K-2nd Grade - Gateway 2

The instructional materials reviewed for Grades K-2 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 Kindergarten, Unit 4, Understanding Addition and Subtraction, Lesson 2, students demonstrate conceptual understanding as they use physical objects to represent addition and determine the total number of objects in two groups (K.OA.1). The Warm-Up activates background knowledge about cardinality and quantifying counter cubes and chips through the Instructional Routine Which One Doesn’t Belong? Students continue this thinking in Activity 1, where the teacher asks students what they notice and wonder about the two groups of physical objects, engaging in a Think-Pair-Share paired with printed sentence frames in the Student Edition. As partners work together to determine the total number of objects in the two groups, the materials direct the teacher to remind students to use the language they heard in the Warm-Up during Math Language Routine [MLR] 2: Collect and Display which supports them with applying prior knowledge to new tasks. MLLs are fully supported with participating in the student-to-student discourse during MLR2, where the teacher adds language partners to use to describe addition to an anchor chart started in a previous lesson titled “Words About Adding and Subtracting.” The Activity concludes with a whole-class discussion around what partners noticed and wondered about determining the total of two groups of physical objects. An ML/EL Support provides for MLLs’ full and complete participation in the whole-class discussion by encouraging multimodal instruction, stating, “Encourage students to use gestures, such as joining hands, when sharing descriptions to support visualization.” Activity 2 provides ample opportunities for MLLs to use and develop language around addition in the Instructional Routine Mix and Mingle. The MLD Resources for this lesson are for Activity 2, and they support MLLs by participating in Mix and Mingle where they work in partners to determine the total of two groups of physical objects. The student page of the MLD Resources contains printed sentence frames such as, “I have ____ cubes. My partner has ____ cubes. We have ____ cubes altogether,” alongside a bilingual English-Spanish word bank. These sentence frames mirror the printed sentence frames in the Student Edition, supporting MLLs with engaging in the exact same task as their peers. 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 encouraging MLLs to point or gesture to the manipulatives. In summary, the lessons’ embedded features such as the virtual manipulatives, the ML/EL Support, 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 physical 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 K-2 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 experienced previously 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 2, Unit 4, Addition and Subtraction on the Number Line, Lesson 11, students continue work from the previous lessons to develop fluency with adding and subtracting within 100 using strategies based on place value, properties of operations, and the relationship between the operations (2.NBT.5). The Warm-Up activates background knowledge from the previous lessons, inviting students to determine if addition equations with many addends are true or false using the Instructional Routine True or False? Students work towards independently demonstrating procedural skills and fluency during the mental math portion of the Instructional Routine. Activity 1 begins with the teacher activating background knowledge around the context of the real-world scenarios, supporting MLLs’ full and complete participation with drawn visuals of the context. Students work first independently, and then in partners to solve two problems involving addition and subtraction using number lines and equations. The MLD Resources for this lesson are for this portion of Activity 1, and they support MLLs in participating in the student-to-student discourse with the following sentence frames printed in the student page of the MLD Resources: “I drew ____ on my number line because… My partner drew ____ on their number line because…. The representations are different because…” 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 gesture to parts of the solution strategies. These supports help move MLLs towards independently demonstrating an understanding of procedural skills and fluency when solving addition and subtraction problems. The Activity concludes with the teacher facilitating a whole-class discussion where students share their number line representations. MLLs are supported in fully participating in the whole-class discussion through a Think-Pair-Share and through Math Language Routine [MLR] 7: Compare and Connect, where the teacher prompts students to notice how properties of operations and the relationship between addition and subtraction supported the students in using the number line representation to solve problems. Activity 2 continues with similar work, with MLLs’ full and complete participation supported through MLR8: Discussion Supports with sentence frames and an ML/EL Support encouraging MLLs to orally rehearse with a partner before sharing with the class. 