3rd-5th Grade - Multilingual Learner Supports

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in extensive work with grade-level problems to meet the full intent of grade-level standards. The materials provide some strategies for MLLs’ participation in grade-level problems, but they do not apply these supports consistently across units and sessions.  Also they are often not tailored to the specific language demands of individual sessions.

The materials provide authentic, real-world contexts that engage students in solving meaningful, language-rich mathematical tasks and encourage them to share their thinking orally, in writing, and through drawings or models. The materials provide language supports for MLLs’ participation in grade-level problems at two levels: in notes titled, MLL in the sessions and in Work Place guides, and embedded in session facilitation. In the resource titled, Supporting Language Development with Discussion Structures & Routines, the materials describe how math routines and discussion structures embedded in session facilitation support MLLs in using the language needed to participate in grade-level problems. It states, “Math routines and discussion structures are part of students’ everyday experience in the Bridges classroom. Bridges supports multilingual learners in developing the language skills and vocabulary needed to explain and justify their thinking, respond to the thinking of classmates, discover and describe patterns, and make conjectures and generalizations… These practices have been shown to support language development and deepen mathematical understanding.” Then, the resource lists the following discussion structures and math routines embedded within sessions, along with a description of the routine and why it is useful:

• Discussion structures: Think-Pair-Share, Noticing & Wondering, Open Strategy Sharing, Gallery Walk, Compare & Connect, What’s Best & Why?, Math Forums

• Math Routines: Choral Counting, Quick Images, Dot Talks, Would You Rather?, Same & Different, Which One Doesn’t Belong?, Guess My Rule, What Comes Next?, I Have, You Need, Number Talks, Number Strings, Problem Posing

While math routines and discussion structures provide support for MLLs by providing predictable, language-rich structures, the materials do not include educational teacher guidance to fully and completely support MLLs with accessing the mathematical content discussed in each math routine and discussion structure. 

In addition, the introduction to each grade level in the Teacher Edition contains two sections that outline how the materials support MLLs with participation in grade-level problems. The Community of Learners section outlines considerations for successfully developing a community of learners, including suggestions that support MLLs’ full and complete participation such as, “Encourage active engagement from all students. The Think-Pair-Share routine allows students to process ideas individually and rehearse their explanation with a partner before engaging in whole-group discussion.” The Language Supports section provides an explanation of the instructional approaches of the program for MLLs, including general recommendations to support math language development (see the report for 3e.MLL for details). These general recommendations are periodically found in MLL notes at point-of-use within session facilitation and Work Place guides. These notes are repetitive in nature, typically falling into one of these general recommendations: flexibly pairing MLLs to leverage home language usage, encouraging multimodal expression, providing clarifying questions and sentence frames and starters, and referencing the ABCs of Math Talk poster and the Word Resource Cards. The Work Place guides feature similar recommendations for each Work Place game, leaning more heavily on sentence frames and starters that are specific to the game. The teacher guidance for supporting students with authentically using the sentence frames and starters is brief and generic, suggesting that the teacher print the sentence frames and starters and make them available while students play the Work Place games. Across the MLL notes in both the session facilitation and the Work Place guides, the materials infrequently reference the ABCs of Math Talk poster and frequently reference the Word Resource Cards. This does not support MLLs’ full and complete participation. Within sessions, the MLL notes are found infrequently, and often remain general in nature and not specific to the task, which limits their impact on MLLs’ ability to access grade-level problems. Additionally, the placement of the MLL notes within sessions often does not correspond with the section of the session that directly addresses grade-level standards.

As a result, the linguistic access points that MLLs need with grade-level problems, such as intentional scaffolds for productive and receptive language, suggestions for structured academic discourse, amplification of language (such as explicit attention to morphology), and support for language functions, are inconsistently applied. MLLs may successfully play the Work Place games or complete the Problems & Investigations tasks, but the materials do not consistently provide language scaffolds to support MLLs’ ability to use and develop precise mathematical language within grade-level problems.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ conceptual understanding of key mathematical concepts. The materials consistently engage students in reasoning about mathematics through structured oral interactions and the use of concrete and visual representations, which promotes conceptual understanding. However, while these experiences create natural opportunities to use and develop language, the materials do not provide systematic, embedded supports to ensure that MLLs develop reading, writing, and academic English in a deliberate way.

Across the grade band, the materials provide students with the opportunity to find relationships within and between concrete representations, visual representations, and various abstract written strategies. The sessions’ instructional design fosters multimodal ways of building conceptual understanding alongside rich oral discourse. For example, in Grade 4, Unit 2, Multidigit Multiplication & Early Division, Module 3, Session 1, Problems & Investigations, students demonstrate conceptual understanding of multi-digit multiplication problems using the ratio table strategy. The lesson begins with a whole-class discussion about two different ratio tables, helping students understand how the ratio table represents multiplication and division. The materials invite students to think-pair-share to make sense of what the problem is asking, providing MLLs with an entry point into the problem situation. Then, after students work independently on two problems, the materials direct the teacher to facilitate a whole-class discussion in which students share their strategies for solving the problems. The materials encourage student-to-student discourse during this whole-class discussion, stating, “Provide opportunities for students to request clarification or to rephrase. Ask students to justify their thinking to provide an atmosphere where students are comfortable asking questions and sharing.” The session concludes with students completing problems with a partner using self-selected solution strategies, and the teacher is directed to look for students who use various concrete and visual models to share in the whole-class discussion. Students are encouraged to estimate and justify their strategies, reinforcing their conceptual understanding of multiplication and division. These tasks provide MLLs with authentic opportunities to use language to build conceptual understanding around multiplication problem situations (4.NBT.5).

