3rd-5th Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations for supporting MLLs’ full and complete participation in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide some strategies for MLLs’ participation in grade-level problems, but they do not apply these supports consistently across chapters and lessons. 

The materials provide a consistent instructional design, both at the chapter-level and the lesson-level. Each chapter features several language-rich components that the Implementation Handbook describes as supporting balance across the three aspects of rigor. These components provide MLLs with opportunities to use and develop language.  

• Big Idea of the Chapter: “informal explorations before chapter learning begins”

• Chapter Vocabulary: “opportunities for students to review past vocabulary using a graphic organizer to make sense of words rather than just memorize their definitions”

• Career Performance Tasks: “tasks centered around applying and connecting mathematical concepts with a focus on the chapter career themes”

• STEAM Video Performance Tasks: “the video highlights mathematics put to work in a STEAM context, and the accompanying task gives students an opportunity to apply the reasoning to solve STEAM tasks of their own”

• Big Idea Tasks: “open-ended tasks focused on assessing the aspects of rigor and mathematical practices”

• Connecting Big Ideas Activities: “data-centered activities focused on application across multiple chapters”

• Chapter Game: “a fun and competitive context for students to review key skills from the chapter”

• Chapter Centers: “additional activities for students to review the content of the chapter”

Within these chapter-level components of the instructional design, the materials provide embedded prompts that attempt to support connections among the three aspects of rigor and mathematical practices, student reflection, or opportunities for discourse. The Chapter Vocabulary and Career Performance Tasks contain English Learner Support notes that contain language supports inconsistently aligned with the language proficiency levels of Entering-Emerging, Developing-Expanding, and Bridging-Reaching. These notes provide language supports for one specific aspect of each task but do not consistently provide for MLLs’ full and complete participation. For example, in Grade 5, Chapter 3, Add and Subtract Decimals, the Chapter Vocabulary uses a graphic organizer and matching task to engage students with the review vocabulary words estimate, compatible numbers, expanded form, standard form, and word form. Students participate in a whole-class discussion stating each review vocabulary word aloud before discussing and completing the graphic organizer. The English Learner Support note invites teachers to support one part of one of the review vocabulary words, compatible, by discussing the everyday meaning of the word and contrasting it with the mathematical meaning. The note suggests that teachers invite students to complete the sentence frame, “To estimate the difference, use the compatible numbers ____ and ____. The estimate is ____.” While these suggestions provide support for the word compatible in compatible numbers, the note does not support the vocabulary words estimate, expanded form, standard form, and word form, and thus does not provide for MLLs’ full and complete participation in the task. 

Additionally, each chapter begins with a section titled, Mathematics of the Chapter, which features a note titled, Nick’s Notes: Language Routines. These notes contain one suggested Language Routine with brief instructions about implementing the suggested routine. For example, in Grade 5, Chapter 2, Numerical Expressions, Nick’s Note: Language Routines states, “Critique, Correct, & Clarify: Most Valuable Mistake. To use this routine, strategically select and present student work that is incorrect, has an unclear solution, or shows a common error. Students analyze the work, pair-share what was done correctly, identify where the error occurred, and co-craft a solution to be discussed as a whole class.” While regularly embedded Language Routines are generally supportive of MLLs’ participation in grade-level tasks by providing tasks with predictable language usage when repeated over time, this is the only reference to Language Routines in the chapter. This one-time reference is brief in nature, and it does not include specific details about implementing the routine within the specific language demands of each lesson.

At the lesson-level, the consistent instructional design includes a language-rich start to each lesson through an Investigate section where students make observations and activate or build background knowledge. The majority of the lesson is spent with teacher-led prompts and activities that focus on explicit instruction of mathematical strategies, new mathematical terminology, and key concepts. Lessons end with an opportunity for students to engage in practice focused on applying the procedures and strategies from the lesson. The materials provide lesson-embedded strategies and scaffolds in notes called English Learner Supports in two spots within each lesson: within the explicit instruction of the lesson and within the practice portion of the lesson. These notes feature language supports aligned with the lessons’ tagged WIDA English Language Development Standards, with the supports delineated by the language proficiency levels of Entering-Emerging, Developing-Expanding, and Bridging-Reaching (see the report for 3.1.MLL-1 for more details). Generally, the English Learner Support notes align to the WIDA key language uses of explain, inform, or argue, and feature language supports in three categories: support for new mathematical vocabulary, suggestions for MLLs to leverage home language as a resource, or sentence frames to support MLLs with participating in student-to-student discourse. Within the lesson facilitation, these notes often support MLLs’ participation in one specific problem or one small aspect of the task. Within the practice portion of the lesson, these notes often present an additional activity that serves as a summary of the lesson. Because of these points, the English Learner Support notes do not allow for MLLs’ full and complete participation in grade-level problems across lessons. Additional evidence illustrating these limitations appears in the reports for 2a.MLL-2c.MLL, and for each of the mathematical practices in the reports for 2e.MLL-2l.MLL. 

