K-2nd Grade - Multilingual Learner Supports

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 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. 

The instructional materials reviewed for Grades K-2 of Amplify Desmos Math partially meet expectations for intentionally developing language in ways valued by disciplinary practices over time, across lessons, units, and throughout the course. 

The Math Language Development section of each grade's Course Overview outlines the material’s belief in the interdependence of content, language, and practices. It states, “At Amplify Desmos math, we acknowledge that there is a strong interconnection between mathematical content, practices, and language. We believe that developing mathematical language is critical for all learners, while recognizing and supporting the unique needs of Multilingual/English Learners. Our approach to math language development focuses on when, how and why students are using language to make sense of and share their mathematical ideas. Every lesson in Amplify Desmos math includes opportunities for all students to develop mathematical language as they experience the content, while providing intentional support for Multilingual/English Learners. We purposefully progress language throughout the units by cultivating students’ language and supporting students in making their arguments and explanations stronger, clearer, and more precise as they progress from lesson to lesson.”  

The materials show partial evidence of intentional disciplinary language development aligned to mathematical content and practices. Disciplinary language development consists of functional language development alongside mathematical vocabulary development. Overall, the materials provide some, but not comprehensive, support for the ongoing development of disciplinary language. While they promote language-rich classrooms and consistently build mathematical vocabulary, support for functional language development is inconsistent and lacks clear progression. The materials lack a clearly articulated, longitudinal plan for developing language as a disciplinary practice beyond moments embedded within mathematical content or practices. 

The materials provide opportunities for, and encourage, students to use informal and everyday ways of communicating; the lesson design provides opportunities for teachers to connect students’ informal language with more precise mathematical language. However, the materials do not provide a plan or explicit guidance for teachers to bridge between students’ informal and everyday ways of communicating and more precise mathematical ways of communicating. For example, in the Navigating This Program section of each grade’s Course Overview, the materials describe their structured approach to problem-based learning, which features lessons that begin with a Warm-Up, and then engage students with one to two instructional Activities, which feature Launch, Monitor, and Connect sections. Each lesson ends with a Synthesis and a Show What You Know moment. This lesson design supports students’ use of informal and everyday ways of communicating within Warm-Ups that feature Mathematical Language Routines or Instructional Routines like Notice and Wonder, which invite students to use everyday language to describe what they notice and wonder about a mathematical situation. Within the lesson, Activities encourage disciplinary language usage within partner, small-group, and whole-group discourse. Lessons close with a Synthesis, which provides an opportunity for students to summarize mathematical learning by either listening to or orally practicing precise language usage. Therefore, the materials support students in using informal and transitioning to more formal language usage, but the materials do not provide a plan or explicit guidance for teachers to bridge the two. 

The instructional materials reviewed for Grades K-2 of Amplify Desmos Math partially meet the expectations for including language goals/objectives at the lesson level that are clear, measurable, and support language development in service of content learning. Most lessons include Language Goals that are tied directly to the content goals and are clearly focused on at least one domain of language and one language function. However, the materials inconsistently feature Language Goals at the lesson level that are measurable and contain language structures.

The materials provide language and content goals under the heading of Today’s Goals, and the Language Goals are clearly labeled. For example, in Grade 1, Unit 7, Geometry & Time, Lesson 1, the materials list the Language Goal as, “Describe similarities between different three dimensional shapes. (Speaking and Listening)” This Language Goal is clear and tied directly to the content objective of, "Identify objects that look like three-dimensional shapes." The Language Goal clearly lists the language domains of speaking and listening, and includes the language function describe. However, this Language Goal does not feature language structures, and there is no guidance for assessing the quality, specificity, or complexity of MLLs’ language usage when they are describing similarities and differences in three dimensional shapes. 

Furthermore, not all lessons contain labeled Language Goals. In some lessons, Today’s Goals feature content goals without labeled Language Goals.  The content goals do not provide the same level of detail about language usage and development as the labeled Language Goals do. For example, in Kindergarten, Unit 4, Understanding Addition and Subtraction, Lesson 15, Today’s Goals are, “Interpret the meaning of the plus and minus signs. Represent Add To, Result Unknown and Take From, Result Unknown story problems in more than 1 way and solve them.” There are no Language Goals listed for this lesson. In this grade band, approximately ten lessons do not include Language Goals. For these lessons, the Math Language Development Resource includes an overview of the language demands of one specific activity in the lesson. For example, for Lesson 15, the Math Language Development Resource states the following bullet points outlining the language usage for Activity 1 Exploring Expressions, “Support discussions as students work toward the Goal: Represent Add To, Result Unknown and Take From, Result Unknown story problems in more than 1 way and solve them. Interpret and communicate language using the language from the activity, such as expression, add, subtract.” While these statements provide teachers with an overview of MLLs’ language usage during this specific activity, it does not contain the same level of detail about language usage and development as the lesson-level Language Goals.

These examples explicitly demonstrate that the materials include lesson-level Learning Goals that describe the language-rich mathematical tasks. They partially meet the expectation that goals are included in every lesson and are consistently measurable and supported with explicit scaffolds for language structure and form.

The instructional materials reviewed for Grades K-2 of Amplify Desmos Math partially meet the expectations of the guiding teachers on how to match students with language supports, progressing along a continuum, and to be responsive to students’ current language development in relation to the content. The materials provide language support at varying language proficiency levels. However, the materials contain minimal teacher guidance on how to match students with language supports, progressing along a continuum.