Although the sessions engage MLLs in rich oral discourse, they do not provide the type of sustained opportunities for the intentional development of all four domains of language, specifically reading and writing. Opportunities for students to engage in sustained reading or extended writing tasks are rare, and when written tasks are present, such as recording thinking in math journals, the materials do not provide explicit instruction in sentence structure, morphology, or syntax. Without these intentional language supports, the success of MLLs depends heavily on teacher facilitation and the incidental repetition of vocabulary during conversation. Visuals and manipulatives provide powerful visual entry points and work to build conceptual understanding, but without intentional language supports, MLLs may struggle to connect these concrete and pictorial representations to abstract symbols and numbers and precise mathematical language.

In summary, the materials promote conceptual understanding by engaging students in mathematical reasoning through oral interactions and concrete and visual representations, but they lack systematic language supports for MLLs.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ procedural skill and fluency. Sessions provide frequent opportunities for students to build procedural fluency through aspects of the instructional design that invite oral explanation and partner discourse around procedural fluency, like Warm-Ups, Number Corners, and practice problems. While these experiences promote accurate and efficient computation, the materials do not systematically embed linguistic supports needed to ensure that MLLs develop academic English while mastering procedures.

Throughout the grade band, students encounter carefully sequenced tasks that emphasize flexible strategies and efficient procedures alongside rich oral discourse. In Grade 3, Unit 7, Extending Multiplication & Fractions, Module 1, Session 2, Problems & Investigations, students engage in the routine Same & Different to compare two visual multiplication models and equations with unknowns (3.OA.7). Students first Think-Pair-Share similarities and differences in the pictures, providing MLLs with the opportunity to use comparison language when discussing multiplication. The teacher then facilitates a whole-class discussion, recording students’ observations and prompting them to identify which comparisons are mathematical. The teacher facilitates a whole-class discussion around how a letter is used to represent an unknown value, supporting students with thinking about different strategies to identify missing values based on the information given. 

While aspects of the instructional design focusing on procedural skills and fluency give MLLs repeated chances to use language, the materials do not intentionally develop language around communicating how and why an algorithm works. Manipulatives such as colored tiles and base ten pieces provide strong visual anchors to support procedural skills. But, without intentional language support around using these tools to calculate accurately, efficiently, and with flexibility, MLLs will manipulate the materials without fully connecting them to precise mathematical terminology. Without this intentional connection, students must rely on teacher questioning and incidental repetition to intentionally develop the academic language associated with independently demonstrating procedural skills. As a result, MLLs may develop procedural fluency yet lack the structured language practice needed to express their strategies independently.

In summary, the materials support the development of procedural skills and fluency by engaging students in rich oral discourse, but they lack systematic language supports for MLLs. 

Despite these opportunities, supports for MLLs remain incidental. Reading is largely limited to interpreting numerical expressions or short word problems. Writing expectations focus on recording equations or brief observations without providing sentence frames, word banks, or explicit guidance for constructing mathematical sentences. The vocabulary cards for dividend, divisor, and quotient display numbers in problems but no visual representations of the concepts, reducing their usefulness for language development. Teachers are encouraged to clarify and restate student responses, but the materials themselves do not provide systematic attention to morphology (e.g., divide vs. division), syntax, or etymology. Multimodal resources such as arrays, ratio tables, and number strings are plentiful, yet they are not paired with bilingual glossaries or labeled visuals that would help MLLs independently connect procedures to academic language.

These pieces of evidence show that Bridges 3–5 successfully builds procedural skill and fluency through engaging routines and strategic practice. However, because explicit language amplification is missing, reading and writing are limited, and discourse supports depend on teacher facilitation, the materials partially meet expectations for supporting MLLs’ full and complete participation in the development of procedural skill and fluency.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet expectations for supporting MLLs’ full and complete participation in the intentional development of students’ ability to apply mathematics in real-world and mathematical contexts. Across units, students encounter authentic application tasks that require them to read multi-step word problems, write solutions with precise units, and justify reasoning orally and in writing. These activities promote mathematical reasoning and the transfer of skills to new contexts, but the materials do not systematically provide the language supports needed to ensure that MLLs can access and express the embedded language demands.

