## Reveal Math

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### Overall Summary

The materials reviewed for Reveal Math Grade 2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence, and in Gateway 2, the materials meet expectations for rigor and practice-content connections.

###### Alignment
Meets Expectations
###### Usability
Meets Expectations

### Focus & Coherence

The materials reviewed for Reveal Math Grade 2 meet expectations for focus and coherence. For focus, the materials assess grade-level content and partially provide all students extensive work with grade-level problems to meet the full intent of grade-level standards. For coherence, the materials are coherent and consistent with the CCSSM.

##### Gateway 1
Meets Expectations

#### Criterion 1.1: Focus

Materials assess grade-level content and give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Reveal Math Grade 2 partially meet expectations for focus as they assess grade-level content and partially provide all students extensive work with grade-level problems to meet the full intent of grade-level standards.

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Materials assess the grade-level content and, if applicable, content from earlier grades.

The materials reviewed for Reveal Math Grade 2 meet expectations for assessing grade-level content, and if applicable, content from earlier grades. Summative Assessments include Unit Assessments (Forms A and B), Unit Performance Tasks, Benchmark Assessments, and an End of the Year Summative Assessment. Also included in the digital Teacher Center are editable, auto- scored assessments. Unit 1 does not include a Unit Assessment or Performance Task.

Examples of grade-level assessment items include:

• In Unit 2, Place Value to 1,000, Digital Unit Assessment, Form B, Item 15, “Artem uses base-ten blocks to make a number. He uses 3 hundreds, 4 ones, and 1 ten. Is the number Artem makes greater than, less than, or equal to 304? Explain your answer.” (2.NBT.4)

• In Unit 3, Patterns within Numbers, Performance Task, Part C, “Beth buys 6 green balloons and 7 pink balloons. Explain how you know Beth has an odd number of balloons. How could Beth get to an even number of balloons?” (2.OA.3)

• In Unit 9, Strategies to Add 3-Digit Numbers, Unit Assessment, Form A, Item 4, “Colleen read 361 pages in a book. She reads 10 more pages. How many pages has Colleen read in all? A. 362 pages, B. 371 pages. C. 461 pages, D. 471 pages.” [371 books] (2.NBT.7)

• Benchmark Assessment 2, Item 2, “Look at the equation. ? - 23 = 52. Which is the unknown number? A. 29, B. 31, C. 72, D.  75.” [75] (2.NBT.5)

• Summative Assessment, Item 9, “What time is shown on the clock? A. 2:10, B. 1:50, C. 2:50, D. 10:10.” [1:50] (2.MD.7)

##### Indicator {{'1b' | indicatorName}}

Materials give all students extensive work with grade-level problems to meet the full intent of grade-level standards.

The materials reviewed for Reveal Math Grade 2 partially meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. Within the materials all standards are represented and most meet the full intent of the grade-level standard. However, the materials provide limited opportunities for all students to engage in extensive work with grade-level problems in standards 2.NBT.6, 2.MD.7, and 2.G.2. Additionally, the materials do not provide opportunities for students to meet the full intent of standard 2.NBT.4.

Examples where the materials engage all students in extensive work with grade-level problems to meet the full intent of the standard include:

• In Lesson 5-2, More Strategies to Add Fluently Within 20, Launch, Notice & Wonder, students are shown a visual representing a case of six noodle boxes with 2 rows of 3 in each row and one box out to the side.  “Teaching Tip: Have students think about how they could lift the boxes of noodles out of the container two at a time. This can help them visualize the doubles. Understanding that the contained boxes of noodles can be represented as doubles will help the students realize the total number of boxes of noodles can be represented as near doubles.” This exercise provides the opportunity to fully engage with the standard 2.OA.2, fluently add and subtract within 20 using mental strategies. By end of grade 2, know from memory all sums of two one-digit numbers.

• In Lesson 6-10, Solve Two-Step Problems Using Subtraction, Practice & Reflect, On My Own, Exercise 1, “Edwin has 36 t-shirts. 15 of his t-shirts are white, 7 are blue, and the rest are green. How many green t-shirts does Edwin have?” Students can use any strategy to represent and solve this two-step word problem. This exercise engages the students with the full intent of 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem.

