: Compare Units in a Given System, Narrative states, “One student spins a spinner to get a measurement and a unit. They ask their partner a ‘would you rather?’ question, comparing the given measurement to a quantity that they choose, using a different unit in the same measurement system. The partner answers the question and explains their reasoning.”

The materials reviewed for Imagine IM Grade 3 through Grade 5 provide opportunities for teachers to use a variety of grouping strategies. Suggested grouping strategies are consistently provided in the Activity Launch guidance and include whole groups, small groups, pairs, and individual configurations. Examples include:

• In Grade 3, Unit 7, Two-dimensional Shapes and Perimeter, Lesson 3, Activity 2, Launch states, “Groups of 2. ‘Now you’re going to play Mystery Quadrilateral with your partner. Re-read the directions for the game, then think about some words that may be helpful as you play.’ (side, angle, right angle, equal, skinny, tall, slanted). 1 minute: quiet think time. Share and record responses. Give each group a folder containing a set of the quadrilateral cards from the previous lesson. ‘How could you use the images of all the quadrilaterals on your paper as you play?’ (They can help me think about questions I could ask. I could mark off quadrilaterals as I figure out that they’re not the mystery quadrilateral.) Give students access to counters and let them know they can be used to cover shapes during the game.” Activity, “‘Play Mystery Quadrilateral with your partner. Be sure to take turns hiding the shape and guessing the shape.’ 10-15 minutes: partner work time.”

• In Grade 4, Unit 4, From Hundredths to Hundred-Thousands, Lesson 3, Activity 1, Launch states, “Groups of 3–4.” Activity, “If creating a giant number line, lead the activity as outlined in the Activity Narrative. Otherwise, ask students to work with their group on the first two problems. Pause and discuss: How students knew where to put each decimal. How the number line could help us see the least and greatest. ‘Take a few quiet minutes to complete the rest of the activity.’ 5–6 minutes: independent work time.”

• In Grade 5, Unit 4, Wrapping Up Multiplication and Division With Multi-Digit Numbers, Lesson 5, Activity 2, Launch states, “Groups of 2. Activity: 8-10 minutes: independent work time. 2-3 minutes: partner discussion.”

The materials reviewed for Imagine IM Grade 3 through Grade 5 offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. These suggestions are provided within the Teacher Guide in a section called Universal Design for Learning and Access for Students with Diverse Abilities, and Assessment Guidance. As such, they are included at the program level and not specific to each assessment. Examples include:

• Teacher Course Guide (Flipbook) Universal Design for Learning and Access for Students with Diverse Abilities states, “Supplemental instructional strategies, included in Access for Students with Diverse Abilities of each lesson, increase access, reduce barriers and maximize learning. Each support is aligned to the Universal Design for Learning Guidelines (udlguidelines.cast.org), and based on one of the three principles of UDL, providing alternative means of engagement, representation, or action and expression. These supports offer additional ways to adjust the learning environment so that students can access activities, engage in content, and communicate their understanding. Supports are tagged, with the areas of cognitive functioning they are designed to address, to help identify and select appropriate supports for students. Designed to facilitate access to Tier 1 instruction by capitalizing on students’ strengths to address obstacles related to cognitive functions or challenges, these strategies and supports are appropriate for any student who needs additional support to access rigorous, grade-level content. Use these lesson-specific supports, as needed, to help students succeed with a specific activity, without reducing the mathematical demands of the task. Phase them out as students gain understanding and fluency. Use a UDL approach and students’ IEPs, their strengths, and their challenges to ensure access. When students may benefit from alternative means of access or support, draw on ideas from the tables below or visit udlguidelines.cast.org for more information.”

• Teacher Course Guide (Flipbook) Universal Design for Learning and Access for Students with Diverse Abilities, Accessibility for Students with Visual Impairments states, “For students with visual impairments, accessibility features are built into the materials: 1. A palette of colors distinguishable to people with the most common types of color blindness. 2. Tasks and problems are designed so that success does not depend on the ability to distinguish between colors. 3. Mathematical diagrams, presented in scalable vector graphic (SVG) format, can be magnified, without loss of resolution, and rendered in Braille. 4. Where possible, text associated with images is not part of the image file, but rather included as an image caption accessible to screen readers. 5. Alt text on all images makes interpretation easier for users accessing the materials, with a screen reader. All images in the curriculum have alt text: a very short indication of the image’s contents, so that the screen reader doesn’t skip over as if nothing is there. Some images have a longer description to help students’ with visual impairments recreate the image in their mind. Understand that students with visual impairments likely will need help accessing images in lesson activities and assessments. Prepare appropriate accommodations. Accessibility experts, who reviewed this curriculum, recommended that eligible students have access to a Braille version of the curriculum materials, because a verbal description of many of the complex mathematical diagrams is inadequate to support their learning.”