Across the grades, the materials engage students regularly in applying mathematics in routine and non-routine contexts, including single- and multi-step problems. These applications provide repeated opportunities for students to demonstrate their ability to transfer and apply mathematical concepts and skills. The sessions’ instructional design fosters multimodal ways of solving application problems alongside rich oral discourse. For example, in Grade 3, Unit 8, Bridge Design & Construction: Data Collection & Analysis, Module 1, Session 2, Problems & Investigations, students investigate bridge design by listening to the teacher read aloud and  informational text from Kids Discover: Bridges. They participate in a whole-class discussion where they interpret photo captions and diagrams, and the teacher records observations on a Know-Wonder-Learn chart. The session continues with students working in partners to estimate and weigh various amounts of pencils. MLLs use language as they discuss strategies to estimate the weight of the pencils before weighing them. Finally, students learn how to play the Work Place 8B game Wacky Discus. Students work in partners solve a non-routine problem involving making a rectangular discus with an area of 24 square centimeters that will travel the farthest in the class. MLLs use language as they collaborate with their partner to design their rectangular discus; the materials state, “Ask students to discuss with a partner how they might determine the dimensions of the rectangle, then have volunteers share with the class. Record the dimensions shared on the record sheet.” The materials continue to invite MLLs to use language as they iterate on their rectangular discus design. This session provides ample opportunities for MLLs to use the reading, writing, speaking, and listening language demands to apply mathematics to non-routine problems involving weighing and measuring where solution strategies are not pre-determined (3.MD.2).

While these experiences provide rich opportunities for MLLs to use all four language modalities, the materials do not embed the language supports necessary for MLLs to fully access the linguistic demands of solving routine and non-routine application problems. Specifically, the materials lack systematic language development of the reading, writing, speaking, and listening demands within application tasks when students are asked to use language to self-select a solution strategy, write equations, and justify solutions. Visuals and manipulatives such as pan balances, measuring tapes, and record sheets offer MLLs multimodal entry points to the task but are not paired with explicit linguistic supports for MLLs to develop academic language. Key mathematical vocabulary are introduced within sessions but rarely accompanied by morphology breakdowns, cognate connections, or a reference to the Word Resource Cards. Without intentional language development around the language needed to solve application problems, MLLs’ success relies largely on teacher facilitation and the chance repetition of vocabulary in discourse.

In summary, while the materials engage students in authentic application of mathematical concepts, but they lack systematic language supports for MLLs.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP1: Make sense of problems and persevere in solving them. While the materials provide supports for MLLs engaging in MP1, they do not consistently ensure MLLs’ full and complete participation.

Across Grades 3-5, students engage in open-ended tasks that support key components of MP1 by prompting them to make sense of mathematical situations, develop and revise strategies, and persevere through challenges. Embedded in the session facilitation, the teacher guidance provides MLLs with multiple entry points to engage with MP1 multimodally through storytelling, partner discussions, physical movement, and mathematical recording. The ABCs of Math Talk poster provides sample questions and sentence frames organized into language functions such as add, connect, and clarify. The sample questions and sentence frames support interdisciplinary language connections since they are generic in nature. For example, under the language function clarify, the following questions and sentence frames are listed:

• “Why did you use that strategy?”

• “How did you get that answer?”

• “When you said ____ did you mean ___?”

• “I would like to know why…” 

The materials reference the ABCs of Math Talk poster within session facilitation, most frequently in the teacher guidance for the Math Forums. The sample questions and sentence frames for the language functions add, connect, and clarify could support MLLs’ use and development of language around making sense of problems. However, the materials present the ABCs of Math Talk poster as supporting the Math Teaching Practice of facilitating meaningful mathematical discourse and not as explicitly supporting MLLs’ full and complete participation in making sense of problems. The onus is on the teacher to intentionally integrate the ABCs of Math Talk as a language support for MLLs to engage in MP1. 

Additionally, language supports to ensure MLLs’ full and complete participation in engaging with MP1 are inconsistently applied in Sessions, Work Places, and Number Corners. The materials do not consistently include explicit language scaffolds to support MLLs with understanding the information in a problem or to determine if their answer makes sense, which would strengthen MLLs’ ability to engage in MP1. Furthermore, the lack of targeted strategies to sustain MLLs’ engagement means that some MLLs may struggle to persevere in problem solving without heavy teacher guidance. For example:

• In Grade 3, Unit 3, Multidigit Addition & Subtraction, Module 2, Session 3, Problems & Investigations, students engage in the instructional routine Number Talk where students mentally solve a multidigit subtraction problem. Through a whole-class discussion, students hear a variety of solution strategies, determine if answers make sense, and reflect on the problem solving process. There is a lack of language support for MLLs to participate fully in the whole-class discussion and for MLLs to produce language related to describing their solution strategy or compare their solution strategy to other students’ solution strategies. The session continues with students working in partners to solve multidigit subtraction problems, first through estimating the answer, then working through and explaining the precise calculations. There are no language supports provided for MLLs to engage in student-to-student discourse applying the language functions such as  estimate and explain. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, as many sessions and Number Corners do not have specific language support or have inconsistent guidance on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP1. MLLs are supported to enter and engage in problem solving, but they are not consistently scaffolded to sustain their perseverance or to use language that supports sense-making and evaluation. These missed opportunities prevent the materials from fully developing the iterative and reflective aspects of MP1 for MLLs.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet the expectations of providing support for MLLs’ full and complete participation in the intentional development of MP2: Reason abstractly and quantitatively. While the sessions’ instructional design offers meaningful opportunities for MLLs to engage in reasoning, the supports are not consistent or comprehensive to ensure full participation for all MLLs.

