3rd-5th Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL 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 consistently provide for full and complete participation by MLL students.

The Instructional Design document in the Additional Resources for each grade outlines how the instructional design of the materials support students participating in extensive work with grade-level problems. Each lesson’s instructional design features a predictable structure:

• Warm-Ups activate prior mathematics content knowledge from previous lessons, units, or grade levels, providing MLLs with a preview of the language they will use within the lesson.

• Whole-Class Instruction features several activities where teachers guide students to solve problems in partners, small groups, or as a whole class. Within Instruction, the materials embed Think and Talk activities where students have “opportunities to engage in mathematical discourse, helping them to learn clearly and effectively express their mathematical strategies and conclusions.” 

• Ample opportunities for practice, including Guided Practice, Independent Practice, and a Personalization day before assessments. Within this practice, the materials feature robust differentiation that is both teacher-led and student-led. The differentiation is primarily driven by mathematical content needs and not the language demands of the activity or practice problem.

Additionally, the Instructional Design document provides course-level teacher guidance for setting up a safe and supportive learning environment, specifically during Think and Talk activities. These suggestions include ideas for establishing groups, such as forming groups of 2-3 students and varying the groups so students hear a wide range of perspectives, and additional guidance for before, during, and after Think and Talk activities, such as establishing norms, monitoring student-to-student discourse, and debriefing small group conversations with the whole class. This guidance may support MLLs’ full and complete participation in grade-level mathematics by contributing to a positive, inclusive learning environment, which research suggests helps lower MLLs’ affective filter, which facilitates risk-taking in content learning and English language usage. 

Lessons feature linguistic supports for MLLs in the Language Tip, which is located in the Additional Supports section of each lesson. The Language Tips provide suggested linguistic scaffolds for either one specific problem of the lesson, one specific activity of the lesson, or linguistic scaffolds that can apply to the entire lesson. Language Tips do not provide consistent strategies that address all four domains of language, reading, writing, speaking, and listening, with supports for writing and reading being the least supported domains. The linguistic scaffolds in the Language Tips generally include, but are not limited to: ideas for supporting mathematical vocabulary (such as the teacher to creating anchor charts or students creating personal picture dictionaries), supports for English-Spanish cognates, suggestions for multimodal instruction such as acting out or gesturing, ideas for visual supports and diagrams that are specific to the mathematical concepts of the lesson, and sentence frames and starters. While there are consistent references to sentence frames within the Language Tips, the sentence frames are cloze sentence frames, limiting to a precise expected answer rather than supporting open-ended responses by MLLs. Therefore, these limiting sentence frames simplify rather than amplify language structures and forms. Periodically, the Language Tips feature variations of language routines. For example, in Grade 4, Unit 12, Measurement, Lesson 12.8, the Language Tip mirrors the language routine Collect and Display, stating, “Support language learners with the Think and Talk in #6 by having students discuss in pairs first. As you listen to their discussions, write down key words and phrases you hear. For example, you might write subtract, regroup, day, 24 hours, and 60 minutes. Then have students respond again using the words and phrases you recorded. This repetition with support will help build students' confidence and ability to explain their thinking using mathematical language.” While this Language Tip mirrors the teacher and student actions of the language routine Collect and Display, it is not explicitly called out as such. This lack of explicit teacher guidance reduces clarity about how language routines support MLLs’ full and complete participation.

The materials include a helpful overview of how each unit will address the standards for mathematical practices [MPs] throughout the lessons in a section titled Math Practices in each Unit Overview. For example, Grade 5, Unit 5, Add and subtract fractions, the Math Practices section states the following for MP4: “In Unit 5, students model with mathematics as they write expressions to solve word problems involving fractions and mixed numbers. Emphasize that there can be multiple expressions that accurately represent a single situation… Highlight the importance of connecting each term in an expression to the context of the problem.” However, this overview is general and without any mention of linguistic scaffolds to support MLLs’ full and complete participation.

In conclusion, the materials provide some strategies for MLLs’ participation in grade-level problems, mainly within the lesson-level Language Tips. However, these strategies do not consistently provide for full and complete participation by MLL students.

