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.”

The materials reviewed for Reveal Math Grade 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include:

• The Implementation Guide provides a program guide, which includes a program overview, the program components, unit features, instructional model, lesson walk-through, and a brief description of the different unit components, such as Math is…, focus, coherence, rigor, and language of math.  

• The Implementation Guide provides pacing for each unit; mapping out the lessons in each unit and how many days the unit will take.

• The Unit Planner contains an overview of the Lessons within the unit, Math Objective, Language Objective, Key Vocabulary, Materials to Gather, Rigor Focus, and Standard.

• The Unit Overview provides a description for teachers as to how the unit connects to Focus, Coherence, and Rigor. 

• Within each lesson, the Language of Math section, provides teachers with specific information about the vocabulary used in lessons and how to utilize vocabulary cards to enhance learning experiences. 

• In Unit 4, Use Patterns to Multiply by 0, 1, 2, 5, and 10, Unit Overview, Effective Teaching Practices, Pose Purposeful Questions, “In order to guide students toward new concepts or extend their understanding of concepts, purposeful questions are used. When questions are purposeful, they provide focus toward a particular goal or concept. These questions ensure that students are not just repeating information, but are also encouraged to discover the answers on their own. When learning is more discovery based, students comprehend mathematical ideas and relationships better. Additionally, listening to students’ answers to purposeful questions is a great way to assess students’ current knowledge. Students’ answers help guide instruction toward the concepts that need to be expanded upon to help students reach full comprehension.”

• In Unit 8, Fraction Equivalence and Comparison, Unit Overview, Math Practices and Processes, Make Sense of Problems and Persevere in Solving Them, “To help students build proficiency with making sense of problems and solving them, they need opportunities to interact with different types of problems. Some suggestions for making sense of problems include:

  • students restate what problems are asking, such as how to determine which fraction is larger when the denominators are the same;

  • students use various representations to visualize equivalent fractions. Encourage students to use fraction charts, fraction circles, and fraction tiles to see the correlations between these representations and to justify their actions.

  • students relate the concepts they have learned previously to current concepts to uncover connections between numerators and denominators when deciding whether two fractions are equivalent.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. The materials provide information about planning instruction, and give suggestions for presenting instructional strategies and content, as well as mathematical practices. Examples include:

• In Lesson 12-1, Measure Liquid Volume, Notice & Wonder, Teaching Tip, “Have students draw on their previous learning by encouraging them to think about when they have measured the length of an object using inches, feet, centimeter, and meters. Students can build on their prior knowledge of comparing the length of two measurements to compare liquid volumes.” 

• In Lesson 12-11, Show Measurement Data on a Line Plot, Bring It Together, Language of Math, “ Students need multiple opportunities to practice the language of mathematics. Throughout the lesson, ask them the meaning of the term scale in the context of a line plot. Encourage students to use words such as halves, fourths, and data to help them become comfortable discussing mathematical modeling with precise language.”

The materials reviewed for Reveal Math Grade 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level. Examples of how individual units, lessons, or activities throughout the series are correlated to the CCSSM include:

• In the Digital Teacher Center, Program Overview: Learning & Support Resources, Implementation Guide, Correlations, identifies the standards included in each lesson. This guide also indicates whether the standards are considered major, supporting, or additional standards. 

• Each Unit Planner includes a pacing guide identifying the standards that will be addressed in each lesson.

• In Lesson 4-4, Use Patterns to Multiply by 1 and 0, the materials identify standards 3.OA.7, fluently multiply and divide within 100 and 3.OA.9, identify arithmetic patterns and explain them using properties of operations. The lesson also identifies the MPs 5 and 7. 

• In Lesson 10-6, Explain the Reasonableness of a Solution, the materials identify standard 3.OA.8, solve two-step word problems using the four operations. The lesson also identifies the MPs 1 and 6. 

