3rd-5th Grade - Gateway 3

The materials reviewed for Eureka Math² Grade 3 through Grade 5 provide strategies for informing stakeholders, including students, parents, or caregivers, about the program and suggestions for how they can help support student progress and achievement. 

The materials reviewed for Eureka Math² Grades 3-5 provide strategies for informing students, parents, and caregivers about the mathematical program and suggestions for how parents and caregivers can support student progress and achievement. The program provides a Eureka Math² Family Math page and Family and Community Support resources that provide families with information and resources related to the program.

The overview of each module’s Teach book includes a Support for Families section that identifies resources available to support learning at home. For example, Grade 3, Module 3, Module Resources, Instructional Design & Curriculum Components, Support for Families states, “The resources in the Apply book give students more practice with the concepts learned in class. The three components in Apply that support students in deepening their understanding of the concepts covered in the daily lesson are Family Math, Practice Partners, and Terminology.” Family Math Letters are available to caregivers in English and Spanish.

Family Math Letters provide families with information about the mathematics students are learning and suggestions for supporting learning. Family Math Letters (Levels K-5) state, “Our Family Math Letters provide a topic overview that includes a content narrative, images of models and strategies, and key terminology. It also includes ideas for topic-related math activities that may be done at home or in school.” In Levels 3-5, Family Math Letters are included in the Apply book.

Practice Partners provide additional guidance for families supporting students at home. Practice Partners (Levels 1–5) state, “Each Practice has a parallel supporting Practice Partner that shows problems like those worked in class and an example of the thinking that helps students solve those problems. Practice Partners serve as a useful tool for students to solve the Practice and Remember problems, as well as a guide for families who may be supporting their student with the Practice and Remember problems at home.”

The materials reviewed for Eureka Math² Grade 3 through Grade 5 provide various 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 a consistent lesson structure: Fluency, Launch, Learn, Land. According to the Grade 3-5 Implementation Guide, Lesson Structure, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 60-minute instructional period. Fluency provides distributed practice with previously learned material. It is designed to prepare students for new learning by activating prior knowledge and bridging small learning gaps. Launch creates an accessible entry point to the day’s learning through activities that build context and often create productive struggle that leads to a need for the learning that follows. Every Launch ends with a transition statement that sets the goal for the day’s learning. Learn presents new learning related to the lesson objective, usually through a series of instructional segments. This lesson component takes most of the instructional time. Suggested facilitation styles vary and may include direct instruction, guided instruction, group work, partner activities, interactive video, and digital elements. The Problem Set, an opportunity for independent practice, is included in Learn. Land helps you facilitate a brief discussion to close the lesson and provides students with an opportunity to complete the Exit Ticket. In the Debrief portion of Land, suggested questions, including key questions related to the objective, help students synthesize the day’s learning. The Exit Ticket provides a window into what students understand so that you can make instructional decisions.”

Examples of varied approaches across the consistent lesson structure include:

• Grade 3, Module 2, Topic A, Lesson 3, Teach Book, Launch, students analyze representations of objects and their weights, identify relationships among the representations, and explain and justify their reasoning through the Which One Doesn’t Belong? routine. “Students engage in discussion about the combined weights of objects. Introduce the Which One Doesn’t Belong? routine. Display the picture of the four scales. Invite students to examine the four scales in the picture. Give students one minute to find a category in which three of the items belong, but a fourth item does not (e.g., number of objects on the scale). Invite students to explain their chosen categories and to justify why one item, or group of items, does not fit. Highlight responses that include reasoning about combining the weights of objects to make a total weight or otherwise adding, subtracting, multiplying, or dividing the weights of objects. Ask questions that invite students to use precise language, make connections, and ask questions of their own. Sample questions: ‘The pictures have different numbers of objects. What does that make you think about?’ (The marker doesn’t belong because it’s only 1 object and does not have smaller parts. The ten-stick doesn’t belong because it is 10 things put together into 1 object. The other pictures do not have anything put together.) ‘Is there a relationship between the number of objects and the weight?’ (The ten-stick is 10 grams, so we know each cube is 1 gram. There are two pencils that weigh 10 grams, so I wonder if each pencil is 5 grams.) Select one or two pictures that generate good discussion and consider asking the following questions. ‘(Ten-stick) If all we know is what we see in the picture, how can we find the weight of each cube?’ (Divide 10 grams by 10.) ‘(Pencils and marker) How can you find the combined weight of the pencils and the marker, without weighing them together?’ (Add their weights together.) ‘(Marker) How can we find the weight of four markers by using only the information in this picture?’ (Multiply 10 grams by 4.) Transition to the next segment by framing the work. ‘Today, we will represent and solve word problems involving weight.’”