• Teacher Course Guide (Flipbook) Assessment Guidance, Diagnostic Assessments section, provides additional teacher guidance on accommodating students during assessments. It suggests that students who may not perform well on diagnostic assessments can continue to engage with grade-level tasks using appropriate supports: “Address prerequisite skills while continuing to work through the on-grade tasks and concepts of each unit, instead of abandoning the current work in favor of material that addresses only prerequisite skills.” 

• The Imagine IM platform complies with WCAG 2.1 AA standards for all student-facing features, supporting the use of assistive technology and promoting accessibility for students with disabilities. Teachers can personalize assessments by modifying question types, removing distractors, or adding audio or visual supports, allowing for individual or small-group assignments without altering academic expectations. Imagine Learning Classroom incorporates accessibility throughout product development using automated and manual testing, user feedback, and regular updates to accessibility documentation, including VPATs. Accessible print formats and recommended text-to-speech tools are also available.

The materials reviewed for Imagine IM Grade 3 through Grade 5 partially provide a range of representations of people and incorporate guidance and structures that reference students’ cultural, social, and community backgrounds. Student-facing materials include multicultural names such as Kiran, Mai, Elena, and Han. When relevant to the mathematical task, characters are illustrated and shown engaging with the content in varied contexts, including rural, urban, and international settings. There are instructional videos titled Inspire Math Video: Introduce/Reinforce/Review, which “showcase the mathematics of the unit in a real-world, engaging context.” These materials do not exhibit demographic bias regarding who achieves success in the mathematical scenarios.

Lesson contexts include examples that reference cultural and community practices. For example:

• In Grade 3, Unit 7, Two-Dimensional Shapes and Perimeter, Lesson 14, Activity 1, students are introduced to wax shapes and use a variety of shapes to create their own. The Launch states, “Groups of 2. Display the image. ‘Today’s lesson is going to focus on African wax prints. African wax prints are colorful cotton fabrics commonly used for clothing in West Africa. Take a minute to think about the pattern. What do you notice? What do you wonder?’ (The pattern is colorful. There are rhombuses in the pattern. There are triangles in the pattern. There are quadrilaterals that aren’t rhombuses, rectangles, or squares in the pattern. How do they make these patterns? What other shapes could be used to make these patterns? What types of clothing are made with this cloth? Where can you buy this type of fabric?) 1 minute: partner discussion. Share responses. ‘You’re going to create your own wax print pattern. Independently read over the directions and think about how you’ll create your pattern.’ 2–3 minutes: quiet think time. ‘Are there any questions about how you’ll create your wax print pattern?’ Answer any questions students have. Give each student a sheet of dot paper and colored pencils, crayons, or markers.”

• In Grade 4, Unit 6, Multiplying and Dividing Multi-Digit Numbers, Lesson 26, Activity 2, students describe and use patterns to make paper flowers. In the activity, students are working on a problem related to preparing for a Quinceanera. Student Task Statement states, “Create a plan for creating paper flower garlands for a quinceañera. In your plan include: A pattern for the paper flower garlands you will create. How many paper flower garlands you can make in 3 hours. How much tissue paper and string you will need to complete the paper flower garlands. Explain or show your reasoning.”

• In Grade 5, Unit 2, Fractions as Quotients and Fraction Multiplication, Lesson 17, students engage in an activity where they create mosaics using rectangles with fractional side lengths. The Lesson Narrative states, “In this lesson, they apply what they learned about multiplying whole numbers and fractions to make mosaic art pieces out of rectangles and they use the area of the pieces to estimate how much it costs to recreate the mosaic with hard material like stone, tile, and glass.” Students use paper rectangles to represent fractional dimensions and then collaborate to create mosaics, calculate areas, and compare the total areas represented.

Lesson structures introduce students to the curriculum and classroom routines while supporting the development of a math community. The Teacher Course Guide (Flipbook), Problem-Based Teaching and Learning, Community Building states, “Each lesson offers opportunities for the teacher and students to learn more about one another, develop mathematical language, and become increasingly familiar with the curriculum routines.” These lessons include routines that facilitate discussion, shared norms, and opportunities to learn about classmates and mathematics simultaneously.

The Teacher Course Guide (Flipbook) contains references to research and guidance that emphasize student identity and lived experience. For example, in the section titled Community Building, the overview states, “In a math community, all students have the opportunity to express their mathematical ideas and discuss them with others, which encourages collective learning. ‘The classroom is a critical container for empowering marginalized students. It serves as a space that reflects the values of trust, partnership, and academic mindset that are at its core’ (Hammond, 2015).” All Students Are Capable Learners of Mathematics states, “It is through these classroom structures that teachers have daily opportunities to learn about and leverage students’ understandings and experiences, and to position each student as a capable learner of mathematics.”

