6th to 8th Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades 6-8 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. 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 Facilitate Guides for 6-A1 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.” While there are other Instructional Routines and Math Language Routines 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 6, Unit 2, Introducing Ratios, Lesson 7, Activity 2, where students determine the least common multiple of two numbers through annotating a virtual hundreds grid. The materials invite students to apply solution strategies independently and check with their partner after determining the least common multiple of each set of numbers. There are no language supports for MLLs to make sense of and apply solution strategies independently.  No supports are provided for MLLs to fully participate in the partner discussion checking their answers. The Activity continues with the teacher presenting a real-world scenario involving desserts, where partners work together to apply the concept of least common multiple. The materials invite the teacher to support partners with prompts such as, “How does this situation compare to the Warm Up’s situation?” The materials do not provide linguistic support for MLLs to fully participate in the partner discussion of analyzing and making sense of the problem as it relates to finding the least common multiple. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 1.  

• In contrast, MLLs are supported in Grade 6, Unit 5, Decimal Arithmetic, Lesson 5, Activity 1, where students use area and fraction multiplication to make sense of multiplying decimals with one non-zero digit. After participating in the Warm-Up where teachers activate background knowledge about calculating area of rectangles with decimal numbers as side lengths, students use area models to decide whether a multiplication equation with decimal numbers is true. The materials direct partners to use the area model to show or explain why the product makes sense, and to type their response in the digital platform. The ML/EL Support offers a suggested language support for MLLs engaging in the writing portion of this activity, stating, “Invite students to talk through their thinking with a partner before writing it down.” This oral rehearsal supports MLLs with full engagement in the task by integrating speaking and writing, providing a low-risk environment to make sense of the product before constructing a written response. The Activity continues with partners solving new multiplication expressions given corresponding area models, using a variety of solution strategies and discussing similarities and differences in their solution strategies using the area models as a reference. The Activity concludes with partners examining a fictional student, Jayden’s, solution strategy, where the materials direct students to show or explain how they would use the solution strategy to solve a new multiplication 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 sequence their explanation. Specifically, the MLD Resources offer teacher prompts such as, “What was Jayden’s first step? Second step? Third step?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language to encouraging MLLs to use the provided sentence frames and starters. 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 6-8 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 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. There are Instructional Routines and Math Language Routines that support the language needed to engage in MP2, but the materials do not call out any specific routine as supporting MP2. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP2. Additionally, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 8, Unit 4, Linear Equations and Linear Systems, Lesson 8, Activity 1, where students reason abstractly and quantitatively to generate expressions representing the position of two vehicles and determine when they will meet. First, students engage with a distance and time table, describing how it connects with an animation of vehicles moving on a road from the Warm-Up. The teacher asks students, “How can we see the constant rate in the table?” and “What will it look like in the table when the vehicles meet?” These prompts engage students with MP2 by asking students to attend to the meaning of quantities. The materials do not provide linguistic supports for MLLs to fully and completely participate in the whole-class discussion. Then, students work individually to determine missing values in the table using self-selected strategies, on paper or by entering them into the digital platform. Then, the Activity concludes with a whole-class discussion where the teacher discusses the variety of students’ self-selected strategies. The materials do not provide linguistic supports for MLLs to fully and completely participate in choosing and communicating about their self-selected strategy, or to participate in the whole-class discussion. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2. 

• In contrast, MLLs are supported in Grade 7, Unit 4, Proportional Relationships and Percentages, Lesson 2, where students solve problems involving percent increase and percent decrease using tape diagrams and tables. The Warm-Up activates background knowledge about tape diagrams, and the language needed to discuss them through the instructional routine, Which One Doesn’t Belong? The ML/EL Support suggests that the teacher invites MLLs to orally rehearse their ideas before sharing whole-class, supporting MLLs’ full and complete participation in the task. In Activity 2, students engage in a card sort activity where students match word problems to tape diagrams, working with a partner to come to consensus on whether situations represent percent increase or decrease. The materials direct the teacher to highlight language that helps students distinguish between equations for percent increase and decrease. The MLD Resources for this lesson are for Activity 2, and they provide teacher guidance to support MLLs with using and developing the language needed to distinguish between percent increase and decrease. Specifically, the MLD Resources offer teacher prompts such as, “Which tape diagram shows an increase? A decrease?” and “In this situation, is there more or less fruit than last year?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from leveraging home language to encouraging MLLs to use the provided sentence frames and starters, to directing MLLs to annotate words or numbers that suggest a percent increase or decrease. 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 6-8 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. 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 Facilitate Guides for 6-A1 describes how the Instructional Routine Decide and Defend supports MP3: “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).” While there are other Instructional Routines and Math Language Routines 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 6, Unit 2, Introducing Ratios, Lesson 1, Activity 1, where students work in partners to develop ratio thinking to orally justify reasoning about a real-world scenario involving pizzas and pizza toppings. The Activity begins with a digital interactive which activates background knowledge about pizzas and pizza toppings. Then, partners create their own pizzas and apply ratio thinking as they calculate the amount of different toppings, in ounces, for various numbers of additional pizzas. Partners justify, orally and in writing, the oven temperature to bake four pizzas. The materials do not provide language supports for MLLs to fully participate in the partner discussion and written response. The Activity concludes with a whole-class discussion in which the teacher invites students to justify ratio reasoning around the amount of toppings when doubling the number of pizzas. The materials do not provide language supports for MLLs to fully participate in this whole-group discussion. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 2.  