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 K-2 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 Kindergarten, Unit 5, Make and Break Apart Numbers Within 10, Lesson 7, students solve routine application problems involving number composition and decomposition (K.OA.2). In the Warm-Up, students activate background knowledge around determining the total of two groups of objects through the Instructional Routine Which One Doesn’t Belong? In Activity 1, students apply that language and knowledge to represent and solve a routine application Put Together/Take Apart, Both Addends Unknown word problems involving a real-world scenario involving apples. The materials support MLLs’ understanding of the real-world scenario and the word problem through Math Language Routine [MLR] 6: Three Reads. Then, the teacher directs partners to work together to solve the application problem using self-selected solution strategies, stating, “Show your thinking using objects, drawings, numbers, or words.” When partners finish, the materials direct the teacher to facilitate a whole-class discussion to connect students’ self-selected solution strategies to an equation that begins with the sum. An ML/EL Support directs the teacher to restate and record MLLs’ thinking using precise mathematical language, linking language to concepts. Then, students engage in a Think-Pair-Share around what is similar and different about the solution strategies and answers. The materials further support MLLs by engaging in comparing solution strategies in this 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 as, “The answers are ____ [the same/different] because… This answer matches the story problem because…" 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 focus on crafting their explanation in their home language to encourage MLLs to point or gesture to the manipulatives. As the lesson continues, students continue to work with partners to engage with and connect several other solution strategies for solving routine application problems involving different real-world scenarios. 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 K-2 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 (MP1, MP3, MP6).” 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 1, Unit 2, Addition and Subtraction Story Problems, Lesson 12, Activity 1, where students make sense of situations in which they need to add or subtract to make the number of cubes in two connecting cube towers equal. Before partners work together using connecting cubes, the materials direct the teacher to read these directions aloud, “Use cubes to show how Kainoa and James could make their towers have an equal number of cubes.” Then, the materials direct the teacher to say the following slightly rephrased prompt: “For each problem, begin by building connecting cube towers that have the same number of cubes as the towers built by Kainoa and James.” The materials do not provide linguistic supports for MLLs to understand the task directions, including the meaning of the term equal as it connects to the teacher prompt using the phrase “...the same number of cubes.” As partners work, the materials do not offer scaffolds or linguistic supports for MLLs to engage in student-to-student discourse to monitor their progress in solving problems or to determine if their answer makes sense. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2.  

• In contrast, MLLs are supported in Grade 2, Unit 1, Working with Data and Solving Comparison Problems, Lesson 15, Activity 2, where students work in partners to match situations, tape diagrams, and equations to support them with making sense of problem types. Before matching, the teacher directs students to take turns reading each story word problem aloud, connecting reading and listening skills. The MLD Resources for this lesson are for Activity 2, and the Student Page provides support for MLLs to make sense of the problem situations through visuals of key vocabulary with the printed term in English and Spanish. After partners understand the information in the six word problems, they work together to match each word problem to a corresponding tape diagram and equation that represent the problem, discussing with their partner how they knew the cards matched. The materials support MLLs’ full and complete participation in this student-to-student discourse through MLR8: Discussion Supports—Pressing for Details, which contains sentence frames to help students understand a variety of solution strategies. After partners have completed all of their matches, they work together to choose one word problem and write to describe how they knew the tape diagram and equation represents the situation. The Student Page of the MLD Resources features sentence frames to support MLLs with the productive language demands of the written descriptions. The Activity concludes with a whole-class discussion in which students reflect on the problem-solving process and deepen their understanding of problem types through teacher prompts such as, “Which tape diagram matches the story problem? How do you know?” The MLD Resources support MLLs’ full and complete participation in the whole-class discussion with linguistic supports that correspond to these teacher prompts. These linguistic supports are 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 them with making sense of the matches. 