• In Lesson 7-11, Solve More Problems Involving Length, Explore & Develop, Develop the Math, Digital Guided Exploration: Solve More Problems Involving Length, “Diane draws a line 26 centimeters long. Oliver draws a line 15 centimeters long. How much longer is Diane’s line than Oliver’s line?” In Activity-Based Exploration, Activity Debrief, “Have students explain the equations and strategies they used to solve the problem. Invite students to share how they used a number line to solve the equation.” Practice & Reflect, On My Own, Exercises 3 and 4, “How can you make a drawing and write an equation to represent the problem? Use the number line to solve.” This meets the full intent of both 2.MD.5, use addition and subtraction within 100 to solve word problems involving lengths that are given in the same units, e.g., by using drawings (such as drawings of rulers) and equations with a symbol for the unknown number to represent the problem, and 2.MD.6, represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

• In Lesson 9-7, Explain Addition Strategies, Practice and Reflect, On My Own, Exercise 5, Stem Connection, “Deven mixed 427 minutes of music and 508 minutes of nature sounds.  How many minutes of audio did he mix? Explain what strategy you used and why.” Exercise 6, Extend your thinking, states, “Use two different addition strategies to find the sum of 129 + 287.  Which strategy do you think is more useful for these numbers?  Why?” In Lesson 10-8, Explain Subtraction Strategies, Practice and Reflect, On My Own, “Fill in the correct answer to complete the sentence.” Exercise 1, “To count on to find the difference of 493 - 217, start at ____.”  [217] Exercise 2, “To count back to find the difference of 872 - 549, start at ____.” [872] Exercises 6 and 7, “Use a subtraction strategy to solve. Then explain the subtraction strategy you used.” Exercise 6, “867- 189 = _____.”  Exercise 7, “Hallie has 500 blocks. She used 268 blocks to build a house. How many blocks does Hallie have left?” These exercises provide extensive work with grade-level problems and address the full intent of the standard 2.NBT.9, explain why addition and subtraction strategies work, using place value and the properties of operations.

• In Lesson 10-9, Solve Problems Involving Addition and Subtraction, Explore & Develop, Develop the Math, Activity-Based Exploration, “Instruct students to work with partners to write a two-step word problem with 3-digit numbers on a piece of paper. Then have students trade word problems with another group to solve. Have students record addition and subtraction equations to represent their word problem. They may also use drawings or base-ten blocks to represent the problem. Then, invite students to choose a strategy to solve each equation. Have pairs trade and solve word problems as the time allows.” In Differentiate, Reinforce Understanding, Differentiation Resource Book, Exercise 2, “Molly has 395 marbles. Isabela has 122 more marbles than Molly. Collin has 147 fewer marbles than Isabela. How many marbles does Collin have?” [370 marbles] These exercises address the full intent of standard 2.NBT.7, add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method. Understand that in adding or subtracting three-digit numbers, one adds or subtracts hundreds and hundreds, tens and tens, ones and ones; and sometimes it is necessary to compose or decompose tens or hundreds.

The materials provide limited opportunities for all students to engage in extensive work with grade-level problems for standards 2.NBT.6, 2.MD.7, and 2.G.2. Additionally, the materials do not provide opportunities for students to meet the full intent of standard 2.NBT.4. Examples include:

• In Lesson 2-5, Compare 3-Digit Numbers, Differentiate, Build Proficiency, Digital Additional Practice Book: Compare 3-Digit Numbers, Exercise 1, “How can you compare the numbers? Use >, <, or =.” Two numbers, 880 and 808, are written in a place value chart. Students compare the values of the hundreds place and then the values of the tens place. Students write the symbol ”>” in the circle between the numbers 880 and 808. While this lesson provides students with opportunities to use the symbols >, =, and <, to compare numbers, outside of this lesson students are provided with limited opportunities to engage with the full intent of 2.NBT.4, compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record the results of comparisons. In Lesson 4-9, Solve two-Step Problems with Comparison, Differentiate, Digital Building Proficiency, Digital Station: Apples & Oranges (Compare Numbers to 100), Directions: “Fill the cart. Choose the bag with more fruit.” Example: “64, 67”.  In Lesson 8-2, Launch, Digital Number Routine, Greater Than or Less Than, Directions: “Is the value of the expression greater than or less than 50? How do you know?  25 + 22, 18 + 43”. While students are provided with extensive practice, they do not use the symbols to compare the numbers thus not meeting the full intent of the standard.