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 Takeoff by IXL partially meet expectations of providing support for MLLs’ full and complete participation in the conceptual understanding of key mathematical concepts. Generally, lesson Warm-ups provide students with the opportunity to activate or build prior knowledge, and Whole-Class Instruction invites the teacher to connect prior knowledge to new tasks. 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. 

The materials offer opportunities for students to explore and make sense of mathematical ideas while engaging with multiple representations to formalize procedures, supporting conceptual understanding. The Instructional design document in each grade level’s Additional resources outlines how the materials leverage consistent models, stating, “Takeoff enables students to make meaningful connections in math by using the same models across grade levels and topics.” This aspect of the material’s instructional design supports MLLs by fostering multimodal ways of building conceptual understanding. However, while the materials include language supports for MLLs to participate in this multimodal instruction, these supports do not consistently provide for full and complete participation by MLL students. 

For example, in Grade 5, Unit 4, Volume, Lesson 4.3, students build conceptual understanding as they relate volume to area, and specifically the operations of multiplication and addition (5.MD.3, 4). The Warm-up activates students’ background knowledge from the previous two lessons, focusing on finding the volume of rectangular prisms that are packed with unit cubes by calculating the area of the base and using repeated addition or multiplication by the number of “layers” in the prism.  This supports MLLs by providing a preview of the language students will use within the lesson. Through the lesson facilitation of the Whole-Class Instruction, teachers guide students to calculate the volume of rectangular prisms that are not packed with unit cubes, but instead labeled with measurements in centimeters, meters, and inches. The Language tip encourages teachers to review customary and metric units of length and their abbreviations, adding them to students’ visual glossaries they began in Lesson 4.1. Additionally, the Language tip encourages the teacher to support MLLs whose home language is Spanish through highlighting the differences in the abbreviations of units in English and Spanish. This Language tip supports MLLs with making sense of the transition from concrete unit cubes to measurements in more abstract units of length. However, the materials do not provide language supports for MLLs’ full and complete participation in the Whole-Class Instruction where students write expressions representing the area of the base and the volume of rectangular prisms, nor where students apply the associative property by recognizing that two prisms that are oriented differently can have the same volume when they have the same dimensions. 

In summary, the materials promote conceptual understanding by engaging students in mathematical reasoning through activating prior knowledge and through concrete, visual, and abstract representations, but they lack systematic language supports for MLLs’ full and complete participation in building conceptual understanding.

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 Takeoff by IXL partially meet expectations of providing support for MLLs’ full and complete participation in developing procedural skills and fluencies. Generally, lessons’ Guided and Independent practice provide students with the opportunity to work on accuracy, efficiency, and flexibility within procedural skills and fluency. When students working in the digital platform solve a question incorrectly, the platform provides a step-by-step explanation and allows students to watch a video tutorial or review a worked example before attempting the problem. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the intentional development of students’ procedural skills and fluencies. 

For example, in Grade 5, Unit 1, Whole number place value and multiplication, Lesson 1.6, students develop procedural skills and fluencies as they multiply multi-digit numbers by two-digit numbers using the standard algorithm (5.NBT.5). The Language tip encourages teachers to support MLLs with reading and interpreting word problems through reading the word problems three times with a different focus each time. However, the materials do not provide language supports for MLLs’ full and complete participation in developing procedural skills and fluencies around multiplying large numbers using the standard algorithm, as is expected in the Think and Talk activity of problem #4, where students examine a fictional student’s solution strategy. 

In summary, the materials promote procedural skills and fluencies through focusing on accuracy, efficiency, and flexibility, but they lack systematic language supports for MLLs’ full and complete participation in procedural skills and fluencies.

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 Takeoff by IXL partially meet expectations of providing support for MLLs’ full and complete participation in utilizing mathematical concepts and skills in engaging applications. Generally, during Whole-class instruction, the materials provide limited opportunities for teacher-guided routine and non-routine problem solving. The materials inconsistently offer language supports necessary for MLLs to fully and completely participate in solving routine and non-routine application problems. 