Across both the chapter-level and lesson-level supports, the materials contain three features to support MLLs’ participation in grade-level problems: a visual glossary, text-to-speech technology, and a Family Letter. The visual glossary is available in English/Spanish in the print Student Experience, along with vocabulary flashcards for the new vocabulary of the chapter. In the digital learning experience, the materials provide a visual glossary in 16 languages. The materials feature text-to-speech technology, and the Implementation Handbook states that the technology “enables students to listen to text using high-quality, natural-sounding voices, available in multiple languages.” The functionality of the text-to-speech technology was inconsistent and not intuitive to navigate. The Family Letter is available in English and Spanish in the digital experience, and it outlines the big picture of the mathematics and vocabulary of the chapter along with a QR code linking to additional resources to support student learning throughout the chapter. 

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations of providing support for MLLs’ full and complete participation in the conceptual understanding of key mathematical concepts. The materials provide opportunities for students to explore and make sense of mathematical ideas while engaging with multiple representations to formalize procedures, supporting conceptual understanding. To do this, the materials provide students with the opportunity to apply prior knowledge to new tasks, inviting students to find relationships within and between concrete representations, visual representations, and abstract written strategies. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the intentional development of students’ conceptual understanding of key mathematical concepts. For example:

• MLLs are not fully supported in participating in Grade 5, Chapter 5, Multiply Decimals, Lesson 5.3, where students draw to model multiplying decimals and whole numbers (5.NBT.7). The WIDA English Language Development [ELD] Standards are as follows: “Interpret mathematical explanations by evaluating a pattern or structure that follows a given rule. Construct mathematical explanations that share a solution with others.” In the first Key Concept, students participate in a whole-class, guided modeling by the teacher of how to shade a hundreds grid to represent a multiplication expression. The lesson facilitation states, “Require students to use precise vocabulary demonstrating place value. Students should say ‘twenty-three hundredths’ instead of ‘point two three’ or ‘point twenty-three’.” There are no language supports provided for MLLs to use and apply precise vocabulary. The Key Concept continues with students building conceptual understanding as they complete several problems similar to the guided example, with teacher prompts for the whole class to compare examples to look for a pattern or structure. The English Learner Support Box includes targeted scaffolds that connect language to the mathematical task by having students use the terms shade and shaded to describe their work, supporting meaning-making of vocabulary in context. Visual modeling and guided questioning provide opportunities for listening, speaking, and demonstrating understanding through actions. However, the scaffolds are primarily limited to short, teacher-directed exchanges and do not consistently support independent language production. Additionally, the supports are not aligned to the language demands of the task of interpreting mathematical explanations by evaluating a pattern or structure. As a result, while the materials provide meaningful strategies that support access to conceptual understanding, they do not consistently ensure full and complete participation for all MLLs as it relates to the tagged WIDA standards.

• In contrast, MLLs are fully supported in Grade 3, Chapter 6, Relate Area to Multiplication, Lesson 6.3, where students compare two rectangles to connect physical dimensions to unit squares and interpret the meaning of factors and products in an area model (3.MD.5a, 5b, 7a). The WIDA ELD Standards are as follows: “Construct mathematical explanations that describe a solution and steps used to solve a problem with others. Construct mathematical arguments that justify conclusion steps and strategies in simple patterns.” In the first Key Concept, students use visual array models, with and without unit squares, to explain how multiplication and repeated addition both represent the total number of unit squares, reinforcing conceptual understanding of area. Students work with partners to interpret and label rows, columns, and areas using standard units while determining the area of rectangles. The English Learner Support note guides MLLs to interpret and label the units of the dimensions and the total area through structured sentence frames and teacher prompts such as, “What unit of length is used in the dimensions of the rectangle?” These scaffolds support across proficiency levels for MLLs explaining their reasoning and constructing mathematical explanations, which is directly aligned to the academic task and the tagged WIDA ELD Standards.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations of providing support for MLLs’ full and complete participation in developing procedural skills and fluencies. The materials offer opportunities for students to encounter sequenced tasks that emphasize flexible strategies and efficient procedures alongside occasional student-to-student discourse. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in opportunities for students to develop procedural skills and fluencies. For example:

• MLLs are not fully supported in participating in Grade 5, Chapter 4, Multiply Whole Numbers, Lesson 4.6, where students multiply multi-digit whole numbers (5.NBT.5). The WIDA English Language Development [ELD] Standards are as follows: “Interpret mathematical explanations by analyzing problem-solving steps. Construct mathematical explanations that share a solution with others.” During the In-Class Practice, students build towards procedural skills and fluency when they independently solve problems involving multi-digit multiplication using self-selected solution strategies. The English Learner Support note includes scaffolded questioning and sentence frames across proficiency levels, guiding students to compare the equations in the solution strategy with a partner. However, these supports offer minimal opportunities for MLLs to understand the steps to multiply multi-digit numbers or independently generate explanations of the procedural steps. As a result, the materials do not consistently ensure MLLs’ full and complete participation while developing procedural skills and fluency.

• In contrast, MLLs are supported in Grade 3, Chapter 4, Division Facts and Strategies, Lesson 4.8, where students divide using strategies such as the relationship between multiplication and division or properties of operations (3.OA.7). The WIDA ELD Standard is as follows: “Construct mathematical explanations that describe a solution and steps used to solve a problem with others.” During the In-Class Practice, students build towards procedural skills and fluency when they independently solve problems involving division using self-selected solution strategies. The English Learner Support note includes scaffolded questioning and sentence frames across proficiency levels, guiding students to describe the steps they used to solve the problem, check their answer by working backward, and connect division and multiplication procedures. This allows MLLs to engage in procedural practice that is intertwined with reasoning, discussion, and reflection, which aligns with the tagged WIDA ELD Standard for this lesson.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations of providing support for MLLs’ full and complete participation in utilizing mathematical concepts and skills in engaging applications. The materials engage students in applying mathematics in routine and non-routine contexts, including single- and multi-step problems. These applications provide opportunities for students to demonstrate their ability to transfer and apply mathematical concepts and skills. However, the materials inconsistently offer language supports necessary for MLLs to fully access the linguistic demands of solving routine and non-routine application problems. For example:

• MLLs are not fully supported in participating in Grade 4, Chapter 3, Multiply by One-Digit Numbers, Lesson 3.8, where students solve multi-step multiplication word problems (4.OA.3). The WIDA English Language Development [ELD] Standards are as follows: “Interpret mathematical explanations by identifying a concept or an entity. Construct mathematical explanations that describe data and/or steps to solve a problem.” During the In-Class Practice, students work independently to solve application problems. An English Learner Support note provides suggested scaffolds for one exercise of the In-Class Practice, amplifying language around the multiple uses of the word that in the word problem and clarifying what the word is referencing each time. While this language support provides MLLs with access to beginning to solve one word problems, the materials do not provide linguistic scaffolds for MLLs’ full and complete participation in solving the other application problems in the lesson, nor do they provide supports for the language demands outlined in the tagged WIDA ELD Standards of interpreting and constructing mathematical explanations.