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 K-2 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 Kindergarten, Unit 1, Math in Our World, Lesson 12, Activity 2, where students reason abstractly and quantitatively when they create equivalent groups using objects and drawings. The Activity begins with the teacher introducing the task, stating, “I am planning an activity for our class and I would like to make sure there are enough math tools for everyone.” The materials direct partners to work together to ensure each student on their printed Student Edition has one pattern block, and then to use the pattern blocks or draw pictures to show their thinking. Then, the teacher asks partners, “Are there enough? How do you know?” There are no linguistic supports for MLLs to fully participate in the student-to-student discourse in which they determine when students have the same quantity and explain how they know when to stop counting. The Activity concludes with a whole-class discussion in which the teacher calls upon students to share various solution strategies. The materials direct the teacher to facilitate a Think-Pair-Share in which partners discuss how they knew when to stop getting pattern blocks to share with the students. An ML/EL Support suggests that the teacher leverage the Think-Pair-Share as an opportunity for MLLs to orally rehearse before contributing to the whole-class discussion. While this suggestion supports MLLs with participating in the whole-class discussion, it does not provide the linguistic scaffolds necessary for MLLs to orally share how they determined when students have the same quantity, nor to explain how they knew when to stop counting. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in Grade 2, Unit 4, Addition and Subtraction on the Number Line, Lesson 10, where students reason abstractly and quantitatively when they use subtraction strategies within 100 and represent their strategies on number lines. The Warm-Up features a Number Talk which activates background knowledge on specific subtraction strategies based on the size of the subtrahend. In Activity 1, students work first independently, then in partners, to find the value of three different subtraction expressions using self-selected solution strategies. The teacher directs partners to compare solution strategies, and specifically number line representations, when each student has finished finding the value of each expression. 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 interpret and compare number line representations of subtraction strategies. Specifically, the MLD Resources offer teacher prompts such as, “What is similar about the way these subtraction strategies are represented on the number line? What is different?” and “Where did you start? Where did your partner start?” 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. 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 Activity concludes with the teacher inviting students to Think-Pair-Share about the prompt, “What conjectures can you make about representing subtraction on a number line?” An ML/EL Support provides MLLs with full and complete participation in explaining how each step reflects the quantities and operations in the expressions, stating, “If possible, pair students with different levels of English language proficiency together as they make conjectures. This will provide a structured opportunity for MLLs to interact with and receive feedback from their peers with varied language backgrounds.” Finally, the teacher facilitates a whole-class discussion to support students with understanding the relationship between the number line representations and the expressions, which the materials state is structured using MLR8: Discussion Supports - Make a Conjecture. The materials direct the teacher to record students’ conjectures on chart paper, prompting the class to consider if each conjecture is always true or not. 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 K-2 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 2, Unit 7, Adding and Subtracting within 1,000, Lesson 5, where students construct viable arguments when adding within 1,000 using self-selected solution strategies. The materials direct partners to work collaboratively using base-ten blocks to calculate the value of four addition expressions. The materials do not provide linguistic supports for MLLs to fully participate in the student-to-student discourse in which they explain their self-selected solution strategies. After calculating the sums, the materials direct students to explain to their partner how they found the value of two of the addition expressions. There are no linguistic supports for MLLs to create their explanations nor to critique their partner’s explanations. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2. 