For example, in Grade 5, Unit 5, Add and subtract fractions, Lesson 5.4, students engage in application problems when they solve subtraction word problems involving fractions with unlike denominators (5.NF.2). In problem #5, the lesson facilitation directs teachers to facilitate a whole-class guided discussion where students use fraction strips to solve a subtraction word problem involving fractions. In the guided discussion, the teacher highlights responses that mention equivalent fractions and then discusses how the fraction strip model shows the answer to the word problem. The Language tip provides linguistic supports for the Compare and talk activity at the end of the Whole-class instruction, and it does not provide language supports for MLLs’ full and complete participation in solving the application word problem in problem #5.

In summary, the materials provide opportunities for teacher-guided routine and non-routine problem solving, but they lack systematic language supports for MLLs’ full and complete participation in solving routine and non-routine 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 Takeoff by IXL partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP1: Make sense of problems and persevere in solving them. The materials provide linguistic supports for MLLs to participate in the intentional development of MP1, but these supports do not consistently provide for full and complete participation by MLL students. 

The materials invite students to use and develop language when making sense of problems through whole-group discourse. For example, the materials often direct the teacher to facilitate a whole-class discussion around a specific problem where students work to understand the information in the problem and the questions asked, determine if their answer makes sense, and reflect on and revise their solution strategy. The materials provide video tutorials within the online practice, allowing MLLs access to a worked example with model language around how to make sense of problems. However, the materials inconsistently offer clear lesson-level linguistic supports for MLLs to fully and completely participate in MP1. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 8, Perimeter, where students make sense of problems involving the perimeter of polygons. The Math practices section in the Unit Overview describes how students engage with MP1, stating, “As students work through problems in this unit, encourage them to start by making meaning of each problem and identifying entry points to a solution. Specifically, discuss with them how to tell whether a problem is asking for perimeter or area (area is the space inside a shape, while perimeter is the distance around it). In addition, working with geometric properties like area and perimeter can stretch students' abilities to visualize what problems are asking. Encourage them to draw diagrams, label given diagrams, and find other ways to make otherwise difficult-to-picture scenarios concrete and easy to visualize.” This section of the Unit Overview also outlines how Lessons 8.4 and 8.5 provide opportunities for teachers to reinforce the general supports of drawing and labeling diagrams and “finding other ways” to visualize the concepts of area and perimeter. These suggestions are general in nature and do not contain teacher guidance for language supports that are lesson-specific, limiting their effectiveness. Furthermore, in Lesson 8.4, the Language Tip does not provide specific teacher guidance for teachers to apply the suggestions in the Unit Overview. Instead, the Language tip suggests that teachers support students with working to understand the context of the word problems in #2, 4, and 5 by previewing the contexts and inviting students to make personal connections to them. While this suggestion may support MLLs with making sense of the problems to determine whether each problem involves area or perimeter, it does not provide guidance for the teacher to support students with using a variety of solution strategies, monitoring and evaluating their progress in solving problems, or determining if their answer makes sense. Additionally, problem #2 in Lesson 8.4 features a Think and Talk activity, and the materials do not provide linguistic scaffolds for MLLs’ full and complete participation in the student-to-student discourse of the activity. 

• In contrast, MLLs are supported in Grade 5, Unit 3, Expressions, where students make sense of multi-step word problems as they write and evaluate numerical expressions. The Math practices section in the Unit Overview describes how students engage with MP1, stating, “In this unit, students apply their understanding of the order of operations as they write and interpret expressions to solve multi-step word problems. Encourage them to analyze each situation, break it into smaller steps, and write expressions that represent those steps. Have students compare the problems in Lesson 3.4 #3, and emphasize that even when the numbers and operations are the same, the order may be different. Prompt students to explain how they decided which step to do first. This helps them look beyond the numbers to understand the full situation, which is an important part of making sense of problems and persevering in solving them.” The Language tip in Lesson 3.4 provides specific suggestions for supporting MLLs with making sense of the multi-step word problems, such as reading problems aloud to the class, inviting MLLs to work together to make sense of the contexts and identify key information, referencing a color-coded anchor chart from a previous lesson, and explicitly connecting the symbolic notation with verbal reasoning while providing an example. The Language tip states, “Be on the lookout for opportunities to pull back support as students become more independent,” which supports MLLs with using and devising a solution strategy independently. 