• In Lesson 5-9, Add More Than Two Numbers, Practice & Reflect, On My Own, Exercise 3,  “What is the sum? Use any addition strategy to solve. 51 + 29 + 14 = ___.” [94] Exercise 5, “20 + 33 + 25 + 12 = ___.” [90] While this lesson provides students with opportunities to add three and four addends, outside of this lesson students are provided with limited opportunities to engage with  the full intent of 2.NBT.6, add up to four two digit numbers using strategies based on place value and properties of operations.

• In Lesson 8-4, Tell Time to the Nearest Five Minutes, Practice & Reflect, On My Own, Exercises 2-5, “What time is shown on the analog clock? Write the time.” In Lesson 8-5, Be Precise When Telling Time, Practice and Reflect, On My Own, Exercises 1-6, “What time of the day does the event take place? Write a.m. or p.m.” Lesson 8-5 focuses only on determining if an event takes place in the a.m or p.m. and does not ask students to tell time on a clock as exercises have times given. Students are provided with limited opportunities to engage with 2.MD.7, tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.

• In Lesson 12-6, Partition a Rectangle into Rows and Columns, Differentiate, Digital Additional Practice Book: Partition a Rectangle into Rows and Columns, Exercises 1 (shows a rectangle partitioned into 2 rows of 4), and 2 (shows a rectangle partitioned into 3 rows of 5), “How many rows, columns, and squares is the rectangle partitioned into? Write an equation to find the total number of squares.” Exercises 3 (shows a rectangle that can be partitioned into 3 rows of 4), and 4 (shows a rectangle that can be partitioned into 4 rows of 6), “How can you partition the rectangle using equal-sized squares? Draw to show your work.” Exercise 5, “A rectangular board game is divided into 5 rows and 6 columns of squares. How many squares are on the board? Explain your reasoning.” This lesson meets the full intent of 2.G.2, partition a rectangle into rows and columns of same-size squares and count to find the total number of them. While mathematically reasonable since this is the last lesson in Reveal Math Grade 2, this demonstrates the representation of partitioning a whole into equal parts (3.NF.1),as well as, setting up area models by finding the area of a rectangle with whole-number side lengths by tiling it (3.MD.7). This will limit the experiences of partitioning for students leaving grade 2 entering grade 3 and provides limited opportunities for students to engage in extensive work with grade-level problems.

#### Criterion 1.2: Coherence

Each grade’s materials are coherent and consistent with the Standards.

The materials reviewed for Reveal Math Grade 2 meet expectations for coherence. The materials: address the major clusters of the grade, have supporting content connected to major work, make connections between clusters and domains, and have content from prior and future grades connected to grade-level work.

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When implemented as designed, the majority of the materials address the major clusters of each grade.

The materials reviewed for Reveal Math Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade.

Within the materials, at least 65% of instructional time addresses the major work of the grade, including supporting work connected to major work. For example:

• There are 12 Units, of which 11 address major work, or supporting work connected to major work of the grade, approximately 92%.

• There are 92 lessons, of which 85 address major work, or supporting work connected to major work, approximately 92%.

• There are 153 days of instruction, 137 of which address major work, or supporting work connected to major work, approximately 90%.

The materials contained discrepancies regarding the number of days per unit, and guidance was not given as to how those days were accounted for, therefore, a lesson level analysis is most representative of the materials. As a result, approximately 92% of the instructional materials focus on major work of the grade.

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Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The materials reviewed for Reveal Math Grade 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of supporting work engaging simultaneously with major work of the grade, when appropriate include:

• In Lesson 3-5, Addition Patterns, Practice and Reflect, On My Own, Exercise 8, Extend Your Thinking, the supporting work of 2.OA.3, determine whether a group of objects (up to 20) has an odd or even number of members, connects to the major work of 2.OA.2, fluently add and subtract within 20 using mental strategies, as students find doubles that add to an even or odd sum. “The red team scored 9 points. The blue team scored 6 points. Is the total number of points an even or odd number? Explain how you know.”

