3rd-5th Grade - Gateway 2

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math meet expectations of providing support for MLLs’ full and complete participation in the conceptual understanding of key mathematical concepts. The materials provide embedded, intentional supports that promote conceptual understanding of grade-level mathematics through activating prior knowledge, pairing concrete, visual, and abstract representations, and engaging students in scaffolded tasks that are aligned with the depth and intent of the standards.

In every unit, the materials consistently provide opportunities for students to explore and make sense of mathematical ideas before engaging with multiple representations to formalize procedures, supporting conceptual understanding. To do this, the materials embed various representations, structured discourse, and Mathematical Language Routines [MLRs] to promote deep conceptual understanding. For example:

• Concrete and visual representations and virtual manipulatives such as counters or cubes and 5- and 10-frames are used alongside MLRs to solidify understanding of grade-level mathematics.

• Sentence frames and starters encourage students to explain their reasoning, compare strategies, and make sense of concrete and visual representations.

• Activities and tasks require students to use and develop language when moving between representations (concrete, visual, and abstract), aligning with the standards’ call for conceptual understanding.

• The MLD Resources provide a strong and explicit structure for teachers to support MLLs’ full participation in one Activity per lesson, including a summary of the language demands of the Activity, Spanish cognates, teacher prompts paired with linguistic supports categorized into Emerging/Expanding/Bridging, and a student-facing page frequently containing sentence frames and starters, graphic organizers, and/or bilingual English-Spanish word banks.

For example, in Grade 5, Unit 5, Place Value Patterns and Decimal Operations, Lesson 7, students demonstrate conceptual understanding as they apply place value language and reasoning to round decimal numbers (5.NBT.4). In the Warm-Up, the teacher asks students Think-Pair-Share what they notice and wonder about a digital interactive number line showing a skier traveling to the closest whole number on a number line diagram. This visual representation supports MLLs with applying prior knowledge around rounding whole numbers to new tasks. In Activity 1, students continue this thinking when they work with partners to round decimal numbers using the same dynamic digital interactive paired with representations of the digital interactive printed in their Student Editions. MLLs are fully supported in participating in the student-to-student discourse with Math Language Routine [MLR] 2: Collect and Display, where the teacher adds language partners to use to describe the process of rounding to an anchor chart titled “Rounding Process.” Activity 2 provides ample opportunities for MLLs to use and develop place value language while rounding decimal numbers with a partner. The MLD Resources for this lesson are for Activity 2, and they support MLLs with using place value language in student-to-student discourse with printed sentence frames such as, “To round 6.382 to the nearest _____ [whole number/tenth/hundredth], I would think about…” alongside a bilingual English-Spanish word bank. The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from crafting their explanation in their home language to modeling how MLLs can restructure their first responses, possibly in everyday language, to more precise mathematical language using the provided sentence frames. In summary, the lessons’ embedded features such as the virtual manipulatives, the MLRs, and the MLD Resources paired with many opportunities for students to use and develop language provide MLLs with full and complete participation in the lesson.

The materials fully support MLLs with the language needed to engage in conceptual understanding by providing structured opportunities for students to explain their thinking, compare strategies, and use precise mathematical vocabulary. Across all units, concrete, visual, and abstract representations are intentionally connected through MLRs and language supports that deepen understanding and encourage reasoning. Embedded supports such as virtual manipulatives, the MLRs, sentence frames, and the MLD Resources ensure MLLs can access, use, and develop the disciplinary language necessary for full participation in building conceptual understanding.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math meet expectations of providing support for MLLs’ full and complete participation in developing procedural skills and fluencies. The materials feature embedded, intentional language supports that support MLLs with systematically building procedural fluency and provide MLLs with the opportunity to use and develop language related to explanation, justification, and synthesis.

In every unit, the materials consistently provide opportunities for MLLs to use and develop the language needed to engage with procedural skills and fluencies as called upon in the standards. To do this, the materials contain various instructional design features that support MLLs’ productive language, or speaking or writing, specifically where lessons require students to explain or justify their thinking or synthesize their learning related to developing procedural skills. For example:

• The digital Fluency Practice cards feature dynamic visual representations that support MLLs' understanding of abstract expressions. As MLLs practice using these cards, the adaptive technology slowly removes the interactive representations as students need the scaffolds less.

• Daily Lesson Practice and Additional Practice feature fluency practice and spiral review with language and visual representations similar to those students previously experienced within lessons, providing MLLs with coherent practice towards mastery. 

• Within lessons, sentence frames and starters encourage students to explain their reasoning and synthesize their learning related to developing procedural skills and fluencies.