The Teacher Course Guide (Flipbook), Advancing Mathematical Language and Access for Multilingual Learners, MLR8 Discussion Supports, suggests using a variety of strategies to help engage students, “Instructional moves and strategies support inclusive discussions about mathematical ideas, representations, contexts, and strategies (Chapin, O’Connor, & Anderson, 2009). Combine and use these instructional moves and strategies to support discussion during almost any activity. These include multimodal strategies for helping students make sense of complex language, ideas, and classroom communication. Over time, students may begin using these strategies themselves to prompt each other to engage more deeply in discussions. Examples of Possible Strategies: Show central concepts multi-modally by using different types of sensory inputs: act out scenarios or invite students to do so, show videos or images, use gestures, and talk about the context of what is happening.” Spanish-language materials are available, including student resources, teacher prompts, and family support content.

The Teacher Course Guide (Flipbook), Key Structures in This Course, Student Journal Prompts, guide the teacher to include life experiences of students when learning math. “John Dewey (1933) asserted that students make sense of the world through metacognition, making connections between their lived experiences and their knowledge base, and argued that education should offer students opportunities to make connections between school and their lived experiences in the world. Ladson-Billings encourages the idea that teachers must help students effectively connect their culturally- and community-based knowledge to the learning experiences taking place in the classroom.”

The materials reviewed for Imagine IM Grade 3 through Grade 5 provide supports for different reading levels to ensure accessibility for students.

Teacher Course Guide (Flipbook), Universal Design for Learning and Access for Students with Diverse Abilities, Representation states, “Reduce barriers and leverage students’ individual strengths by inviting students to engage with the same content in different ways. Supports that provide multiple means of representation include suggestions for offering alternatives to the ways information is presented or displayed, developing students’ understanding and use of mathematical language and symbols, and describing organizational methods and approaches designed to help students internalize learning.”

Teacher Course Guide (Flipbook), Advancing Mathematical Language and Access for Multilingual  Learners, Mathematical Language Routines states, “MLRs, included in select activities of each unit, offer all students explicit opportunities to develop mathematical and academic language proficiency. These ‘embedded’ MLRs are described in the Teacher Guide for the lessons in which they appear. MLR6 Three Reads states, “Use this routine to ensure that students know what they are asked to do, create opportunities for students to reflect on the ways mathematical questions are presented, and equip students with tools used to actively make sense of mathematical situations and information (Kelemanik, Lucenta, & Creighton, 2016). This routine supports reading comprehension, sense-making, and meta-awareness of mathematical language. How It Happens: In this routine, students are supported in reading and interpreting, three times, a mathematical text, a situation, a diagram, or a graph, each time with a particular focus. At times, withhold the intended question or main prompt until the third read so that students can concentrate on making sense of what is happening before rushing to find a solution or method. First Read: ‘What is this situation about?’ After a shared reading, students describe the situation or context. This is the time to identify and resolve any challenges with non-mathematical vocabulary. (1 minute) Second Read: ‘What can be counted or measured?’ After the second read, students list all quantities in the situation that are countable or measurable. Examples: ‘number of people in a room’ rather than ‘people,’ ‘number of blocks remaining’ instead of ‘blocks.’ Record the quantities as a reference to use when solving the problem after the third read. (3–5 minutes) Third Read: ‘What are different ways or strategies we can use to solve this problem?’ Students discuss possible strategies. They may find it helpful to create diagrams to represent the relationships among quantities identified in the second read, or to represent the situation with a picture (Asturias, 2012). (1–2 minutes)” 

• In Grade 4, Unit 3, Extending Operations to Fractions, Lesson 19, Activity 2, Launch states, “MLR6 Three Reads. Display only the problem stem, without revealing the question(s). ‘We are going to read this problem 3 times.’ 1st Read: ‘Jada and Noah are hiking at a park. Here is a map of the trails. The length of each trail is shown. What is this situation about?’ 1 minute: partner discussion. Listen for and clarify any questions about the context. 2nd Read: ‘Jada and Noah are hiking at a park. Here is a map of the trails. The length of each trail is shown.’ (Display the trail map). ‘Name the quantities. What can we count or measure in this situation?’ 30 seconds: quiet think time. 2 minutes: partner discussion. Share and record all quantities. Reveal the question(s). 3rd Read: Read the entire problem, including question(s) aloud. ‘What are some strategies we can use to solve this problem?’ 30 seconds: quiet think time. 1–2 minutes: partner discussion.”