• In contrast, MLLs are supported in the Performance Task for Grade 3, Chapter 10, Understand Time and Measurement, where students apply their understanding of time and measurement to solve problems relating to a real-world situation (3.MD.1, 2, 3.OA.8). The English Learner Support note suggests that the teacher pairs MLLs with home language peers instead of working independently. Scaffolded supports across proficiency levels align language to the language demands of the task by prompting MLLs to critically examine which units of measure they should be working in given the information provided and the real-world situation. Together, these linguistic scaffolds support MLLs in using prior knowledge to solve application problems.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP2: Reason abstractly and quantitatively. The materials employ representations moving from concrete to representational to abstract, giving MLLs accessible entry points into the mathematical task and support MLLs with access to abstract symbols. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in reasoning abstractly and quantitatively. For example:

• MLLs are not fully supported in participating in Grade 3, Chapter 6, Relate Area to Multiplication, Big Idea Tasks #2, students are asked to find an area by multiplying. This task asks students to find the area of a rectangle, explain whether there is more than one possibility for the area measure, and show thinking. Additionally, students are expected to engage with MP2 when asked to determine whether there are multiple possible area measures for a rectangular garden with a perimeter of 40 feet, and explain their thinking. The Big Idea Tasks do not provide support to assist MLLs in producing the language to demonstrate their understanding of reasoning abstractly and quantitatively, such as encouraging students to consider units involved in a problem, attending to the meaning of quantities, representing situations symbolically, or explaining what the numbers in an equation means.

In contrast, MLLs are supported in Grade 4, Chapter 5, Divide Multi-Digit Numbers by One-Digit Numbers, Lesson 5.4, where students reason abstractly and quantitatively when they use models to find quotients and remainders. In this lesson, students are asked to consider what the numbers in the models and corresponding equations represent for each division problem. In Investigate, students work with whole number quotients and remainders and learn how to write the results, as due to the context of a problem, the remainder will be interpreted differently. The English Learner Support note provides linguistic support for MLLs to develop MP2 by directing teachers to, “Explain that the phrase left over means ‘still there.’ Have students use the phrase as they discuss the models they are creating in the Look Ahead. Support EL students in the following ways: Entering–Emerging: Help students describe each model by providing the sentence frames ‘I have blocks. I make equal groups. There are __ blocks left over.’... ” This guidance supports MLLs by explaining what the numbers in an equation represent and making sense of the relationship between problem scenarios and mathematical representations. Students apply this understanding in Exercise 15 of the In-Class Practice, where students independently solve a division problem and make sense of the remainder. The Talk About It guides teachers to write the corresponding equation to the problem scenario after students have solved the problem, prompting partners to discuss how the equation and remainder are related to the problem. This partner discourse provides MLLs with another opportunity to reason abstractly and quantitatively as they discuss what the numbers in an equation represent based on the problem scenario.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP3: Construct viable arguments and critique the reasoning of others. The materials invite students to use and develop language when constructing viable arguments and critiquing the reasoning of others throughout practice problems and with the occasional student-to-student discussion. As stated in the report for 1d.MLL, the program’s English Learner Support notes generally align to the WIDA key language uses of explain, inform, or argue; the language functions explain and argue align with the language demands of MP3. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in MP3. For example: 

• MLLs are not fully supported in participating in Grade 3, Chapter 6, Relate Area to Multiplication, Lesson 6.1, where students construct viable arguments and critique the reasoning of others when they apply measurement skills when counting tiles to find area of a shape. Exercise 9 of the In-Class Practice asks students, “You Be the Teacher: Your friend uses 4 color tiles to cover the rectangle and says the area is 4 square units. Is your friend correct?  Explain.” The Talk About It includes a teacher prompt aligned to MP3: “What questions can you ask your friend to help them understand their mistake?“ While the English Learner Support note provides linguistic support for MLLs by directing teachers to model the meanings of “gap” and “overlap” using tiles, this guidance does not support full and complete participation in Exercise 9 as it does not provide language support for MLLs to critique the reasoning of others. These supports do not consistently provide for full and complete participation by MLL students in the development of MP3. 

In contrast, MLLs are supported in Grade 5, Chapter 2, Numerical Expressions, Lesson 2.5, where students construct viable arguments and critique the reasoning of others when they write a number as a product of its prime factors and use mathematical terms, representations, and concepts in their justifications. On the Support for All Learners page, the English Learner Support note provides linguistic support for MLLs to construct viable arguments by directing teachers to first review the meanings of the math vocabulary applied throughout the lesson: factor, prime factor, tree, and factor tree. Then, the note suggests that the teacher guide students to apply that vocabulary as they make a factor tree for the number 60 and to construct an argument for why the factor tree is accurate. The linguistic supports across proficiency levels provide suggested sentence frames to support MLLs with describing the prime factors of 60. This guidance provides strategies and support for MLLs to participate in the development of MP3 through support of mathematical terms, representations (factor trees), and sentence frames for their justification.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP4: Model with mathematics. The materials engage students in tasks that support MP4 by reasoning with quantities, representing situations symbolically, and interpreting numbers and symbols in context to connect real-world scenarios with mathematical representations. However, the materials do not consistently provide the explicit language supports necessary for MLLs’ full participation in MP4. For example:

• MLLs are not fully supported in participating in Grade 3, Chapter 1, Understand Multiplication and Division, Lesson 1.3, where students model with mathematics when they use an array and equal groups to multiply. In this lesson, students use counters to build equal rows, make a model of their choice to represent a situation, describe the model, and then write an equation to match their model. In Exercise 20 of the In-Class Practice, students are given a word problem and asked, “What are some models you can use to visually represent this problem? How can you use each of these models to write an equation?” An English Learner Support note earlier in the lesson provides support for MLLs to understand what an array is, stating, “When describing an array, lay a pencil horizontally across the counters to show each row. Similarly, lay a pencil vertically to show each column. Remind EL students that each row has the same number of objects.” However, this support lacks detailed linguistic scaffolds for developing MP4, such as MLLs describing what they can do with models and how a model relates to the problem situation, as asked in In-Class Practice Exercise 20. 

• In contrast, MLLs are supported in Grade 5, Chapter 10, Divide Fractions, Lesson 10.3, where students model with mathematics when they develop a model for solving real-life problems by writing division expressions and equations that explain situations. In Problem 11 of Practice, students are asked to engage in modeling with mathematics with the problem: “Connect to Real Life: You need one-half pound of clay to make a pinch pot. Use a model to find how many pinch pots you can make with 12 pounds of clay?” The materials further prompt MP4 engagement with the teacher prompt: “What division equation models this situation? What multiplication equation models this situation?”An English Learner Support note directs the teacher to remind MLLs that they can use multiplication to check division, and to connect multiplication equations with division equations. The note provides further supports for MLLs with language supports across proficiency bands, such as, “Developing–Expanding: ‘What do you multiply to check your answer? Explain.’ Provide sentence frames: The division equation is___ . So, I multiply ___ and ___ , and check that the product is ___.” These linguistic supports provide language for MLLs to interpret the results and check to see whether their answer makes sense while using real-life contexts to help students represent problems.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP6: Attend to precision. The materials provide teacher guidance for explicit instruction for students to communicate using grade-level appropriate vocabulary with accurate definitions. However, there is limited teacher guidance around supporting MLLs to formulate clear explanations, state the meaning of symbols, calculate accurately and efficiently, or use precise labels. Therefore, language supports are inconsistently applied for MLLs to engage in MP6. For example:

• MLLs are not fully supported in participating in Grade 3, Chapter 13, Find Area to Multiplication, Big Idea Tasks #3, where students communicate with precision when they find an area by multiplying. This task asks students to draw two different rectangles that have a perimeter of 30 inches and find the areas. Students are asked to explain whether it is precise to say that the two rectangles are the same size. The Big Idea Tasks do not provide support to assist MLLs in producing the language to communicate precisely to explain whether the rectangles are the same size, calculate areas accurately, or use appropriate units to label area and perimeter. 

In contrast, MLLs are supported in Grade 4, Chapter 10, Relate Fractions and Decimals, Lesson 10.1, where students attend to precision when they write a fraction or mixed number involving tenths as a decimal. In the Key Concept, the teacher provides explicit instruction on the new vocabulary terms tenth, decimal, decimal point, and tenths place using the chapter’s vocabulary cards, verbal descriptions, written definitions, and visual representations such as a place value chart and a base ten model. In Exercise 15 of the In-Class Practice, students apply the meaning of these definitions when they are asked to provide a written explanation describing if 0.5 and 5.0 have the same value. The materials support students, including MLLs, in communicating using grade-level vocabulary through a teacher prompt that invites students to first use a base ten model to represent each value, then talk with a partner about whether the numbers have the same value before students independently write a response. Additionally, the materials invite teachers to listen for students to apply the new vocabulary terms of the lesson. In addition, the English Learner Support box on the Support for All Learners page, provides support for MLLs to understand the difference in meaning between tens and tenths through engaging with a place value chart, chorally repeating decimal numbers, and writing decimal numbers as fractions.