Explanations of the role of the specific grade-level mathematics are present in the context of the series, and teacher materials provide information to allow for coherence across multiple course levels. This allows the teacher to make prior connections and teach for connections to future content. Examples include:

• The Unit Overview includes the section, Coherence, identifying What Students Have Learned, What Students Are Learning, What Students Will Learn. In Unit 3, Multiplication and Division, What Students Have Learned, “Repeated Addition and Arrays Students used repeated addition to find the total number of objects in an array. (Grade 2), Equal Groups of Students determined whether a group of objects was odd or even by pairing objects into two equal groups. (Grade 2), Relate Addition and Subtraction Students add and subtract within 100 using the relationship between addition and subtraction. (Grade 2)” In What Students are Learning, “Understand Multiplication Students understand that multiplication represents the total number of objects in equal groups., Understand Division Students understand that division can represent equal sharing or equal grouping., Relate Multiplication and Division Students use representations to understand the relationship between multiplication and division.” In What Students Will Learn, “Multiply Within 100 Students use patterns and multiplication properties to multiply within 100. (Units 4 and 5), Divide Within 100 Students use strategies to divide within 100. (Unit 9), Relate Multiplication and Division Students use the relationship between multiplication and division to solve division equations. (Unit 9)”

• Each lesson begins by listing the standards covered within the lesson, indicates whether the standard is a major, supporting or additional standard and identifies the Standards for Mathematical Practice for the lesson. Each lesson overview contains a coherence section that provides connections to prior and future work. In Lesson 7-6, Represent a Fraction greater Than One on a Number Line, Coherence, Previous, “Students represented fractions as one or more parts (Unit 7). Students represented fractions on a number line by partitioning the distance into equal parts (Unit 7).” Now, “Students identify fractions greater than 1 on a number line., Students recognize a fraction with a numerator greater than the denominator represents a number greater than one whole.” Next, “Students find equivalent fractions and compare fractions with the same numerator or the same denominator (Unit 8)., Students add and subtract fractions (Grade 4).”

The materials reviewed for Reveal Math Grade 3 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials explain the instructional approaches of the program. Examples include:

• Digital Teacher Center, Program Overview: Learning & Support Resources, Teacher Welcome Letter Template specifies “Reveal Math, a balanced elementary math program, develops the problem solvers of tomorrow by incorporating both inquiry-focused and teacher-guided instructional strategies within each lesson.” 

• Teacher Guide, Volume 1, Welcome to Reveal Math, the overall organization of the math curriculum has five goals:

  • “The lesson model offers two instructional options for each lesson: a guided exploration that is teacher-guided and an activity-based exploration that has students exploring concepts through small group activities and drawing generalizations and understanding from the activities.

  • The lesson model incorporates an initial sense-making activity that builds students’ proficiency with problem solving. By focusing systematically on sense-making, students develop and refine not just their observation and questioning skills, but the foundation for mathematical modeling.

  • Both instructional options focus on fostering mathematical language and rich mathematical discourse by including probing questions and prompts.

  • The Math is… unit builds student agency for mathematics. Students consider their strengths in mathematics, the thinking habits of proficient “doers of mathematics,” and the classroom norms that are important to a productive learning environment.

  • The scope and sequence reflects the learning progressions recommended by leading mathematicians and mathematics educators. It emphasizes developing deep understanding of the grade-level concepts and fluency with skills, while also providing rich opportunities to apply concepts to solve problems.”

The Implementation Guide, located in the Digital Teacher Center, further explains the instructional approaches of specific components of the program. Examples include: 

• Unit Features, Unit Planner, “Provides at-a-glance information to help teachers prepare for the unit. Includes pacing: content, language, and SEL objectives; key vocabulary including math and academic terms; materials to gather; rigor focus; and standard (s).”

• Unit Features, Readiness Diagnostic, “Offers teachers a unit diagnostic that can be administered in print or in digital. The digital assessment is auto-scored. Assesses prerequisite skills that students need to be successful with unit content. Item analysis lists DOK level, skill focus, and standard of each item. Item analysis also lists intervention lessons that teachers can assign to students or use in small group instruction.”