The materials reviewed for Imagine IM Grade 3 through Grade 5 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable. 

Teacher Course Guide (Flipbook), Imagine IM Program Components includes, “Consumable full-color Student Workbooks (units 1–8 or 9 depending on grade level) – available in English and Spanish. Include full lessons with learning goals, Warm-Ups, activities, and practice problems with space for student thinking and work. Provides QR codes to digital family resources at point of use.” The guide further explains, “Print: Exclusive print versions of Teacher Guides and Student Workbooks connect directly to the digital components, ensuring that the integrity of the rich IM content is maintained in any classroom implementation model. Digital: The Imagine IM digital student experience includes access to Student Workbook content, interactive lessons, videos, virtual manipulatives, digital centers, digital task statements, digital practice sets, digital Cool-downs, digital assessments, and more! A comprehensive digital platform with interactive tools and features for multi-dimensional teaching.” Flexibility and adaptability are highlighted: “Editable digital lesson cards can be projected or assigned to students, which allows options to meet the needs of all students. Lessons can be copied, edited, and customized as needed.” The platform also provides opportunities for live engagement: “Interactive Teaching Tools: Live Learn allows for synchronous instruction virtually within the platform. Teachers can transition from asynchronous work time to a live session with one click. Student progress is visible in the moment.” The guide describes the interactive annotation feature: “Annotation Tool – daily instruction comes alive through the ability to write, draw, model, and share student work directly on the lesson cards. Teachers can annotate lesson plans and full-screen views.” An example includes:

• In Grade 3, Unit 3, Wrapping Up Addition and Subtraction within 1,000, Lesson 3, Activity 3.1, students use strategies to add within 1,000. Activity Narrative, “The purpose of this activity is for students to add within 1,000, using any strategy that makes sense to them. The expressions in this activity give students a chance to try different strategies, such as adding hundreds to hundreds, tens to tens, and ones to ones, reasoning with numbers close to a hundred, and using a variety of representations. Students who use base-ten blocks or draw number-line diagrams choose appropriate tools strategically.” Activity, “‘Work with your partner to add these numbers in any way that makes sense to you. Explain or show your reasoning.’ Monitor for an expression that students represent in a variety of ways, such as by: Using base-ten blocks. Drawing a number line. Writing their reasoning in words. Writing equations. Identify students who use different representations, and select them to share during the Activity Synthesis. A virtual manipulative can be found on the next card.” Teacher instructions state, “You can change the type of workspace by clicking the Workspace icon in the bottom right corner. You can clear the workspace by clicking the Reset icon in the bottom right corner. The toolbar has three tabs: The Objects tab enables you to select blocks. The Shapes tab enables you to annotate the workspace with text, numbers, including fractions, and shapes. The Tools tab enables you to use various math representations and tools. You can add blocks to the workspace in two ways: By dragging blocks from the toolbar. By clicking the blocks in the toolbar. Within the workspace, click to select and drag blocks. When you select a block, a drop-down menu will appear: The arrow icon will rotate the block. The break icon will decompose a larger valued block into smaller valued blocks. The regroup icon composes the smaller valued blocks back into the larger valued block. The copy icon will add or copy a block. The trash icon will remove a block. The lock icon enables you to highlight blocks to group and lock them to the workspace. In addition to the trash can icon, you can remove blocks from the workspace by dragging the counters to the side or bottom of the workspace. At the bottom of the white workspace you can: Select whole numbers or decimals. Select which base-ten blocks to show. Select to automatically count the individual block and/or all the blocks. Change the colors. Select place-value disks. Use the pens and eraser at the bottom to draw and write in the workspace. The icons on the bottom left, let you: Undo an action. Redo an action. Zoom in or out. Center the workspace. Choose a language.”