• In contrast, MLLs are supported in Grade 8, Unit 5, Functions and Volume, Lesson 14, Activity 3, where partners calculate the volume of popcorn containers and justify their reasoning. As partners are working, the ML/EL Support suggests that teachers provide the following sentence frame to support MLLs with explaining their choice orally or in writing: “The ___ is the better deal because ___.” Then, the class engages with the Decide and Defend routine in which the teacher invites students who made different choices to use reasoning to convince their classmates. The MLD Resources for this lesson are for Activity 3, and they provide teacher guidance to support MLLs with using and developing the language needed to create their own conjectures orally and in writing using diagrams and numbers. Specifically, the MLD Resources offer a graphic organizer to support MLLs with organizing their thinking and calculations, and teacher prompts such as, “What is the radius for each container?” These prompts are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from annotating the terms, diameter and height, on the diagram, supporting MLLs in applying the use of additional sentence frames with the bilingual English-Spanish word bank, and orally rehearsing with a partner before putting their arguments in writing. 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 6-8 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 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. There are Instructional Routines and Math Language Routines that support the language needed to engage in MP4, but the materials do not designate any specific routine as supporting MP4. This lack of explicit teacher guidance reduces clarity of how the routines support MLLs’ full and complete participation in MP4. Additionally, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 8, Unit 5, Functions and Volume, Lesson 6, where students draw graphs of functions based on videos of real-world scenarios and make sense of different strategies to support graphing functions that represent those events. In Activity 2, students watch a real-world video of water being poured into a bowl, and then they engage in the Notice and Wonder routine to help them make sense of the scenario and identify the important information needed to construct a graph that models the situation. Then, the teacher directs partners to sketch a graph representing the relationship between the volume of water in the bowl and time, requiring students to create a mathematical model of the situation. The ML/EL Support suggests that teachers encourage MLLs to paraphrase their partner’s ideas, yet the ML/EL Support does not offer clear, explicit guidance to support MLLs with this paraphrasing. Also, the ML/EL Support does not offer a suggestion to support the language needed to engage with MP4, such as describing how their graph represents the scenario or explaining what each part of the graph means in the context of the video. The materials tell the teacher to monitor for students attending to specific estimates of water volume at different time points in the graph, yet the materials do not offer language supports for MLLs to produce the language needed to identify important information from the video. The activity concludes with the teacher facilitating a whole-class discussion to support students with making connections between the real-world scenario and the graph with prompts such as, “Why is the rate of change greater in the middle section of the graph?” The materials do not offer language supports for MLLs to fully participate in the whole-class discussion or to evaluate whether their graph is reasonable and revise their model, if needed. Additionally, the Math Language Development [MLD] Resources for this lesson are for Activity 3. 

