K-2nd Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades K–2 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 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 1, Unit 12, Geometry, Lesson 12.8, the Language tip mirrors the language routine Collect and Display, stating, “Language learners may need support to discuss three-dimensional shapes in #3. Pair students and have them discuss what they notice. Then display common phrases that you hear. Discuss these phrases as a class and clarify how to use each one to describe the rectangular prisms. It may also be helpful for students to add some of these phrases to their personal dictionaries.” 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 2, Unit 1, Addition and subtraction within 20, the Math practices section states the following for MP4: “Across Unit 1, students discuss the benefits and drawbacks of different methods for adding and subtracting. They also have opportunities to practice critiquing others’ reasoning, both in discussions with their peers and through exercises designed to address common misconceptions… Prompt students to practice thinking critically about others' work by considering why Polly’s answer might seem reasonable at first glance.” 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 K-2 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 1, Unit 11, Addition and subtraction within 100, Lesson 11.8, students build conceptual understanding as they transition from adding two-digit numbers using place value models to adding two-digit numbers by working in the abstract, breaking apart both numbers by place value (1.NBT.4). The Warm-up activates students’ background knowledge around breaking apart two-digit numbers by place value, supporting MLLs by providing a preview of the place value language students will use within the lesson. The Whole-class Instruction includes Teacher notes to guide students to apply this prior knowledge to the new task of adding two-digit numbers mentally, without a recording. The Language tip includes teacher guidance for teachers to anticipate the language demands of the homonym record, providing language supports rooted in teacher guidance to facilitate a discussion around the different meanings of the word. However, the materials do not provide language supports for MLLs’ full and complete participation in adding two-digit numbers mentally by breaking apart both numbers by place value, as is described in problem #6.

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 K-2 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 Kindergarten, Unit 6, Addition and subtraction, Lesson 6.10, students develop procedural skills and fluencies as they identify related addition and subtraction facts (K.OA.5). The Language tip encourages teachers to encourage home language usage when students complete problem #5, suggesting that teachers partner MLLs with students who speak the same home language to explain how they identify related facts. However, the materials do not provide language supports for MLLs’ full and complete participation in identifying related addition and subtraction facts throughout the lesson, as in problem #3, where students engage in a real-world scenario to make sense of related facts, or in problem #4, where students use linking cubes to model related addition and subtraction facts.

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 K-2 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 1, Unit 5, More addition and subtraction stories, Lesson 5.5, students engage in application problems when they represent and solve add to, take from, put together, and take apart word problems (1.OA.1). The Language tip includes teacher guidance for teachers to anticipate the language demands of reading and comprehending the contexts of the word problems by inviting students to share their background knowledge around the contexts and specific terms associated with those contexts. However, the materials do not provide language supports for MLLs’ full and complete participation in solving application problems, such as choosing their own solution strategy. 

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 K-2 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 2, Unit 4, Subtraction within 100, where students critique the solution strategies of others’ strategies for subtracting. The Math practices section in the Unit Overview describes how students engage with MP3, stating, “Throughout Unit 4, students compare and contrast different strategies and methods for subtracting. In Lessons 4.2, 4.6, and 4.9, students evaluate how others have solved problems. When they spot errors, like in Bella's work in #15 of Lesson 4.2, encourage them to explain what's correct, what's not, and what they would do differently.” In Lesson 4.2, the Language tip does not provide linguistic scaffolds for critiquing Bella’s work in problem #15. 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 Kindergarten, Unit 11, Measurement, where students construct viable arguments and critique the reasoning of others while comparing two objects by length, height, width, area, volume, capacity, or weight. The Math practices section in the Unit Overview describes how students engage with MP3, stating, “Throughout the unit, students critique others' reasoning as a way of addressing common errors, like not lining up objects when comparing length, width, or height (#5 in Lesson 11.1 and #6 in Lesson 11.2) and assuming bigger objects weigh more (#4 in Lesson 11.3). Use prompts like ‘Do you agree?’ and ‘Why or why not?’ to get students thinking carefully about each claim. Help them draw on what they know, like how it feels to hold a beach ball or a bowling ball, to explain their thinking. These conversations give students a chance to clarify their own ideas and learn from different points of view.” Lesson 11.3 begins with the materials prompting students to compare the weight of physical objects by closing their eyes and holding each object, stating which objects are heavier or lighter. This use of real objects paired with precise mathematical terminology supports MLLs in using and applying the terms when constructing arguments and critiquing others later in the lesson. The Language tip supports MLLs by previewing the terms heavy and light with the support of gestures so that they can understand these key terms and effectively construct viable arguments when prompted during the lesson. Additionally, the Language tip provides teacher guidance around anticipating the language demands of the homophones weight/wait and the homonyms light (as in opposite of heavy) and light (as in brightness). In problem #4, the materials ask that students critique a functional student’s reasoning about an object that takes up more space as being heavier than a smaller object, prompting, “Do you agree with Rob?” To effectively critique Rob’s reasoning, MLLs must be able to use and apply the math vocabulary terms heavy, light, and weight, and understand the difference between the meaning of the homophones weight/wait. 