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 Takeoff by IXL 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 consistent representations across grade levels, 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 lesson-level linguistic supports for MLLs to fully and completely participate in MP2. For example:

• MLLs are not fully supported in participating in Grade 4, Unit 11, Multiply fractions and whole numbers, Lesson 11.3, where students reason abstractly and quantitatively when they solve problems that involve multiplying fractions by whole numbers, moving between contexts, models, and equations, explaining how each number or step they perform maps back to the original context. The Language tip states, “In #2, Shane finds 5\times\frac{7}{8} by thinking about it as 5 groups of \frac{7}{8}. Consider explicitly telling language learners that one way to read a multiplication expression is by replacing the multiplication sign with groups of. Not only will this help them understand Shane's idea, connecting notation and verbal descriptions helps strengthen conceptual understanding and reinforce language skills.” While explicitly connecting the multiplication sign with the phrase groups of may support MLLs with understanding what the symbols in an expression represent, the Language Tip does not provide specific linguistic scaffolds for MLLs to fully engage with the productive language of explaining or discussing what the symbols in an expression represent, or to understand the relationship between problem scenarios and mathematical representations.

• In contrast, MLLs are supported in Grade 5, Unit 12, Measurement and data, where they reason abstractly and quantitatively when they convert units and interpret line plots, considering the units involved in problems and attending to the meaning of quantities. The Math practices section of the Unit overview describes how students engage with MP2, stating, “Support students as they identify the necessary operations and conversion factors, and encourage them to explain their reasoning as they represent quantities in equivalent forms. In situations involving mixed or fractional units (Lessons 12.1–12.3 and 12.6), prompt students to interpret remainders in context and connect them to fractional values. For example, in #10 of Lesson 12.1, when they convert 40 feet to yards (40\div3 =13 R1), emphasize that the remainder of 1 represents 1 foot. Ask what part of a yard that foot represents; this will lead students to reason that 1 foot is /frac{1}{3} of a yard.” The Language tip in Lesson 12.1 provides specific suggestions for supporting MLLs with considering and attending to the meaning of the measurement units, such as creating a personal picture dictionary for measurement units (inch, foot, yard, mile), with students drawing objects of relative size. This grounds abstract unit names in concrete, visual referents. Additionally, the Language tip provides linguistic scaffolds for MLLs to fully participate in the Think and Talk activity of problem #4, where they represent situations symbolically, stating, “First, have them annotate the models in #4 to help them focus on the information they need for the discussion. They can label each bar with smaller units or larger units. They can also show which operation they used for each conversion by drawing an arrow from the top bar to the bottom one and labeling it multiply or divide.” The Language tip further supports MLLs with engaging in MP2 through guiding questions such as, “Do larger or smaller units cover more or less distance?” and “Do you need more or less larger units or smaller units to cover the same distance?” These guiding questions encourage MLLs to explain what the symbols in an expression represent.

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 Takeoff by IXL 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 provide linguistic supports for MLLs to participate in the intentional development of MP3, but these supports do not consistently provide for full and complete participation by MLL students. 

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. The Instructional design document in each grade level’s Additional resources describes how the program integrates the language domain of writing into constructed responses, stating, “Takeoff by IXL includes many opportunities for students to share their thinking and approaches in writing, both in daily learning activities and in open response questions. In these activities, students make claims and justify their reasoning while using clear, precise mathematical language to articulate their thoughts.” However, the Instructional design document does not provide teacher guidance on how to support MLLs with writing their constructed responses. Additionally, within lessons, the materials inconsistently offer clear lesson-level linguistic supports for MLLs to fully and completely participate in MP3. For example: 

• MLLs are not fully supported in participating in Grade 3, Unit 2, Understand multiplication, where students have many opportunities to critique others’ reasoning as they develop a conceptual understanding of multiplication. The Math practices section in the Unit overview describes how students engage with MP3, stating, “In #11 in Lesson 2.7, for example, students are asked to identify and explain the error Austin made in solving a multiplication equation with a number line (he started the jumps at 2 instead of 0). By correcting this error, students practice critiquing others' work and solidify their understanding of how to use number lines to represent multiplication.” In Lesson 2.7, the Language tip does not provide linguistic scaffolds for critiquing Austin’s work in problem #11. The problem offers the opportunity to perform error analysis of the response provided, yet MLLs are not supported in this task.