• The Math Language Development [MLD] Resources provide a strong and explicit structure for teachers to support MLLs’ full participation in one Activity per lesson, including a summary of the language demands of the Activity, Spanish cognates, teacher prompts paired with linguistic supports categorized into Emerging/Expanding/Bridging, and a student-facing page frequently containing sentence frames and starters, graphic organizers, and/or bilingual English-Spanish word banks.

For example, in Grade 4, Unit 4, From Hundredths to Hundred Thousands, Lesson 18, students continue work from the previous lessons to develop fluency with subtracting multi-digit whole numbers in problems involving decomposition (4.NBT.4). The Warm-Up activates background knowledge from the previous lessons, inviting students to estimate a difference using the Instructional Routine Estimation Exploration. Students work towards independently demonstrating procedural skills and fluency during the mental math portion of Estimation Exploration. Then, in Activity 2, students progress toward fluency and procedural skill being interwoven with conceptual understanding as they compare two fictional students’ solution strategies for solving multidigit subtraction problems. MLLs are supported with comparing these abstract solution strategies and fully participating in the whole-class discussion through an ML/EL Support that invites the teacher to annotate the strategies with student language, and encourage students to refer to the annotated display throughout the discussion, supporting MLLs with linking language to concepts. MLLs are further supported with Math Language Routine [MLR] 7: Compare and Connect, with teacher prompts such as, “What is similar and different about the strategies?” Then Activity proceeds with partners working together to develop flexibility through solving one subtraction problem using the same two solution strategies. The Activity concludes with the teacher facilitating a whole-class discussion again comparing the same two solution strategies that partners just applied, providing MLLs with ample opportunities to use and develop language around procedural skills and fluency. The MLD Resources for this lesson are for this portion of Activity 2, and they support MLLs in participating in the whole-class discourse with the following sentence frames printed in the student page of the MLD Resources: “The expanded form algorithm and the standard algorithm are ____[similar/different] because… In the _____ [expanded form/standard form] algorithm, decomposition is shown by…” These sentence frames are printed in English and Spanish, and alongside them is a bilingual English-Spanish word bank. The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from crafting the steps in their home language to encouraging MLLs to point to parts of the solution strategies or point to words in the word bank. These supports help move MLLs towards independently demonstrating an understanding of procedural skills and fluency when solving multidigit subtraction problems. In summary, the lessons’ embedded features such as the MLRs and the MLD Resources paired with many opportunities for students to use and develop language provide MLLs with full and complete participation in the lesson.

In every unit, the materials consistently provide opportunities for MLLs to use and develop the language needed to engage with procedural skills and fluencies as called for in the standards. The materials embed structured supports such as MLRs, sentence frames, and the MLD Resources to promote productive language use when explaining reasoning, justifying steps, and synthesizing learning related to procedures. These features, along with coherent visual and linguistic supports in daily and digital practice, move MLLs toward independently demonstrating procedural fluency. 

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math meet expectations of providing support for MLLs’ full and complete participation in utilizing mathematical concepts and skills in engaging applications. The materials feature embedded, intentional language supports that support MLLs with engaging in applying mathematical concepts and skills in routine and non-routine tasks as well as partner and whole-class discourse focusing on mathematical reasoning. 

In every unit, the materials consistently provide opportunities for MLLs to use and develop language when making sense of and solving application problems. To do this, lessons frequently invite students to choose and apply their own solution strategy while engaging in real-world and mathematical application tasks. The materials often introduce concepts using real-world scenarios, self-select prescribed or unique solution strategies, and invite students to synthesize and apply their learning to new contexts. The Math Language Development [MLD] Resources provide a strong and explicit structure for teachers to support MLLs’ full participation in one Activity per lesson, including a summary of the language demands of the Activity, Spanish cognates, teacher prompts paired with linguistic supports categorized into Emerging/Expanding/Bridging, and a student-facing page frequently containing sentence frames and starters, graphic organizers, and/or bilingual English-Spanish word banks. 