• Grade 4, Module 1, Topic B, Lesson 5, Teach Book, Launch, students analyze place value representations, identify relationships among the representations, justify which representation does not belong, and discuss how units can be composed and renamed. “Introduce the Which One Doesn’t Belong? routine. Display the picture of the four charts. Invite students to study the picture of the charts. Give students 1 minute to find a category in which three of the items belong, but a fourth item does not. When time is up, invite students to explain their chosen categories and to defend why one item does not fit. Highlight responses that emphasize reasoning about place value units, about composing units, and about place value representations. Ask questions that invite students to use precise language, to make connections, and to ask questions of their own.” Sample questions include: “‘Which one doesn’t belong?’ (Chart A does not belong because the units are written with numbers instead of words. Chart C does not belong because the rest of the charts are labeled with the units and that one isn’t. The disks are labeled with 1. Chart B does not belong because it has thousands, and the rest of the charts only go to hundreds. Chart D does not belong because there are fewer than 10 hundreds, and the rest of the charts have more than 10 of a unit.) ‘How many more hundreds does chart D need to rename to the next largest unit? How do you know?’ (1 more because that would be 10 hundreds, which could be renamed as 1 thousand.) ‘What larger unit can be composed with 10 ones? 10 tens?’ (1 ten. 1 hundred.) ‘How can the one in chart C be renamed as tens and ones?’ (They can be renamed as 1 ten 5 ones.) ‘How can the tens in chart A be renamed as hundreds and tens?’ (They can be renamed as 1 hundred 3 tens.)” Students then turn and talk about how the thousands in chart B can be renamed.

• Grade 5, Module 5, Topic D, Lesson 27, Teach Book, Learn, students work with a partner to apply their understanding of volume as they plan and design a sculpture composed of right rectangular prisms. “Pair students. Distribute one Sculpture Guidelines card to each student pair. Direct one student from each pair to remove Sculpture Recording Sheet from their book. Allow students time to read the guidelines and to review the recording sheet. Invite students to turn and talk about the guidelines and share ideas they have for the design of their sculptures. Then invite them to share. ‘What ideas do you have for the design of your sculpture?’ (We want our sculpture to have prisms arranged in a random way, like some modern art we have seen before. We want our sculpture to look like an animal. We want our sculpture to look like a castle.) ‘To make the right rectangular prisms in your sculpture, you will have three bases to choose from. You will cut them out, and you can change the volumes by changing their heights. Watch me cut one of the prism patterns and make a prism.’ Demonstrate cutting the Base 6 cm by 3 cm pattern.”

Students have opportunities to share their thinking, receive feedback from teachers and peers, monitor their progress, and adjust their strategies or apply feedback to future work. Examples include:

• Grade 3, Module 1, Topic E, Lesson 23, Teach Book, Universal Design for Learning: Action & Expression, students self-evaluate their problem-solving approaches after comparing solution strategies and consider whether they would use the same strategy in a similar problem. “After the class compares solution strategies, encourage students to monitor their own progress by prompting them to evaluate the success of their problem-solving approach. For example, provide guiding questions for students to ask themselves. How did I do? Did I show my thinking? Did my strategy work? Will I use the same strategy to solve a similar problem next time? Why or why not?”

• Grade 4, Module 3, Topic A, Lesson 2, Teach Book, Universal Design for Learning: Action & Expression, students monitor the effectiveness of their selected strategy and consider whether they need to adjust their approach. “Support students in monitoring their own progress by encouraging them to engage in self-questioning as they select a strategy. Emphasize the importance of adjusting strategies or changing course if a strategy is not working. Model using a think-aloud while asking questions such as the following: Is my strategy working? Should I do anything differently?”

• Grade 5, Module 2, Topic A, Lesson 3, Teach Book, Universal Design for Learning: Engagement, students receive teacher feedback that identifies successful aspects of their work, areas for improvement, and how they can apply what they learn from errors to future work. “Consider providing feedback throughout the lesson that emphasizes individual effort, encourages setting goals for improvement, and acknowledges the value of finding and correcting errors. Use feedback such as the following: Your effort really shows here when you correctly labeled the total in your tape diagram. You partitioned the tape correctly and identified the unknown part with a question mark. That really shows your effort. Let’s talk about what you can do next time to be sure you have the correct number of parts shown in your tape. Let’s talk about what you can do next time to accurately label the total in your tape diagram. When you are learning something new, it is normal to make mistakes. What is important is to learn from mistakes and apply that learning next time.”

The materials reviewed for Eureka Math² Grade 3 through Grade 5 provide opportunities for teachers to use a variety of grouping strategies. 

The materials provide teacher guidance for varied types of student interaction and a variety of grouping formats, including whole-group, small-group, partner, and individual work. 