• In Lesson 3-6, Patterns with Arrays, Practice and Reflect, On My Own, Exercise 5, the supporting work of 2.OA.4, use addition to find the total number of objects arranged in rectangular arrays, connects to the major work of 2.NBT.2, count within 1000; skip-count by 5s, 10s, and 100s, as students use skip counting to find the total number of objects. “How can you skip count to find the number of counters in the array? Choose the correct answer.” Students are shown an array with two rows of four and given the answer choices, “A. 2, 4, B. 4, 8, C. 4, 8, 12, D. 2, 4, 6, 8, 10.” [B]

• In Lesson 8-3, Solve Money Problems Involving Dollar Bills and Coins, Explore & Develop, Develop the Math, the supporting work of 2.MD.8, solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $and ¢ symbols appropriately, connects with the major work of 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems, as students solve different types of problems involving money up to$100/100 cents. In the Activity-Based Exploration, the teacher gives students index cards to create denominations of bills (3-$20 bills, 5-$10 bills, 2-$5 bills, and 10-$1 bills). “Have partners take turns choosing a number between 50 and 100 to represent an amount of dollars. The other partner is to model that amount of money with as many combinations of index cards as possible. Repeat with other numbers.”

• In Lesson 8-4, Tell Time to the Nearest Five Minutes, Explore & Develop, Develop the Math, Activity-Based Exploration, the supporting standard of 2.MD.7, tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m., connects to 2.NBT.2, count within 1000; skip-count by 5s, 10s, and 100s, as students skip count by 5s telling time. Directions, “Have partners write a number from 1-12 and choose a card from the Time Cards pile. Tell them the number written down represents the hour and the card represents the minutes. Instruct groups to show their time on an analog clock and on a digital clock. Have students repeat the activity with a new number and a new card.”

• In Lesson 11-3, Solve Problems Using Bar Graphs, Differentiate, Build Proficiency, Digital Additional Practice Book: Solve Problems Using Bar Graphs, Exercises 3-6, connect the supporting work of 2.MD.10, draw a picture graph and a bar graph (with single-unit scale) to represent a data set with up to four categories, to the major work of 2.NBT.5, fluently add and subtract within 100, as students answer questions about data represented in a bar graph about birds. “Use the bar graph to answer the questions. Exercise 3, What bird was seen the most? Exercise 4, How many more yellow finches were seen than blue jays? Exercise 5, How many fewer cardinals were seen than robins? Exercise 6, How many birds were seen in all? Explain.”

• In Lesson 11-6, Show Data on a Line Plot, Practice and Reflect, On My Own, Exercises 4 and 5, connect the supporting work of 2.MD.9, generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot, where the horizontal scale is marked off in whole-number units, to the major work of 2.MD.1, measure the length of an object by selecting and using appropriate tools, as students record length measurements of crayons and make a line plot to represent the data. “How can you use your own data to make a line plot?  Measure the length of 10 crayons.  Exercise 4, Record the measurements. Exercise 5, Make a line plot of the data.”

##### Indicator {{'1e' | indicatorName}}

Materials include problems and activities that serve to connect two or more clusters in a domain or two or more domains in a grade.

The materials reviewed for Reveal Math Grade 2 meet expectations for including problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials contain connections from supporting work to supporting work and connections from major work to major work throughout the grade-level materials when appropriate. The supporting standards 2.MD.C, work with time and money, and 2.MD.D, represent and interpret data did not have connections to other supporting standards, but the separation is mathematically reasonable as they connect to major work of the grade.

Connections between major clusters or domains include:

• In Lesson 6-2, More Strategies to Subtract Fluently within 20, Practice & Reflect, On My Own, Exercise 6, connects the major work of 2.OA.A, represent and solve problems involving addition and subtraction, to the major work of 2.OA.B, add and subtract within 20, as students use addition to solve a subtraction problem. “Jack is finishing his homework. There are 17 math problems. He finishes 8 problems. How many problems does he have left to finish? Show your work using addition to subtract.”

• In Lesson 6-9, Solve One-Step Problems Using Subtraction, Differentiate, Build Proficiency, Digital Additional Practice Book: Solve One-Step Problems Using Subtraction, Exercise 2, connects the major work of 2.OA.A, represent and solve problems involving addition and subtraction, to the major work of 2.NBT.B, use place value understanding and properties of operations to add and subtract, as students use subtraction strategies to solve one-step word problems. “How can you represent and solve the word problem? Fill in the equation and use any strategy to solve. Jamal has 48 crayons. He gives his brother 23 crayons. How many crayons does Jamal have left? ____ - ____ = ____.”