• In contrast, MLLs are supported in Grade 6, Unit 2, Introducing Ratios, Lesson 10, where students analyze tables of equivalent ratios representing a real-world scenario, determining unknown values in a ratio table and deciding how they might use the ratio table to make decisions about the future. After the teacher activates background knowledge around the real-world scenario of preparing for a natural disaster, students calculate the recommended amount of specific items to hand on hand. In Activity 2, students work in small groups to make a poster that communicates their recommended number of items to prepare for a natural disaster. They describe how the mathematical model of the ratio table relates to the problem situation and use math they know to solve problems arising in everyday situations. The MLD Resources for this lesson are for Activity 2, and they provide teacher guidance to support MLLs with using and developing the language needed to analyze a worked example in which they check to see whether the answers make sense and determine if they need to change an answer. Specifically, the MLD Resources offer teacher prompts such as, “Does this seem like the right number of paper towel rolls? Why?” and “How would you change the recommended ratio to make this number more reasonable?” These prompts 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 use the English-Spanish word bank containing everyday terms such as bed and cotton balls. These everyday terms are featured within the lesson facilitation and slides with drawn visual images, providing linguistic support for MLLs. After small groups create their posters and participate in a Gallery Tour routine, the materials direct the teacher to facilitate Math Language Routine 7: Compare and Connect, where students analyze and compare each other’s strategies in a whole-class discussion. 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 6-8 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 tools through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when choosing appropriate tools, recognizing insights and limitations of different tools, and knowing how to use a variety of tools. There are Instructional Routines and Math Language Routines that support the language needed to engage in MP5, but the materials do not provide any specific routine as supporting MP5. This lack of explicit teacher guidance reduces clarity about how the routines support MLLs’ full and complete participation in MP5. Additionally, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 7, Unit 3, Measuring Circles, Lesson 3, Activity 1, where partners use three methods–using string, using tape, or by rolling–to measure round objects and determine the relationship between circumference and diameter. The Launch directs the teacher to demonstrate measuring a circular object using those three methods, which are supported by images for students. Then, the teacher facilitates a whole-class discussion which engages students with MP5 using the prompt, “Why might you get two different answers for the diameter of the same object?” The materials then direct the teacher to encourage students to consider the limitations and advantages of each method of measuring. The Math Language Development [MLD] Resources for this lesson are for this Activity, yet they do not provide linguistic support for MLLs to engage with the whole-class discussion around the limitations and advantages of each method of measuring. Instead, the MLD Resources focus linguistic supports on MLLs using and applying the concept of proportionality through describing the relationship of the circumference and diameter of a circle.

• In contrast, MLLs are supported in Grade 6, Unit 5, Decimal Arithmetic, Lesson 8, Activity 1, where partners use area models and vertical calculations to solve a decimal multiplication problem using place value reasoning. The Activity begins with a whole-class discussion where students examine two different solution strategies for multiplying decimal numbers using Math Language Routine [MLR] 7: Compare and Connect. MLR7 supports MLLs with using and applying the language needed to engage with MP5 by encouraging them to analyze and compare the two different solution strategies. The teacher prompts in this activity explicitly focus on strategic strategy use and the advantages and disadvantages of each strategy: “How are their strategies alike? How are they different?” and “What are some advantages of using Kwame’s strategy? Tiara’s strategy?”. The Activity closes with a whole-class discussion where the teacher asks students to consider how to decide which strategy to use. The MLD resources for this lesson are for Activity 1, and they further amplify language access by providing a Venn diagram, with sentence starters, for comparing the two solution strategies. The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from explaining the strategies in their home language to using the bilingual English-Spanish word bank to revise and refine their explanations in English from the sentence starters. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP5 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 MP5. 

The instructional materials reviewed for Grades 6-8 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 6, Unit 5, Decimal Arithmetic, Lesson 2, Activity 1, where the materials encourage students to read decimals aloud using place-value terms, such as “two hundred seventy-one thousandths.” ML/EL Support states, “Consider creating or reviewing an anchor chart about how to read decimals using place value to support their mathematical understanding. (Reading and Speaking)” However, the materials do not provide a model anchor chart or guidance about what to include in the anchor chart to support MLLs with participating fully in the task. Additionally, the Activity continues with the teacher facilitating the Decide and Defend routine in which students respond to prompts such as, “What evidence or language was most convincing to you?” The materials do not provide guidance on how teachers can support MLLs with using and applying the language from the anchor chart during the Decide and Defend routine in order to formulate a clear explanation. The Math Language Development [MLD] Resources for this lesson are for Activity 1, but they focus linguistic supports on justifying opinions, reading closely, and writing to describe, rather than on using and applying precise place value vocabulary. The materials do not provide specific guidance about how teachers can utilize the listed Spanish cognates, the bilingual English-Spanish word bank, or the suggested anchor chart to support MLLs with communicating using precise vocabulary during the Decide and Defend routine. 