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 K-2 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 Kindergarten, Unit 3, Two-dimensional shapes, where students model with mathematics when they use what they know about the attributes of different shapes to solve shape puzzles. The Math practices section in the Unit Overview describes how students engage with MP4, stating, “In Lesson 3.9, students use pattern blocks and drawings to build new shapes and solve shape puzzles, choosing and positioning pieces to create the correct composite shape. Across the unit, students begin to see how they can apply principles of geometry to better understand and describe the world around them.” In Lesson 3.9, problem #3 directly engages students in MP4 by having them solve a shape puzzle where they "join three to six triangles in different ways to make a variety of bigger shapes," then trace their chosen shape and write how many triangles they used. The shape puzzle is inherently multimodal, involving kinesthetic manipulation of pattern blocks, visual representation through tracing, and written quantification. The materials guide teachers to have students share and discuss their shapes, yet there are no linguistic supports for MLLs to use what they know about the attributes of shapes to solve the shape puzzle. The Language tip for the lesson encourages teachers to have MLLs orally rehearse their thinking before having a whole-class discussion, which allows MLLs access to the task. However, the materials do not provide specific linguistic scaffolds to support MLLs in using and applying the language of mathematical modeling.

• In contrast, MLLs are supported in Grade 1, Unit 1, Addition and subtraction stories, where students model with mathematics as they use a variety of solution strategies to model addition, subtraction, and compare stories. The Math practices section in the Unit Overview describes how students engage with MP4, stating, “Students use linked cubes, drawings, and number sentences to model addition stories (Lessons 1.1–1.3), subtraction stories (Lessons 1.4–1.5), and compare stories (Lessons 1.6–1.7). Encourage them to explore a variety of modeling strategies and to discuss why some approaches may be more effective than others. Emphasize the advantage of using simple shapes, such as circles, rather than detailed illustrations to more clearly and quickly represent objects from a story. Throughout the unit, prompt students to explain the connections between models, number sentences, and word problem contexts.” In Lesson 1.2, the Language tip provides teacher guidance to use color coding to support MLLs with making connections between their models and the problems, giving a specific example for problem #2. The materials support MLLs’ full and complete participation in this opportunity to model with mathematics by recommending that MLLs use cubes to match colors to their color-coding to model their solution strategy for problem #2. Next, MLLs are encouraged to explain how the models represent their problem with the support of sentence stems such as, “The blue cubes show ____. The orange cubes show ____.” This provides a targeted opportunity for MLLs to use and develop the language of connecting models and problems while providing linguistic supports for MLLs to strategically engage in multimodal instruction.

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 K-2 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 2, Unit 4, Subtraction within 100, where students attend to precision as they learn to be precise when recording the subtraction strategies they use with numbers and symbols. The Math practices section in the Unit Overview describes how students engage with MP6, stating, “Encourage students to check that their written work matches the method they used. For example, for #8 in Lesson 4.5, if they choose to break apart 27 to subtract, they should show how they subtract 20 and 7 from 56. Alternatively, if they use compensation, they should show how they subtract 30 and add 3 back. Emphasize that recording their work precisely helps others understand their thinking.” In lesson 4.5, the Language tip provides generic suggestions for MLLs to state the meaning of symbols, guiding teachers to “provide ample opportunities” for MLLs to explain what the numbers and symbols mean and to “draw extra attention to the operation symbols.” However, the Language tip lacks specific linguistic supports for how teachers should carry out the generic suggestions; this lack of explicit teacher guidance reduces clarity of how the suggestions support MLLs’ full and complete participation in MP6.