• In contrast, MLLs are supported in Grade 2, Unit 2, Adding and Subtracting Within 100, Lesson 20, Activity 1, where students construct arguments based on their conceptual understanding of interpreting and solving one- and two-step story problems. Students work independently to use their own language to justify in writing whether student work samples show a correct solution for a two-step story problem where only 2 values are given. The materials support MLLs with understanding the functional language demands of the independent task through a teacher prompt that provides the appositive “... look closely at…” for the language function “analyze.” The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with the written language demands of creating a justification and critiquing the reasoning of others. Specifically, the MLD Resources offer teacher prompts such as, “Is there an unknown in the story problem? What is it?” and “How does that help you determine who is correct?” 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. 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 Activity concludes with the teacher facilitating a whole-class discussion leveraging MLR8: Discussion Supports—Pressing for Details, which supports MLLs with developing the language needed to engage with MP3 through the teacher prompting students to add details to their justifications. The materials further support MLLs’ full and complete participation in the whole-class discussion through an ML/EL Support that states, “Provide students with wait time to formulate and rehearse a response 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 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 K-2 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 2, Unit 3, Measuring Length, Lesson 11, Activity 2, where students work independently to solve and compare one- and two-step problems involving length within 100. While the real-world scenario is familiar to students because it is continued from the word problems in Activity 1, there are no linguistic supports for MLLs to read, make sense of, represent, or solve the two new word problems in Activity 2. Then, the materials direct students to represent and solve the final word problem with a partner. There are no linguistic supports provided for the student-to-student discourse involving using equations, diagrams, and strategies to determine and compare unknown values. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. Activity 2 concludes with a whole-class discussion where the teacher outlines what is known and unknown from the last word problem. MLLs are supported in participating in the whole-class discussion around identifying the important information in the problem through MLR8: Discussion Supports–Sentence Frames, which provides two sentence frames structured to answer the teacher prompts. In summary, throughout this lesson, MLLs are partially supported in using and developing the language needed to engage in MP4. 

• In contrast, MLLs are supported in Kindergarten, Unit 3, Flat Shapes All Around Us, Lesson 11, Activity 1, where students find, describe, and draw shapes they notice at school to connect geometry to real-life objects. Activity 1 begins with the teacher activating background knowledge from previous lessons around the language used to describe shapes based on their attributes, referencing previously co-created anchor charts. Then, students model with mathematics as they apply this language when identifying, drawing, and describing shapes they observe in their environment. The MLD Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs when working with a partner to find shapes in their environment. Specifically, the MLD Resources offer teacher prompts such as, “How can you describe the object you found?” and “How many corners does it have? Sides?” 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 partners search for and describe shapes in their environment, the materials direct the teacher to facilitate the Think-Pair-Share routine for students to discuss what they notice about shapes in a photograph of a school cafeteria. MLLs are fully supported in participating in the student-to-student discourse with MLR 8: Discussion Supports–Pressing for Details, which features teacher prompts to guide students to use precise mathematical language when describing shapes. MLLs are future supported through an ML/EL Support, encouraging multimodal instruction with the teacher pointing and gesturing to relevant parts of the shapes as students share their thinking. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP4 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 ML/EL Supports and the MLD Resources do not support the language needed for MLLs to engage with MP4.

The instructional materials reviewed for Grades K-2 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 Kindergarten, Unit 6, Numbers 0–20, Lesson 10, Activity 2, where students make equations true by determining missing parts. Continuing from Activity 1 where students make equations true with the support of ten frames, Activity 2 invites students to work in partners to make equations true by determining missing parts without the support of ten frames pre-printed for students. Instead, the materials direct partners that they can use objects, drawings, or ten frames to help them, then to explain to their partner how they know each equation is true. There are no linguistic supports for the student-to-student discourse in which MLLs work with their partner to strategically select a tool and orally justify their tool selection and answer. Then, the materials invite the teacher to facilitate the Mix and Mingle routine in which partners join with another partner pair and explain how each pair determined how to make true equations. The materials do not provide the linguistic scaffolds necessary for MLLs to orally share how they used their self-selected tools to make true equations. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in Grade 2, Unit 2, Adding and Subtracting Within 100, Lesson 10, Activity 1, where students choose and use appropriate tools such as place value mats and base-ten blocks to represent addition and subtraction strategies, explain what they notice about different approaches, and connect concrete models and diagrams to equations that show their reasoning. Activity 1 begins with the teacher reading two word problems aloud while students follow along, linking the listening and reading language domains. Then, the materials direct students to solve the two word problems independently, self-selecting which representation they will use to solve each problem. The materials also direct the teacher to make available place value mats and base-ten blocks for students to self-select as they work. MLLs are fully supported in completing Problem 3 which asks students to independently write to describe what they notice about each strategy in Problems 1 and 2. The MLR Resources for this lesson are for Activity 1, and they provide teacher guidance to support MLLs with the language demands of the independent writing task. Specifically, the MLD Resources offer teacher prompts such as, “What do you know about Jada’s and Shawn’s strategies? What is similar? What is different?” and “Why does each strategy get the same answer?” The Student Page of the MLD Resources features corresponding sentence frames to support MLLs with the productive language demands of Problem 3. 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 descriptions. Additionally, MLLs are further supported with the written language demands of Problem 3 through Math Language Routine 1: Stronger and Clearer Each Time; the lesson facilitation in the Launch directs teachers to partner students, have them share their written responses, and encourage listeners to ask clarifying questions using provided sentence stems. Furthermore, an ML/EL Support suggests that teachers further support MLLs by displaying yes/no questions that support MLLs while making sense of the steps of each strategy in Problems 1 and 2, helping them compare and contrast those steps in the written task of Problem 3. 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 K-2 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 1, Unit 6, Measuring Lengths up to 120 Length Units, Lesson 5, Activity 2, where students attend to precision as they apply their understanding of measuring length accurately to measure the lengths of objects using paper clips. The Activity begins with the teacher introducing the task, stating, “Measure and record the length of each picnic item on your own. Then, you will compare your measurements with your partner. If you disagree about a length, work together to measure again.” There are no linguistic supports for MLLs to fully participate in the student-to-student discourse in which they attend to precision as they measure objects without gaps or overlaps. After measuring four objects and comparing the measurements, the materials direct students to write how they know the measurement of one object is correct. The materials do not provide linguistic support for MLLs to formulate a clear explanation or to use and apply precise language in their written explanations. The Activity concludes with a whole-class discussion in which the teacher calls upon students to share their written explanations, with no linguistic supports for MLLs to fully participate to explain how they knew their measurement was correct. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in participating in Grade 1, Unit 5, Adding Within 100, Lesson 12, Activity 2, where students attend to precision as they add two digit numbers using different strategies and explain their strategy choices. In this independent Activity, students find the value of three addition expressions using self-selected strategies. Then, they independently analyze two of the problems they solved and construct a written response to explain their strategy choices. An ML/EL Support provides MLLs with an initial entry point into the task, stating, “Strategically pair students with partners who speak the same primary language. Allow students to share and receive feedback in their primary language before sharing in English.” The MLD Resources for this lesson are for Activity 2, and they provide teacher guidance to support MLLs with the language demands of formulating a clear written explanation using grade-level appropriate vocabulary. Specifically, the MLD Resources offer teacher prompts such as, “Did you use the same strategy to solve Problems 4 and 5? Why or why not?” and “What did you do first? Next?” 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 sequencing language, key vocabulary with visuals and terms written in English and Spanish, and a bilingual English-Spanish word bank. Additionally, after students construct their written responses, the lesson facilitation directs teachers to implement MLR1: Stronger and Clearer Each Time in which students give each other feedback by using sentence starters such as, “What do you mean by…?” and “Can you tell me more about…?” The Activity concludes with a whole-class discussion where the teacher facilitates a Think-Pair-Share for partners to discuss how they selected efficient strategies. 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 K-2 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 encouraging students to 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 prior knowledge 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 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 2, Unit 1, Working with Data and Solving Comparison Problems, Lesson 2, Activity 1, where students play a game in which they use patterns to generalize whether adding or subtracting two numbers will produce a target value. In the Launch, the teacher demonstrates how to play the game before releasing partners to play. The materials do not provide linguistic supports for MLLs to understand the game directions. While partners play the game, the materials direct the teacher to prompt students to consider looking for structures within mathematical expressions while playing the game: “How can you use what you know about addition to find the sum of the two numbers?” There are no linguistic supports for MLLs to fully participate in the student-to-student discourse where they engage with MP7 during the gameplay. The Activity concludes with the teacher facilitating a Think-Pair-Share that engages students with looking for patterns or structures to make generalizations with the prompts, “What do you notice about the expressions? Why do all the expressions have the same value?” The materials do not provide supports to ensure MLLs’ full and complete participation in the student-to-student and whole-class discourse.