• In Lesson 7-10, Solve Problems Using Length, Explore & Develop, Work Together, connects the major work of 2.MD.B, relate addition and subtraction to length, to the major work of 2.NBT.B, use place value understanding and properties of operations to add and subtract, as students solve subtraction word problems involving length using strategies based on the relationship between addition and subtraction. “Adele has 33 yards of ribbon. She uses some ribbon. Now she has 16 yards of ribbon. How much ribbon does Adele use? Make a drawing and write an equation to help you solve the problem.”

Connections between supporting clusters or domains include:

• In Lesson 12-6, Partition a Rectangle into Rows and Columns, Practice & Reflect, On My Own, Exercise 3, connects the supporting work of 2.G.A, reason with shapes and their attributes, to the supporting work of 2.OA.C, work with equal groups of objects to gain foundations for multiplication, as students count to find the total number of squares, identify how many in each row and column, and write a repeated addition equation. “How many rows, columns, and squares is the rectangle partitioned into? Write an equation to find the total number of squares.” Students are shown a rectangle that is partitioned into 4 rows and 5 columns.

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Content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

The materials reviewed for Reveal Math Grade 2 meet expectations that content from future grades is identified and related to grade-level work, and materials relate grade-level concepts explicitly to prior knowledge from earlier grades.

Content from future grades is identified within the chapters, units, and lessons; and is connected to grade-level work. Examples include:

• In Lesson 3-7, Use Arrays to Add, Coherence, Now, includes 2.OA.4, use addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns; write an equation to express the total as a sum of equal addends. “Students use arrays to find the sum of equal addends.” In Next, “Students use patterns to solve addition problems (Unit 5). Students will represent multiplication with arrays (Grade 3).” 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, and 3.OA.1, interpret products of whole numbers, e.g., interpret 5 × 7 as the total number of objects in 5 groups of 7 objects each.

• In Lesson 5-5, Decompose Two Addends to Add, Coherence, Now, includes 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction. “Students decompose addends by place value to find partial sums to help them add 2-digit numbers.” In Next, “Students decompose one added to add (Unit 5). Students solve two-step word problems with four operations (Grade 3).” 3.OA.8, solve two-step word problems using the four operations.

• In Unit 7, Measure and Compare Lengths, Coherence, What Students Are Learning, includes 2.MD.3, estimate lengths using units of inches, feet, centimeters, and meters. “Students estimate length in customary and metric units.” In What Students Will Learn, “Students measure and estimate liquid volumes and masses of objects using standard units. (Grade 3).” 3.MD.2, measure and estimate liquid volumes and masses of objects using standard units of grams(g), kilograms(kg), and liters(l).

• In Lesson 11-5, Understand Line Plots, Coherence, Now, includes 2.MD.9, generate measurement data by measuring lengths of several objects to the nearest whole unit, or by making repeated measurements of the same object. Show the measurements by making a line plot. “Students use a line plot to interpret measurement data.” In Next, “Students generate measurement data to halves and fourths of an inch and show the data on line plots (Grade 3).” 3.MD.4, generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch. Show the data by making a line plot.

Examples where the instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades include:

• In Lesson 4-1, Represent and Solve Add To Problems, Coherence, Now, includes 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems. “Students apply their understanding of representing word problems with drawings and equations by solving addition word problems.” In Previous, “Students used arrays to find the sum of equal addends (Unit 3). Students added and subtracted within 20 to solve word problems (Grade 1).” 1.OA.1, use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

• In Unit 6, Strategies to Fluently Subtract within 100, Coherence, What Students Are Learning includes 2.OA.1, use addition and subtraction within 100 to solve one-and two-step word problems. “Students solve one-and two-step word problems involving subtraction.” In What Students Have Learned, “Students added fluently within 20. (Grade 2, Unit 5). Students subtracted within 20 to solve world problems. (Grade 1).” 2.NBT.5, fluently add and subtract within 100 and 1.OA.1, use addition and subtraction within 20 to solve word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions.

• In Lesson 11-2, Understand Bar Graphs, Coherence, Now, includes 2.MD.10, draw a picture graph and a bar graph to represent a data set with up to four categories. “Students learn the parts and purpose of a bar graph. Students compare a bar graph and a picture graph.” In Previous, “Students organized, represented, and interpreted data with up to three categories (Grade 1). Students used tally charts to draw picture graphs (Unit 11).” 1.MD.4, organize, represent, and interpret data with up to three categories.

##### Indicator {{'1g' | indicatorName}}

In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification.