• Unit Features, Spark Student Curiosity Through Ignite! Activities, “Each unit opens with an Ignite! Activity, an interesting problem or puzzle that: Sparks students’ interest and curiosity, Provides only enough information to open up students’ thinking, and Motivates them to persevere through challenges involved in problem solving.”

• Instructional Model, “Reveal Math’s lesson model keeps sense-making and exploration at the heart of learning. Every lesson provides two instructional options to develop the math content and tailor the lesson to the needs and structures of the classroom.” Each lesson follows the same structure of a “Launch, Explore & Develop, Practice & Reflect, Assess and Differentiate.” Each of these sections is further explained in the instruction manual.

• Number Routines, in each lesson there is a highlighted number routine for teachers to engage students with. These routines “are designed to build students’ proficiency with number and number sense. They promote an efficient and flexible application of strategies to solve unknown problems…”

The Implementation Guide, located in the Digital Teacher Center, discusses some of the research based features of the program. Examples include: 

• Implementation Guide, Effective Mathematical Teaching Practices, “Reveal Math’s instructional design integrates the Effective Mathematics Teaching Practices from the National Council of Teachers of Mathematics (NCTM). These research-based teaching practices were first presented and described in NCTM’s 2014 work Principles to Action: Ensuring Mathematical Success for All.”

• Implementation Guide, Social and Emotional Learning, “In addition to academic skills, schools are also a primary place for students to build social skills. When students learn to manage their emotions and behaviors and to interact productively with classmates, they are more likely to achieve academic success Research has shown that a focus on helping students develop social and emotional skills improves not just academic achievement, but students’ attitudes toward school and prosocial behaviors (Durlak et al., 2011)...”

• Implementation Guide, Support for English Learners, Lesson-level support, English Learner Scaffolds, each lesson has an “English Learner Scaffolds” section to support teachers with “scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, Developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language Development Standards.”

• Implementation Guide, Math Language Routines, throughout the materials certain language routines are highlighted for teachers to encourage during a lesson, these routines were developed by a team of authors at Center for Assessment, Learning and Equity at Standard University and are “based on principles for the design of mathematics curricula that promote both content and language.” In the implementation guide, the material lists all eight Math Language routines and their purposes, “MLR1: Stronger and Clearer Each Time - Students revise and refine their ideas as well as their verbal or written outputs.”

• Implementation Guide, Math Probe - Formative Assessment, each unit contains a Math Probe written by Cheryl Tobey. Math Probes take time to discover what misconceptions might still exist for students. Designed to ACT, “The teacher support materials that accompany the Math Probes are designed around an ACT cycle - Analyze the Probe, Collect and Assess Student Work, and Take Action. The ACT cycle was originally developed during the creation of a set of math probes and teacher resources for a Mathematics and science Partnership Project.”

The materials reviewed for Reveal Math Grade 3 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

The Digital Teacher Center, Program Resources: Course Materials, Planning Resources, Materials List: Grade 3 specifies the comprehensive materials list. The document specifies classroom materials (e.g., playing cards, dot cube, whiteboards, etc.), materials from a manipulative kit (e.g., pattern blocks, plastic coins, color tiles, etc.), non-consumable teaching resources (e.g.,place value charts to 1,000s, blank fact triangles, pattern blocks, etc.), and consumable teaching resources (e.g., problem-solving tool, tiling figures, bar graphs, etc.).

In the Teacher Edition, each Unit Planner page lists materials needed for each lesson in the unit, for example, Unit 7, Fractions, Materials to Gather:

• “Lesson 7-1 - blank cubes, grid paper, index cards, scissors

• Lesson 7-2 - fraction circles, index cards

• Lesson 7-3 - rulers

• Lesson 7-4 - blank cubes, fraction tiles

• Lesson 7-5 - blank cubes, fraction tiles

• Lesson 7-6 - fraction circles, fraction tiles, markers, whiteboards.”

