3rd Grade - Gateway 2

The materials reviewed for Reveal Math Grade 3 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials develop conceptual understanding throughout the grade level, with teacher guidance, through discussion questions and conceptual problems with low computational difficulty. Examples include:

• In Lesson 2-12, Solve Two Step Problems Involving Addition and Subtraction, Launch, students are shown a picture and told, “Lea earns points playing her favorite dance video game. She plays the next level and earns more points. Lea needs points to buy a new song for the game.” Students are asked conceptual questions, such as, “What operation(s) might you use to solve the problem? What information would you need to answer one of the questions?” These questions build their conceptual understanding of 3.OA.8, solve two step word problems using the four operations. 

• In Lesson 5-1, Understand the Distributive Property, Explore & Develop, Activity-Based Exploration, students are given color tiles and grid paper. The teacher asks students to “explore different ways they can decompose a factor to find the product of 6 x 8. They may represent their strategy with an array using color tiles or a drawing on grid paper.” This provides students an opportunity to build their conceptual understanding of 3.OA.5, apply properties of operations as strategies to multiply and divide. 

• In Lesson 10-1, Patterns with Multiples of 10, Bring It Together, students are asked “How would you explain the pattern with multiples of 10 to a friend? How can knowing the pattern with multiples of 10 help you find products?” These questions support conceptual development of standard 3.NBT.3. multiply one-digit whole numbers by multiples of 10 in the range 10-90 using strategies based on place value and properties of operations. 

The materials provide opportunities for students to independently demonstrate conceptual understanding through concrete, semi-concrete, verbal, and written representations. Examples include:

• In Lesson 2-2, Round Multi-Digit Numbers, Extend Thinking, Exercise 2, “Write three numbers possible for each. A number rounded up to the nearest ten is 20.” This exercise provides students an opportunity to independently develop conceptual understanding of 3.NBT.1, use place value understanding to round to the nearest 10 or 100.

• In Lesson 8.1, Understand Equivalent Fractions, Differentiate, Take Another Look: Recognize Equivalent Fractions, “How can you use the fraction models to determine if the fractions are equivalent? Choose equivalent or not equivalent.” This activity provides students an opportunity to independently develop conceptual understanding of 3.NF.3a, understand two fractions as equivalent if they are the same size, or the same point on a number line.

• In Lesson 12-1, Measure Liquid Volume, Activity Based exploration, students share their responses to the question, “How can you explain to a friend how to measure liquid volume?” The teacher then asks them to explain how they know what the unlabeled marks on the container represent. This activity provides students an opportunity to independently develop conceptual understanding of 3.MD.2, measure and estimate liquid volumes and masses of objects using standard units of grams, kilograms, and liters.

The materials reviewed for Reveal Math Grade 3 meet expectations that the materials develop procedural skills and fluency throughout the grade level. The materials provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade level. 

The materials develop procedural skills and fluency throughout the grade with teacher guidance, within standards and clusters that specifically relate to procedural skill and fluency, and build fluency from conceptual understanding. Examples include:

• Fluency Practice exercises are provided at the end of each unit. Each Fluency Practice includes Fluency Strategy, Fluency Flash, Fluency Check, and Fluency Talk. “Fluency practice helps students develop procedural fluency, that is, the ‘ability to apply procedures accurately, efficiently, and flexibly.’ Because there is no expectation of speed, students should not be timed when completing the practice activity.” Fluency Practice exercises in Grade 3 progress toward 3.OA.7, fluently multiply and divide within 100 using strategies, and 3.NBT.2, fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction. 

• In Lesson 2-6, Use Partial Sums to Add, Explore & Develop, Activity Based Exploration, the teacher presents 378 + 546 = ?. In pairs, students solve, “Discuss what it means to decompose each addend by place value. Have students decompose each addend and share. Then have student pairs use the partial sums strategy to solve. Provide base-ten blocks for support as needed.” This activity develops procedural skill and fluency of 3.NBT.2, fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Lesson 4-1, Use Patterns to Multiply by 2, Differentiate, Reinforce Understanding, in small groups, students “spin a spinner labeled 0-9 and call out the number. The students should write two equations that represent doubling the number.” This activity builds the fluency of 3.OA.7, fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division...