Examples include:

• Grade 3, Module 3, Topic D, Lesson 20, Teach Book Fluency state, “‘Let’s play Ready, Set, Multiply. Today, we will use both hands.’ Have students form pairs and stand facing each other. Model the action: Make two fists and shake them on each word as you say, ‘Ready, set, multiply.’ At ‘multiply,’ open one or both fists and hold up any number of fingers. Tell students that they will make the same motion. At ‘multiply,’ they will show their partner any number of fingers. Consider doing a practice round with students. Clarify the following directions: To show zero, show closed fists at ‘multiply.’ Try to use different numbers each time to surprise your partner. Each time partners show fingers, have them both say the product. Then have partner A say the multiplication equation starting with the number of fingers on their own hands, followed by partner B saying a related division equation. See the sample dialogue under the photograph. Switch roles after each round. Circulate as students play the game to ensure that each student is trying a variety of numbers.”

• Grade 4, Module 3, Topic D, Lesson 15, Teach Book, Learn states, “Use the Numbered Heads routine. Organize students into groups of 3 and assign each student a number, 1 through 3. Present the problem: 83 times as much as 52. Give students 2 minutes to find the product as a group. Remind students that any one of them could be the spokesperson for the group, so they should be prepared to answer. Groups should be prepared to share the following information: their group’s process for finding the partial products; the product; and how place value supports determining the partial products and product.”

• Grade 5, Module 6, Topic C, Lesson 12, Teach Book, Learn states, “Students draw quadrilaterals in the coordinate plane and classify quadrilaterals based on their properties. Divide students into groups of four. Give each group a set of Quadrilateral Cards. Assign one card to each group member and direct students to follow the instructions on the card. When each student has drawn a quadrilateral, tell groups to look at the four quadrilaterals and determine the most specific name for the quadrilateral on each card. Prompt students to use their knowledge of lengths and angles in the coordinate plane and of the properties of quadrilaterals to support their response. When groups are finished, display the graphs of the four quadrilaterals.”

The materials reviewed for Eureka Math² Grade 3 through Grade 5 partially provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials provide accommodations including text-to-speech/read-aloud, reading assessment content in a student's home language where appropriate, additional time, and digital accessibility tools. The materials provide guidance for teachers on implementing accommodations, including enabling text-to-speech for individual students or entire classes, reading assessment directions or problems aloud as necessary, and extending assessment time when appropriate. However, the materials provide limited guidance for teachers on determining which students would benefit from specific accommodations. The identified accommodations support access to assessments without changing the mathematical content or grade-level expectations.

Examples include:

• Great Minds Digital Help Center, Assessments and Reports, Assessments, provides guidance for teachers on enabling text-to-speech for an entire class or individual students. “Enable Text-to-Speech for Assessments, Teachers can enable the text-to-speech/read-aloud feature for entire classes or for specific students. This feature allows students to have text read aloud to them when taking an assessment. Text can be read aloud for both English and Spanish assessments.” The resource provides step-by-step directions for teachers to activate the accommodation: “1. Select Assessments from the main menu. 2. Select Assessment Settings at the top right. 3. Select a class section from the list. 3. To enable text-to-speech for the entire class, click the toggle next to Text to Speech for all students. 4. To enable the option for an individual student, locate their name in the student list and toggle the setting to On. 5. In the pop-up, select Yes, Turn It On to confirm your changes.”

• Grade 1-2 Implementation Guide, Assessment, Exit Tickets, provides teachers with guidance for determining when to extend the allotted time for students to complete Exit Tickets. “Exit Tickets are short, paper-based assessments that close lessons. These assessments use at least one problem, question, or writing prompt to assess whether a student has learned the basic skills and concepts needed for success in upcoming lessons. Items reflect the minimum that students must demonstrate to meet the lesson objective. You may look for evidence of the mathematical practice identified as the focus mathematical practice for the lesson in student work on the Exit Ticket. In a typical classroom, most students with basic understanding can finish within 3-5 minutes. In some settings, honoring the timeframe is more important than requiring students to finish. For example, a student’s inability to finish within 5 minutes may be valuable information. In other settings, you may extend the time to allow all students to finish as appropriate. Exit Tickets are not graded. They are paper-based so that you can quickly review and sort them. Occasionally, an alternative assessment activity may substitute for an Exit Ticket at the end of a lesson.”

• Great Minds Digital Help Center, Student and Family Resources, Use Text-to-Speech Tools, provides guidance for students on using text-to-speech and screen mask tools during assessments. Students can adjust the dictation speed, text highlight color, and speech mode when using text-to-speech. The Screen Mask tool allows students to tint the page and focus on a selected portion of the assessment. “Once the text-to-speech setting has been enabled by their teacher, students can utilize text-to-speech (read aloud) and screen mask tools when taking assessments. Use the Text-to-Speech Tool, Student can utilize the text-to-speech tool to have text and image alt text read aloud to them when taking assessments.” The resource also provides directions for adjusting the available tools, including “Dictation speed: Slow, Medium, or Fast, Text highlight color, Speech mode: Choose to click or hover over the text you want read aloud” and Screen Mask settings for opacity and color.