• In Grade 4, Unit 5, Multiplicative Comparison and Measurement, Lesson 2, Activity 2.1, students represent situations and descriptions of multiplicative comparison, using diagrams and equations. Activity Narrative states “The purpose of this activity is for students to analyze and describe how images and diagrams can show ‘n times as many.’ Students generate ideas for how to use a multiplication equation to represent the comparison. Students begin by interpreting an image in which the multiplier (3) and the numbers are given. They explain how some number of times of the lesser amount can be seen in the greater amount. Next they create their own diagram and see different ways of representing the iterations (groups of) the lesser amount to create the greater amount. During the activity, make connecting cubes accessible for students who may choose to use them for problem solving—either to reason about the quantities or to explain their reasoning.” Activity states, “‘Create a display that shows your thinking about the cubes in each problem and include details to help others understand your thinking.’” ‘How does each representation show ‘times as many’?’ Monitor for students who create diagrams that are similar to connecting-cube images and discrete tape diagrams to share in the Activity Synthesis. A virtual manipulative can be found on the next card.” Teacher instructions state, “You can change the type of workspace by clicking the Workspace icon in the bottom right corner. You can clear the workspace by clicking the Reset icon in the bottom right corner. The toolbar has three tabs: The Objects tab enables you to select connecting cubes. The Shapes tab enables you to annotate the workspace with text, numbers, including fractions, and shapes. The Tools tab enables you to use various math representations and tools. You can add cubes to the workspace in two ways: By dragging the cubes. By clicking the cubes in the toolbar. You can remove cubes from the workspace by dragging the cubes to the side or bottom of the workspace. Within the workspace, click to select and drag cubes. When you select a cube in the workspace, a drop-down menu appears. The paint can icon removes or fills color in a cube. The copy icon will add a cube. The trash icon will delete a cube. The lock icon enables you to highlight groups of cubes to create a locked tower of cubes. You can break larger towers of cubes into smaller towers of cubes by dragging the cubes apart. At the bottom of the white workspace, select the Groups icon to automatically count each group of cubes. Use the pens and eraser at the bottom to draw and write in the workspace. The icons on the bottom left, let you: Undo an action. Redo an action. Zoom in or out. Center the workspace. Choose a language.”

• In Grade 5, Unit 7, Shapes on the Coordinate Plane, Lesson 2, Activity 2.1, students locate and describe points on the coordinate grid. Activity Narrative states, “The purpose of this activity is for students to describe coordinates for points. After playing a round of What’s the Point?, students have an opportunity to write a description of the location of a point in the coordinate grid. The structure of this part of the activity mirrors what students did in the previous lesson when they were describing a rectangle. Some students may use the coordinates on the grid while others may use words to describe the location of the point. Students make choices about how to revise their thinking based on what makes the description stronger and clearer to them. This activity not only supports students developing language to describe the location of a point but also develops a deeper understanding of the coordinate grid. Invite students to use language from the display from an earlier lesson if they find it helpful.” Activity states, “Monitor for students who: Revise their thinking. Refer to the numbers on the coordinate grid to communicate the location of the point. ‘Share your description of the location of the point on the grid with your partner. Take turns being the speaker and the listener. If you are the speaker, share your ideas and writing so far. If you are the listener, ask questions and give feedback to help your partner improve their work.’ Teacher Instructions state, “You can change the workspace from basic to graphing by clicking in the bottom right corner. You can add points and bands or lines to the workspace in two ways: By dragging the points and bands or lines to the first point you want and letting go. By clicking the points and bands or lines in the tray. You can click points on the band or line to drag to new points. You can click the x or y axis and: The plus sign will copy the grid. The trash icon will remove grids. Change the scale. Toggle between one and four quadrants. Toggle between points or grid view. Show or remove axis labels. Lock the grid. Within the workspace, click a point, band, or line and: The plus sign will copy the item. The trash icon deletes the item. The paint can fills or removes color from a band. Use “toggle label” to label the coordinates of your item. At the bottom, you can. Show ordered pair labels. Show a data table of the ordered pairs. Use the pens and eraser at the bottom to draw and write in the workspace. To type, click the T in the top left corner.”

The materials reviewed for Imagine IM Grade 3 through Grade 5 include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable. Examples include:

• Students can submit work through a digital data dashboard, and the teacher can score the assignment/assessment as well as provide feedback on the work to the student. The IL Classroom Guides, For Students section provides instructions for accessing this feedback. The How To Access Your Classes and Assignments guide states, “If your teacher has made comments to any of your work in that class, you will see the ‘New comments’ banner next to the class name” and “Your teacher may leave comments for you to see while you work on your assignment.” The program also includes a Digital QuickStart Guide that provides “overviews of how to navigate the program by unit and lesson, how to access the digital data dashboard, and provides a list of virtual manipulatives available to assign and use with students.” The What’s New in the IL Classroom section details updates to features such as “text to speech enhancements, digital dashboard updates, Live Learn enhancements, and item analysis.”

• Teacher Course Guide (Flipbook) states, “Imagine IM’s enhanced resources are specially tuned to support teachers in planning and facilitating lessons across various instructional environments.” The guide lists features under Teacher Experience, including a “comprehensive digital platform with interactive tools and features for multi-dimensional teaching” and “embedded professional learning with Learning Narrative videos accessible directly from both the print Teacher Guides and in the digital platform.” These resources are designed to support implementation and may be used collaboratively among teachers. The guide also notes, “Teachers are equipped to monitor student progress through digital task statements, innovative staged centers, section checkpoints, and Cool-Downs. These provide real-time feedback and data to inform instructional decisions.” In addition, the materials include embedded opportunities for student discussion and reflection. 