• In the Unit 6 overview, Connect Area and Multiplication, Unit  Routines, “The number routines found at the beginning of each lesson help students build number sense and operational fluency. They also help students develop the thinking habits of mind that are important for proficient doers of math.” Four specific routines are provided: About How Much? (build estimating skills), Decompose It (flexibility with numbers), Where Does It Go? (estimating skills using benchmarks), Would You Rather? (flexibility with number sense and mental math operations, enhance decision making). 

The materials provide opportunities for students to independently demonstrate procedural skills and fluency. Examples include:

• In Lesson 4-4, Use Patterns to Multiply by 1 and 0, Exit Ticket, Exercise 1, “Cho makes a list of multiplication equations to find a pattern. A. What is the product? 3 x 2 = ?  4 x 2 = ?  5 x 2 = ?” This problem provides an opportunity for students to demonstrate procedural skill and fluency of 3.OA.7, fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division...

• In Unit 7, Fractions, Fluency Practice, Fluency Talk, “How can you explain to a friend how to multiply by 2?” Students use the doubling strategy to independently demonstrate fluency with multiplication within 100, 3.OA.7, fluently multiply and divide within 1000, using strategies such as the relationship between multiplication and division or properties of operations.

• In Unit 12, Measurement and Data, Fluency Practice, Fluency Check, “What is the product? 3. 3 x 6 = ___ , 4. 9 x 5 = ___ , 5. 7 x 5 = ___…” Students learn a decomposing strategy to become fluent with multiplication within 100 and practice problems that lend themselves to that strategy, 3.OA.7, fluently multiply and divide within 1000, using strategies such as the relationship between multiplication and division or properties of operations.

The materials reviewed for Reveal Math Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Additionally, the materials provide students with the opportunity to independently demonstrate multiple routine and non-routine applications of the mathematics throughout the grade level. 

The materials provide specific opportunities within each unit for students to engage with both routine and non-routine application problems. In the Digital Teacher Center, Program Overview: Learning & Support Resources, Implementation Guide, Focus, Coherence, Rigor, Application, “Students encounter real-world problems throughout each lesson. The On My Own exercises include rich, application-based question types, such as ‘Find the Error’ and ‘Extend Thinking.’ Daily differentiation provides opportunities for application through the Application Station Cards, STEM Adventures, and WebSketch Explorations. The unit performance task found in the Student Edition offers another opportunity for students to solve non-routine application problems.” 

The materials develop application throughout the grade as students solve routine problems in a variety of contexts, and model the contexts mathematically within standards and clusters that specifically relate to application, both dependently and independently. Examples include:

• In Lesson 2-12, Solve Two-Step Problems Involving Addition and Subtraction, Assess, Exit Ticket, Item 2, “Jayle earned $4187 babysitting. She went shopping and bought headphones for $129 and a carrying case for $26. How much money does she have left?” This exercise allows students to develop and apply mathematics of 3.OA.8, solve two-step word problems using the four operations. 

• In Lesson 5-7, Solve Problems Involving Arrays, Differentiate, Reinforce Understanding, Problem 1, “An egg carton has 3 rows with 6 eggs in each row. How many eggs are in the carton?” This exercise allows students to develop and apply mathematics of 3.OA.3, use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. 

• In Lesson 9-4, Understand Division with 1 and 0, Extend Thinking, Exercise 2, “Mark’s sister checks knitting needles out from the Library of Things. She knits 1 headscarf per month. How many headscarves can she knit in 3 months?” This exercise allows students to develop and apply mathematics of 3.OA.7, multiply and divide within 100. 

The materials develop application throughout the grade as students solve non-routine problems in a variety of contexts, and model the contexts mathematically within standards and clusters that specifically relate to application, both dependently and independently. Examples include:

• In Lesson 2-11, Fluently Subtract within 1000, Extend Thinking, Use It! Application Station, “An elementary school raises $1,000 to buy new playground equipment. The school principal asks you for your ideas of which playground items to purchase. 1. What would you suggest the school to buy? Make 3 different lists. Find each list’s total cost. Justify your reasoning for the 3 lists you made. 2. What other expenses might the school have in order to complete this project? How much might these expenses affect your school’s budget of $1000? What ideas might you suggest? How will you present your ideas to the principal?” This exercise allows students to develop and apply mathematics of 3.NBT.2, fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Unit 6, Connect Area and Multiplication, Application Station, Real World Card, Landscape Architecture, “Landscape architects design outdoor spaces. They plan backyards, parks, company grounds, and other outdoor places. They may add trees, steps, fountains, stone tiles, and more interesting features. Be a landscape architect and plan the outdoor space for a house or business. Use grid paper to draw the perimeter of the building. Then begin to plan its outdoor space. Include trees, flowers, and other geometric landscape features. Consider elements such as tiled patios, walkways, and sitting areas. Label all of the dimensions in your plan. (1) How can you find the area of each part of the outdoor space? Record each and show your work. (2) How can you find the number of tiles you would need for your outdoor space? How is this number related to the area? (3) Write 2 problems about your outdoor space that involve multiplication. Trade your problems with another group.” This exercise allows students to develop and apply mathematics of 3.MD.7, relate area to the operations of multiplication and addition.

• In Lesson 12-2, Estimate and Solve Problems with Liquid Volume, Extend Thinking, “Write three word problems that involve liquid volume. Solve. Write an equation to show your work.” This exercise allows students to develop and apply mathematics of 3.MD.2, add, subtract, multiply or divide to solve one-step word problems involving masses or volumes that are given in the same units.

The materials reviewed for Reveal Math Grade 3 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. Additionally, multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout each grade level. 

All three aspects of rigor (conceptual understanding, procedural skill & fluency, and application) are present independently throughout the grade level. Examples include:

• In Lesson 3-1, Understand Equal Groups, On My Own, Problems 3 and 4, students develop conceptual understanding of one meaning of multiplication as the total number of objects in equal groups. Problem 3, “How can you represent the equal groups? 2 equal groups of 7.” Problem 4, “How can you represent the equal groups? 4 equal groups of 5.” 

• In Lesson 4-2, Use Patterns to Multiply by 5, On My Own, Problems 4 - 11, students build procedural skill and fluency to recall multiplication facts. For example, Problem 4, “5 x 9 = ___.” Problem 5, “___ = 5 x 7.” Problem 7, “25 = 5 x ___.”

• In Lesson 11-4, Solve Problems Involving Area and Perimeter, On My Own, Problem 11, students apply their understanding of area and perimeter as they solve real-world problems. “Two rectangular rooms are covered with 36 square feet of tile but are different lengths. How can this be? Explain.”

The materials provide a balance of the three aspects of rigor as multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single topic/unit of study throughout the grade level. Examples include:

• In Lesson 2-12, Solve Two-Step Problems Involving Addition and Subtraction, On My Own, Problem 5, students use their conceptual understanding of addition and subtraction to solve real-world application problems. “Sam and Ben take turns driving. They traveled 417 miles in May and 454 miles in June. If Sam drove 502 of the miles, how many miles did Ben drive?”

• In Lesson 6-1, Understand Area, Learn, students use their conceptual understanding of area in the real world to develop procedural skill and fluency by counting unit squares to measure area in different units. “Misha is choosing a new rug for her room. How can she decide which rug will cover the greater area?”

• In Lesson 11-5, Solve Problems Involving Measurement, On Your Own, Problem 9, students build upon their procedural skill and fluency with using multiplication and division to solve real-world measurement problems. “Sheila tapes together 4 postcards. The total length of the 4 postcards is 24 inches. How long is each postcard? Write an equation to represent the problem.”

The materials reviewed for Reveal Math Grade 3 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Each Unit Overview, Math Practices and Processes section, identifies one mathematical practice that is prevalent in the unit and gives an overview of its use within the unit. In the Standards section of each lesson, mathematical practices for the lesson are also identified; however, in both sections, the mathematical practice is labeled as MPP Reason abstractly and quantitatively, rather than MP1 or MP 2. Within each of the lesson components, the mathematical practices are not labeled or identified, leaving where they are specifically addressed up for interpretation and possible misidentification.

The materials provide intentional development of MP1: Make sense of problems and persevere in solving them, in connection to grade-level content. Examples include:

• In Lesson 6-1, Understand Area, Own My Own, Exercise 11, “Why might it be important to use unit squares rather than other shapes to tile a figure to determine the area?” Students engage with MP1 as they consider different strategies to determine the area.