In contrast, MLLs are supported in Grade 3, Unit 6, Division fluency, where students critique the reasoning of others and find errors in written division solution strategies. The Math practices section in the Unit overview describes how students engage with MP3, stating, “Students have many opportunities to practice critiquing others' reasoning using what they know about multiplication and division in Unit 6, especially in Lessons 6.1 and 6.4. When students find errors in written work, encourage them to discuss the strategy used, find the source of each error, and explain how to fix it.” The Language tip in lesson 6.1 provides support for MLLs to participate in critiquing the reasoning of others by inviting MLLs to first write down their thoughts independently, then discuss what they wrote with a partner before sharing with the whole class. The Language tip states, “This gives students who understand the math but struggle to explain it a chance to rehearse and build confidence.” Additionally, the Language tip provides a specific language support for problem #19, stating, “Consider having students rephrase Henry's observation out loud so that you can clear up any misconceptions before they start writing.” This provides MLLs with an opportunity to clarify where Henry’s error is before constructing a written error analysis in problem #19.

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 Takeoff by IXL 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 clear lesson-level language supports necessary for MLLs’ full participation in MP4. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 7, Applications of multiplication and division, where students model problem situations using tables, strip models, and equations. The Math practices section in the Unit overview describes how students engage with MP4, stating, “In Lessons 7.4 and 7.5, students represent one- and two-step problems with strip models and equations, using variables for unknowns. Help students connect the model, equation, and story to support flexible problem solving.” The Language tip for Lesson 7.5 does not support MLLs with connecting the model, equation, and story. Instead, the Language tip provides teacher guidance to support MLLs with reading and understanding the various word problems in the lesson, encouraging teachers to pair MLLs with a partner who can help them read the word problems and discuss the contexts. While this may provide MLLs with access to the task, the Language tip does not support MLLs with modeling the mathematical situations from the word problems with an appropriate representation, describing what they do with the representation, or explaining how the representation connects to the problem scenarios.

• In contrast, MLLs are supported in Grade 4, Unit 5, Factors, multiples, and patterns, where students shift from modeling problem situations with number sentences, connecting to diagrams or physical models, to modeling problems with number and shape patterns. The Math practices section in the Unit overview describes how students engage with MP4, stating, “Throughout Lessons 5.7–5.9, be sure to discuss why previous types of modeling fall short (you'd need to write many number sentences or draw many diagrams to represent all of the numbers in a pattern) and the advantages and disadvantages of different representations: tables, lists, and written rules.” The Language tip for lesson 5.8 provides linguistic supports for MLLs to put the problem situations of number and shape patterns into their own words by encouraging MLLs to work with a partner to answer questions and explain the patterns in their home language first. Additionally, the Language tip suggests that teachers support MLLs with understanding the word problem contexts through reading aloud each problem and discussing what students notice about the patterns, recording and displaying their ideas for MLLs to reference as they work with partners to answer questions and explain the patterns they see. 

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

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP5: Use appropriate tools strategically. The materials provide opportunities for students to know how to use a variety of tools. However, there is limited teacher guidance around supporting MLLs to choose appropriate tools and to recognize the insights and limitations of different tools. Therefore, language supports are inconsistently applied for MLLs to engage in MP5. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 11, Compare fractions, where students engage with MP5 when they use a variety of tools to explore fraction equivalence and comparison. The Math practices section in the Unit overview describes how students engage with MP5, stating, “In Lessons 11.4–11.7, highlight how each tool can support different kinds of reasoning. For example, in Lesson 11.4 #6, ask students to explain why a number line might be more helpful than a shape model for identifying fractions that are equivalent to whole numbers. Throughout the unit, give students time to reflect on why a particular model is useful, and encourage them to choose tools purposefully. Asking questions like, ‘What did this model help you see?’ or ‘Would a different tool be more helpful here?’ can lead to more strategic and effective problem-solving.” In Lesson 11.4, the Language tip does not provide specific teacher guidance for teachers to apply the suggestions in the Unit Overview. Instead, the Language tip suggests that teachers support students by pairing MLLs by home language for the Think and talk activities, encouraging them to discuss their answers in their home language before responding in English. Additionally, the Language tip encourages teachers to listen for and display the mathematical terms and phrases students use. While these scaffolds support MLLs with leveraging their home language assets during the Think and talk activities, the Language tip does not provide teacher guidance to support students with choosing appropriate tools or recognizing the insights gained from different tools and their limitations.