The materials reviewed for Reveal Math Grade 2 foster coherence between grades and can be completed within a regular school year with little to no modification.

There are three places within the materials that identify pacing for Grade 2: each Unit Planner of the Teacher Edition; Digital Teacher Center, Program Overview, Learning & Support Resources, Implementation Guide, Pacing; and Digital Teacher Center, Program Resources, Course Materials, Pacing Guide. These three sources contain discrepancies in the number of days per unit.

In the Pacing Guide, the Program Table of Contents: Grade 2, identifies that the instructional materials can be completed in 153 days. For example:

• There are 12 instructional units with 92 days of lessons.

• Each unit includes a Unit Opener: Ignite activity and Units 2-14 have a Readiness Diagnostic for 12 additional days.

• There is a Unit Assessment and Performance Task for each unit with the exception of Unit 1, for 11 days.

• The materials include a Course Diagnostic, Benchmark Assessments (3), and a Summative Assessment, for a total of 5 days.

• Each Unit contains a Unit Review and Units 2-12 contain a Math Probe, for an additional 23 days.

The components listed above account for 143 days. The materials do not give guidance on how to account for the other ten days.

The materials note lessons are 60-64 minutes, and consist of five components plus a Number Routine exercise. For example:

• Number Routine: 5-7 minutes

• Launch: 5-7 minutes

• Explore & Develop: 20 minutes

• Practice & Reflect: 10 minutes

• Assess: 10 minutes

• Differentiate: 10 minutes

### Rigor & the Mathematical Practices

The materials reviewed for Reveal Math Grade 2 meet expectations for rigor and balance and practice-content connections. The materials help students develop procedural skills, fluency, and application. The materials also make meaningful connections between the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

##### Gateway 2
Meets Expectations

#### Criterion 2.1: Rigor and Balance

Materials reflect the balances in the Standards and help students meet the Standards’ rigorous expectations, by giving appropriate attention to: developing students’ conceptual understanding; procedural skill and fluency; and engaging applications.

The materials reviewed for Reveal Math Grade 2 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, spend sufficient time working with engaging applications of mathematics, and do not always treat the three aspects of rigor together or separately.

##### Indicator {{'2a' | indicatorName}}

Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for Reveal Math Grade 2 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 2-1, Understand Hundreds, Explore & Develop, Guided Exploration, “Students extend their understanding of place value to the hundreds place and build on their understanding that a group of 10 tens makes 1 hundred.” Math is Modeling, “Why is a tens rod a good way to show each student’s fingers?” Students work with a partner to skip count by 10s to find the value of 10 tens. Students record their thinking on paper using drawings or numbers. Facilitate Meaningful Discourse, “What do you notice about the number of ten rods and the value of the ten rods? What can you use to represent all 100 fingers? Why do you think we call the base-ten block for one hundred a flat? How do tens relate to a hundred?”  This activity supports conceptual development of 2.NBT.1, understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.

• In Lesson 6-5, Use a Number Line to Subtract, Differentiate, Extend Thinking, Differentiation Resource Book, Exercise 1, “Malena sells jackets and gloves at a store. How can you use the information in the table and draw a number line to show the difference? Explain your answer.” Exercise 1, “How many more jackets are sold on Thursday than Tuesday?” This exercise supports conceptual development of 2.MD.6, represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.)

• In Lesson 9-3, Represent Addition with 3-Digit Numbers with Regrouping, Explore & Develop, Bring it Together, “How can you use base-ten blocks to regroup 10 ones? How can you use base-ten blocks to regroup 10 tens?” During this lesson, students use base ten blocks to represent and solve 3-digit addition equations with regrouping. This provides students with the opportunity to develop conceptual understanding of 2.NBT.7, add and subtract within 1000, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method.

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

• In Lesson 2-1, Understand Hundreds, Practice & Reflect, On My Own, Reflect, “Why is it helpful to group 10 tens as 100?” Students use their understanding of 100 as 10 groups of 10. Each student writes a reflection and students share their reflections with their classmates. This supports conceptual understanding of 2.NBT.1, understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones; e.g., 706 equals 7 hundreds, 0 tens, and 6 ones.)

• In Lesson 3-4, Understand Even and Odd Numbers, Practice & Reflect, On My Own, Exercise 5, “Cleo is washing strawberries. Is the number of strawberries even or odd? Explain how you know.” Students are shown five groups of two strawberries. This activity supports conceptual understanding of 2.OA.3, determine whether a group of objects (up to 20) has an odd or even number of members.