The sessions’ instructional design provides multiple supports that partially serve MLLs in reasoning abstractly and quantitatively. The materials employ representations moving from concrete to representational to abstract, giving MLLs accessible entry points into the mathematical task and support MLLs with making sense of abstract symbols. For example:

• In Grade 4, Unit 3, Module 2, Session 1, Problems & Investigations, students engage in MP2 by reasoning about how smaller regions on a geoboard relate to the larger whole square. They Think-Pair-Share their observations, construct the regions with geobands, and record mathematical relationships in words and equations that contain fractional amounts. Students are encouraged to represent their reasoning through multiple modes—gestures, drawings, or concrete modeling—strengthening their ability to understand the meaning of numbers and symbols on the recording sheet. A note titled, MLL states, “Encourage students to share their thoughts by gesturing or drawing on the display geoboard. For example, they can show relationships by drawing lines on a larger region to show the number of smaller regions that can fit inside.” This language support provides MLLs with a scaffold to understand what the fractional quantities mean in relation to the smaller regions on the geoboard.

However, the materials stop short of ensuring full participation for all MLLs; they lack explicit language scaffolds for the language demands associated with representing situations symbolically or explaining what the numbers and symbols mean in solution strategies. For example:

• In Grade 3, Unit 3, Multidigit Addition & Subtraction, Module 3, Session 2, Problems & Investigations, the teacher introduces a game to practice estimating sums and differences. After randomly generating the digits of a 3-digit number, partners arrange their cards to make a sum or difference as close to the target as they can. The materials direct the teacher to encourage partners to discuss strategies for addition or subtraction and to make base ten manipulatives, whiteboards, and markers available. There are no language supports for scaffolding MLLs’ complete participation in the partner game, nor are there language supports to encourage MLLs to make meaning of the numbers. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not intentional in supporting MLLs with the language demands of engaging in MP2. MLLs have opportunities to reason quantitatively and symbolically, but they are not supported to use language that helps them justify strategies, restate peers’ reasoning, or explain the meaning of symbols. These missed opportunities prevent the materials from fully developing the decontextualizing, contextualizing, and interpreting aspects of MP2 for MLLs.

The instructional materials reviewed for Grades K-2 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP3: Construct viable arguments and critique the reasoning of others. While sessions include entry points and structures that invite MLLs into mathematical argumentation, the supports are not consistent or comprehensive enough to ensure full and sustained participation for all MLLs. 

As described in the report for 2g, students participate in tasks that support key components of MP3 by constructing mathematical arguments, analyzing errors, justifying their thinking with multiple representations, engaging with and evaluating others’ reasoning through questions, and making and testing conjectures while solving problems. The ABCs of Math Talk poster provides sample questions and sentence frames organized into language functions such as add, build, connect, and challenge. The sample questions and sentence frames support interdisciplinary language connections since they are generic in nature. For example, under the language function challenge, the following questions and sentence frames are listed that support students critiquing each other:

• “Why did you… ?”

• “I respectfully disagree because… ”

• “A more efficient strategy might be… ”

The materials reference the ABCs of Math Talk poster within session facilitation, most frequently in the teacher guidance for the Math Forums. The sample questions and sentence frames for the language functions add, connect, and clarify could support MLLs’ use and development of language around constructing viable arguments and critiquing the reasoning of others. However, the materials present the ABCs of Math Talk poster as supporting the Math Teaching Practice of facilitating meaningful mathematical discourse and not as explicitly supporting MLLs’ full and complete participation in constructing arguments and critiquing others. The onus is on the teacher to intentionally integrate the ABCs of Math Talk as a language support for MLLs to engage in MP3. 

Additionally, language supports to ensure MLLs’ full and complete participation in engaging with MP3 are inconsistently applied in Sessions, Work Places, and Number Corners. The materials do not consistently include explicit language scaffolds to support MLLs with constructing viable arguments and critiquing the reasoning of others. For example:

