3rd-5th Grade - Gateway 2

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of students’ conceptual understanding of key mathematical concepts, especially where called for in specific content standards or clusters.

Multiple conceptual understanding problems are embedded throughout the grade level within the Activate, Explore, and Reflect sections, providing students opportunities to engage both independently and with teacher support. The Teacher Implementation Guide, Student Tools for Learning, Making Math Concrete and Visible, notes that “manipulatives bridge the gap between concrete experiences and abstract reasoning. They help students build number sense, visualize ideas, and internalize concepts through hands-on exploration.” The materials therefore, ensure students can access and demonstrate conceptual understanding, including opportunities to do so independently when appropriate. Examples include:

• Grade 3, Module 2, Topic 5, Lesson 4, Explore 2, students develop conceptual understanding as they represent fractional parts and wholes with pattern blocks. The value of the whole changes throughout the activity, requiring students to consider how the fractional value of a piece relates to the whole. Students also encounter fractions greater than one. Directions state, “Direct students to the green triangle pattern block. Have students hold one in their hands. Do you know what fraction the small triangle represents? Why or why not? Sample answer: ‘It is one piece, but I am not sure of the size.’ Tell students the hexagon is one whole and have them think about what fraction the small triangle is. What fraction is the small triangle? ‘1 piece of size one-sixth.’ How do you know it is one piece of size one-sixth? Sample answer: ‘I put 6 small triangles together to create a hexagon.’ Have students think about whether the triangle is still one piece of size one-sixth when the trapezoid is one whole. Is the triangle one piece of size one-sixth of the trapezoid? Why or why not? What fraction is the triangle of the trapezoid? ‘1 piece of size one-third.’” (3.NF.1)

• Grade 4, Module 1, Topic 1, Lesson 3, Explore 1, Question 1, students demonstrate conceptual understanding as they represent multi-digit numbers with base-ten blocks and determine the fewest number of blocks needed. Using an image for question 1 of 1 thousand block, 1 hundred block, 4 ten rods, and 5 unit cubes, students are asked: “For each question, write the number of erasers in the shipment. Then, decide whether the shipment uses the fewest number of packages. When it does, write yes. When it does not, describe how you can repack the shipment. 1. _______ erasers______” (4.NBT.2)

• Grade 5, Module 5, Topic 12, Lesson 4, Reflect and Summarize, Problem 1, students demonstrate conceptual understanding as they determine the volume of right rectangular prisms. Given an image of a prism with a length of 4 units, a width of 3 units, and a height of 2 units, they are asked, “Determine the volume of each figure and the composite figure. Each unit cube in the figures represents 1 cubic centimeter.” (5.MD.5a)

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for providing intentional opportunities for students to develop procedural skills and fluencies, especially where called for in specific content standards or clusters.

The Grade-Specific Fluency Expectations map outlines fluency goals within and across grade levels for ClearMath Elementary. The Module and Topic Fluency Progressions in the Mathematical Progressions and Connections digital book describe how fluency develops across the courses. The Mathematical Progressions and Connections documents for each grade level state, “Fluency Progressions, Fluency encompasses number sense, precision, and efficiency. Number sense is understanding the relationships between quantities and having the ability to flexibly compose and decompose quantities. Precision entails recognizing that the solution is accurate and makes sense. Efficiency is developing strategies that promote using connections between concepts to solve problems in a streamlined way. These three pieces come together when students demonstrate fluency. These components are complex in and of themselves and therefore take time to develop and synthesize.” The fluency map highlights the grade-specific expectations within ClearMath Elementary. Additional fluency practice is available through MATHia Adventure, where students play games that support fluency development. Examples include

• Grade 3, Module 2, Topic 4, Lesson 4, Explore 1, Question 1, students demonstrate procedural skill and fluency as they relate addition and subtraction within 1,000. They complete fact family puzzles and apply this understanding to word problems requiring related equations, such as: “182+ _______ =425.” (3.NBT.2)

• Grade 4, Module 2, Topic 4, Lesson 5, Explore 1, students develop procedural skill and fluency with subtraction of multi-digit numbers using the standard algorithm. Working in pairs, they build models with base-10 blocks for 2,453-1,642 and explain how regrouping is represented, “Task, Display the expression 2,453-1,642. Have students work in pairs to build a model of the subtraction with base-10 blocks. ‘How can you model regrouping for taking away 600 from 400? What difference did you determine for 2,453-1,642?’” (4.NBT.4)

• Grade 5, Module 2, Topic 3, Lesson 4, Reflect, Problem 1, students demonstrate procedural skill and fluency as they multiply multi-digit numbers using the standard algorithm. “Read the story. Then, answer each question. Camila picks 5 cards with the digits 2, 3, 6, 8, and 9 on them. Camila makes the factors 29 and 36. What is the product?” (5.NBT.5)

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of students’ ability to utilize mathematical concepts and skills in engaging applications, especially where called for in specific content standards or clusters.