For example, in Grade 4, Unit 5, Multiplicative Comparison and Measurement, Lesson 7, students solve routine two-step application problems involving multiplicative comparison (4.OA.A). The Warm-Up activates background knowledge from previous grades, inviting students to analyze equations and consider the relationship between multiplication and division using the Instructional Routine True or False? This thinking and language usage continues to Activity 1 where students work independently, then in partners, to write their own two-step application-type problem involving multiplicative comparisons. Before the teacher releases students to write their word problems, the teacher models metacognitive and metalinguistic thinking through co-constructing a two-step routine comparison problem. In this section, the materials move beyond language simplification to actively amplify English language structures, particularly syntax and grammar, within routine application problems; the teacher guidance explicitly highlights grammar by noting, "The verb tense can change to fit the story problem. For example, you can use swim or swam," explicitly drawing students’ attention to how grammatical choices impact meaning. This language amplification continues as students are released to independently write their word problems through a word bank of nouns and verbs printed in the Student Edition. The materials further support MLLs with independently writing a routine application problem through the MLD Resources for this lesson, which are for Activity 1. The student page of the MLD Resources contains printed sentence frames such for MLLs to use in writing, alongside a bilingual English-Spanish word bank and visuals of key vocabulary terms. These resources mirror the word bank of nouns and verbs printed in the Student Edition, giving MLLs access to the same activity as their peers. The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that focus on crafting their explanation in their home language to encourage MLLs to point or gesture to the visuals and word bank. After students finish writing their routine application word problem, the materials continue to support MLLs’ full and complete participation in the independent writing task through Math Language Routine [MLR] 1: Stronger and Clearer Each Time. MLR1 directs students to meet with partners to share their problems and get feedback to make the problems more clear through sentence starters like, “What do you mean by…?” and “What is the first step...?” This supports MLLs with refining their use of academic language, linking language to the concept of multiplicative comparison by emphasizing the phrase “times as many.” In summary, the lessons’ embedded features such as the MLRs and the MLD Resources paired with many opportunities for students to use and develop language provide MLLs with full and complete participation in the lesson.

The materials consistently provide opportunities for MLLs to use and develop the language needed to make sense of and solve application problems. Lessons embed structured supports such as MLRs, sentence frames, and the MLD Resources to promote productive language use when explaining solution strategies, comparing approaches, and applying mathematical approaches to routine and non-routine problems. These design features, along with opportunities for self-selected strategies and discourse-rich discussions, move MLLs toward independently applying mathematical reasoning to new situations. 

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 some strategies and supports for MLLs to fully and completely participate in the intentional development of MP1, but they are not employed consistently throughout the program.

The materials provide opportunities for students to use and develop language when making sense of problems through features embedded within the lesson facilitation or as an ML/EL Support. Examples of features embedded within the lesson facilitation are the Instructional Routines and the Math Language Routines [MLRs]. Specifically, in the PD Library on the digital platform, the Routine Facilitate Guides for K-5 describes how the Instructional Routine Notice and Wonder supports MP1: “This routine helps students make sense of a math representation or context (MP1) before they investigate it more deeply. This routine often appears as a Warm-Up or in the launch of an activity.” Similarly, the Routine Facilitation Guide describes how MLR8: Discussion Supports supports MP1: “This routine supports precise and meaningful student discussion and the deepening of students’ mathematical understandings.” While there are other Instructional Routines and MLRs that support the language needed to engage in MP1, Notice and Wonder is the only routine the materials identify as supporting MP1. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP1.

The materials invite students to use and develop language when making sense of problems through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk as 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 digital interactives, real-world videos, and animated videos that activate background knowledge while supporting students with understanding the information in the problem and the question asked. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 2, Area and Multiplication, Lesson 2, Activity 2, where students work independently to build shapes and then work with a small group to arrange them from smallest to largest using a shared unit of measurement. The materials do not provide linguistic supports for MLLs to participate fully in the collaborative language needed to arrange the shapes by explaining area comparisons with their peers. As groups are working, the materials direct the teacher to monitor groups and identify students who need help getting started by using prompts such as, “How can you compare the areas of your shapes?” There are no linguistic supports provided to students to make sense of problems and persevere in solving them by justifying reasoning using consistent measurement language. The Activity concludes with a whole-class discussion where MLLs are supported through MLR8: Discussion Supports—Sentence Frames which provides two sentence frames for students to add details in their ordering reasoning. In summary, throughout this lesson, MLLs are partially supported in using and developing the language needed to engage in MP1. 

• In contrast, MLLs are supported in Grade 4, Unit 3, Extending Operations to Fractions, Lesson 2, Activity 1, where students work with partners to make sense of problems involving  real-world fractions with the same denominators involving joining and separating with diagrams and equations. The MLD Resources for this lesson are for Activity 1, and the Student Page provides support for MLLs to make sense of the fraction problem situations through visuals of key vocabulary with the printed term in English and Spanish. As partners work together to make sense of each fraction problem situation, the Student Edition supports students with visualizing and representing the joining and separating of fractional parts with printed representations of fractions, already subdivided into the parts described in the word problems. The materials suggest that the teacher provides students with access to manipulatives such as fraction-sized pieces to further support students with making sense of fraction problems. Then, partners use a variety of self-selected solution strategies to solve two fraction problems without pre-printed representations. Finally, the materials direct two partners to come together to form a group of four to make sense of the fraction problems through comparing and contrasting their self-selected solution strategies. The MLD Resources support MLLs’ full and complete participation in this student-to-student discourse with sentence frames such as, “Our representations and answers are ____ [the same/different] because…” alongside a bilingual English/Spanish word bank. Additionally, the MLD Resources provide teacher prompts to support MLLs with comparing and contrasting solution strategies, which are paired with linguistic supports that are categorized into Emerging/Expanding/Bridging. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP1 in this lesson.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program. They are not consistent in supporting MLLs with the language demands of making sense of problems. At times, the ML/EL Supports and the MLD Resources do not support the language needed for MLLs to engage with MP1.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 provide some strategies and supports for MLLs to fully and completely participate in the intentional development of MP2, but they are not employed consistently throughout the program.