• Great Minds Digital Help Center, Assessments & Reports, Assessments, Assessment Settings, provides guidance on how to turn on tools for students when taking the digital version. “Teachers can customize various assessment and scoring settings when assigning an assessment to their class(es). To modify assessment settings, select the Advanced settings option at the bottom left of the assign window. Assessment Settings, Teachers can set a time limit for students to complete the assessment if desired. Teachers can allow access to a basic or scientific calculator tool. Teachers can allow students access to annotation tools, including a highlighter and notepad. If Allow Students to Check Answers is turned on, students can select a multiple-choice option in an assessment, select Check answer, and immediately learn whether their answer is correct or incorrect.” No specific guidance is offered as to which students would benefit from these tools being available. 

• Great Minds Digital Help Center, Assessments & Reports, Assessments, Customize Assessments, provides additional guidance on how to add and remove assessment items from either a printable or digital version. “Teachers and administrators can duplicate assessments from the Great Minds Library. Once an assessment has been copied, items can be added, removed, and rearranged. Additional assessment details, including title, type, and grade level, can also be modified. Copy an Assessment from the Great Minds Library: 1. Select Assessments from the main menu. 2. Select the Great Minds Library tab. 3. Locate the assessment you wish to copy in the library. 4. Click the kebab icon and select Make a copy from the drop-down menu to the right of the assessment. You can now add, remove, and rearrange items in the copied version of the assessment. Any edits to the copied assessment will not change the original assessment in the Great Minds Library. Customize Assessment: You can customize an assessment by modifying the assessment details, or by adding, removing, and/or rearranging items. Update the Assessment Details: To change the assessment title, select the pencil icon to the right of the title at the top of the page. To modify the assessment details, select the gear icon. Add Item, To add items to the assessment, select Find Items at the top of the item list. Search for items by Keyword using the keyword search at the top left. Search for items by Curriculum Attribute (Grade, Module, Lesson, Topic), Language (English or Spanish), or by Standard using the search field on the right. To filter search results, begin typing "grade", "module," "topic," "lesson," or a specific standard code. This will populate filters you can select to narrow your results. You can preview items by selecting the eye icon to the left of the item. Select items by checking the boxes to the left of the item. Select Add Item(s) to add them to the copied assessment. Once you have added all items, click the Back button at the top of the page to return to your draft. Remove and Rearrange Items: To remove items, first select them by checking the boxes to the left of each question, and then select the Remove button at the top of the list. To rearrange items, select the drag bar and drag the item to the desired position in the item list.”

• Grade 3-5 Implementation Guide, Assessment, Module Assessment, provides some guidance on having problems or directions read to students as needed. “Students complete Module Assessments independently, with directions or problems read aloud as necessary. Module Assessments take up to one class period to complete in a typical setting.”

The materials provide guidance on how to implement accommodations and identify some circumstances in which they may be appropriate. However, the guidance does not consistently identify the student needs that would warrant specific accommodations or support teachers in determining which accommodations would be most beneficial for individual students.

The materials reviewed for Eureka Math² Grade 3 through Grade 5  provide a range of representations of people and include detailed instructions and support for educators to effectively incorporate and draw upon students’ different cultural, social, and community backgrounds to enrich learning experiences. 

Examples include:

• Grade 3, Module 4, Topic D, Lesson 13, Teach Book, Learn, students solve a two-step area word problem involving a real-world situation using self-selected strategies. Teacher guidance states, “Students reason about, represent, and solve a two-step area word problem. Display the problem: Ivan washes the outsides of 5 rectangular windows. Each window is 6 feet wide and 8 feet high. What is the total area of the windows that Ivan washes? Prompt students to use the RDW process to solve the problem. Allow students to select their own solution strategies. Circulate and observe student work. Select two or three students to share their work in the next segment. Purposefully choose work that allows for rich discussion about finding large areas. The student work samples demonstrate using multiplication followed by addition and using addition followed by multiplication.” Teachers are also encouraged to adjust the problem's context to reflect students' school or community while maintaining its mathematical complexity. Universal Design for Learning: Engagement states, “Consider adjusting the problem to make it more relevant to students in your class. For example, identify items in the school or community with the dimensions and quantity in the problem and change the problem to reflect the more relevant context. When you select a different context, the units of measure could change, but the quantity 5 and the dimensions 6 by 8 should remain the same to maintain the complexity of the problem.”