As stated in the Criterion 1 summary, see 1d.MLL for the program’s embedded linguistic supports. This report examines how those supports are reflected in relation to the expectations of this specific Indicator, using examples from the materials to illustrate implementation.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP8: Look for and express regularity in repeated reasoning. The materials provide opportunities for students to use and develop language when looking for and expressing regularity in repeated reasoning through Key Concept whole-group discussions and In-Class Practice. However, language supports are inconsistently applied for MLLs to engage in MP8. For example:

• MLLs are not fully supported in participating in Grade 3, Chapter 13, Find Area and Perimeter, Lesson 13.3, where students extend their knowledge of perimeter to finding an unknown side length and consider how finding the missing side length of a rectangle will help them find the missing sides of other quadrilaterals in future problems. During Investigate, Talk About It provides teacher prompts to engage students with repeated reasoning: “The perimeter of another map is also 20 feet, but it is in the shape of a square. How might you adjust your strategy to find the unknown side length? Pair-share and discuss your reasoning.“ An English Learner Support note provides linguistic scaffolds for MLLs to find the missing side length of the map example by encouraging MLLs to compare pairs of opposite sides and complete sentence frames such as, “I know that the map is a ___. The lengths of two opposite sides are ____ and ____. The length of the other side is ____. So, the missing side length is ____ feet.” This support does not make a direct connection to the repeated calculations needed to understand and make a generalization and develop MP8. 

In contrast, MLLs are supported in Grade 5, Chapter 13, Understand Volume, Lesson 13.4, where students look for patterns when trying to understand the relationship between length, width, and height, and the volume to calculate unknown dimensions. In Exercise #6 of the Practice, students determine the side lengths of a cube given the volume. The materials provide teacher prompts to engage students with noticing when calculations are repeated to understand formulas: “What do you notice about the figure? How will that affect the volume equation?” The English Learner Support box on the Support for All Learners page provides support developing the mathematical practice through linguistic scaffolds for using sequencing language to describe the process of finding unknown dimensions. The note directs teachers to write mathematical phrases such as related division equation, unknown values, and volume formula on the board and encourages MLLs to use the language as they complete sequencing sentence frames such as, “First, I write the ____. Then I write the ____. Next, I ____ and write the ____. Finally, I ____ to find the ____.” These linguistic scaffolds support MLLs with noticing repeated calculations to understand algorithms and use repeated reasoning as a tool to find unknown dimensions.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations for intentionally developing language in ways valued by disciplinary practices over time, across lessons, units, and throughout the course. Disciplinary language development consists of functional language development alongside mathematical vocabulary development. In the materials, functional language development is inconsistent and often serves students’ understanding of the mathematical content or practices rather than intentionally advancing disciplinary language development over time, as noted in the reports for Criterion 1. As noted in the report for 2j.MLL, the materials partially support the development of mathematical vocabulary over time. Additionally, the materials do not provide a plan for teachers to bridge between students’ informal ways of communicating and more precise mathematical ways of communicating. 

The materials lack a clearly articulated, longitudinal plan for developing language as a disciplinary practice beyond moments embedded within mathematical content or practices. An example of this exists in Grade 4, Chapter 9, Multiply Whole Numbers and Fractions, where students apply and extend their previous understanding of multiplication to multiply a fraction by a whole number by using repeated addition and iterating unit fractions. There is no framing in the materials of the interdependence of the mathematical concept of multiplying fractions and the language needed to multiply fractions. However, the English Learner Support notes within each lessons’ instructional activities feature language supports that slightly progress in sophistication, beginning with the listed language function of interpreting mathematical explanations in Lessons 9.1 and 9.2, moving to interpreting mathematical arguments in Lessons 9.3, and ending with the most sophisticated constructing mathematical explanations in Lessons 9.5 and 9.6. The specific linguistic scaffolds in each of these notes move from encouraging MLLs to verbally interpret an expression with repeated addition in Lesson 9.1 to providing sentence frames for MLLs to construct mathematical explanations in Lessons 9.5 and 9.6. 