The materials provide opportunities for students to use and develop language when reasoning abstractly and quantitatively through features embedded within the lesson facilitation or as an ML/EL Support. Examples of features embedded within the lesson facilitation are the Instructional Routines and the Math Language Routines [MLRs]. Specifically, in the PD Library on the digital platform, the Routine Facilitate Guides for K-5 describe how specific Instructional Routines and MLRs support MP2:

• Estimation Exploration: This routine strengthens students’ ability to make reasonable estimates for amounts, lengths, or sizes. Over time, this routine promotes a shift from random guessing to using prior knowledge and problem-solving techniques as students make and revise estimates (MP2).

• Stories and Questions: This routine invites students to consider a math story to analyze the relationship between quantities (MP2) and consider how they can use mathematics to model a real-world situation (MP4).

• MLR4: Information Gap: This routine creates a need for students to communicate and allows teachers to facilitate meaningful interactions by giving partners or team members different pieces of necessary information that must be used together to solve a problem (MP2, MP4). 

The materials frequently provide opportunities for students to use and develop language when reasoning abstractly and quantitatively through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk as students consider the units involved in a problem or the meaning of the quantities, analyze the relationships between quantities, and connect real-world scenarios to mathematical representations. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 4, Unit 4, From Hundredths to Hundred Thousands, Lesson 8, Activity 1, where students reason abstractly and quantitatively by building equivalent representations of numbers to understand that a digit in one place is worth ten times the value of the digit to its right. To do this, the materials direct students to work in partners to use a place value mat to represent large numbers in various ways, either by drawing representations of place value tokens or through the digital interactive place value mat with tokens. There are no linguistic supports for MLLs to fully participate in the student-to-student discourse in which they represent situations symbolically and discuss what the symbols mean. Then, the Activity invites partners to create a parallel challenge task for their classmates. The materials do not provide linguistic supports for MLLs to fully participate in creating a challenge task for their peers. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2. 

• In contrast, MLLs are supported in Grade 4, Unit 6, Multiplying and Dividing Multi-Digit Numbers, Lesson 6, Activity 1, where students reason abstractly and quantitatively when they work in partners to create a visual display showing how to multiply 2 two-digit numbers. The materials support MLLs with access to the task through an ML/EL Support that activates background knowledge about the real-world scenario involving flower gardens. Then, partners work together to create their visual display showing how to multiply 2 two-digit numbers, which must include diagrams, words, and equations. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with using and developing the language needed to fully participate in the student-to-student discourse and to justify their thinking with diagrams, words, and equations. Specifically, the MLD Resources offer teacher prompts such as, “What strategy have you used to multiply multi-digit numbers? How could you use that here to help you?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language and gestures to encouraging MLLs to use the provided sentence frames and starters. The Student Page of the MLD Resources features corresponding sentence frames and a bilingual English-Spanish word bank to support MLLs with the productive language demands of the Activity. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP2 in this lesson. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program. They are not consistent in supporting MLLs with the language demands of reasoning abstractly and quantitatively. At times, the ML/EL Supports and the MLD Resources do not support the language needed for MLLs to engage with MP2.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 some strategies and supports for MLLs to fully and completely participate in the intentional development of MP3, but they are not employed consistently throughout the program.

The materials provide opportunities for students to use and develop language when constructing arguments and critiquing others through features embedded within the lesson facilitation or as an ML/EL Support. Examples of features embedded within the lesson facilitation are the Instructional Routines and the Math Language Routines [MLRs]. Specifically, in the PD Library on the digital platform, the Routine Facilitate Guides for K-5 describe how specific Instructional Routines and MLRs support MP3: 

• Decide and Defend: “This routine is intended to support students in strengthening their ability to make arguments and to critique the reasoning of others (MP3). In this routine, students make sense of someone else’s line of mathematical reasoning, decide if they agree with that reasoning, and then draft an argument defending their decision. This includes situations where students are making sense of two students’ different ideas about a situation (Settle a Dispute).” 

• True or False?: This routine encourages students to notice and make use of structure as they use the properties of operations to determine equivalence without having to calculate. Students use what they know about place value, operations, and number relationships to justify and explain their thinking (MP3, MP7).

• MLR8: Discussion Supports: This routine supports precise and meaningful student discussion and the deepening of students’ mathematical understandings (MP1, MP3, MP6). 