• Grade 4, Module 2, Topic D, Lesson 19, Teach Book, Launch, students identify and describe the area and perimeter of rectangles in real-world objects, including a raised garden bed and dump trailer. Teacher guidance states, “Students identify the areas and perimeters of rectangles in pictures of real-world objects. Display the picture of the raised garden bed. ‘Where do you see a rectangle in the picture of a raised garden bed?’ (The frame around the dirt and plants is a rectangle.) ‘How can you describe the perimeter of the raised garden bed?’ (The perimeter is represented by the wooden frame.) ‘How can you describe the area of the raised garden bed?’ (The area is represented by the inside part, where the dirt is.) ‘What would we need to know to find the perimeter of the raised garden bed?’ (We would need to know the length and width of the outside edges of the frame.) Display the picture of the dump trailer. ‘Where do you see a rectangle in this picture of a dump trailer?’ (The bottom of the trailer forms a rectangle. The sides of the trailer form a rectangle.) ‘What is the perimeter of the dump trailer represented by?’ (The perimeter is represented by the sides of the trailer.) ‘What is the area of the dump trailer represented by?’ (The area is represented by the bottom part inside the trailer, or the bed of the trailer.) ‘What would we need to know to find the area or perimeter of the dump trailer?’ (We would need to know the length and width of the bed of the trailer.)” Universal Design for Learning: Representation provides guidance for teachers to connect the contexts to students’ prior experiences with gardens and trailers. “Consider activating students’ prior knowledge of a raised garden bed and dump trailer. Ask students about their experiences working in a garden, seeing beds or planters, and the shapes they noticed. Ask students about the different types of trailers they have seen and the uses of the trailers. Consider displaying additional pictures of garden beds and dump trailers if students are unfamiliar with the contexts.”

• Grade 5, Module 4, Topic E, Lesson 30, Teach Book, Learn, students draw on their personal experiences and collaborate with partners to develop word problems involving decimal operations in real-world situations. Teacher guidance states, “Students brainstorm word problem situations and develop examples for each operation. Invite students to Think–Pair–Share about real-world situations that might involve decimals. Record their ideas as they share them. Possible responses include the following. Buying items at a store, Making a recipe, Measuring ribbon, Running a race, Riding a bike, Filling containers. Invite pairs to choose one situation from the list, or any situation that they thought of that was not shared. Have pairs write one example for each operation that shows how they might use the operation in the situation.” Universal Design for Learning: Engagement encourages teachers to incorporate contexts relevant to students’ lives. “The situations presented are samples. Invite the class to brainstorm real-world situations that are relevant to their lives, which provides the opportunity to anchor instruction in contexts that are familiar and meaningful to students.” Teacher Notes further suggests, “If time allows, consider having pairs write their examples on chart paper and hang them up around the room for all students to see throughout the lesson.”

Throughout the program, illustrations of hands used for counting include different skin shades, and illustrations of students and adults represent people with different appearances and abilities.

The materials provide teachers with instructions and resources for incorporating and drawing upon students’ cultural, linguistic, family, and community knowledge and experiences during instruction. Math Past resources situate mathematics within historical and cultural contexts and provide examples of how people from different cultures and communities developed and used mathematics. The Additional Resources include a Culturally Responsive Teaching Resource with resources for teachers and leaders, including Valuing Students’ Assets and Knowledge, Creating a Culture of High Expectations for All Students, Communicating and Collaborating with Students and Families, Empowering Students as Agents of Change, and Supporting Culturally Responsive Teachers.

Examples include:

• The Supporting Culturally Responsive Teachers resource provides guidance for educators to consider how culture affects communication, incorporates students’ home languages, partners with families and community organizations, and brings real-world issues that are important to students into the mathematics classroom. The resource directs educators to “Ask families about the types of community organizations they think would make good partners for the school and which issues are of concern to them.” In Valuing Students’ Assets and Knowledge, teachers are directed to acknowledge the experiences and knowledge students bring to the classroom, actively identify those assets, and connect them to new learning. The resource directs teachers to “learn about the interests and assets of students and their families.”

• In Communicating and Collaborating with Students and Families, the materials provide specific guidance for incorporating students’ cultural and linguistic backgrounds into instruction. Teachers are encouraged to recognize differences in verbal and nonverbal communication styles, encourage students to use their home languages, and include families as partners in the learning process. The resource states, “In a culturally responsive classroom, teachers encourage students to use their home language and view this as an asset.” It also describes families as “respected partners who are included in the learning process and valued for the funds of knowledge they contribute.” At the lesson level, teachers receive Multilingual Learner Support margin notes, language objectives, and guidance for using strategic, flexible grouping to leverage students’ home languages and knowledge.

• In Empowering Students as Agents of Change, the materials direct teachers to learn about students’ cultural, linguistic, and academic assets and incorporate real-world issues that matter to students into mathematics instruction. The resource states, “As teachers, it's important we take time to learn about students in and out of school, including their cultural, linguistic, and academic assets.” Teachers are also directed to use Data Talks, Data Investigations, and everyday situations in word problems to connect mathematics to issues in students’ schools and communities. These resources provide opportunities for students to use mathematics to investigate issues that matter to them, consider how decisions affect their communities, and propose actions or solutions.