At the beginning of each lesson in the “Materials” section, a list of materials needed for each part of the lesson is provided: 

• In Lesson 7-2, Understand Fractions, Materials, “The materials may be for any part of the lesson: fraction circles and index cards.”

• In Lesson 8-7, Compare Fractions, Materials, “The materials may be for any part of the lesson: Blank cubes (labeled 1,2,3,4,6,8), fraction circles, fraction tiles, grid paper, index cards.”

• In Lesson 10-2, More Multiplication Patterns, Materials, “The materials may be for any part of the lesson: colored pencils, index cards, Multiplication Fact Table, to 10 Teaching Resource.”

The materials reviewed for Reveal Math Grade 3 meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

Each unit, beginning with Unit 2, offers a Readiness Diagnostic that assesses the content of the unit and gives teachers a snapshot of the prerequisite skills the students already possess. Each unit also includes a Unit Assessment that evaluates students’ understanding of and fluency with concepts and skills from the unit. In the Teacher Edition, an Item Analysis lists each item’s DOK level, skill focus, content standard, and a Guided Support Intervention Lesson that teachers can assign or use for small groups or remediation. For example:

• In Unit 3, Multiplication and Division, Unit Assessment (Form A), Item 5 lists “Model Multiplication (Objects)” as the Guided Support Intervention Lesson. This resource can be located in the Digital Teacher Center in the Targeted Intervention section of the Unit.

Unit Performance Tasks include a scoring rubric that evaluates student work for each section on a 2, 1, or 0 point scale. No follow-up guidance is provided for the Performance Task. For example:

• In Unit 6, Connect Area and Multiplication, Performance Task Part A, Rubric (8 points), “2 Points: Students’ work reflects proficiency with finding the area of a rectangle and adding the areas. The students’ answers are all correct. 1 Point: Students’ work reflects developing proficiency with finding the area of a rectangle and adding the areas. Some of the students’ answers are incorrect. 0 Points: Students’ work reflects weak proficiency with finding the area of a rectangle and adding the areas. The students’ answers are incorrect.”

Math Probes analyze students’ misconceptions and are provided at least one time per Unit, beginning with Unit 2. In the Teacher Edition, “Authentic Student Work” samples are provided with correct student work and explanations. An “IF incorrect…, THEN the student likely…Sample Misconceptions” chart is provided to help teachers analyze student responses. A Take Action section gives teachers suggestions and resources for follow up or remediation as needed. There is a “Revisit the Probe” with discussion questions for students to review their initial answers after they are provided additional instruction, along with a Metacognitive Check for students to reflect on their own learning. For example:

• In Unit 5, Use Properties to Multiply by 3, 4, 6, 7, 8, and 9, Math Probe, Analyze The Probe, Targeted Concept, “Use known facts and the Distributive Property to decompose a number multiplied by 7 or 9- and then distribute the 7 or 9 to both addends. Decide which strategies can be used to find the product of the two factors.” Students “Decide which strategies can be used to find the product of two factors.” For example, “Problem 1, Which of these show a strategy for multiplying 7 x 6? Circle all correct strategies. a. 7 x 5 + 7 x 1, b. 7 x 5 + 1, c. 7 x 3 + 7 x 3, d. 7 x 7 + 6.” Targeted Misconceptions: Some students have difficulty determining a decompose and distribute strategy when written in abstract form. They may focus only on the decomposed number and not on the distribution of the 7 or 9. They may interpret the decomposition by addition or subtraction, but they may not recognize the distribution process.” Sample Student work is provided, along with “IF incorrect...THEN the student likely…” explanations of the sample misconception are provided.