While there are other Instructional Routines and MLRs that support the language needed to engage in MP3, Decide and Defend is the only routine the materials state as supporting MP3. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP3.

The materials invite students to use and develop language when constructing viable arguments and critiquing the reasoning of others through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when explaining their strategies, performing error analysis of students’ work, listening to the arguments of others to determine if they make sense, and creating their own conjectures. The materials provide point-of-use sentence frames, often in the Synthesis, that specifically support students with constructing viable arguments and critiquing the reasoning of others. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 5, Unit 1, Volume, Lesson 10, Activity 2, where students determine the volumes of figures created from right rectangular prisms and critique the reasoning of others. Students work with a partner to determine the volumes of figures by removing a right rectangular prism-shaped piece. The materials do not provide linguistic supports for MLLs to fully participate in the student-to-student discourse in which they work collaboratively with partners and explain how to determine volumes by subtracting the volume of the removed piece. Then, partners work collaboratively on a new problem in which they critique similar geometric reasoning from a fictional student, writing their critiques in the Student Edition. There are no linguistic supports for MLLs to create their written critiques. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in Grade 4, Unit 2, Fraction Equivalence and Comparison, Lesson 8, Activity 1, where students work with a partner to create a poster to justify how they know two given fractions are equivalent. Then, the materials direct partners to work together to create their visual display showing how two fractions are equivalent in as many ways as possible, which must include fraction strip diagrams and/or number lines, words, and equations. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with using and developing the language needed to fully participate in the student-to-student discourse and to justify their thinking with diagrams, words, and equations. Specifically, the MLD Resources offer teacher prompts such as, “What is important about the parts on a fraction model?” and “How does the equation connect to your models?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language and gestures to encouraging MLLs to use the provided sentence frames and starters. The Student Page of the MLD Resources features corresponding sentence frames, a bilingual English-Spanish word bank, and visuals annotated with vocabulary terms in English and Spanish to support MLLs with the productive language demands of the Activity. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP3 in this lesson. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program.  They are not consistent in supporting MLLs with the language demands of constructing viable arguments and critiquing the reasoning of others. At times, the ML/EL Supports and the MLD Resources do not support the language needed for MLLs to engage with MP3.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP4: Model with mathematics. The materials provide linguistic supports for MLLs to participate in the intentional development of MP4, but these supports do not consistently provide for full and complete participation by MLL students. 

The materials provide opportunities for students to use and develop language when modeling with mathematics through features embedded within the lesson facilitation or as an ML/EL Support. Examples of features embedded within the lesson facilitation are the Instructional Routines and the Math Language Routines [MLRs]. Specifically, in the PD Library on the digital platform, the Routine Facilitate Guides for K-5 describes how the Instructional Routine Stories and Questions supports MP4: “This routine invites students to consider a math story to analyze the relationship between quantities (MP2) and consider how they can use mathematics to model a real-world situation (MP4).” Similarly, the Routine Facilitation Guide describes how MLR4: Information Gap supports MP4: “This routine creates a need for students to communicate and allows teachers to facilitate meaningful interactions by giving partners or team members different pieces of necessary information that must be used together to solve a problem (MP2, MP4).” While there are other Instructional Routines and MLRs that support the language needed to engage in MP4, Stories and Questions and MLR4 are the only routines the materials identify as supporting MP4. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP4.

The materials frequently provide opportunities for students to use and develop language when modeling with mathematics through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when identifying important information in the problem, modeling the problem with a mathematical representation, and describing how to use the mathematical model. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 1, Introducing Multiplication, Lesson 16, Activity 2, where students create a bar graph and use a scale to represent the data. While the context of the data for the bar graph is familiar to students because it is continued from Activity 1, there are no linguistic supports for MLLs to independently make sense of and choose a scale, and create a bar graph in Activity 2. Then, the Student Edition directs students to discuss why they chose a particular scale with a partner. There are no linguistic supports provided for the student-to-student discourse where students reflect on the advantages or disadvantages of their choices. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1.  

• In contrast, MLLs are supported in Grade 4, Unit 3, Extending Operations to Fractions, Lesson 4, Activity 1, where students solve real-world fraction word problems by representing them with visual models and equations. Activity 1 begins with the teacher reading a real-world fraction word problem aloud while students follow along, linking the listening and reading language domains. To support students with understanding the word problem, the teacher invites students to describe the problem in their own words, identifying the important information in the problem. Then, students model with mathematics as they independently create models, such as visual models and equations, to represent two word problems. After students solve the problems, they discuss their self-selected solution strategies with a partner and describe how their models show the relationships between the amounts in the problems. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs when working with a partner to discuss how the same situation can be represented with different models and investigate how they can use both addition and subtraction to solve problems due to the inverse relationship between these operations. Specifically, the MLD Resources offer teacher prompts such as, “How is your model and your partners’ similar? Different?” and “How are the model and equation connected?” The Student Page of the MLD Resources features corresponding sentence frames to support MLLs with the productive language demands of the Activity. These prompts and sentence frames are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from encouraging MLLs to apply the provided sentence frames and starters to directing MLLs to point or gesture to support their verbal descriptions. After this partner discussion, the materials direct the teacher to facilitate whole-class discourse where the teacher displays different models and students explain how their model represents the problem. MLLs are fully supported in participating in the whole-class discourse with an ML/EL Support encouraging teachers to provide similar sentence frames as in MLD Resources. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP4 in this lesson.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 some strategies and supports for MLLs to fully and completely participate in the intentional development of MP5, but they are not employed consistently throughout the program.