In the Math Language Development Resource, the materials provide guidance for one activity in each lesson by three language proficiency levels—Emerging, Expanding, and Bridging. Included in each language proficiency level are examples of how students may respond, ranging from gestures or single words to longer, complete sentences using academic language. This section advises teachers to, "consider using the sample responses in each column to understand ways that students at different proficiency levels may respond to questions." These resources guide teachers on how to be responsive to students’ current language development while maintaining focus on mathematical content.

In the Math Language Development Resources Overview, the materials provide minimal, course-level guidance to teachers on how to match which level of support may be appropriate for individual students. In the Guidance by Proficiency Level section, the materials state, “Emerging: Look for students to respond with gestures or single words as they begin to understand and use mathematical and contextual vocabulary. Expanding: Look for students to respond using phrases or simple, complete sentences as they develop their English language skills and learn a greater variety of vocabulary and language structures. Bridging: Look for students to respond in longer, complete sentences as they continue developing and applying their English language skills across various contexts, including comprehension and production of content-area texts.” This teacher guidance describes what teachers could look for in how students may typically respond by English language proficiency level. However, this teacher guidance does not provide teachers with lesson-level details about how to match students with language supports considering MLLs’ mathematical knowledge and language assets within specific tasks (e.g., cue teachers to observe, listen, and gather information about students’ current understandings and proficiencies).

Additionally, the materials do not provide teacher guidance on how to adjust supports over time as students develop language proficiency. As a result, while the presence of differentiated supports may help MLLs access content, the lack of instructional guidance limits their effective use.

The instructional materials reviewed for Grades K-2 of Amplify Desmos Math partially meet the expectation of including guidance for intentional and flexible grouping structures for MLLs to ensure equitable participation. The materials provide some guidance for intentional and flexible grouping structures for MLLs but lack guidance to ensure equitable participation for MLLs in group work.

In the Unit Overview materials for each grade, the resource titled, Routine Facilitation Guide contains grouping suggestions in Multilingual/English Learners [ML/EL] Supports for three of the 22 routines: Stories & Questions (a Kindergarten only routine), Think, Pair & Share, and Math Language Routine (MLR) 5: Co-Craft Questions. Each of these ML/EL Supports invites teachers to intentionally pair MLLs who speak the same home language to leverage home language usage.

Periodically within lessons, the materials provide very limited guidance for intentional or flexible grouping structures to support MLLs. For example, in Grade 2, Unit 6, Geometry and Time, the only instance appears in Lesson 8 within an ML/EL Support, which suggests: “If possible, pair students with different levels of English language proficiency together as they make conjectures. This will provide a structured opportunity for Multilingual Learners to interact with and receive feedback from their peers with varied language backgrounds.” While this ML/EL Support acknowledges the value of peer interaction, it is isolated to a single lesson and does not offer broader guidance on grouping practices across the unit. 

In summary, the materials provide limited and inconsistent guidance on intentional and flexible grouping for MLLs, with some suggestions in unit overview materials and in isolated lesson ML/EL Supports. However, they fall short of ensuring equitable participation for MLLs in group work across units.

The instructional materials reviewed for Grade K-2 of Amplify Desmos Math partially meet expectations for providing guidance to encourage teachers to draw upon student home language to facilitate learning. The materials provide guidance to encourage teachers to draw upon the home language to facilitate learning, but the in-lesson guidance is sporadic and inconsistent.

The Multilingual Learner Program Models resource contains teacher-facing guidance on how to integrate Spanish into classroom instruction in various program contexts for MLLs (see report 3.1.MLL-4 for more information). This resource states, “For Spanish-speaking and Spanish-learning students, all Amplify Desmos Math instructional materials and assessments support transadaptation and are completely interchangeable between the Spanish and English editions. Teachers providing instruction in one language can change to or reference the materials in the other language at any point as needed.” The materials emphasize they are currently focused on the Spanish language for biliteracy. This resource is found on the digital platform in the overview for each grade level, meaning this guidance remains broad and program-level rather than lesson-specific. The suggestions are confined to this overview document and do not appear within individual lessons across the curriculum. 

As stated in the report for 3.1.MLL-1, the Math Language Development Resource includes a modified student page for the activity, which includes visuals annotated in English and Spanish, sentence frames in English and Spanish, and a word bank in English and Spanish to use within the sentence frames. The Math Language Development Resources also periodically contain a table of Spanish-English cognates. This resource is not integrated into lessons; it is available digitally, located within the Paper Resources section of each lesson and in print as a separate blackline masters book. 

Within lessons, periodic ML/EL Supports contain suggestions for teachers to leverage home language use. For example, in Grade 1, Unit 5, Adding within 100, Lesson 10, Activity 2, the ML/EL Support states, “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." These ML/EL Supports appear infrequently and sporadically within lessons.

The materials do not include guidance on how teachers can garner home language information that will aid in learning, such as the family’s preferred language of communication, schooling experiences in other languages, literacy abilities in other languages, and previous exposure to academic or everyday English. 

In summary, the materials provide sporadic and inconsistent guidance for teachers to leverage multilingualism as an asset or to strategically use a variety of home languages to help MLLs negotiate mathematical text in English, with some suggestions in unit overview materials and some in isolated lesson ML/EL Supports. Additionally, they fall short of including guidance on how teachers can garner home language information that will aid in learning.