Multiple routine and non-routine applications of mathematics are included throughout the grade level, with single- and multi-step application problems embedded within lessons, including Activate and Explore. Students engage with these applications both with teacher support and independently through tasks such as games, puzzles, and investigations. Materials are designed to provide opportunities for students to independently demonstrate their understanding of grade-level mathematics when appropriate. For example:

• Grade 3, Module 1, Topic 2, Lesson 7, Explore 2, students independently engage in non-routine application as they use art materials to create monsters that follow specific rules (e.g., no more than 10 eyes, teeth, and arms). Students then solve problems with their monsters, such as: “How many eyes do six of your monsters have?” (3.OA.3)

• Grade 4, Module 2, Topic 5, Lesson 2, Reflect, Question 1, students independently demonstrate application through non-routine fraction problems. In Food Fractions, My Just Right Problem, students solve, “Kaya ate \frac{1}{12} of a casserole, Avery ate \frac{5}{12} of it, and Tiago ate \frac{6}{12}  of it. How much of the casserole did Kaya and Tiago eat?” (4.NF.3d)

• Grade 5, Module 5, Topic 12, Lesson 6, Explore 1, students engage in non-routine application of volume in a real-world context as they design a stingray habitat. The problem states, “You are designing a new habitat for stingrays at an aquarium. It will house 6 stingrays and must meet the following requirements: The floor space reserved for the habitat is 15 feet by 20 feet, each stingray needs at least 55 cubic feet of water, there should be a cutout where people can stand to pet the stingrays, this should be large enough to fit 3 people, the tank should have a maximum height of 3 feet, the cost to build the habitat is $4 for each cubic foot, the aquarium has a budget of $3,000.” (5.MD.5)

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade as reflected by the standards.

Multiple aspects of rigor are engaged simultaneously across the materials to develop students' mathematical understanding of individual lessons. Each module within the curriculum supports a variety of instructional approaches that incorporate conceptual understanding, procedural fluency, and application in a balanced way. Examples include:

• Grade 3, Module 1, Topic 2, Lesson 2, Explore 2, Question 1, students engage in conceptual understanding and application as they use pictures of real-world groupings, such as tricycles or paper clips, to build understanding of multiplication patterns and apply fact knowledge to solve a word problem: “How many erasers are in 1 pack? How many erasers are in 6 packs?” (3.OA.3, 3.OA.7)

• Grade 4, Module 2, Topic 5, Lesson 11, Explore 1, Question 1, students engage in conceptual understanding, procedural skill and fluency, and application as they design an obstacle race at least 5 miles long, place fractional distances with denominators of 8 on an unpartitioned number line, and label obstacles such as a “Tunnel at 1\frac{1}{8}” and an “Inflatable wall at 2\frac{2}{8} miles.” (4.NF.3, 4.NF.3c, 4.NF.3d)

• Grade 5, Module 1, Topic 1, Lesson 8, Explore 1, Question 1, students engage in conceptual understanding and application as they apply the formula for volume, relate volume to multiplication and addition, and solve a real-world problem by designing outdoor storage that meets requirements such as “at least 50 cubic feet of storage space,” a cost “not exceed[ing] $250,” and bins that “fit on a patch of grass measuring 3 feet by 15 feet.” (5.MD.5, 5.MD.5b)

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The Teacher's Implementation Guide explains the curriculum’s approach to MP1, Embedding Mathematical Habits of Mind states, “The first Habit of Mind is evident every day in every lesson as students engage in activities, solve problems, and analyze their solutions.”

Opportunities for students to engage with MP1 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP1 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP1 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

• Grade 3, Module 2, Topic 4, Performance Task, provides students with opportunities to engage in MP1 by devising strategies independently to solve a multi-step task involving rounding and adding or subtracting three-digit numbers.