The materials reviewed for Eureka Math² Grade 3 through Grade 5 partially provide support for different reading levels to ensure accessibility for students. 

The materials identify strategies for reducing reading barriers while maintaining access to grade-level mathematics, including wordless context videos, picture supports, vocabulary supports, familiar phrasing, and connections among visual, physical, and oral representations.

The Grade 3-5 Implementation Guide, Lesson Facilitation, Readability states, “A student’s relationship with reading should not affect their relationship with math. All students should see themselves as mathematicians and have opportunities to independently engage with math text. Readability and accessibility tools empower students to embrace the mathematics in every problem. Lessons are designed to remove reading barriers for students while maintaining content rigor. Some ways that Eureka Math² clears these barriers are by including wordless context videos, providing picture support for specific words, and limiting the use of new, non-content-related vocabulary, multisyllabic words, and unfamiliar phonetic patterns.”

Examples include: 

• Grade 3, Module 4, Topic D, Lesson 13, Teach Book, Learn, use a visual to access the word problem before interpreting the situation mathematically. Teacher Note states, “A context video for this word problem is available. It may be used to remove language or cultural barriers and encourage student engagement. Before providing the problem to students, consider showing the video and facilitating a discussion about what students notice and wonder. This supports students in visualizing the situation before being asked to interpret it mathematically.”

• Grade 4, Module 5, Topic A, Lesson 2, Teach Book Learn, receive vocabulary support to distinguish and make sense of mathematical terminology. Teacher Note states, “The term decimal is sometimes used as a shortened way to refer to a decimal point or to a number written in decimal form. Model precision by using the more specific terms, decimal point and decimal form, and support students as they make sense of these terms with familiar phrasing.”

• Grade 5, Module 4, Topic B, Lesson 9, Teach Book, Fluency, students count decimal numbers using different mathematical language to express tenths and hundredths. Teacher Note states, “Students may count by tenths and hundredths in many ways. Choose one way for students to count decimal numbers during the activity. Consider one of the following ways: Zero, zero and one tenth, …, zero and nine tenths, one; Zero, zero point one, …, zero point nine, one; Zero, point one, …, point nine, one.”

The materials reviewed for Eureka Math² Grade 3 through Grade 5 partially integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable. Teachers can utilize interactive tools to engage students in grade-level content. 

According to the Instructional Design & Curriculum Components, “The digital platform provides seamless digital access to items in Teach, Learn, and Apply. It also includes lesson slides, videos, digital interactives, assignments and assessments, implementation videos, asset-based teaching supports, and data science projects and activities.”

The Instructional Design & Curriculum Components, Building Data Literacy, states, “Students live in a data-rich society. Incorporating elements of data science into mathematics instruction helps students develop crucial data literacy skills. Students with strong data literacy skills build knowledge by using data to interpret their world, make connections across content areas, effectively communicate their findings, have increased access to job opportunities, and use data to understand the world and impact their communities. Eureka Math² includes two products designed to work together, Data Talks and Data Investigations. Data Talks give students short, frequent exposure to data while Data Investigations provide time for students to explore data in greater depth.”

The Instructional Design & Curriculum Components, Research-Based, Multimodal, Terminology Support, states, “Lessons invite students to engage with concepts through mathematical discussions and experiences, such as digital interactives, manipulatives, or math language routines, before they learn mathematically precise terminology for the concept.”

The materials provide digital interactives within the Digital Platform; however, the materials do not provide student-facing data collection or modeling tools. Digital interactives are primarily designed for teacher-facilitated use, although teachers can send interactive slides to student devices. The Digital Platform states, “Lessons that include digital interactives are authored so that while you demonstrate the digital interactive, students engage with the demonstrations as a class. Eureka Math² digital interactives help students see and experience mathematical concepts interactively. You can send slides to student devices in classroom settings where it feels appropriate to do so. Use Teacher View to present, send slides to students, monitor student progress, and create student discussions. If you send interactive slides to students from this view, you can choose to view all students’ screens at once or view each student’s activity individually.”

Digital tools support student engagement in mathematics. Materials incorporate digital interactives and context videos throughout the curriculum. In Module Resources, Instructional Design & Curriculum Components, Digital Resources, “The digital platform provides seamless digital access to items in Teach and Learn. It also includes lesson slides, videos, digital interactives, assignments and assessments, implementation videos, asset-based teaching supports, and data science projects and activities.” Digital resources include fluency activities, videos, teacher-led interactives and demonstrations, images and text from Teach or Learn, and pages from Learn, including Classwork, removables, Problem Sets, and Exit Tickets.

The digital materials are fixed in format and cannot be customized for local use.