Exit Tickets are provided at the end of each lesson and evaluate students’ understanding of the lesson concepts and provide data to inform differentiation. Each includes a Metacognitive Check allowing students to reflect on their understanding of lesson concepts on a scale of 1 to 3, with 3 being the highest confidence, and beginning in Unit 2, include an Exit Skill Tracker that lists each item’s DOK, skill, and standard. The Exit Ticket Recommendations chart provides information regarding which differentiation activity to assign based on the student’s score. For example, “If students score…Then have students do” which provides teachers information on what Differentiation activities to use such as Reinforce Understanding, Build Proficiency or Extend Thinking. For example:

• In Lesson 11-1, Understand Perimeter, Exit Ticket, Item 1, “How can you find the perimeter of the figure? Use the grid to answer the question. ___ units.” Exit Ticket Recommendations: “If students score 3 of 3, Then have students do Additional Practice or any of the B (Build Proficiency) or E (Extend Thinking) activities. If students score 2 of 3, Then have students Take Another Look or any of the B activities. If students score 1 or fewer of 3, Then have students do Small Group Intervention or any of the R (Reinforce Understanding) activities.”

The materials reviewed for Reveal Math Grade 3 meet expectations that assessments include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series. 

Reveal Math offers a variety of opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices. While content standards and DOK levels are consistently identified for teachers in the Teacher Edition, and content standards are labeled for students in digital assessments, the standards for mathematical practice are not identified for teachers or students. It was noted that although assessment items do not clearly label the MPs, students are provided opportunities to engage with the mathematical practices.

Unit Readiness Diagnostics are given at the beginning of each unit, beginning with Unit 2. Formative assessments include Work Together, Exit Tickets, and Math Probes. Summative assessments include Unit Assessment Forms A and B, and Unit Performance Tasks at the end of a unit. Benchmark Assessments are administered after multiple units, and an End of the Year (Summative) Assessment is given at the end of the school year. Examples include:

• In Lesson 5-7, Solve Problems Involving Arrays, Assess, Exit Ticket, Item 3, supports the full intent 3.OA.3 (Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities…), and MP7 (Look for and make use of structure) as students look for patterns to make generalizations and solve problems. “Heather has 4 shelves. She puts 8 rolls of toilet paper on each shelf. How many rolls of toilet paper does she have? Draw an array or decompose a doctor to solve.”

• In Unit 8, Fraction Equivalence and Comparison, Performance Task, supports the full intent of 3.NF.3a (Understand two fractions as equivalent if they are the same size, or the same point on a number line), 3.NF.3d (Compare two fractions with the same numerator or the same denominator by reasoning about their size.), and MP5 (Use appropriate tools strategically) as students choose an appropriate tool or strategy that will help them solve the problem. “The students in Ms. Walton’s science club are learning about mealworms. Each student makes a home for their mealworm in a plastic container. They provide mealworms with water, food, and bedding. Then they measure their mealworm. The table shows the lengths of each mealworm. Part A: Which mealworms are the same length? Show how you know by using drawings, number lines, fraction models, or words. Which mealworm is longer - A or B? Explain how you know.”

• In Unit 11, Perimeter, Unit Assessment Form A, Item 2 supports the full intent of 3.MD.8 (Solve real world and mathematical problems involving perimeters of polygons, including perimeter given the side lengths, finding and unknown side length … , and MP2 (Reason abstractly and quantitatively) as students determine the unknown side length of a polygon.     “Rashid uses 48 inches of string to make the figure shown. What is the unknown side length? A. 8 inches, B. 9 inches, C. 10 inches, D. 19 inches.”

• Summative Assessment, Item Analysis, Item 16 supports the full intent of 3.NF.2a (Represent fractions on a number line), and MP6 (Attend to precision) as students plot a fraction on a number line. “Where is $\frac{1}{4}$ on the number line? Place a point on $\frac{1}{4}$.”

The materials reviewed for Reveal Math Grade 3 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

There are multiple locations of supports for students in special populations at the unit and lesson level. These supports are specifically aligned to lessons and standards, making them engaging in a variety of ways. They also scaffold up to the learning instead of simplifying or lowering expectations. 

The Implementation Guide, Support for English Learners, identifies three features at the Unit level:

• “The Math Language Development feature offers insights into one of the four areas of language competence - reading, writing, listening, and speaking - strategies to build students’ proficiency with language.”