• Grade 4, Module 5, Topic 13, Lesson 3, Explore 2, provides students with opportunities to engage in MP1 as they analyze problems, identify needed information, apply a variety of strategies, monitor and evaluate progress, and revise their approaches. In this lesson, students design a playground, determine the area and perimeter of multiple figures, and independently devise strategies to complete their design.

• Grade 5, Module 5, Topic 12, Lesson 2, Explore 1, provides students with opportunities to engage in MP1 by analyzing real-world volume problems. Students work to understand the information in the problem and the questions asked, while teachers prompt them to identify the information needed to solve the problem.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP2:  Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Opportunities for students to engage with MP2 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP2 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP2 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 3, Topic 8, Lesson 8, Explore 1, provides students with opportunities to engage in MP2 by representing situations symbolically. Students write an equation using parentheses and a letter for the unknown to represent situations and then solve them.

• Grade 4, Module 2, Topic 4, Lesson 8, Explore 1, provides students with opportunities to engage in MP2 by considering units in a problem, attending to the meaning of quantities, and representing situations symbolically. In this lesson, students work and discuss in small groups to complete a home makeover activity, creating and solving equations to reach a total as close to $15,000 as possible without going over. Students explain how they selected items and ensured they stayed within budget.

• Grade 5, Module 4, Topic 11, Lesson 5, Explore 2, provides students with opportunities to engage in MP2 by identifying what is known and unknown in a real-world problem and representing the situation with an equation. Teachers observe if students explain what the numbers or symbols in the expression represent and if they can write an equation to match the problem.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Opportunities for students to engage with MP3 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP3 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP3 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 3, Topic 7, Lesson 3, Center 3, provides students with opportunities to engage in MP3 by constructing viable arguments and critiquing the reasoning of others. Students analyze Lina’s partially completed equations for partitioned arrays, justify their strategies orally or in writing using concrete models, drawings, actions, or numbers, and evaluate whether Lina’s reasoning makes sense as they prove how each array was partitioned to find the total area.

• Grade 4, Module 3, Topic 6, Lesson 1, Explore 2, provides students with opportunities to engage in MP3 by constructing viable arguments and critiquing the reasoning of others. Students explain and justify their strategies orally and in writing, and perform error analysis of provided student work by listening to or reading arguments, deciding whether they make sense, and asking clarifying questions. Teachers facilitate a Think-Pair-Share routine in which students investigate patterns and discuss which student work is correct and why.

• Grade 5, Module 5, Topic 12, Lesson 6, Explore 2, provides students with opportunities to engage in MP3 by constructing viable arguments and critiquing the reasoning of others. Students explain and justify their strategies in writing, perform error analysis of provided student work, and determine whether classmates’ designs meet given requirements during a gallery walk. Students mark “yes or no” on their recording sheet and use whiteboards to calculate as they evaluate peer work in small groups.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP4: Model with mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Opportunities for students to engage with MP4 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP4 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP4 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 1, Topic 3, Lesson 1, Explore 1, provides students with opportunities to engage in MP4 by modeling with mathematics. Teachers pose problems connected to previous concepts and prompt students to reflect on how the current picture graph compares to a picture graph created as a class in a prior lesson.

• Grade 4, Module 3, Topic 8, Lesson 1, Explore 1, provides students with opportunities to engage in MP4 by modeling with mathematics. Students draw models of multiplication with unit fractions, use equations to represent their models, and check whether their answers make sense, revising their models when necessary. Teachers facilitate discussion as students share and compare their models and strategies.

• Grade 5, Module 4, Topic 9, Lesson 9, Explore 2, provides students with opportunities to engage in MP4 by modeling with mathematics. Students describe what they do with their models of factors and products, explain how the models relate to the problem situation, and identify where in their models they can find each factor and the product.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Opportunities for students to engage with MP5 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP5 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP5 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 1, Topic 1, Lesson 1, Activate, provides students with opportunities to engage in MP5 by using appropriate tools strategically. Students are given three different tools to use to tile their desks, then compare the tools to identify their limitations and determine which tool would be best. Teachers prompt students to reflect on how the choice of tool supports their mathematical knowledge.

• Grade 4, Module 5, Topic 11, Lesson 4, Explore 2, provides students with opportunities to engage in MP5 by using appropriate tools strategically. Students measure angles using a straightedge and protractor, deciding when and how to use each tool. Teachers facilitate discussion as students recognize the insight each tool provides, its limitations, and when it is appropriate not to use tools.