• In contrast, MLLs are supported in Kindergarten, Unit 10, Three-dimensional shapes, where students learn to communicate about shapes precisely using grade-appropriate mathematical language. The Math practices section in the Unit Overview describes how students engage with MP6 in lessons 10.4 and 10.5 as they expand their vocabulary to describe specific three-dimensional shapes and categorize shapes accurately. The Language tip for lesson 10.4 provides proactive, asset-based supports for MLLs to communicate using grade-level appropriate vocab. The guidance recommends pairing MLLs to discuss what they notice about their shapes before whole-class discussion, creating a low-pressure opportunity for language practice. It suggests having students physically trace a cube's faces to reinforce the term, connecting kinesthetic action to vocabulary. For Spanish-speaking students, the tips explicitly encourage cross-linguistic transfer by noting cognates: cubo (cube) and esfera (sphere). 

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 K-2 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 Kindergarten, Unit 9, Numbers to 100, where students use number system patterns to understand numbers up to 100. The Math practices section in the Unit Overview describes how students engage with MP7, stating, “Later in the unit, students use their understanding of tens and ones to count larger groups more efficiently. In Lessons 9.5–9.7, students count using skip counting and grouping by tens. As they do, prompt them to notice how the tens digit increases while the ones digit stays the same. This regular pattern supports efficient counting and lays the groundwork for future work with place value and computation. Emphasize that using ten as a helpful unit is a strategy students will return to throughout their math learning.” In Lesson 9.6, the Language tip does not provide specific teacher guidance for teachers to apply the suggestions in the Unit Overview. Instead, the Language tip prompts teachers to strategically pair language learners with other students for pronunciation support as they put objects into groups of 10 and count by 10s to find the total, specifically during the opening group activity. This suggestion does not contain teacher guidance for language supports that are specific to MLLs looking to make use of structures within the hundreds chart.

• In contrast, MLLs are supported in Grade 2, Unit 3, Addition within 100, where students deepen their understanding of addition by attending to the structure of the place value system. The Math practices section in the Unit Overview describes how students engage with MP7, stating, “Across multiple lessons, they use strategies like breaking apart numbers into tens and ones (Lessons 3.1, 3.2, 3.5, 3.6), grouping like units with place value blocks (Lessons 3.5 and 3.6), and organizing their work in place value charts (Lesson 3.7). Highlight the common structure across these strategies: they all rely on understanding and leveraging place value.” In Lesson 3.5, the Language tip provides proactive support for the linguistic demands, looking for structures to solve problems by recording work using place value language. The guidance acknowledges that writing 32 as "3 tens and 2 ones" may be more challenging for MLLs than writing 30 + 2, but emphasizes its importance for "the conceptual foundation for the standard algorithm." The Language tip suggests that the teacher display an anchor chart showing multiple representations of the same number (place value blocks, 3 tens and 2 ones, and 30 + 2) to be referenced throughout this unit and the next. This multimodal anchor chart directly supports students in connecting concrete, linguistic, and symbolic representations of place value structure. Importantly, this chart helps students see the underlying pattern: that any two-digit number can be understood as a certain number of tens and a certain number of ones. This visual representation of the structure supports students in looking for and recognizing the consistent pattern across numbers, which is the foundation for making generalizations about place value.

The instructional materials reviewed for Grades K–2 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.

For example, in Grade 2, Unit 6, Measuring length, Lesson 6.8. In this lesson, teachers are advised to strategically group beginning MLLs who understand measurement concepts with peers who have stronger language skills but may need mathematical support. This guidance reflects an intentional approach to grouping based on complementary strengths and provides an opportunity for peer-supported interaction during discussion and written work.

While this example demonstrates some guidance for intentional grouping structures for MLLs, this type of guidance is 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 K–2 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 Kindergarten, Unit 1, Numbers to 5, Lesson 1.1, the Language tip states, “Students may already know how to count in their home language. Encourage these students to count the objects first in their home language and then in English to reinforce the relationship between them.” 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.