• In Lesson 5-6, Use a Number Line to Add, Practice & Reflect, On My Own, Exercise 1, “How can you use a number line to add? Fill in the numbers to complete the equation. 1. 33 + ___ = ___.” Students complete the equation by using bars shown on the number line. This supports conceptual understanding of 2.MD.6, represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1, 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

• In Lesson 9-2, Represent Addition with 3-Digit Numbers, Practice & Reflect, On My Own, Exercise 2, “What is the sum?  Use base-ten shorthand to show your work. 206 + 481 = ____.”  This activity supports conceptual understanding of 2.NBT.7, add and subtract within 1000.

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Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency.

The materials reviewed for Reveal Math Grade 2 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 skill 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 2 progress toward 2.OA.2, fluently add and subtract within 20 using mental strategies, and 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Unit 4, Fluency Practice, Fluency Strategy, Exercise 1, “How can you make a 10 to find 7 + 6? Explain.”  Fluency Flash, “What is the sum?  Make a 10 to add.” Exercise 2, “9 + 4 = ___.”  These activities provide an opportunity to develop procedural skill and fluency of 2.OA.2, fluently add and subtract within 20 using mental strategies.

• In Lesson 5-1, Strategies to Add Fluently Within 20, Explore & Develop, Learn, “How can you find the total number of snack bars using mental math? You can use the strategies you know to find 8 + 5 using mental math. One way to find the sum is to count on. Another way to find the sum is to decompose one addend to make a 10.” This activity supports the development of 2.OA.2, fluently add and subtract within 20 using mental strategies.

• In Lesson 6-3, Represent Subtraction with 2-Digit Numbers, Explore & Develop, Work Together, “There are 55 napkins in a stack. Some people use 31 of them. How can you use base-ten blocks to find how many napkins are left in the stack?” Teacher guidance encourages teachers to, “Point out different strategies students may use to demonstrate subtraction as they arise. Strategies might include removing or covering up the change number of base-ten blocks.” This activity builds procedural skill and fluency of 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction, from conceptual understanding of addition and subtraction.

• In Lesson 6-4, Represent 2-Digit Subtraction with Regrouping, Explore & Develop, Activity- Based Exploration, “Directions: Present this problem to students: 51 - 14 = ? Instruct students to represent and solve the equation using base-ten blocks.” Math is Thinking, “How can you take away 4 ones when there is only 1 ones unit?” This activity provides an opportunity for students to develop procedural skill and fluency of 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Unit 6, Strategies to Fluently Subtract within 100, Math Probe, Directions, “Determine if the strategy shown is a correct approach to do this subtraction: 45 - 17. Do not actually perform the calculations.” Exercise 1, “45 - 10 - 7. Does this strategy work? Circle Yes or No. Explain why you chose Yes or No.” This exercise shows the development of the cluster 2.NBT.B, use place value understanding and properties of operations to add and subtract, relating to the procedural skill and fluency of 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

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

• In Lesson 5-3, Strategies to Fluently Add within 100, Practice & Reflect, On My Own, Exercise 7, “What is the sum? Show your thinking. 31 + 13 = ___.” This exercise provides students with an opportunity to independently demonstrate procedural skill and fluency of 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Unit 6, Strategies to Fluently Subtract within 100, Unit Assessment, Form A, Item 14, “Armond eats 17 berries. He eats 9 blueberries. The rest are blackberries. How many blackberries does Armond eat? Show your work using addition to subtract.” Students have used this strategy throughout Unit 6 and this provides an opportunity for students to demonstrate procedural skill and fluency of 2.OA.2, fluently add and subtract within 20 using mental strategies.

• In Unit 6, Strategies to Fluently Subtract within 100, Unit Review, Performance Task, Reflect, “What are some different strategies for subtracting 2-digit numbers? Which strategy do you think is the most helpful?” This exercise allows students to independently demonstrate procedural skill and fluency of 2.NBT.5, fluently add and subtract within 100 using strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.

• In Unit 7, Measure and Compare Lengths, Fluency Practice, Fluency Check, Exercise 3, “What is the sum or difference?  12 - 5 = ____.” This activity provides an opportunity for students to demonstrate procedural skill and fluency of 2.OA.2, fluently add and subtract within 20 using mental strategies.