• In contrast, MLLs are supported in participating in Grade 6, Unit 2, Introducing Ratios, Lesson 2, in which students are introduced to the term ratios and learn how to describe them. In the Warm-Up, students engage with multiplicative thinking during a Number Talk that’s structured with a string of four related multiplication expressions. In Activity 1, the materials activate background knowledge about a real-world scenario involving pizzas. The teacher prompts students to experience the concept of a ratio before introducing the term, stating, “The ratio of tomato to pepperoni is 3 to 4. What do you think the word ratio means?” The materials invite the teacher to co-create a class definition of the term ratio using students’ language and the glossary. The MLR Resources for this lesson are for Activity 1, and they center around supporting MLLs with fully and completely participating in co-creating a class definition. Specifically, the MLD Resources offer linguistic supports categorized into Emerging/Expanding/Bridging that involve MLLs completing a Frayer model graphic organizer to define the term ratio. The suggestions include inviting MLLs to work with a partner to write a definition in their own words in their home language to co-creating examples and non-examples of ratios. As the Activity progresses, the materials invite the teacher to listen for students using ratio language while working in partners to complete ratio problems. The ML/EL Support states, “Encourage students to paraphrase each other’s ideas to help make connections and incorporate ratio language.” The Activity ends with the teacher facilitating MLR2: Collect and Display in which the teacher guides students to refine the class definition of ratio using students’ language from throughout the activity. 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 6-8 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 6-A1 describes how the Instructional Routines Number Talks and Which One Doesn’t Belong 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.” While there are other Instructional Routines and Math Language Routines [MLRs] that support the language needed to engage in MP7, Number Talks and Which One Doesn’t Belong are the only routines the materials specify as supporting MP7. This 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 looking for and making use of structure through whole-group and student-to-student discourse. For example, the materials often direct the teacher to invite students to think-pair-share or turn and talk when looking for patterns or structures to solve problems, analyzing a problem to look for more than one approach, and decomposing complex problems into simpler, more manageable parts. However, the materials inconsistently offer clear linguistic supports for MLLs to fully and completely participate in the language-rich discussions. For example:

• MLLs are not fully supported in participating in Grade 7, Unit 2, Introducing Proportional Relationships, Lesson 7, Activity 1, where students decide if equations represent proportional relationships. Individually, students read two real-world scenarios, complete a table, write an equation, determine if the relationship is a proportional relationship, and write to explain their thinking. The materials suggest an optional application of MLR6: Three Reads, where students individually read each story three times with a different lens each time. While MLR6: Three Reads supports MLLs with independently making sense of the real-world scenario, the individual application of the MLR reduces opportunities for MLLs to make meaning of the relationship represented in the scenario through student-to-student discourse. Additionally, there are no language supports provided for students to determine if the relationship is a proportional relationship or to write to explain their thinking. As the Activity progresses, the teacher invites students to engage with MP7 with whole-group discourse focusing on prompts such as, “What does the constant of proportionality tell us about the story?” The materials do not provide linguistic support for MLLs to participate fully in the whole-group discussion where students look for and make use of structure to generalize which types of equations do or do not represent proportional relationships. Also, the Math Language Development [MLD] Resources for this lesson are for Activity 2.  

• In contrast, MLLs are supported in Grade 6, Unit 6, Expressions and Equations, Lesson 7, Activity 1, in which partners describe, compare, and make generalizations from various strategies for determining the number of border tiles for a square. Partners examine three fictional students’ strategies for counting and writing expressions representing the number of border tiles for a seven-by-seven square. The materials prompt students to discuss how each of their expressions are alike. To support MLLs with fully participating in the student-to-student discourse to notice when calculations are repeated, the materials direct the teacher to facilitate MLR7: Compare and Connect. This MLR engages MLLs with the language needed to engage with MP7, such as, “Where do we see the same information in Lucia’s expression? Kyrie’s? Manuel’s?” The MLD resources for this lesson are for Activity 1, and they further support MLLs’ full and complete participation with MP7 with sentence frames for comparing and making generalizations from the three solution strategies, such as, “I see _____ in both _____’s and ____’s work.” and “All three students used…” The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from gesturing to the perimeter of the square to using the bilingual English-Spanish word bank to fill in the sentence frames. The activity concludes with a whole-class discussion in which the teacher connects students’ generalizations from examining the three fictional students’ expressions to an expression with variables that represents the number of border tiles for any square. The MLD Resources paired with the language-rich lesson provide MLLs with full and complete participation in MP7 in this lesson. 

In summary, while language supports are present in the materials, they are not employed throughout the program.  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 MP7. 