The materials frequently provide opportunities for students to use and develop language when using appropriate tools through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when choosing appropriate tools, recognizing insights and limitations of different tools, and knowing how to use a variety of tools. There are Instructional Routines and Math Language Routines that support the language needed to engage in MP5, but the materials do not provide any specific routine as supporting MP5. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP5. Additionally, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 5, Unit 2, Fractions as Quotients and Fraction Multiplication, Lesson 4, Activity 1, where students use their understanding of the relationships between division and fractions to write and solve equal-sharing story problems. Activity 1 begins with ample support for MLLs to engage with the task. First, the teacher reads aloud the directions for the Activity while students follow along, linking the listening and reading language domains. Then, the materials direct partners to work together to write two fraction division word problems. An ML/EL Support provides a home-language pairing suggestion for MLLs to leverage home language when writing fraction word problems. The Math Language Development [MLD] Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with the language demands of the writing task. Specifically, the MLD Resources offer teacher prompts such as, “What is needed to write a division story problem?” The Student Page of the MLD Resources features corresponding sentence frames to support MLLs with the productive language demands of the Activity. However, these supports do not directly relate to MLLs engaging with MP5, including selecting and using tools, or explaining why specific tools are appropriate. After partners write two fraction word problems, the materials direct partners to join with another pair and take turns sharing their word problems. The Student Edition invites these groups of four students to engage with MP5 with the prompt, “What tools could you use to represent each part of the story problem you wrote? Why would you choose these tools?” The materials do not provide language supports for MLLs to engage in this student-to-student discourse, to choose appropriate tools, or to reflect on the insights gained from different tools and their limitations.  

• In contrast, MLLs are supported in Grade 4, Unit 4, From Hundredths to Hundred Thousands, Lesson 5, Student Edition, Activity 1, where students use appropriate tools and models such as number lines or diagrams to compare decimals, explain why particular tools are useful, test conjectures about decimal comparison strategies, and share how their chosen representations support their reasoning. In Launch, the teacher reads aloud the directions for the Activity while students follow along, linking the listening and reading language domains. The teacher activates background knowledge around choosing appropriate tools strategically by asking, “What tools or models have we used already to represent fractions? How can you use those to help you compare?” Then, partners work together to compare six sets of decimals, self-selecting the use of diagrams, number lines, or fraction models to help them solve each problem. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with the language demands of selecting tools in the student-to-student discourse. Specifically, the MLD Resources offer teacher prompts such as, “What strategy do you use to compare two decimals?” and “How could you use a number line to prove your thinking? A diagram? Equivalent fractions?” The Student Page of the MLD Resources features corresponding sentence frames to support MLLs with the productive language demands of the Activity. These prompts and sentence frames are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from encouraging MLLs to apply the provided sentence frames and starters to directing MLLs to point or gesture to support their verbal descriptions. The Activity concludes with the teacher facilitating a whole-class discussion in which students share their responses, any tools or models they used, and a reflection on why they chose the tool or model and how it helped them to compare decimals. MLLs are supported in participating in the whole-class discussion with an ML/EL Support that states, “Provide students with wait time to process the questions, formulate a response, and rehearse what they will say with a partner before sharing with the class.” The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP5 in this lesson.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 linguistic supports for MLLs to participate in the intentional development of MP6, but these supports do not consistently provide for full and complete participation by MLL students. 

The materials frequently provide opportunities for students to use and develop language when attending to precision through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when communicating using appropriate vocabulary, labeling tables and graphs appropriately, and stating the meaning of symbols. Often, the materials provide point-of-use sentence frames and bilingual English-Spanish word banks in the Math Language Development [MLD] Resources that specifically support students with using precise vocabulary when formulating explanations. Generally, the materials invite students to engage with a mathematical concept, both through speaking and listening during mathematical discourse and through the use of visuals or manipulatives, before attaching a precise new vocabulary term to the concept. The materials support teachers with anticipating the vocabulary demands of the unit with the Language Development section of the Overview for each Unit. This section outlines the new vocabulary and contextual vocabulary of the Unit, including lesson tags, and also provides a list of review vocabulary. 