The materials reviewed for Eureka Math² 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. 

Great Minds Digital Help Center, Curriculum & Instruction, Navigation, provides a Teacher Platform Overview that describes the digital resources available to teachers and methods for sharing resources with students. “Resources, Teachers have access to curriculum materials and resources for all Great Minds products licensed to their organization. Select a grade level at the top left. Navigate to a specific module and other resource categories using the tabs. Drill down into the selected module using the drop-down menus. You can download individual resources from the resource card, or you can select a resource to preview it. When viewing an individual resource, teachers can: Navigate to other resources in the section using the Next and Previous arrows. Download or print the resource using the buttons at the top left. Use the language drop-down to access the Spanish version of the resource (if available). PDF resources can be annotated using the in-platform annotation tools. Student-facing resources can be shared with students in multiple ways: Copy the shareable link to send to students or embed in an LMS, Share the resource to Google Classroom, Assign the resource to students in Great Minds.”

The Teacher Platform Overview also describes reporting features available to teachers: “Reports: In Reports, teachers can access visual assessment reports for their classes. For more information on each type of report, see the below articles: Student Report, Assessment Report, Class Standards Report, Single Standards Report.”

The digital platform provides mechanisms for teachers to distribute resources and assignments to students and review student assessment information. However, the evidence does not demonstrate that teachers and students or students and other students use digital technology to communicate, jointly complete mathematical work, exchange mathematical thinking or feedback, or otherwise collaborate with each other.

The digital technology supports student-to-student and teacher-to-student collaboration.

The materials reviewed for Eureka Math² Grade 3 through Grade 5 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic. 

The materials use a consistent design across modules, topics, and lessons, including recurring lesson structures, icons, color coding, headings, and organizational features. Student materials use consistent font sizes, placement of directions, and designated space for students to show their mathematical thinking. Printable Student Task Statements, Assessment PDFs, and Learn books provide space for students to record calculations and responses. Teacher materials organize content by module, topic, lesson, and lesson component and use consistent formatting and navigation features.

According to the Grade 3–5 Implementation Guide, visual design includes:

• Lesson Overview states, “Each lesson begins with two pages of information to help you prepare to teach the lesson. Language Objectives describe the primary language domain of each lesson (reading, writing, speaking, or listening). They also describe the modes of communication (collaborative, interpretive, or productive) and any math language that students will use during the lesson. Key Questions help focus your instruction and classroom discourse. Achievement Descriptors (ADs) are standards-aligned descriptions that detail what students should know and be able to do based on instruction. The number of ADs addressed in each lesson varies depending on the content. Turn to the Resources section at the end of the Teach book to see the proficiency indicators for each AD. Proficiency indicators help you assess your students’ level of proficiency. The Lesson at a Glance is a snapshot of the lesson framed through what students should know, understand, and do while engaging with the lesson. It includes information about the tools, representations, and terminology used in the lesson. The Agenda shows the sequence and recommended time length of the sections of the lesson. Materials lists the items that you and your students need for the lesson. Lesson Preparation provides guidance about materials that need to be created, assembled, or placed in advance.”

• Lesson Structure states, “Each lesson is structured in four sections: Fluency, Launch, Learn, and Land. Lessons are designed for one 60-minute instructional period.” Lessons consistently present Fluency, Launch, Learn, and Land in the same sequence.

• Visual Design states, “In the Teach book, color coding and other types of text formatting are used to highlight facilitation recommendations and possible statements, questions, and student responses. These are always suggestions and not a script. Each section includes a bold line of text that gives the purpose for that section. These purpose statements, taken together, support the overall objective of the lesson. Dark blue text shows suggested language for questions and statements that are essential to the lesson. Light blue text shows sample student responses. Text that resembles handwriting indicates what you might write on the board. Different colors signal that you will add to the recording at different times during the discussion. Bulleted lists provide suggested advancing and assessing questions to guide learning as needed.”

• Inside Learn, “Learn is students’ companion text to the instruction in Teach. It contains all the pages your students need as you implement each lesson. The components that go with each lesson are indicated by icons in the student book. The magnifying glass icon indicates a lesson page that students use during the guided or directed portion of the lesson. The gears icon indicates the Problem Set. This is a carefully crafted set of problems or activities meant for independent practice during the lesson. Items from the Problem Set may be debriefed in Land, or you may use the items as formative assessment or for deeper discussion about a specific aspect of the instruction. An orange bar on the side of a page indicates a removable, a student page that should be removed from the Learn book. A removable may be used inside a personal whiteboard so students can practice skills several times in different ways, or it may be cut, assembled, or rearranged for an activity during a lesson or across multiple lessons.”