• In Lesson 10-4, Two-Step Problems Involving Multiplication and Division, Launch, Numberless Word Problem, Be Curious, “What math do you see in the problem? Mason brings juice boxes to soccer practice. He needs more than one juice box for each of the players. The juice boxes are in packages.” Students engage with MP1 as they work to understand the information presented in a numberless problem, and use a variety of strategies to solve the problem.

• In Lesson 11-4, Solve Problems Involving Area and Perimeter, Differentiate, Extend Thinking, “Draw and label two or more figures with the same area but different perimeters. Be sure to include the units.” Students engage with MP1 as they analyze and make sense of the problem.

The materials provide intentional development of MP2: Reason abstractly and quantitatively, in connection to grade-level content. Examples include:

• In Lesson 2-6, Use Partial Sums to Add, Practice & Reflect, Exercise 8, “How can you find the sums in a different way?” Students engage with MP2 as they work to understand the relationships between problem scenarios and mathematical representations.

• In Lesson 4-6, Solve Problems Involving Equal Groups, Own My Own, Exercise 1, “How can you write a multiplication and division equation for the problem? Write a ? for the unknown. 1. Eight friends share 40 apple slices. If each friend receives the same amount of apple slices, how many does each person receive?” Students engage with MP2 as they represent situations symbolically.

• In Teacher’s Guide, Lesson 9-1, Use Multiplication to Solve Division Equations, Guided Exploration, “Students use the relationships between multiplication and division to understand division as an unknown-factor problem. They use fact triangles to rewrite a division equation as an unknown-factor problem to help solve the division equation.” Students engage with MP2 as they work to understand the relationship between multiplication and division.

The materials reviewed for Reveal Math Grade 3 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. 

Each Unit Overview, Math Practices and Processes section, identifies one mathematical practice that is prevalent in the unit, and gives an overview of its use within the unit. In the Standards section of each lesson, mathematical practices for the lesson are also identified; however, in both of these sections, the mathematical practice is labeled MPP: Construct viable arguments and critique the reasoning of others, rather than MP3 Construct viable arguments and critique the reasoning of others. Additionally, the math practices are not identified within the lesson sections, therefore leaving where they are specifically addressed up for interpretation and possible misidentification.

Examples of intentional development of students constructing viable arguments in connection to grade-level content, including guidance for teachers to engage students in MP3 include:

• In Lesson 3-4, Understand Equal Sharing, Own my Own, Exercise 11, students justify their strategies and thinking as they solve,“Emma picks 32 peaches, She needs 8 peaches for each batch of jam. If she makes 4 batches, will she have any peaches left over? Justify your answer.”

• Teacher’s Guide, Lesson 9-7, Divide by 9, Pose the Problem, students answer the following prompts to explain how the multiplication fact table relates to division. “How can you use the rows and columns of the multiplication fact table to find a product? How do the factors in a multiplication equation relate to the numbers in a division equation? Do you think quotients are represented in the multiplication fact table? Explain.”

• In Lesson 11-4, Solve Problems Involving Area and Perimeter, Launch, Be Curious, Is It Always True?, students explain and justify their thinking orally and with drawings. “Two rectangles with the same perimeters always have the same areas. Is the statement always true? How do the areas and perimeters of rectangles compare? How can models help you think about the areas and perimeters of rectangles? How can your models help you draw conclusions about the relationship between perimeters and areas of rectangles?”

Examples of intentional development of students critiquing the reasoning of others in connection to grade-level content, including guidance for teachers to engage students in MP3 include:

• In Lesson 2-5, Addition Patterns, Explore & Develop, Work Together, students critique the reasoning of others as they perform error analysis of provided student work. “Nisha writes 135 + 232 = 167. She says her sum is correct because an odd number added to an even number equals an odd sum. Do you agree with her reasoning? Explain.”

• In Lesson 9-3, Divide by 5 and 10, Own My Own, Exercise 10, students critique the reasoning of others as they perform error analysis of provided student work. “Maya says she can use a related multiplication fact ot help her find the unknown in 30? = 10. Do you agree? Explain.”