• In Grade 4, Unit 6, Multiplication & Division, Data & Fractions, Module 2, Session 4, Problems & Investigations, students are supported in reasoning about perimeter and area through hands-on modeling. In the Rectangle Sort activity, students must explain their reasoning about how Yasmeen sorted rectangles and justify why one specific example, the square, works in both groups. There are no language supports for MLLs to explain their reasoning or justify the placement of the square. The teacher invites one student to place red linear pieces on a display to outline a rectangle representing a perimeter of 16 inches and invites another to use colored tiles to show an area of 16 square inches. The materials contain a note titled, MLL which states, “Invite volunteers to summarize what they need to do to complete this task. Encourage multilingual students to summarize the details of the task in the language they find most comfortable speaking for the benefit of other students who speak that language.” While these supports promote initial access through understanding the task instructions, they do not consistently scaffold how MLLs can extend their reasoning into constructing or critiquing arguments with mathematical precision. Then in the Same Perimeter, Different Area task, students must make a poster that includes their recommendation on the dimensions of the soccer practice zone and provide the reason they chose those dimensions. During the Gallery Walk routine in the following session, the materials invite students to critique other possible options. There are no language supports provided for MLLs to participate fully in the Gallery Walk where they critique the reasoning of others.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not intentional in supporting MLLs with the language demands of constructing arguments and critiquing the reasoning of others.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet the expectations for providing strategies and support for MLLs’ full and complete participation in the intentional development of MP4: Model with mathematics. While sessions include entry points and structures that invite MLLs into mathematical modeling, the supports are not consistent or comprehensive enough to ensure full and sustained participation for all MLLs. 

Across Grades 3-5, students engage in tasks that support MP4 by reasoning with quantities, representing situations symbolically, and interpreting numbers and symbols in context to connect real-world scenarios with mathematical representations. Session features such as visuals, manipulatives, and contextual stories create conditions where MLLs can begin to model situations with representations and connect different representations for the same problem. However, the materials do not consistently provide the explicit language supports necessary for MLLs’ full participation. For example:

• MLLs are not fully supported in participating in Grade 5, Unit 4, Multiplying & Dividing Whole Numbers & Decimals, Module 2, Session 2, when students engage in MP4 as they use ratio tables to model the costs of making and selling bracelets for a school fundraiser. The real-world context of Bryan’s Bracelets helps students connect mathematics to a meaningful situation, and the ratio table serves as a tool for recording known information, identifying relationships, and predicting future sales or fundraising goals. Students use multiplication and division equations to complete the tables and participate in Think-Pair-Share routines to describe their strategies. Teachers are encouraged to annotate ratio tables with student input and use arrows to highlight multiplicative relationships, supporting students in connecting quantities to symbolic representations. These features provide MLLs with some access to modeling by offering visuals, mathematical representations, and a real-world context. However, the lesson does not consistently include explicit language supports to help MLLs articulate the connections between the context, the ratio table, and the equations. As a result, MLLs have partial access to MP4, with opportunities to engage in modeling but limited scaffolds to fully express their reasoning about the models.

• In contrast, MLLs are supported in Grade 3, Unit 1, Addition & Subtraction Patterns, Module 3, Session 2, which begins with a whole-class discussion of a scavenger hunt from a previous session in which students found classroom realia of different lengths. Students compare and review their results from the scavenger hunt and then solve problems involving adding lengths of objects together. After students solve one addition expression independently using self-selected solution strategies, the materials direct the teacher to model various students’ solution strategies using an empty number line and a measuring tape. These features provide MLLs with some access to modeling by connecting expressions, various representations, and classroom realia. The session continues with students working independently or with a partner finding sums of similar length problems. A note titled, MLL states, “Help students interpret the questions by using objects or pictures of objects to represent the objects in the problems. Alternatively, use objects of the given lengths and line them up.”  With these provided scaffolds (model a story context with multiple representations and to describe what they do with the models), this program provides MLLs with full participation in MP4 in this session.

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, and they are not consistent in supporting MLLs with the language demands of modeling with mathematics.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics 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 support for MLLs full and complete participation in MP6 sometimes, but those supports are not employed consistently throughout the program.

As described in the core report for 2j, the materials support precise language by modeling accurate mathematical language, ensuring students understand and apply precise definitions. The Word Resource Cards help students attend to the precision of mathematical language with cards printed with a nonlinguistic model of the word and a definition on the back. However, there is limited teacher guidance around supporting MLLs to formulate clear explanations utilizing the Word Resource Cards or providing feedback to students on the accurate use of mathematical language. Therefore, language supports are inconsistently applied for MLLs to engage in MP6 in Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in Grade 4, Unit 3, Fractions & Decimals, Module 4, Session 3, Problems & Investigations, where students practice placing fractions and decimals on a number line, with a focus on precision and mathematical reasoning. Students estimate and record the location of 1 on a horizontal number line, considering the placement of other values like 0.50. Students use number tags to represent values such as fractions and decimals, collaboratively place them on a class number line, and justify their thinking to the class. The materials provide no language support for any aspect of the activity. Specifically, the materials lack in language supports for MLLs’ use of precise language to describe their thinking and their receptive language needs of listening to another student explain.

• In contrast, MLLs are fully supported in Grade 5, Unit 3, Place Value & Decimals, Module 2, Session 2, where the session begins with a Number String activity where students engage in mentally finding the difference of two decimal numbers. The materials direct teachers to give wait time while students mentally calculate the differences and determine how they found each difference; wait time supports MLLs with attending to the precision of the calculations along with the precise use of language to describe their solution strategy. Then, the session introduces Work Place 3B Draw & Compare Decimals, in which students play a game with partners in which they use randomly generated numbers to build, represent, read, and compare decimal numbers, justifying their comparisons. The Work Place Guide provides teacher guidance around supporting students’ precise use of language through the following section of the Assessment & Differentiation table: “If you see that students read decimal numbers as whole numbers… Work with students to use base ten number pieces to find the values of the digits in each place.” Specifically to support MLLs’ participation in the activity, a note titled, Multilingual Learners outlines several options for language support: 

  • “Have students restate the directions in their own words, using the cards to demonstrate. 