Images, graphics, and mathematical models communicate information and support student understanding of mathematical concepts. Each module includes a table of contents that identifies topics and lessons by page number and uses bold, orange text to distinguish sections. Module overviews include visuals of sample student work, manipulatives, or mathematical representations used within the topics. Lessons also include visuals that correspond to the mathematical content.

For example, Grade 3, Module 5, Module Overview, Topic C, includes a double number line labeled with fractions with a denominator of 8 that corresponds to students’ work representing and comparing fractions on a number line. The overview states, “Fractions on the Number Line Students continue to formalize their understanding of fractions as numbers by representing fractions from 0 to 1 on a number line. They partition number lines with fraction tiles, and they compose and decompose 1 whole by using strategies similar to those used with number bonds and tape diagrams in topic B. Students relate a fraction’s value to its size, its location on a number line, and its distance from 0 to find pairs of equivalent fractions. They generalize their understanding of fractions on a number line to build a ruler that they use to measure lengths within fractions of an inch and to create line plots representing fractional length data.” Module overviews across the grade band use similar structures to pair descriptions of mathematical content with corresponding visuals and representations.

Student materials use consistent organizational features. Each Learn book begins with a table of contents that identifies the topics and lessons within the module. A What’s Included section describes the recurring components of the Learn resource and includes visuals identifying these components. Grade 4, Learn, Module 6, What’s Included, states, “Welcome to Learn, students’ companion text to the instruction in Teach. This resource contains all the pages that students need, including in-class work pages, glossaries, and opportunities for practice. Lesson pages needed during the lesson are labeled by lesson number and include learning outcomes. Pages that include an orange bar are meant to be separated from the book and used during class. The Problem Set, which follows the new learning of the lesson, offers daily independent practice with problems organized from simple to complex for easy differentiation. An Exit Ticket is a brief, formative assessment of key learning in the lesson. The back of each Exit Ticket includes space for students to reflect on their understanding of the day’s objective. Spiral Review reinforces skills and concepts through distributed and interleaved practice.”

Each Learn book also includes a Terminology section with definitions, corresponding visuals, and lesson references for mathematical terms introduced within the module. For example, Grade 4, Learn, Module 6, Terminology, states, “These terms are introduced in the module. Use the blank space to make notes and drawings. cup A cup (c) is a unit for measuring liquid volume. 2 cups equal 1 pint. A small school milk carton holds 1 cup. (Lesson 20).” An accompanying visual shows a small milk carton to represent the unit of measure.

The materials reviewed for Eureka Math² Grade 3 through Grade 5 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.  

Eureka Math² integrates digital resources with lesson materials and provides point-of-use guidance for their use. Teacher guidance identifies lesson-specific digital interactives and explains how teachers can use the tools to support students in representing mathematical ideas, exploring mathematical relationships, identifying patterns, explaining their thinking, and solving problems.

Examples include:

• Grade 3, Module 3, Topic B, Lesson 8, Teach Book, Learn, Teacher Note, provides guidance for using the Associative Property Arrays digital interactive to support students in visually decomposing quantities. “The digital interactive Associative Property Arrays supports students breaking apart a quantity visually. Consider allowing students to experiment with the tool individually or demonstrating the activity for the whole class.”

• Grade 4, Module 2, Topic C, Lesson 14, Teach Book, Launch, directs teachers to use the Distributing Pencils digital interactive to support students in representing division through decomposing units. Teachers “open and display the Distributing Pencils digital interactive” and present a problem in which a principal distributes 1 case of pencils, 3 boxes of pencils, and 6 individual pencils equally among 4 teachers. Teachers use the interactive to decompose 1 case into 10 boxes and then decompose a remaining box into 10 individual pencils as students determine how the pencils can be distributed equally. Students turn and talk throughout the demonstration to explain how the quantities should be decomposed and distributed.

• Grade 5, Module 5, Topic A, Lesson 1, Teach Book, Learn, guides teachers to use the Geometry World: Side Length Explorer digital interactive to support students in investigating relationships among the angle measures of quadrilaterals. Teachers “open and display the Geometry World: Side Length Explorer digital interactive,” display a quadrilateral, and have students discuss what they notice about its angles. Teachers adjust the vertices to demonstrate that “the 4 angle measures in a quadrilateral always sum to 360°.” Students then Think–Pair–Share about the relationship between the angles of the quadrilateral and the degrees in a circle and use the relationship to determine whether the sum of the angle measures is a property of quadrilaterals.

The Great Minds Digital Help Center also provides guidance for teachers on accessing and implementing student-facing digital resources. Teachers can assign PDFs and videos to a class or individual students, provide instructions, determine how students submit work, and review student submissions. Teachers can also copy direct links to student-facing resources for use in other digital systems.

The Grade 3-5 Implementation Guide provides additional guidance for implementing digital resources and identifies virtual manipulatives, how-to videos, downloadable activities, and assessment and reporting resources available to support instruction.