• The English Language Learner feature provides an overview of the lesson-level support.”  

• The Math Language Routines feature consists of a listing of the Math Language Routines found in each lesson of the unit.” 

The Implementation Guide, Support for English Learners, also identifies three features at the Lesson level:

• Language Objectives: “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus for the lesson for English Learners. The language objective also identifies the Math Language Routines for the Lesson.”

• English Learner Scaffolds: “English Learner Scaffolds provide teachers with scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, Developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language Development Standards. With these three levels, teachers can scaffold instruction to the appropriate level of language proficiency for their students.”  

• Math Language Routines: “Each lesson has at least one Math Language Routine specifically designed to engage English Learners in math and language.”  

The Implementation Guide, Differentiation Resources, provides a variety of small group activities and resources to support differentiation to sufficiently engage students in grade level mathematics. Examples include: 

• Reinforce Understanding: “These teacher-facilitated small group activities are designed to revisit lesson concepts for students who may need additional instruction.”  

• Build Proficiency: “Students can work in pairs or small groups on the print-based Game Station activities, written by Dr. Nicki Newton, or they can opt to play a game in the Digital Station that helps build fluency.”  

• Extend Thinking: “The Application Station tasks offer non-routine problems for students to work on in pairs or small groups.”   

The Implementation Guide, Differentiation Resources, provides a variety of independent activities and resources to support differentiation to sufficiently engage students in grade level mathematics. Examples include:

• Reinforce Understanding: “Students in need of additional instruction on the lesson concepts can complete either the Take Another Look mini-lessons, which are digital activities, or the print-based Reinforce Understanding activity master.”

• Build Proficiency: “Additional Practice and Spiral Review assignments can be completed in either print or digital environment. The digital assignments include learning aids that students can access as they work through the assignment. The digital assignments are also auto-scored to give students immediate feedback on their work.”  

• Extend Thinking: “The STEM Adventures and Websketch activities powered by Geometer’s Sketchpad offer students opportunities to solve non-routine problems in a digital environment. The print-based Extend Thinking activity master offers an enrichment or extension activity.”  

The Teacher Edition and Implementation Guide provide overarching guidance for teachers on how to use the supports provided within the program. Examples include:

• Teacher Edition, Volume 1, Lesson Model: Differentiate, for every lesson, there are multiple options for teachers to choose to support student learning. Based on data from Exit Tickets, students can reinforce lesson skills with “Reinforce Understanding” opportunities, practice their learning with “Build Proficiency” opportunities, or extend and apply their learning with “Extend Thinking” opportunities. Within each of these opportunities, there are options of workstations, online activities and independent practice for teachers to elect to use. 

• Implementation Guide, Targeted Intervention, “Targeted intervention resources are available to assign students based on their performance on all Unit Readiness Diagnostics and Unit Assessments. The Item Analysis table lists the appropriate resources for the identified concept or skill gaps. Intervention resources can be found in the Teacher Center in both the Unit Overview and Unit Review and Assess sections.”  The Item Analysis can be found in the Teacher Edition. Intervention resources include Guided Support, “Guided Support provides a teacher-facilitated small group mini-lesson that uses concrete modeling and discussion to build conceptual understanding” and Skills Support, “Skills Support are skills-based practice sheets that offer targeted practice of previously taught items.”  Both of these can be located in the Digital Teacher Center.

The materials reviewed for Reveal Math Grade 3 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Each unit opens with an “Ignite!” activity that poses an interesting problem or puzzle to activate prior knowledge and spark students’ curiosity around the mathematics for the unit. In the Digital Teacher Center, “What are Ignite! Activities?” video, contributing author Raj Shah, Ph.D., explains, “An Ignite! Activity is an opportunity to build the culture of your classroom around problem-solving, exploration, discovery and curiosity.” The activity gives teachers, “the opportunity to see what the students can do on their own, without having to pre-teach them anything.” This provides an opportunity for advanced students to bring prior knowledge and their own abilities to make insightful observations. 