There are Instructional Routines and Math Language Routines [MLRs] that support the language needed to engage in MP6, but the materials do not provide any specific routine as supporting MP6. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP6. The materials offer point-of-use linguistic supports that do not consistently provide for full and complete participation by MLL students. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 6, Measuring Length, Time, Liquid Volume, and Weight, Lesson 6, Activity 1, where students attend to precision when they work in small groups to generate data by measuring objects in their school and represent the data on a line plot. The materials direct small groups to make a plan to walk around the school and select and measure 10 objects to the nearest half or quarter inch, recording the lengths in tables. There are no supports ensuring MLLs have a meaningful role in group collaboration, nor are there linguistic supports for MLLs to attend to precision as they measure objects to the nearest half or quarter inch. The Activity concludes with a whole-class discussion around what students notice about their length measurements. MLR8: Discussion Supports - Revoicing provides a suggestion for teachers to revoice student statements with more mathematically precise language. While this MLR supports MLLs with using precise, grade-level appropriate language, it does not provide MLLs with support for formulating a clear explanation about what they noticed about their length measurements. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2. 

• In contrast, MLLs are supported in participating in Grade 5, Unit 1, Volume, Lesson 3, where students attend to precision as they solve for volume by using different strategies. The Warm-Up features a What Do You Know About ____? routine which activates background knowledge and language about rectangular prisms. In Activity 1, students work in partners to build rectangular prisms and describe their structures in a written response. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with the language demands of formulating a clear written description using grade-level appropriate vocabulary. Specifically, the MLD Resources offer teacher prompts such as, “How can you describe the rectangular prism?” and “How many layers are there? In each layer, how are the cubes arranged?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language and gesturing to encouraging MLLs to use the provided sentence frames and starters. To further support MLLs’ full and complete participation in the task, the Student Page of the MLD Resources features corresponding sentence frames designed to support MLLs with applying descriptive language, key vocabulary with visuals and terms written in English and Spanish, and a bilingual English-Spanish word bank. The lesson facilitation and an ML/EL Support repeat some of the support from the MLD Resources. The materials direct the teacher to facilitate MLR2: Collect and Display to provide a word bank of grade-level appropriate vocabulary to students. An ML/EL Support states, “Add an image of a rectangular prism to the display and provide annotations that highlight key features of the layered structure.” After students construct their written description, MLLs have an opportunity to develop and apply the same descriptive language; the materials direct two partner groups to join together, trade prisms with each other, and verbally describe the prism using the same language and grade-level appropriate vocabulary. In this section of the Activity, the materials support MLLs with understanding the term decompose through a teacher prompt that provides the appositive “... take apart…” The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP6 in this lesson. 

In summary, while language supports are present in the materials, they do not consistently provide for full and complete participation by MLL students. At times, the MLD Resources do not support the language needed for MLLs to engage with MP6.

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 some strategies and supports for MLLs to fully and completely participate in the intentional development of MP7, but they are not employed consistently throughout the program.

The materials provide opportunities for students to use and develop language when looking for and making use of structure through features embedded within the lesson facilitation or as an ML/EL Support. An example of a feature embedded within the lesson facilitation is the Instructional Routines. Specifically, in the PD Library on the digital platform, the Routine Facilitation Guides for K-5 describes how the Instructional Routines Number Talks, Which One Doesn’t Belong, Choral Count, How Many Do You See?, and True or False? support MP7: “Number Talks: This routine encourages students to look for and make use of structure in expressions to calculate their values (MP7). Which One Doesn’t Belong: This routine supports students in looking for and making use of structure (MP7). Students use their existing ideas and language to decide which of four mathematical objects is different from the others. All sets of objects are designed so that each of the objects ‘doesn’t belong’ in some way, which helps students focus on their reasoning and communication rather than their answer. Choral Count: This routine provides students with an opportunity to practice counting as a class. As students count aloud, the count sequence is displayed so that students can notice patterns or structures across numbers (MP7). How Many Do You See: This routine supports students’ development of counting strategies, subitizing, and utilizing visual and mathematical structures (MP7). True or False?: This routine encourages students to notice and make use of structure as they use the properties of operations to determine equivalence without having to calculate. Students use what they know about place value, operations, and number relationships to justify and explain their thinking (MP3, MP7). There are other Instructional Routines and Math Language Routines [MLRs] that support the language needed to engage in MP7, and the lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP7.