• In Grade 3, Unit 3, Wrapping Up Addition and Subtraction within 1,000, Lesson 21, About this lesson, Lesson purpose, “In this lesson, students put together a wish list of supplies they would like to get for their classroom given a large collection of choices and their costs. They are given a budget and freedom to decide how to spend the money. As they make choices, students round the costs before they check the total amount they are spending. Students then compare their wish list with another group. Groups compare their wish lists and how much they spent in each category.” Activity synthesis states, “Invite groups to share how their strategies compare to those of their partner groups. Invite partner groups to share their comparisons with the whole class, using ‘how much less?’ and ‘how much more?’ statements.” This lesson shows an example of collaboration between student to student.

• In Grade 4, Unit 1, Factors and Multiples, Lesson 5, About this lesson, Math Community, “Before the lesson, explain to students that norms are expectations that help everyone in the room feel safe, comfortable, and productive doing math together. Offer an example, such as: ‘It may help us share our ideas as a whole class if we have the norm ‘Listen as others share their ideas.’’ Tell students to think about norms that help everyone do math as they work today, and that you will record these norms during the Lesson Synthesis.’” Lesson synthesis states, “Math Community, Ask students to reflect on both individual and group actions while considering the question ‘What norms, or expectations, were we mindful of as we did math together in our math community?’ Record responses in the ‘Norms”’ ​column of the poster.” This lesson is an example of collaboration between teacher to student.

• In Grade 5, Unit 1, Finding Volume, Lesson 1, About this lesson, Math Community, “In the Lesson Synthesis, students discuss what it means to be a part of a mathematical community. Prepare a space, such as a piece of chart paper, titled ‘Math Community,’ ​and a T-chart with the headers ‘Doing Math’ and ‘Norms.’​ ​Partition each column into two sections: ‘Students’ and ‘Teacher.’ The two sections encourage students and the teacher to be mindful that both respective parties are responsible for the way math is being done in the classroom. In this lesson, students will add their ideas to the ‘Doing Math’​ section. In upcoming lessons, students will add to and revise their contributions, including drafting classroom norms.” Lesson synthesis states, ‘“Today we explored volume and compared the solid objects that our group built. What does it look and sound like to do math together as a mathematical community? What was I doing? What were you doing?’ (We talked to each other and to the teacher. We had some quiet time to think. We shared our ideas. We thought about the math ideas and words we knew. You were writing down our answers. You were waiting until we gave the answers.) Add students’ responses to the ’Doing Math’ column of the chart. This lesson is an example of collaboration between teacher and student.

The materials reviewed for Imagine IM Grade 3 through Grade 5 have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The images, graphics, and models support student learning and engagement and communicate information or support student understanding. Examples include: 

• Grade 3, Unit 4, Relating Multiplication to Division, Lesson 2, Warm-Up, Narrative, “The purpose of this Warm-Up is to elicit the idea that many different questions could be asked about a situation, which will be useful when students solve problems in a later activity.” Warm-Up states, “What do you notice? What do you wonder? Students may notice: Some apples are in boxes. Some apples are still on the tree. There are 9 boxes of apples. Some may wonder: How did the apples get into the boxes? How many apples are in boxes? Does each box have the same number of apples?” The image that is used is clear and supports student learning and engagement.

• Grade 4, Unit 7, Angles and Angle Measurement, Lesson 1, Warm-Up, Narrative, “This Warm-Up prompts students to generate formal and informal geometric language (Lines, points, straight, curved), which will be used in an upcoming task, by familiarizing themselves with a context and the mathematics that might be involved in the task.” Warm-Up states, “What do you notice? What do you wonder? Students may notice: There are different colored lines. All the points form a circle. The lines start at one point and end at another point. The lines are straight but go in different directions. The lines make a circle in the middle. Students may wonder: How are the straight lines making a circle? Are any of the lines curved?” The image that is used is clear and supports student learning and engagement.

• Grade 5, Unit 7, Shapes on the Coordinate Grid, Lesson 7, Activity 1, Activity Synthesis, “Invite previously selected students to share. ‘Clare says ‘Some rhombuses are squares and some rectangles are squares.’ Do you agree with her?’ (Yes, we saw with the toothpicks that a rhombus can be a square but it doesn’t have to be. Rectangles are squares when the 4 sides are equal, but the 4 sides don’t need to be equal, so not all rectangles are squares.) Display or draw a diagram like the one below or use the diagram from a previous lesson and ask, ‘How does the diagram show the relationship between rhombuses and rectangles?’ (It shows that squares are both rhombuses and rectangles.)” The image that is used is clear and supports student learning and engagement.