While a slight progression exists in Grade 4, Chapter 9, there is no discernable progression of disciplinary language development in the previous chapter in Grade 4, Chapter 8, Add and Subtract Fractions. In this chapter, the English Learner Support notes within each lessons’ instructional activities list language functions that shift irregularly between interpreting mathematical explanations to constructing mathematical explanations to constructing mathematical arguments with no clear progression of language sophistication over time. 

Therefore, the materials provide some, but not consistent, intentional support for the ongoing development of disciplinary language. While they consistently build mathematical vocabulary, support for functional language development is inconsistent and lacks clear progression. Consequently, the materials do not effectively equip teachers to foster MLLs’ language growth in a deliberate and sustained way.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet expectations for providing teacher guidance to support MLLs and to utilize the strategies, supports, and/or accommodations found. The materials provide useful suggestions for language supports at point-of-use within lessons which often support teachers in anticipating potential language demands along a progression of language acquisition. However, the materials do not provide comprehensive guidance to teachers that is inclusive of all levels of understanding in instructing MLLs, including how to consistently observe and respond to potential language demands, challenges, and opportunities in a lesson.

As noted in the 3e.MLL report, each lesson in every chapter includes at least one English Learner Support note that is aligned to the lessons’ tagged WIDA standard(s) and that offer linguistic scaffolds to support MLLs with understanding and applying the mathematical language of the lesson. For example, in Grade 5, Chapter 11, Convert and Display Units of Measure, Lesson 2, the tagged WIDA standards are, “Construct mathematical explanations that share a solution with others,” and, “Construct mathematical explanations that describe data and/or the steps to solve a problem.” The lesson opens with students activating background knowledge around conversions in metric units. The English Learner Support note offers anticipatory linguistic scaffolds, provided along a progression of language acquisition, to support MLLs with constructing mathematical explanations about carrying out metric conversions: 

• “Entering-Emerging: Point out parts of the first Example. ‘Are you converting mass or capacity? What unit do you need to convert? What is the unit in the answer?’ Help EL students use phrases to answer. Repeat for the second Example.

• Developing-Expanding: ‘What type of measure is this? What unit do you need to convert? What do you convert to? What is the answer?’ Help EL students answer using short sentences. Ask similar questions about the second Example.

• Bridging-Reaching: Have EL students take turns asking and answering questions about the measure, unit, target unit, and answer in each Example.”

However, while the lesson-embedded English Learner Support notes guide teachers to anticipate potential language demands within lessons, they do not provide consistent teacher guidance on how to observe and respond to the potential language demands and opportunities in lessons. Additionally, the English Learner Support notes do not provide comprehensive guidance to teachers that is inclusive of all levels of understanding in instructing MLLs. In the Grade 5 example, the linguistic scaffold provided in the Entering-Emerging language proficiency levels, and paralleled in the Developing-Expanding language proficiency levels, includes the vague guidance of helping MLLs answer using phrases or short sentences without details about how to do that. The suggestion in the Bridging-Reaching language proficiency level is the exact task that is written into the Guiding Student Learning section of the lesson. These are representative examples of trends found across chapters and grade levels, and these types of support are not sufficiently educative for teachers at all levels of understanding in instructing MLLs. 

Some guidance is found at the chapter level in the Mathematics of the Chapter section, where Laurie’s Notes: Language Routines outlines one Language Routine per chapter. As stated in the 3e.MLL report, this is the only reference to the Language Routines in the chapter. Teacher guidance for implementing the Language Routines is not embedded at the lesson-level, limiting its usability and utility, specifically for teachers without background in implementing math language routines.

In conclusion, the materials demonstrate a clear and sustained commitment to supporting MLLs through frequent lesson-embedded guidance that addresses language demands alongside mathematical content.However, the materials do not provide comprehensive guidance to teachers that is inclusive of all levels of understanding in instructing MLLs.

The instructional materials reviewed for Grades 3-5 of Math & YOU partially meet the expectations of the guiding teachers on how to match students with language supports, progressing along a continuum, and to be responsive to students’ current language development in relation to the content. While the materials provide language support at varying language proficiency levels, they do not guide teachers on how to match students with language supports at those language proficiency levels.