The materials invite students to use and develop language when noticing and making use of structure through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when looking for patterns or structures to solve problems, analyzing a problem to look for more than one approach, and decomposing complex problems into simpler, more manageable parts. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 5, Unit 6, More Decimal and Fraction Operations, Lesson 3, Activity 2, where students work in partners to multiply whole numbers by powers of 10 and record the resulting products. After completing four problems, partners are directed to look for and explain the structure within the problems as they discuss the prompt, “What connections can you make between the power of 10 and each product?” There are no linguistic scaffolds for MLLs to engage in the student-to-student discourse while completing the four problems or discussing the place value structure within the problems. The Activity concludes with the teacher facilitating a whole-class discussion on this teacher prompt that engages students further in MP7, using the place value structure to make generalizations: “What conclusions can you make about the product of any whole number and a power of 10?” While the materials do not provide language supports for MLLs to fully participate in the whole-class discussion, an ML/EL Support provides teachers with a linguistic scaffold for the multiple meaning term shifting as it relates to the Key Takeaway of digits shifting to the left when multiplying by a power of 10. 

• In contrast, MLLs are supported in Grade 3, Unit 4, Relating Multiplication to Division, Lesson 8, where students examine a multiplication table and identify relationships among products. In Activity 1, students work with partners to fill in a portion of a multiplication chart and discuss this prompt that engages them to look for patterns and make generalizations: “What patterns do you notice? Why do you think they occur?” The Launch invites the teacher to facilitate this student-to-student discourse using MLR8: Discussion Supports - Sentence Frames: “A pattern I notice is… For example, …” and “I think this happens because…” This supports MLLs’ full participation in Activity 1. Activity 2 continues to engage students in a portion of a multiplication chart, looking for patterns and generalizations as they color all the even products. The materials invite partners to engage in the same prompts as in Activity 1, and MLR8: Discussion Supports - Active Listening. This MLR supports MLLs with fully participating for a second time in similar student-to-student discourse by inviting them to begin their partner work by restating their partner’s descriptions in their own words before adding on their ideas. The MLD resources for this lesson are for Activity 2, and they further support MLLs’ full and complete participation with MP7 with sentence frames for looking for structure in the multiplication charts, such as, “Where do you see the even products on the chart?” and “What do you notice about their factors?” The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from gesturing to using the bilingual English-Spanish word bank to fill in the sentence frames. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP7 in this lesson. 

The instructional materials reviewed for Grades 3-5 of Amplify Desmos Math 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 some strategies and supports for MLLs to fully and completely participate in the intentional development of MP8, but they are not employed consistently throughout the program.

The materials frequently provide opportunities for students to use and develop language when looking for and expressing regularity in repeated reasoning through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk as they create or describe a general process or algorithm, use repeated reasoning as a tool, or notice when calculations repeat. There are Instructional Routines and Math Language Routines [MLRs] that support the language needed to engage in MP8, but the materials do not provide any specific routine to support MP8. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP8. Additionally, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 5, Unit 7, Geometry and Patterns, Lesson 9, Activity 2, where students look for and express regularity in repeated reasoning when they generate two number patterns using different rules and describe the relationship between the patterns using multiplication. First, students work independently to generate two number patterns using different rules. Then, students participate in a Think-Pair-Share about what they notice about the corresponding terms. Here, the materials provide language support by directing the teacher to record students’ noticings, supporting MLLs by pairing spoken and written English. As the Activity continues, the materials do not provide any additional language supports for MLLs’ full and complete participation. Students work in partners to write in the Student Edition to identify a consistent multiplicative relationship between corresponding terms and generalize the relationships using multiplication, with no linguistic supports for the writing language demands. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in Grade 3, Unit 4, Relating Multiplication to Division, Lesson 9, Activity 2, where students look for and express regularity in repeated reasoning when they complete equations to represent two smaller rectangles that compose a larger one, then justify how adding the smaller products shows the Distributive Property. When working in the digital platform, MLLs are supported with initial access to the task through use of a dynamic, self-checking digital interactive that allows them to repeatedly compose and decompose rectangles and analyze the expressions that correspond with each rectangle. Partners work collaboratively to complete several equations that represent two smaller rectangles that compose a larger one. Then, the materials ask partners to justify how adding the smaller products shows the Distributive Property. The MLD Resources for this lesson are for Activity 2, and they provide teacher guidance to support MLLs with this student-to-student discourse in which MLLs engage in the language of MP8. Specifically, the MLD Resources offer teacher prompts such as, “How do you know that the rectangles you made fit inside the 7x8 rectangle?” and “What happens when you add the side lengths of 2 of the rectangles together?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language to using gestures and manipulatives. To further support MLLs’ full and complete participation in the task, the Student Page of the MLD Resources features corresponding sentence frames designed to support MLLs with justifying the application of the Distributive Property and a bilingual English-Spanish word bank. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP8 in this lesson. 

In summary, while language supports are present in the materials, they are not employed throughout the program, but these supports do not consistently provide for full and complete participation by MLL students. At times, the MLD Resources do not support the language needed for MLLs to engage with MP8.