The teacher and student materials follow a consistent layout and structure across lessons and units, including repeated phases such as Warm-Ups, Instructional Activities, Lesson Synthesis, and Cool-Down. Instructional elements are labeled and sequenced in the same order throughout the materials.

• Teacher Course Guide (Flipbook), Key Structures in This Course, Coherent Progression, “Every unit, lesson, and activity has the same overarching design structure: The learning begins with an invitation to the mathematics, is followed by a deep study of concepts and procedures, and concludes with an opportunity to consolidate understanding of mathematical ideas.”

• Teacher Course Guide (Flipbook), How To Use The Imagine IM Resources, “Each grade level contains eight or nine units. Units contain 8–28 lesson plans. Depending on the grade level, units have pre-unit Practice Problems in the first section, a Checkpoint after each section, and an End-of-Unit Assessment. In addition to lessons and assessments, units have aligned center activities to support the unit content and ongoing procedural fluency.”

Narratives throughout the materials help guide teacher understanding and maintain coherence. 

• Teacher Course Guide (Flipbook), What’s in an Imagine IM Lesson, Narratives Tell The Story, “The story of each grade is told in eight or nine units. Each unit has a narrative that describes the mathematical work that will unfold in that unit. Each lesson and each activity in the unit also has a narrative. The Lesson Narrative explains: The mathematical content of the lesson and its place in the learning sequence. The meaning of any new terms introduced in the lesson. How the mathematical practices come into play, as appropriate. The Activity Narrative explains: The mathematical purpose of the activity and its place in the learning sequence. What students are doing during the activity. What to look for, while students are working on an activity, to orchestrate an effective Activity Synthesis. Connections to the mathematical practices, when appropriate.”

Student materials, in printed consumable format, include appropriate font size, direction amount and placement, and space on the page for students to show their mathematical thinking. There is ample space in the printable Student Task Statements, Assessment PDFs, and workbooks for students to capture calculations and write answers. Organizational features such as the table of contents and internal references are present and clearly labeled, supporting navigation across units and lessons.

The materials reviewed for Imagine IM Grade 3 through Grade 5, provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Teacher Course Guide (Flipbook) provides descriptions of the digital technology embedded within the program. In the Teacher Experience section under Interactive Teaching Tools, the guide states, “Live Learn allows for synchronous instruction virtually within the platform. Teachers can transition from asynchronous work time to a live session with one click. Student progress is visible in the moment.” In the Program Components section under Digital, the guide notes that “The Imagine IM digital experience offers tools to enhance instruction and incorporate blended learning.” It further explains that these embedded features are designed to improve usability, including “for planning and instruction: Unit Launch videos, assignable digital lessons and assessments, embedded teaching notes, unit mapping plans, and more; for lesson delivery: a lesson player with editable lesson cards, Live Learn, and the annotation tool; and for student engagement: digital centers, virtual manipulatives, digital tasks and practice problems, and more.” Additionally, a lesson titled How to Use Live Learn is available in the Imagine IM Updates section under What’s New in IM Classroom? on the program website, offering teachers further guidance on using this embedded technology.

Imagine IM provides a Digital QuickStart Guide that offers teachers an overview of how to navigate the program by unit and lesson, access the digital data dashboard, and identify virtual manipulatives that can be assigned and used with students. Ongoing updates to the program are available in the What’s New in the IL Classroom section, which includes information on recent enhancements such as text-to-speech features, digital dashboard improvements, updates to the Live Learn tool, and item analysis functionality.

Teacher guidance is provided within lessons for the use of embedded technology to support and enhance student learning, as demonstrated in the following example:

• In Grade 3, Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 9, Activity 9.2, Activity Narrative states, “The purpose of this activity is for students to tell and write time to the nearest minute as they draw times on blank clocks.” Launch states, “‘Let's use what you know about telling time to the nearest minute to practice writing times on clocks.’ ‘What are some important things to remember when you are drawing the time on a blank clock?’ (Show the difference between the minute and hour hand clearly. The minute hand should be longer than the hour hand. Be careful in drawing the location of each hand.)” Student Task Statement, “1. Draw hands on each clock to show the given time. A. 2:36 PM. B. 3:18 PM.” Teacher instructions state, “You can change the type of workspace by clicking the Workspace icon in the bottom right corner. You can clear the workspace by clicking the Reset icon in the bottom right corner. The toolbar has three tabs: The Objects tab enables you to add blocks of time to the clock and a number line to show elapsed time. The Shapes tab enables you to annotate the workspace with text, numbers, including fractions, and shapes. The Tools tab enables you to use various math representations and tools. Within the workspace, click to select hands and drag to count minutes or hours around the clock or on the number line. By clicking the number line, you can move the blue dots below to change time intervals. Click an object for a drop-down menu to appear: The clock hand icons will add or remove the minute and/or hour hand. The minute icon adds or removes minutes from the clock. The copy icon will add another clock to the workspace. The trash icon will remove objects. The lock icon will group and lock objects to the workspace. The paint can icon fills or removes color to a block. At the bottom of the white workspace, you can: Select the geared icon to make the hour and minutes hand move together. Select the free icon to make the hour and minute hand move separately. Select the clock icon to add or remove the hour and/or minute hands as well as the minute labels. Select the digital clock icon to show a digital clock. Select the 24-hour icon and digital clock icon to show a 24-hour digital clock. Select tracker to track time with color. Use the pens and eraser at the bottom to draw and write in the workspace. The icons on the bottom left, let you: Undo an action. Redo an action. Zoom in or out. Center the workspace. Choose a language.”

• In Grade 4, Unit 1, Factors and Multiples, Lesson 1, Activity 1.1, Activity Narrative states, “The purpose of this activity is for students to find the area of a rectangle by tiling and multiplying the side lengths. Students use inch tiles to build rectangles with a given side length and find the area of those rectangles. They work together to compare and explain the strategies used to find the area of rectangles and make connections between strategies. Students observe how the area of rectangles with a given width varies as the length changes and make predictions about what areas are possible with the given widths.” Launch states, “Display the rectangle in the student book. ‘Look at the rectangle on your page and describe it to a partner.’ (It has 6 units. There are 2 rows and 3 columns.) Give each group 10 tiles. ‘Build all the rectangles you can using all 10 tiles. Describe them to a partner.’ ‘Who has a rectangle that is 2 tiles wide, 5 tiles wide, 10 tiles wide?’ Draw each rectangle as students share their responses. A virtual manipulative can be found on the next card.” Teacher instructions state, “You can change the type of workspace by clicking the Workspace icon in the bottom right corner. You can clear the workspace by clicking the Reset icon in the bottom right corner. The toolbar has three tabs: The Objects tab enables you to add tiles to the workspace. The Shapes tab enables you to annotate the workspace with text, numbers, including fractions, and shapes. The Tools tab enables you to use various math representations and tools. You can add tiles to the workspace in two ways: By dragging the tiles from the toolbar. By clicking the tile in the toolbar. Within the workspace, click to select and drag tiles. When you select a tile, a toolbar will appear: The paint can icon allows you to change the color of the tiles. The square icon toggles the fill for the tiles. The copy icon will add tiles to the workspace. The trash icon will remove tiles. The lock icon enables you to highlight tiles to group and lock them to the workspace. At the bottom of the white workspace, you can: Add or remove grid lines. Label groups of tiles in the workspace. Use the pens and eraser at the bottom to draw and write in the workspace. The icons on the bottom left, let you: Undo an action. Redo an action. Zoom in or out. Center the workspace. Choose a language.”

• In Grade 5, Unit 7, Shapes on the Coordinate Grid, Lesson 3, Activity 3.1, Activity Narrative states, “The purpose of this activity is for students to plot several points with the same vertical or horizontal coordinate and observe that they lie on a horizontal or vertical line respectively. Students also plot points on the axes for the first time. Before plotting the points on a grid with grid lines, students first estimate the location of the points. This encourages them to think about the coordinates as distances (from the vertical axis for the first coordinate and from the horizontal axis for the second coordinate).” Launch states, “‘You and your partner will each complete a different set of 4 problems independently. After you’re done, discuss your work with your partner.’” Student Task Statement, “Partner A. Estimate to plot and label the location of each point. 2. Plot and label the same points on the coordinate grid.” Teacher instructions state, “You can change the workspace from basic to graphing by clicking in the bottom right corner. You can add points and bands or lines to the workspace in two ways: By dragging the points and bands or lines to the first point you want it and letting go. By clicking the points and bands or lines in the tray. You can click points on the band or line to drag to new points. You can click the x or y axis and: The plus sign will copy the grid. The trash icon will remove grids. Change the scale. Toggle between one and four quadrants. Toggle between points or grid view. Show or remove axis labels. Lock the grid. Within the workspace, click a point, band, or line and: The plus sign will copy the item. The trash icon deletes the item. The paint can fills or removes color from a band. Use ‘toggle label’ to label the coordinates of your item. At the bottom, you can: Show ordered pair labels. Show a data table of the ordered pairs. Use the pens and eraser at the bottom to draw and write in the workspace. To type, click the T in the top left corner.”