The materials provide general guidance that supports teachers in responding to students’ current language usage in relation to mathematical content. As noted in the 3e.MLL report, within The Implementation Handbook: Grades K-5, teachers are prompted to monitor and attend to the language students use. For example, the High Expectations for All: Supporting Student Learning section of the Implementation Handbook offers the following vague suggestion, “Consider these (English Learner Support) notes during planning to identify challenges that multilingual learners might encounter during the lesson and plan appropriate supports.” This guidance is general in nature and does not provide specific conditional guidance related to language development of MLLs (e.g. “If MLLs struggle with ____, then provide ___.”). In the Implementation Handbook, the Assessment System: Monitoring Student Learning section provides general conditional guidance as it relates to portions of the lesson design. This guidance is not specific to language development of MLLs. For example, this section of the Implementation Handbook encourages teachers to monitor students’ written work and oral conversations during the Investigate portion of the lesson design, specifically to, “listen to what language students use to describe what they noticed and attend to their strategies to interpret the approaches they discovered while making sense of the tasks.” The materials then encourage teachers to make responsive instructional decisions during the Investigate, such as, “Use mathematical language that can serve as a building block for the Key Concept. Leverage informal strategies used by students that can be formalized into generalizable approaches. Identify additional support needed before formalizing learning and introducing mathematical vocabulary." While these supports are responsive in nature and relate to students’ language usage, they are general and are not uniquely positioned as attending to MLLs’ current language development in relation to mathematical content. As a result, responsiveness is present but not consistently operationalized.

Within lessons, the materials rely on predefined WIDA language proficiency level bands (e.g., Entering–Emerging, Developing–Expanding, Bridging–Reaching) without providing sufficient guidance on how teachers should determine MLLs’ current language proficiency level to match students with language supports during instruction, particularly in contexts where WIDA proficiency data is unavailable, outdated, or insufficiently granular. Additionally, the materials do not include teacher guidance on how to adjust supports over time as students develop language proficiency or address how teachers should respond to variability within the wide ranges of language development within the bands. 

In conclusion, while the materials offer general guidance for monitoring and responding to students’ language use during mathematics instruction, this guidance is broad, lacking specificity to MLL language development. Additionally, while lesson-level supports rely on WIDA language proficiency bands, the materials do not provide sufficient direction for matching MLLs with language supports.

The instructional materials reviewed for Grade 3-5 of Math & YOU partially meet expectations for providing guidance to encourage teachers to draw upon student home language to facilitate learning. The materials offer translated resources, but they lack specific teacher-facing guidance on how to integrate MLLs’ home languages into daily classroom instruction. The materials partially provide guidance to teachers on how to draw upon MLLs’ home language as a resource for learning, but this guidance is inconsistent and lacks specificity connected to MLLs learning grade-level mathematics content.

The materials feature a suite of multilingual access tools—including multilingual glossaries, text-to-speech, Spanish-language Teacher and Student Editions, and translated family letters—that collectively position multilingualism as an instructional asset. These tools provide meaningful opportunities for students to access content in their home language, especially through the Spanish-language editions and the 16-language digital translation options when using the Digital Experience. Practically, the digital translation tools inconsistently translate text, especially when mathematical symbols are present. While these tools are robust in structure, they appear unevenly embedded and referenced across the instructional cycle.

For example, in Grade 4, Chapter 5, Divide Multi-Digit Numbers by One-Digit Numbers, Lesson 5.6, the Learning Target is, “Use partial quotients to divide two-digit numbers and find remainders.” A portion of the English Learner Support note for the lesson states, “Entering-Emerging: ‘Point to one rower in the picture. Now point to several rowers.’ Have students use their home language to discuss and solve the problem with a  partner. Then help them complete the frames ‘There are ____ rowers. Each group needs to have ____ rowers. You need ____ more rowers. Here are ____ groups of 4 rowers.’.” However, while the Implementation Handbook asserts that the English Learner Support notes appear “in every lesson,” this is one of nine references to home language usage in Grade 4. Additionally, the majority of the nine references appear in the Support for All Learners section of the lesson, hence not embedded at point-of-use within lesson facilitation. This demonstrates an inconsistent application of the materials providing guidance to encourage teachers to draw upon student home language to facilitate learning. 

Given these patterns, the materials encourage teachers to draw upon MLLs’ home language to facilitate learning grade-level mathematics content but not consistently. Additionally, the materials do not include guidance on how to garner information that will aid in learning, including the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic or everyday English.