• In contrast, MLLs are supported in Grade 5, Unit 11, Divide decimals, where students engage in MP5 when they self-select solution strategies for dividing decimals by whole numbers and other decimals. The Math practices section in the Unit Overview describes how students engage with MP5, noting that the unit "introduces multiple methods for dividing decimals, which students compare and evaluate in different contexts" to develop "the critical thinking skills needed to select the best tool for any given problem." This section specifically references Lesson 11.3, encouraging teachers to "use problems like #5 to compare these methods and prompt students to explain their preferences," discussing how "place value sketches provide more concrete visual support, while area models are often quicker to draw." The Language tip for Lesson 11.3 suggests a color-coding strategy for the Think and talk activity where students use matching colors to highlight corresponding parts of Jon's and Luca's work: one color for the dividend, a different color for the divisor, and a third color for the quotient. Additionally, the Language tip recommends students "include a key to show which colors represent the dividend, divisor, and quotient" and encourages them to "refer to the color-coded models to help them use math vocabulary" throughout the lesson. This visual organization directly supports MLLs to compare and contrast solution strategies, which supports them with choosing and applying a variety of solution strategies.

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

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL 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 to introduce new vocabulary and for students to use and apply definitions accurately. However, there is limited teacher guidance around supporting MLLs to 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, Unit 4, Area, where students attend to precision as they practice reporting area measurements accurately and precisely. The Math practices section in the Unit Overview describes how students engage with MP6, stating, “Be sure to model proper use of units in both written and verbal communication, beginning with Lesson 4.1. Make sure students understand how missing or incorrect units affect an answer's meaning. For example, if students record an answer in inches instead of square inches, it has a completely different meaning (it represents a length instead of an area). Similarly, if they leave units off of their final answers, people trying to understand the results wouldn't have a way to interpret what the numbers mean.” In Lesson 4.1, the Language tip does not provide specific teacher guidance for teachers to apply the suggestions in the Unit overview. Instead, the Language tip suggests that teachers support students with introducing the terms area, unit square, and square unit by adding them to the year-long vocabulary list and through amplifying the English language structure of putting adjectives before nouns. Additionally, the Language tip includes generic suggestions such as “draw attention” to the difference between a unit square and a square unit, and to “encourage students to use the new terms in discussions.” These suggestions are general in nature and do not contain teacher guidance for language supports that are specific to MLLs, specifying units of measure, limiting their effectiveness. 

• In contrast, MLLs are supported in Grade 5, Unit 13, Coordinate plane and patterns, where students attend to precision as they work with coordinate planes, writing coordinates with the correct notation and using precise mathematical vocabulary. The Math practices section in the Unit Overview describes how students engage with MP6, stating, “As students move into plotting data (Lessons 13.2–13.4), encourage them to attend to details as they choose axis labels, create scales, and plot points to ensure their graphs accurately show the data. In Lesson 13.4, help students see that precision is essential for solving problems related to plotting or interpreting data on graphs. Encourage them to continuously check their work to ensure their models are reliable.” In Lesson 13.2, students write and plot ordered pairs from tables and plot points on a coordinate plane when given ordered pairs. The Language tip recommends color-coding to support MLLs in explaining how the x- and y-coordinates are represented on the graph, supporting them in using and labeling tables and graphs appropriately. Additionally, the Language tip provides sentence frames to support MLLs with communicating using grade-level appropriate vocabulary, such as, “The x-coordinates represent ____. The y-coordinates represent ____. The ordered pair ____ means that ___.”