The instructional materials reviewed for Grades 6-8 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 Grade 6, Unit 8, Describing Data, Lesson 7, where students are introduced to the concept of mean as the average. The Warm-Up activates background knowledge on a real-world scenario involving arcade games with an ML/EL Support that states, “Invite students to share what they know about arcade games and tickets to increase access to the task. (Reading and Listening)” Then, in Activity 1, partners engage with digital manipulatives to interpret the concept of mean as distributing a total equally among a group. The Activity concludes with the materials directing the teacher to facilitate a whole-class discussion, stating, “Discuss Ava’s strategy. Consider asking, ‘Why did Ava add all the tickets? Why did Ava divide by 4?’ Share captured strategies for calculating the mean. Invite students to describe a general strategy for determining the mean no matter how many tickets or players there are. (MP8)” The materials do not provide language supports for MLLs to recognize a general process for finding the mean and apply this reasoning across different data sets. The Math Language Development [MLD] Resources for this lesson are for Activity 1, but they focus linguistic supports on understanding the new term mean. The materials do not provide specific guidance about how teachers can support MLLs with creating, describing, or explaining the general process for finding the mean of a data set.

• In contrast, MLLs are supported in Grade 8, Unit 7, Exponents and Scientific Notation, Lesson 6, Activity 2, where students generalize the properties of exponents as they write rules for how exponents work. Small groups build off of a card sort from the Warm-Up to co-create their own rules for three situations involving exponents. MLLs are supported in co-creating exponent rules by the teacher facilitating MLR1: Stronger and Clearer Each Time, which states, “Consider continuing to use this routine by inviting students to write a first draft and use feedback to make their thinking stronger and clearer. (optional)” Although the MLR is listed as optional, the student print edition is formatted with locations for students’ first draft rule and second draft rule. As small groups co-create and co-write exponent rules, MLLs are supported with an ML/EL Support that states, “Encourage students to paraphrase each other’s ideas to help them make connections and incorporate vocabulary from the unit. (Speaking and Listening)” The MLD resources for this lesson are for Activity 2. They further support MLLs’ full and complete participation with sentence frames and a bilingual English-Spanish word bank to help MLLs co-create exponent rules, such as, “I think the rule might be….” and “The rule would be clearer if we…” The MLD Resources also provide teacher prompts that are paired with linguistic supports categorized into Emerging/Expanding/Bridging that range from color-coding similarities between examples and annotating patterns they notice. 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 6-8of 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 6-8 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  language function. However, the materials inconsistently feature language goals at the lesson level that are measurable and that contain language structures.

The materials provide language and content goals under the heading of Today’s Goals. In some lessons, Today’s Goals include references to language use or development, partially fulfilling the purpose of a language goal, even though the materials do not explicitly name them as language goals. For example, in Grade 7, Unit 7, Angles, Triangles, and Prisms, Lesson 5, the materials list Today’s Goals as, “Determine whether three segments will form a triangle. Justify whether three segments form a triangle. (Writing, Speaking, and Listening)” The second goal clearly lists the language domains of writing, speaking, and listening, and the language function justify. However, this 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 justifying whether three segments form a triangle.

Furthermore, not all lessons include Today’s Goals that address students’ language use and development. For example, in Grade 6, Unit 6, Expressions and Equations, Lesson 11, Today’s Goals states, “Evaluate numerical expressions that have an exponent and one or more other operations.” This goal does not contain information on what MLLs will be able to say, depict, and/or write when evaluating multistep numerical expressions. In this grade band, approximately ten lessons do not include Today’s goals with specific language information. 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 11, the Math Language Development Resource states the following bullet points outlining the language usage for Activity 2 Exponent Expressions, “Interpret (Reading and Listening) and communicate (Speaking and Writing) using the language from this activity, such as decide, defend, exponent.” While this statement provides 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 Today’s Goals that feature language information.

These examples explicitly demonstrate that while 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 6-8 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 do not guide teachers 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 6-8 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: Tell a Story, 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 7, Unit 8, Probability and Sampling, Lesson 10 contains an ML/EL Support that states, "Consider grouping students with different English language proficiency levels, so students can listen to and learn from their peers." 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 6-8 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 that 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 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 7, Unit 8, Probability and Sampling, Lesson 15, Activity 1, the ML/EL Support states, “Invite students to write their response to Problem 5 first in their primary language and then translate it to English during the second draft.” 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.