• In Lesson 10-5, Solve Two-Step Problems, Differentiate, Extend Thinking, Differentiation Resource Book, Exercise 2, students solve two-step word problems using the four operations to critique the reasoning of others. “Do you agree or disagree with the solution given? Circle your answer and explain your reasoning. Lewis dog sits for 3 weekdays on each of 4 weeks in a month. He also dog sits all weekend one week in a month. He calculates the number of days he has spent dog sitting.”

The materials reviewed for Reveal Math Grade 3 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. 

Each Unit Overview, Math Practices and Processes section, identifies one mathematical practice that is prevalent in the unit, and gives an overview of its use within the unit. In the Standards section of each lesson, mathematical practices for the lesson are also identified; however, in both sections, the mathematical practice is identified as MPP Model with mathematics, rather than MP4. Additionally, the math practices are not identified within the lesson sections, therefore leaving where they are specifically addressed up for interpretation and possible misidentification. 

Examples of intentional development of students modeling with mathematics in connection to grade-level content, including guidance for teachers to engage students in MP4 include:

• In Lesson 3-2, Use Arrays to Multiply, Practice & Reflect, Own My Own, students solve, “How can arrays represent multiplication?” Students engage with MP4 as they describe the model (array) and how it relates to the problem situation (multiplication).

• In Lesson 5-1, Understand Area, Extend Thinking, students, “Draw three or more different figures with areas of 18 square units. Label the sides of each figure. A = 18 square units.” Students model the situation with appropriate representations of figures with 18 square units.

• In Lesson 12-11, Teacher’s Guide, Show Measurement Data on a Line Plot, Activity-Based Exploration, students measure classroom items and students are asked, “How can a line plot help you understand a data set? How can you use a number line to show the data another way?” Students engage with MP4 as they describe what they do with the models and how the models relate to the problem situation.

Examples of intentional development of students using appropriate tools strategically in connection to grade-level content, including guidance for teachers to engage students in MP5 include:

• In Lesson 2-2, Round Multi-Digit Numbers, Guided Exploration, Math is...Choosing Tools, students answer, “Why is a number line helpful for rounding?” Students consider how a number line helps them round to the nearest 10 or 100.

• In Lesson 7-4, Represent One Whole as a Fraction, Math is…Choosing Tools, students answer, “What other tools could you use to show that a fraction with the same numerator and denominator is equal to 1?” Students utilize number lines, fraction strips/tiles, or cubes.

• In Lesson 13-4, Teacher’s Guide, Draw Quadrilaterals with Specific Attributes, Guided Exploration, students examine descriptions of quadrilaterals and are asked, “What tools could you use if you don’t have a ruler? Students brainstorm how to use other items as an appropriate tool if a ruler is not available.” Students engage with MP5 as they consider what other tools they might use to measure if a ruler is not available.

The materials reviewed for Reveal Math Grade 3 meet expectations that there is intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students in connection to the grade-level content standards, as expected by the mathematical practice standards.  

Each Unit Overview, Math Practices and Processes section, identifies one mathematical practice that is prevalent in the unit, and gives an overview of its use within the unit. In the Standards section of each lesson, mathematical practices for the lesson are also identified; however, the mathematical practice is labeled MPP Attend to precision, rather than MP6: Attend to precision. Additionally, the math practices are not identified within the lesson sections, therefore leaving where they are specifically addressed up for interpretation and possible misidentification.

The instructional materials address MP6 in the following components:

• In the Digital Teacher Center, Program Overview: Learning & Support Resources, Implementation Guide, Language of Math, Unit-level Features, “The Language of Math feature highlights math terms that students will use during the unit. New terms are highlighted in yellow. Terms that have a math meaning different from everyday means are also explained.” Math Language Development, “This feature targets one of four language skills - reading, writing, listening, speaking - and offers suggestions for helping students build proficiency with these skills in the math classroom.” Lesson Level Features, “The Language of Math feature promotes the development of key vocabulary terms that support how we talk about and think about math in the context of the lesson content.” Each Unit Review also includes a vocabulary review component which references specific lessons within the unit.

Examples of intentional development of MP6: attend to precision, in connection to the grade-level content standards, as expected by the mathematical practice standards, including guidance for teachers to engage students in MP6 include:

• In Lesson 2-4, Use Addition Properties to Add, Differentiate, Extend Thinking, Exercise 1, “Mr. Reneke is a manager at the Holiday Hotel and is checking his bank deposit. He is adding $205, $450, and $295. How can he use both properties of addition to add more efficiently?” Students attend to precision as they calculate accurately and efficiently.