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

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP7: Look for and make use of structure. The materials provide opportunities for students to look for patterns or structures to solve problems and decompose complex problems into simpler, more manageable parts. However, the materials inconsistently offer clear lesson-level linguistic supports for MLLs to fully and completely participate in MP7. For example: 

• MLLs are not fully supported in participating in Grade 3, Unit 1, Addition and subtraction within 1,000, where students build on their understanding of the structure of the place value system to add and subtract. The Math practices section in the Unit Overview describes how students engage with MP7, stating, “In Unit 1, highlight methods and strategies that depend on this structure, such as rounding to the nearest ten or hundred in Lesson 1.1, using addition and subtraction strategies from earlier grades in Lesson 1.3 and Lesson 1.4, and in new strategies covered in Lessons 1.9, 1.10, 1.12, and 1.13.” The suggestion of “highlight methods and strategies that depend on this structure” is general in nature and does not contain teacher guidance for language supports that are specific to looking for structures to make generalizations. Furthermore, in Lesson 1.1, the Language tip does not contain teacher guidance to support MLLs with using and developing language related to looking for and explaining structures. Instead, it focuses on vocabulary support for the terms estimate and round. 

• In contrast, MLLs are supported in Grade 5, Unit 6, Multiply fractions, where students decompose "complicated" problems into "simpler" parts when they build on familiar structures (e.g., arrays, equal groups, and area models) to make sense of fraction multiplication. The Math practices section in the Unit Overview describes how students engage with MP7, stating, “Later in the unit, students use area models to multiply fractions by other fractions (Lesson 6.4), fractions greater than 1 (Lesson 6.7), and mixed numbers (Lesson 6.8). Discuss how these models connect to the area models students previously used to multiply and divide whole numbers. Emphasize how area models rely on the familiar concept of decomposition, allowing students to break each factor into smaller, more manageable parts.” In Lesson 6.8, the Language tip suggests color-coding numbers in multiplication expressions and area models as a visual reference for explaining the structure of the area model in their work. Additionally, the Language tip provides specific sentence frames for discussing the area model structure: "The length/width of this rectangle represents the whole number/fraction part of the factor ____." and "I found the area of this rectangle by ____." These sentence frames directly support MLLs in articulating how they have decomposed the mixed numbers into their parts, i.e., whole numbers and fractions, and how they are finding the area of each simpler rectangular region. The guidance also encourages students to use the positional phrases top left, top right, bottom left, and bottom right to precisely identify which part of the decomposed area model they are referring to, further supporting MLLs with using and developing the language of structural decomposition.

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

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL 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 language when looking for and expressing regularity in repeated reasoning within Think and talk activities. However, language supports are inconsistently applied for MLLs to engage in MP8. For example:

• MLLs are not fully supported in participating in Grade 4, Unit 6, Divide by 1-digit numbers, where students look for and express regularity in repeated reasoning when they use a variety of solution strategies to divide multi-digit numbers by one-digit numbers. The Math practices section in the Unit Overview describes how students engage with MP8, stating that across lessons, students should "notice the common thread" between division methods: "each step involves dividing a portion of the dividend based on the divisor, subtracting that portion to find what remains, and then repeating the process until the entire dividend is accounted for." This section emphasizes that when "students recognize this repeated reasoning across division methods, they strengthen their division fluency." In Lesson 6.6, the Language tip provides general collaborative support, suggesting that students "work in pairs to solve #4–5, and have them take turns explaining their process" to allow "repetition and collaboration" to "solidify students' conceptual learning." While this suggestion encourages peer interaction, it does not provide specific linguistic structures to help MLLs articulate the repeated reasoning they observe, nor to compare methods and articulate the regularity across them. Students are expected to engage in sophisticated comparative reasoning in problem #3 of the lesson without the embedded language scaffolds for MLLs to express their observations about the common thread across division methods.