• In contrast, MLLs are supported in Grade 2, Unit 5, Numbers to 1,000, Lesson 6, Activity 2, where students make different three-digit numbers using the same digits and represent each number in standard form and expanded form. In Launch, the teacher reads the task directions and problems aloud while students follow along, linking the listening and reading language domains. Students then work in partners to make as many three-digit numbers as they can with randomly drawn number cards, recording the numbers in standard form and expanded form in the Student Edition. MLLs are fully supported in participating in the student-to-student discourse where they apply prior knowledge of place value to interpret the same value represented in different ways through both MLR8: Discussion Supports–Sentence Frames and an ML/EL Support. MLR8 suggests that the teacher provide a sentence frame to support partner discourse related to looking for and explaining the structure within mathematical representations: “I noticed ____ in standard form, so I wrote ____ in expanded form.” The ML/EL Support suggests the teacher provide MLLs with wait time and an opportunity for oral rehearsal before MLLs share their thinking with the whole class. Additionally, 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 MLLs to see and decompose "complicated" into "simpler" things, such as, “How can you represent the number in expanded form?” and “What is the value of each digit? How many hundreds are there? Tens? Ones?” 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 complete 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 K-2 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 as supporting 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 Kindergarten, Unit 4, Understanding Addition and Subtraction, Lesson 19, Activity 2, where students look for and express regularity in repeated reasoning as they determine the values of subtraction expressions with 0 or 1 and identify patterns in the results. Students work first independently, and then in partners to find and compare the value of six subtraction expressions that are paired with visuals quantifying both the minuend and the subtrahend. Then, the materials direct partners to discuss what they notice about adding or subtracting 0 or 1 that is always true. The Student Edition provides the sentence frames, “I notice____. I wonder ____.” While the sentence frames support MLLs with the productive language needed to participate in the student-to-student discourse, they do not provide linguistic scaffolds for MLLs to use and develop language related to MP8, such as recognizing the consistent patterns of subtracting 0 and subtracting 1, or articulating general rules to justify their conclusions. The Activity concludes with a whole-class discussion in which the teacher facilitates a Think-Pair-Share about what is always true about subtracting 0 and 1. Similarly, while the Think-Pair-Share provides MLLs with an opportunity to engage in student-to-student discourse, it does not provide the linguistic scaffolds for MLLs to use and develop the language related to noticing repeated calculations nor to explain a general rule. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1. 

• In contrast, MLLs are supported in Grade 2, Unit 2, Adding and Subtracting Within 100, Lesson 8, Activity 2, where students look for and express regularity in repeated reasoning when they analyze subtraction expressions and recognize the consistent pattern of when decomposition of a ten is required. The Activity begins with the teacher facilitating a whole-class discussion that the materials state is based off of MLR8: Discussion Support - Make a Conjecture. Here, the materials support MLLs with understanding the functional language demands of making a conjecture through this teacher prompt with direct instruction about conjectures: “Now, you will make a conjecture. A conjecture is a statement you believe is true based on the current information you have. Mathematicians make conjectures and then test them to see if they are always true.” Then, the teacher facilitates a Think-Pair-Share about what conjectures students could make about when they would need to decompose a ten to subtract. The materials provide additional language support by directing the teacher to record students’ conjectures on chart paper, supporting MLLs by pairing spoken and written English. After this whole-class discussion where students make a general rule for decomposition in subtraction, partners work together to test and revise the general rule they made by finding the value of three subtraction expressions. The MLD Resources for this lesson are for Activity 2, and they provide teacher guidance to support MLLs with testing and revising the general rule. Specifically, the MLD Resources offer teacher prompts such as, “I needed to decompose a ten because...” and “I did not need to decompose a ten because…” 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 describing the general rule, the key vocabulary term decompose with visuals and terms written in English and Spanish, 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.