• Grade 5, Module 1, Topic 1, Lesson 4, Center 1, provides students with opportunities to engage in MP5 by using appropriate tools strategically. Students use connecting blocks to determine volume and discuss why gaps or overlaps make the model ineffective. Teachers facilitate a conversation about the benefits and limitations of the tool as students demonstrate its use to solve volume problems.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP6: Attend to precision, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Opportunities for students to engage with MP6 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP6 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP6 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 2, Topic 4, Lesson 6, Explore 1, provides students with opportunities to engage in MP6 by attending to precision. Students specify units of measure, label number lines, and use tables and graphs appropriately. Teachers prompt students to identify which direction to label vertical and horizontal number lines, recognize multiples of 10, and locate specific numbers on their number line.

• Grade 4, Module 5, Topic 11, Lesson 1, Explore 1, provides students with opportunities to engage in MP6 by attending to precision. Students state the meaning of symbols, use definitions accurately, and communicate using grade-level vocabulary and conventions. Teachers direct students to say and read definitions of points, rays, lines, and line segments, explain their reasoning to peers when recognizing geometric figures, and label figures accordingly.

• Grade 5, Module 4, Topic 9, Lesson 5, Center 3, provides students with opportunities to engage in MP6 by attending to precision. Students calculate fractions as quotients by rewriting them as multiplication equations, ensuring calculations are accurate and efficient. 

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP7: Look for and make use of structure, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Opportunities for students to engage with MP7 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP7 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP7 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 1, Topic 2, Lesson 6, Explore 2, provides students with opportunities to engage in MP7 by looking for and making use of structure. Students decompose arrays into smaller parts and use the distributive property to create multiplication equations.

• Grade 4, Module 3, Topic 6, Lesson 2, Explore 1, provides students with opportunities to engage in MP7 by looking for and making use of structure. Students complete rule tables, identify which rules represent additive and multiplicative comparisons, and explain the structures within the tables. Teachers ask students how they can determine whether a rule represents an additive or multiplicative comparison.

• Grade 5, Module 5, Topic 14, Lesson 3, Explore 2, provides students with opportunities to engage in MP7 by looking for and making use of structure. Students identify and record the attributes of quadrilaterals, then discuss patterns in these attributes with a partner to make generalizations about quadrilateral properties.

The materials reviewed for ClearMath Elementary Grades 3 through 5 meet expectations for supporting the intentional development of MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Opportunities for students to engage with MP8 appear throughout the year. The Teacher's Implementation Guide identifies lessons and sections in which to observe MP8 through Habits of Mind call-out boxes, topic overviews, and lesson facilitation notes. Each Topic Overview provides “student look-for’s” that describe how students will develop proficiency with the practice. Facilitation notes supply teacher prompts that connect MP8 to the grade-level content standards. The Assessment Guide also aligns MPs to Re-Engagement Lessons, where students reflect on their problem-solving.

The Teacher's Implementation Guide, Embedding Mathematical Habits of Mind states, “The Habits of Mind emphasize problem-solving, reasoning, constructing arguments, and modeling with mathematics to promote critical thinking and real-world application. ClearMath Elementary engages students in these practices by encouraging them to make sense of mathematics and demonstrate their reasoning through problem-solving, writing, discussion, and modeling.” ClearMath Elementary further states that “every lesson engages students in mathematical problem solving, guiding them to explore, discover, and reason. The interleaving of mathematical content and practices ensures students develop these habits of mind across all domains. The focus on discourse requires students to share ideas, evaluate reasoning, and refine understanding while using precise language and persevering in problem-solving.”

Examples include:

• Grade 3, Module 1, Topic 2, Lesson 1, Explore 1, provides students with opportunities to engage in MP8 by looking for and expressing regularity in repeated reasoning. Students create a skip-counting table and use repeated reasoning as a tool to generate multiplication equations.

• Grade 4, Module 3, Topic 6, Lesson 9, Explore 1, provides students with opportunities to engage in MP8 by looking for and expressing regularity in repeated reasoning. Students develop strategies for multiplying one-digit numbers by multiples of 10, 100, and 1,000, and explain their reasoning as they notice repeated calculations. Teachers encourage students to recognize the similarity in the process when factors appear in a different order, supporting generalizations and efficient strategies.

• Grade 5, Module 2, Topic 4, Lesson 3, Explore 2, provides students with opportunities to engage in MP8 by looking for and expressing regularity in repeated reasoning. Students discuss why 10\times10\times10 can be written as 10^{3} and make generalizations about exponential notation.