• In contrast, MLLs are supported in Grade 5, Unit 2, Whole number division, where students look for and express regularity in repeated reasoning as they use a variety of solution strategies to divide multi-digit numbers by two-digit numbers. The Math practices section in the Unit Overview describes how students engage with MP8, stating that across lessons in the unit, students “refine division strategies by identifying patterns and using repeated reasoning to work more efficiently.” Additionally, this section states that students build toward more efficient strategies in Lesson 2.6, prompting teachers to connect each step of the standard algorithm to strategies they've used. The Language tip for Lesson 2.6 focuses on using visual cues, gestures, and color-coding for MLLs to connect verbal instructions to the standard algorithm. Additionally, the Language tip states, “These cues help connect your verbal instructions to the written work they see. As students record their work, encourage them to write out each step of their calculations, just as they did with partial quotients. This helps make their thinking visible and keeps the focus on the structure of the algorithm, rather than getting stuck on new terminology or formatting.” This Language tip provides specific teacher guidance to support students in finding connections between the partial quotients method and the standard algorithm, and to describe a general algorithm.

The instructional materials reviewed for Grades 3-5 of Takeoff by IXL partially meet the expectation of including guidance for intentional and flexible grouping structures for MLLs to ensure equitable participation. The materials include some guidance for intentional and flexible grouping structures for MLLs; however, they do not include guidance to ensure equitable participation for MLLs in group work.

One example of grouping guidance appears in Grade 4, Unit 4, Multiply by 2-digit numbers, Lesson 4.2. In the Language tips, teachers are advised to support language learners during a Think and talk activity by having students discuss in pairs before sharing with the whole group. Students are encouraged to discuss what an area model would look like and draw it together before responding to subsequent questions. While this guidance offers a flexible structure for peer discussion, it does not include explicit direction for forming groups based on language proficiency or home language, nor does it provide scaffolds tailored to varying levels of English proficiency.

While this example demonstrates some guidance for intentional grouping structures for MLLs, they are isolated and not representative of the curriculum as a whole.  Across the vast majority of lessons and units in the grade band, teacher guidance related to grouping MLLs is limited and inconsistently provided. When present, grouping guidance appears within lesson-level Language tips rather than as part of a consistent framework across units and lessons; the materials do not provide overarching guidance to support teachers in forming flexible groups based on language proficiency, home language, or task demands. Additionally, the materials do not offer strategies for monitoring group interactions to ensure that MLLs are active and valued contributors. As a result, the materials lack sufficient guidance to ensure equitable participation for MLLs in group work.

In summary, the materials include limited examples of guidance for intentional and flexible grouping structures for MLLs. However, this guidance is inconsistent and does not extend to ensuring equitable participation across lessons and units.

The instructional materials reviewed for Grades 3–5 of Takeoff by IXL partially meet the expectations of providing guidance to encourage teachers to draw upon students' home language to facilitate learning.

The digital platform provides a variety of digital translation options, including glossaries in Spanish, Arabic, and Chinese, along with digital translation and audio support available in more than 100 languages when enabled by teachers or administrators (see the report for 3n.MLL for more details). While these features offer one level of access, the materials do not provide teacher guidance on how to actively and intentionally integrate these translated resources into instruction to support conceptual understanding or mathematical discourse. While family letters are available in English and Spanish, there is no broader guidance on using linguistic background information strategically to inform instruction.

The materials also miss opportunities to support teachers in systematically understanding MLLs’ linguistic backgrounds, such as families’ preferred languages of communication, prior schooling experiences in other languages, literacy abilities in those languages, or exposure to academic or everyday English. As a result, multilingualism is not presented as an asset to be strategically leveraged during instruction.

In limited instances, the materials briefly acknowledge home language as a resource. For example, in Grade 3, Unit 2, Understand multiplication, Lesson 2.2, the Language tip states, "This lesson introduces multiplication equations. Consider adding related vocabulary like factor, product, and times to the vocabulary list you started earlier in the year, and encourage students to use this vocabulary as they discuss multiplication equations throughout the unit. If these words are similar in students' home languages, consider pointing that out to help students understand their meanings. For example, in Spanish, these words are factor, producto, and multiplicar.” This guidance positions home language as an asset and is applicable across linguistic backgrounds; however, such examples are few and inconsistently applied across the grade band. When home language is referenced in Language Tips, it is most often limited to Spanish rather than inclusive of students’ full linguistic repertoires.

In summary, the materials do not provide consistent, asset-based guidance around home MLLs’ home language usage, nor sufficient instructional strategies for leveraging students’ full linguistic resources.