  • Provide sentence frames for students to use to explain their thinking. Sentence frames can be found on the Bridges Educator Site.

  • Suggest partnerships that allow students to play in the language they are most comfortable speaking or that provides support in mathematical discourse, interaction, language development, or understanding the game’s rules.

  • Play a sample game in a small group and allow opportunities for students to request clarification and rephrasing.”

In conjunction, the embedded and MLL-specific language supports (wait time, targeted support for reading decimal numbers, clarification of the game rules, sentence frames, and home language usage) allow MLLs to use precise language within the game.

In summary, MLLs engage in tasks with opportunities to attend to precision, but the materials do not consistently provide language supports that help students articulate precise explanations, interpret peer reasoning, or refine their use of mathematical language. These missed opportunities prevent MLLs from fully developing the habits of precise communication expected in MP6.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics 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. While MLL specific language supports are available in some sessions where students are engaging in MP7, their purpose is not intentionally to scaffold the language demands associated with looking for and explaining structure to make generalizations.

Across Grades 3-5, students engage in tasks that highlight MP7 by recognizing patterns, identifying structure, and breaking down complex problems. Sessions encourage comparing strategies, justifying reasoning, and reflecting on how structure supports deeper understanding through teacher-facilitated discussion. Language supports for MLLs to engage fully and completely in MP7 are inconsistently applied within Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in Grade 5, Unit 3, Place Value & Decimals, Module 1, Session 4, where students examine patterns in the base ten number system to investigate exponents and exponential notation. Students engage in a Think-Pair-Share and a whole-class discussion to notice patterns and establish the connection between a visual representation of base ten manipulatives and their mathematical representation using exponents. While students have opportunities to use and develop place value language, there are no language supports for MLLs to fully engage in the class discussion, or to support the language demands of describing patterns. Then, students work with partners to co-create a base ten mat using the visual representations of base ten manipulatives, discussing patterns in the base ten number system as they work. There is a lack of language supports to ensure MLLs’ full participation in the collaborative partner work.

• In contrast, MLLs are supported in Grade 5, Unit 6, Graphing, Geometry & Volume, Module 2, Session 2, where students examine a hierarchy of shape properties that contains a visual representation of the shape noted with the shape names. As students share observations about the patterns of how the shapes are arranged in the hierarchy with the class, a note titled, MLL states, “Invite students to identify the different types of quadrilaterals. Have them point to the appropriate Word Resource Cards instead of, or in addition to, naming them.” This language support offers MLLs a scaffold for engaging in the whole-class discussion around describing patterns in the structure of a hierarchy of shapes. 

In summary, while language supports are present in the materials, they are not employed consistently throughout the program, as many sessions and Number Corners do not have specific language supports on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP7. MLLs engage in tasks with opportunities to look for and make use of structure, but the scaffolds provided are limited or absent, leaving students without consistent support to describe, generalize, and explain patterns. These missed opportunities prevent MLLs from fully developing the habits of identifying and communicating structure as expected in MP7.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics 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 supports for MLLs engaging in MP8 primarily through notes titled, MLL, but those notes are inconsistently applied throughout the program.

Throughout Grades 3-5, the materials provide opportunities for students to use and develop language when looking for and expressing regularity in repeated reasoning through Work Place math stations that include partner games and the Number Corners bulletin display that incorporates whole group discussion. Language supports are inconsistently applied for MLLs to engage in MP8 in Sessions, Work Places, and Number Corners. For example:

• MLLs are not fully supported in participating in Grade 3, Unit 5, Linking Multiplication & Division, Module 1, Session 2. Examples are located in  Problems and Investigations, where students use repeated reasoning when building on a pattern, and connecting the pattern to multiplication and division equations. The materials direct students to Think-Pair-Share about the patterns they notice within a chart from a previous session displaying the multiples of 4s. Then, students work with a partner to write multiplication and division equations describing those patterns. The teacher facilitates a whole-class discussion connecting the visuals from the chart to the multiplication and division equations the students recorded, with prompts such as, “If there are 12 legs, how many horses are there?” There are no language scaffolds to support MLLs with participating fully in the whole-class discussion around describing patterns with equations. Then, the materials direct the teacher to display the Word Resource Cards for the terms dividend, divisor, and quotient, connecting the terms to the equations students recorded. The Problems & Investigations section ends with students completing a student book page in partners where they extend their thinking by examining a completed pattern chart and recording observations. The materials lack language supports for MLLs to write observations in their student book page. The teacher facilitates a whole-class discussion aimed at supporting students with noticing repeated calculations to make generalizations, with prompts such as, “How many legs would be in the 10th row? The 20th? Explain how you know.” The materials do not provide language supports for MLLs to engage with the language functions of noticing repeated calculations and making generalizations. 