The Teacher Edition, Unit Resources At-A-Glance page includes a Workstations table which, “offers rich and varied resources that teachers can use to differentiate and enrich students’ instructional experiences with the unit content. The table presents an overview of the resources available for the unit with recommendations for when to use.” This table includes Games Station, Digital Station, and Application Station. 

Within each lesson, there are opportunities for students to engage in extension activities and questions of a higher level of complexity. The Practice & Reflect, On My Own section of the lesson provides an Item Analysis table showing the aspect of rigor and DOK level of each item. The Exit Ticket at the end of each lesson provides differentiation that includes extension through a variety of activities.

Additionally, there are no instances of advanced students doing more assignments than their classmates.

The materials reviewed for Reveal Math Grade 3 meet expectations for providing strategies and supports for students who read, write, and/or speak in a language other than English to regularly participate in learning grade-level mathematics.

The materials provide strategies for all students to foster their regular and active participation in learning mathematics, as well as, specific supports for English Learners. 

In the Implementation Guide, Support for English Learners, Unit-level support, “At the unit level are three features that provide support for teachers as they prepare to teach English Learners. The Math Language Development feature offers insights into one of the four areas of language competence - reading, writing, listening, and speaking - and strategies to build students’ proficiency with language. The English Language Learner feature provides an overview of lesson-level support. The Math Language Routines feature consists of a listing of the Math Language Routines found in each lesson of the unit.” The Unit Overview also includes a Language of Math section highlighting key vocabulary from the unit. These sections provide an overview of the strategies present within the unit ,and give guidance as to possible misconceptions or challenges that EL students may face with language demands. Included within the Unit Review is a Vocabulary Review that includes an Item Analysis for each item as well as what lesson/s the term was found in.  

At the lesson level, there are supports to engage ELs in grade-level content and develop knowledge of the subject matter. These involve oral language development and reading and writing activities. The Teacher Edition and Implementation Guide outline these features. Examples include:

• Language Objective, “In addition to a content objective, each lesson has a language objective that identifies a linguistic focus of the lesson for English Learners. The language objective also identifies the Math Language Routine of the lesson.”

• Math Language Routine, “Each lesson has at least one Math Language Routine specifically designed to engage English Learners in math and language.” Math Language Routines (MLR), listed and described in the Implementation Guide include: Stronger and Clearer Each Time, Collect and Display, Critique, Correct, and Clarify, Information Gap, Co-Craft Questions and Problems, Three Reads, Compare and Connect, Discussion Supports.

• English Learner Scaffolds, “English Learner Scaffolds provide teachers with scaffolded instruction to help students make meaning of math vocabulary, ideas, and concepts in context. The three levels of scaffolding within each lesson - Entering/Emerging, developing/Expanding, and Bridging/Reaching are based on the 5 proficiency levels of the WIDA English Language development Standards. With these three levels, teachers can scaffold instruction to the appropriate level of language proficiency of their students.”

• Language of Math, ”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.”

• Number Routines such as “Would You Rather?” or “Math Pictures” and Sense-Making Routines such as “Notice and Wonder” or “Which Doesn’t Belong?” provide opportunities to develop and strengthen number sense and problem solving through discussion or written responses.

Most materials are available in Spanish such as the Student Edition, Student Practice Book (print), Student eBook, Math Replay Videos, eGlossary, and Family Letter (digital).

The materials reviewed for Reveal Math Grade 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent, and when appropriate, are connected to written methods.

Physical manipulatives needed for each unit and lesson can be found in the Teacher Edition, Unit Planner, at the beginning of each unit under “Materials to Gather”. Each lesson also identifies needed materials in the “Materials” section on the first page of each lesson.

Virtual manipulatives can be found online under “e-Toolkit”. Manipulatives are used throughout the program to help students develop a concept or explain their thinking. They are used to develop conceptual understanding and connect concrete representations to a written method.