• In Lesson 6-1, Understand Area, Activity Based Exploration, the teacher asks, “Have you fully covered the figure? How do you know? How do you know you’ve used the fewest number of tiles to cover the figure? How can you determine how many tiles to cover the figure? At what part of the figure makes the most sense to begin placing your tiles? the middle? a corner?” Students attend to precision as they use tiles to cover a figure without gaps or overlaps, and calculate the area.

• In Lesson 7-6, Represent a Fraction Greater Than One on a Number Line, Own my Own, Exercise 2, “How can you label the missing fractions on the number line? Which fractions are greater than 1? Circle them.” Students attend to precision as they label a number line with fractional increments. 

Examples of where the instructional materials attend to the specialized language of mathematics, including guidance for teachers to engage students in MP6 include:

• In Unit 3, Multiplication and Division, Unit Review, Vocabulary Review, Exercise 1 and 2, “You can use _____ to find the product of two or more numbers. When you share objects equally among groups, you can use _____ to determine the number of objects in each group.” Students have a list of words to use, “Use the vocabulary to complete each sentence. (division, equal groups, factors, multiplication, product, quotient)” Students attend to the specialized language of mathematics as they complete sentences using vocabulary from the unit.

• In Lesson 6-3, Use Multiplication to Determine Area, Explore & Develop, Work Together, “How can you find the area of the square using the side length?” Students attend to the specialized language of mathematics as they explain how to calculate area using only the side length of a square.

• In Lesson 10-2, More Multiplication Patterns, Practice & Reflect, Own my Own, Exercise 8a, “Circle the multiplication facts that will have an even product. 4 x 5, 3 x 6, 1 x 9, 2 x 4, 5 x 7, 5 x 2, 7 x 8, 10 x 6 Explain why the products are even.” Students attend to the specialized language of mathematics  as they explain why the products are even using factors and products.

The materials reviewed for Reveal Math Grade 3 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

Each Unit Overview, Math Practices and Processes section, identifies one mathematical practice that is prevalent in the unit, and gives an overview of its use within the unit. In the Standards section of each lesson, mathematical practices for the lesson are also identified; however, the mathematical practice is labeled MPP  Look for and make use of structure, rather than MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning. Additionally, the math practices are not identified within the lesson sections, therefore leaving where they are specifically addressed up for interpretation and possible misidentification. 

Examples of intentional development of students looking for and making use of structure, to meet its full intent in connection to grade-level content, including guidance for teachers to engage students in MP7 include:

• In Lesson 2-4, Use Addition Properties to Add, Guided Exploration, Math is...Structure, students answer “How can changing the order of addends make it easier to add?” Students engage with MP7 as they consider how changing the order of the addends makes it easier to add numbers.

• In Lesson 7-3, Represent Fractions on a Number Line, Guided Exploration, Math is… Structure, students answer “How is partitioning a number line like partitioning a shape?” Students engage with MP7 as they relate partitioning a number line to partitioning a shape.

• In Lesson 13-1, Describe and Classify Polygons, Guided Exploration, Math is...Structure, students answer “Why is categorizing and naming shapes important?” Students engage with MP7 as they classify pattern blocks into groups.

Examples of intentional development of students looking for and expressing regularity in repeated reasoning, including guidance for teachers to engage students in MP 8 include:

• In Lesson 2-5, Addition Patterns, Guided Exploration, Math is...Generalizations, students answer “Why is it true that the sum of two odd numbers is always even?” Students engage with MP8 as they consider why the sum of two odd addends is always even.

• In Lesson 5-1, Understand the Distributive Property, Own My Own, Reflect, “How can decomposing a factor help solve a multiplication equation?” Students engage with MP8 as they describe a general process and method.

• In Lesson 7-2, Understand Fractions, Activity-Based Exploration, Math is...Generalizations, students answer, “What happens to the size of each equal part as the digit in the denominator increases? Explain why.” Students engage with MP8 as they “conclude that as the digit in the denominator increases, the size of the parts decreases because the whole is partitioned into more pieces.”