• In contrast, MLLs are supported in Number Corners Grade 5, November, Day 14, Calendar Collector: Meters, Meters & More Meters, where students are invited to share observations, predictions, and questions about a conversion table displaying centimeters and meters. The materials direct students to complete the table independently and the teacher to circulate and provide support, as needed. This facilitation is paired with a note titled, MLL & Support which states, “Consider using sentence frames such as these to support and facilitate student discourse:

  • I know that a ________(measurement) is ________(fraction) of a ________(measurement).

  • I know that there are ________(number) ________(measurements) in every ________(measurement).”

These sentence frames amplify the language forms that allow MLLs to engage in MP8, specifically by communicating patterns in the table through phrases such as “of a” and “in every.”

In summary, while language supports are present in the materials, they are not employed consistently throughout the program.  Many sessions and Number Corners do not have specific language support or have limited guidance on how to use strategies and scaffolds to support MLLs’ full and complete participation in MP8. MLLs engage in tasks with opportunities to look for and express regularity in repeated reasoning, but the scaffolds provided are limited or absent, leaving students without consistent support to notice repeated calculations, make generalizations to create or explain an algorithm, and evaluate the reasonableness of answers. These missed opportunities prevent MLLs from fully developing the habits of generalization as expected in MP8.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet the expectations of intentionally developing language in ways valued by disciplinary practices over time, across lessons, units, and throughout the course. 

The first page of the introduction to each grade level outlines the guiding principles of The Math Learning Center, including the interdependence of content and language, stating, “Bridges teachers… promote discourse, draw out student thinking, and embed assessment in their instruction through deliberate noticing and purposeful questioning.” The materials show partial evidence of supporting students with this interdependence and intentional development of disciplinary language. Disciplinary language development consists of functional language development alongside mathematical vocabulary development. In the materials, functional language development is inconsistent and often serves students’ understanding of the mathematical content rather than explicitly advancing disciplinary language development over time, as noted in the reports for 2a.MLL-2c.MLL. The materials lack a longitudinal plan for developing language as a disciplinary practice beyond moments embedded within mathematical content. As noted in the report for 2j.MLL, the materials partially meet the expectations for supporting precision of mathematical language over time.

For example, in Grade 3, Unit 6, Geometry, Modules 1 and 2, there is no intentional disciplinary language development embedded across Sessions. While students are occasionally prompted to explain their thinking or describe shapes, these prompts are isolated and lack scaffolding, modeling, or progressive sophistication over time. For instance, in Module 1, Sessions 1 and 2, students use everyday language to describe shapes, engaging in Instructional Routines like Which One Doesn’t Belong and Guess My Rule. In Session 5, the materials state, “As students share their reasoning, prompt them to be precise in their use of shape names and attributes (e.g., straight sides, equal lengths, number of angles).” While the materials draw teachers’ attention to the use of mathematically precise vocabulary, there is no teacher guidance to support students with bridging from everyday language to more mathematically precise vocabulary. Similarly, in Module 2, Session 4, students are told to, “... provide enough information through labeled sketches and equations to demonstrate how they know their figure has the designated value.” The materials do not contain guidance on how teachers can support this explanation or how it connects to prior or future language use and development. 

Therefore, across the Problems & Investigations sections of the Sessions, there are inconsistent language supports for functional language or mathematical vocabulary to progressively develop students’ disciplinary language use. Each Work Place Guide contains language supports in a note titled Multilingual learners; periodically these language supports offer suggestions to support MLLs’ disciplinary language use. For example, in Module 1, Work Place 4c Hexagon Spin & Fill, a note titled Multilingual learners suggests four language supports. One of the suggestions supports MLLs’ mathematical vocabulary usage: “As you talk about the pattern blocks, hold them up each time. Use the color and shape name to identify the blocks.” One of the suggestions supports MLLs with engaging with the language function of explaining, stating, “Provide sentence frames for students to explain their thinking. Sentence frames can be found on the Bridges Educator Site.” The referenced sentence frames for this Work Place state, “I need ___ pieces to build my shape. I used the ___ tangram pieces to make a ___.” These language supports are at point-of-use and do not contain information related to supporting MLLs with developing disciplinary language across Sessions, Modules, or Units. 

Overall, the materials provide some, but not consistent, support for the ongoing use and development of disciplinary language across Sessions and Modules. Support for functional language development and mathematical vocabulary development lacks a clear progression. While Sessions encourage the use of everyday language, they do not offer explicit guidance for teachers to bridge from everyday language to more mathematically precise vocabulary.

The instructional materials reviewed for Grades 3-5 of Bridges in Mathematics partially meet the expectations that materials provide explanations of the instructional approaches of the program for MLLs and the identification of research-based strategies. The materials explain the instructional approaches of the program for MLLs through general recommendations. The materials provide a cited list of literature and research that influenced the design of Bridges in Mathematics but do not include explanations of how the literature base is used in the instructional approaches of the program for MLLs.

The Introduction to each grade level provides an explanation of the instructional approaches of the program for MLLs. Before listing general recommendations, the materials state, “Bridges Teachers Guides include specific support suggestions to assist teachers with providing access and opportunity for all students, including multilingual learners (MLLs).” The materials then list the following recommendations:

• “Flexibly pair multilingual learners with peers who demonstrate a range of language skills to allow flexible use of language and to support sensemaking. While MLLs should sometimes be paired with other MLLs, it is not appropriate to always pair MLLs together.

• Allow students to work and collaborate in the language they are most comfortable speaking. Provide support in understanding the content, participating in mathematical discourse, and interacting with peers.

• Give students multiple opportunities to share their ideas in different ways, including orally, in writing, and through gestures, drawings, and the use of models. Provide time for students to rehearse an explanation first with the teacher, a partner, or small group before sharing out. When students present orally, allow them to use visual representations to accompany and explain their work.

• Ask clarifying questions to probe student ideas. Productive questions include:

  • ‘How did you find ______? Can you show me how you found ________?’

  • ‘How did you use this tool to _________? Can you show me?’

  • ‘What did you do first? What did you do next?’

  • ‘I see you drew/wrote _____________. Can you tell me about that part?’

• Provide sentence frames to support students in expressing ideas during Work Places and other instructional activities. Consider writing sentence frames on the board or posting them somewhere visible to students during math forums (grades 3–5), strategy shares, and whole-class math games to support language and facilitate the sharing of ideas.

• Use the Word Resource Cards or Math Vocabulary app to provide visual support for vocabulary development. Show students the Word Resource Card and provide opportunities for them to discuss and share their prior knowledge related to the word or phrase. Unpack the vocabulary in the session using visuals and examples to clarify meaning for students. Ask students, ‘Can you restate that using (insert specific vocabulary word)?’ to support the use of the vocabulary used in the session.

• Pair visual supports and gestures with language whenever possible. Visuals and gestures not only support MLLs but all learners with varying language needs. Visuals help to clarify students’ understanding of the content as well as shared directions.”

The above recommendations frame the material’s MLL approach, which aligns broadly with best practices for language development. However, the recommendations are framed generically for “…all students, including MLLs…” which does not outline the explicit purpose of ensuring MLLs are able to meet the standards by using language to perform disciplinary practices. Furthermore, while the recommendations reflect widely accepted practices, there are no direct citations between these recommendations and specific research-based frameworks or findings.

The Bridges Educator Site includes a document entitled Literature Base for Bridges in Mathematics Third Edition (extended), which lists citations of “influential works in mathematics education.” This introduction to this document states, “… these works influenced the design of Bridges in Mathematics Third Edition.” This document references several established sources in language development for MLLs, including:Bresser et al. (2009), Chval et al. (2021), Hill & Flynn (2006), and the Multilingual Learning Toolkit developed by the American Institute for Research.While the materials identify their literature base of influential works, this document does not reference these citations in the instructional approach for MLLs located in the Introduction to each grade level. The materials do not indicate how the strategies from these sources were selected, adapted, or systematically embedded throughout the curriculum for the explicit purpose of ensuring MLLs are able to meet the standards by using language to do disciplinary practices.

The instructional materials reviewed for Grade 3-5 of Bridges in Mathematics partially meet expectations for providing guidance to encourage teachers to draw upon student home language to facilitate learning. The materials offer Spanish translated resources, but they lack specific teacher-facing guidance on how to integrate MLLs’ home languages into daily classroom instruction. The materials partially provide guidance to teachers on how to draw upon MLLs’ home language as a resource for learning, but this guidance is inconsistent and lacks specificity connected to MLLs learning grade-level mathematics content.

The materials present multilingualism as an asset in learning grade-level mathematics. The Guiding Principles section of the Introduction to each grade level states, “Bridges teachers… both in and out of the classroom, honor and build upon students' cultural resources, knowledge bases, languages, and prior experiences with mathematics.” The Language Support section of the Introduction to each grade level lists general recommendations for language supports for MLLs, including, “Allow students to work and collaborate in the language they are most comfortable speaking. Provide support in understanding the content, participating in mathematical discourse, and interacting with peers.” While the materials present multilingualism as an asset, the recommendations to leverage home language usage are not comprehensive, because they do not include specific teacher guidance on using home language to support MLLs in learning grade-level mathematics content.

Similar evidence is found periodically at point-of-use within sessions and Work Place Guides. For example, in Grade 4, Unit 2, Module 2, Session 3, Problems & Investigations provides the following teacher guidance: “Encourage students to share their thinking in the language they feel most comfortable speaking. Work collaboratively with students to understand each student’s thinking, as it is expressed in any language. Multilingualism in academic language supports students’ literacy in general.” This teacher guidance is found infrequently within sessions and Work Place Guides and is not consistently focused on supporting MLLs in learning grade-level mathematics content.

Additionally, the materials do not include guidance on how to garner information that will aid in learning, including 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.