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Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

The materials reviewed for Reveal Math Grade 2 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 4-2, Represent and Solve Take From Problems, Explore & Develop, Learn, “Jon brings some juice boxes to share with his class. His classmates drink 8 of the juice boxes. There are 11 juice boxes left. How many juice boxes did Jon bring?” Pose Purposeful Questions, “What words in the problem help you determine if you need to add or subtract? What is the unknown? How do the quantities relate to one another?” Students use a bar diagram to represent the problem. This exercise provides an opportunity for students to develop the mathematics of 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems. In Assess, Exit Ticket, Exercise 2, “Write an equation to represent the problem using ? for the unknown. Then solve. Kim has 11 lemons. She uses some lemons to make lemonade. There are 7 lemons left. How many lemons does Kim use to make lemonade? Equation: ______ Solve: _____.” This exercise allows students to independently apply mathematics of 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems.

• In Lesson 7-11, Solve More Problems Involving Length, Explore & Develop, Learn, “Diane draws a line 26 centimeters long. Oliver draws a line 15 centimeters long. How much longer is Diane’s line than Oliver’s line?” Pose Purposeful Questions, “What information is given in the problem? Have you solved similar problems to this before? Explain. What operation do you think you will use to solve this problem?” This exercise allows students to develop the mathematics of 2.MD.6, represent whole numbers as lengths from 0 on a number line diagram with equally spaced points corresponding to the numbers 0, 1 2, …, and represent whole-number sums and differences within 100 on a number line diagram.

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Materials include standards correlation information that explains the role of the standards in the context of the overall series.

The materials reviewed for Reveal Math Grade 2 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 4-2, Represent and Solve Take From Problems, the materials identify the standard 2.OA.1, use addition and subtraction within 100 to solve one- and two-step word problems involving situations of adding to, taking from, putting together, taking apart, and comparing, with unknowns in all positions, e.g., by using drawings and equations with a symbol for the unknown number to represent the problem. The lesson also identifies MP2, reason abstractly and quantitatively and MP4, model with mathematics.

• In Lesson 7-5, Estimate Length Using Customary Units, the materials identify standard 2.MD.3, estimate lengths using units of inches, feet, centimeters, and meters. The lesson also identifies MP6, attend to precision and MP4, model with mathematics.

The teacher materials contain explanations of the role of the specific grade-level mathematics, including prior and future content connections. 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, Patterns within Numbers, What Students Have Learned, “Counting  Students counted by 1s within 120. (Grade 1) Look for Patterns  Students looked for patterns in numbers within 120. (Grade 1) Determine Equal Groups Students analyzed whether two sides of an equation were equal. (Grade 1)” What Students Are Learning, “Pattern Recognition Students describe and use patterns when counting by 1s and skip counting by 5s, 10s, and 100s within 1,000. Determine Even and Odd Numbers Students determine whether a number is even or odd. Determine Equal Groups Students write an equation to express an even number as a sum of two equal addends. Use Arrays to Add Students use arrays to find the sum of equal addends.”  What Students Will Learn, “Pattern Recognition  Students identify patterns with doubles, products of 5, and products of 10 in the multiplication table. (Grade 3) Use Arrays to Multiply Students will represent multiplication with arrays. (Grade 3)”

• 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. Each lesson overview contains a Coherence section that provides connections to prior and future work. In Lesson 6-1, Strategies to Subtract Fluently within 20, Coherence, Previous, “Students used strategies to subtract within 20 (Grade 1). Students added fluently within 20 (Unit 5).” Now, “Students use the count on strategy to find a difference within 20. Students use the count back strategy to find a difference within 20.” Next, “Students learn more strategies to fluently subtract within 20 (Unit 6). Students solve two-step word problems with four operations (Grade 3).”

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Materials provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The materials reviewed for Reveal Math Grade 2 provide strategies for informing all stakeholders, including students, parents, or caregivers about the program and suggestions for how they can help support student progress and achievement.

The Digital Teacher Center, Program Overview: Learning & Support Resources, Get Started with Reveal Math, provides support for both students and families in the form of a family letter and a digital presentation. The Family Letter: Welcome to Reveal Math, gives an overview of what students will learn throughout the year. The Digital Walk-Through: Welcome to Reveal Math, is a video presentation for students showing them how to navigate the online materials and resources. The Administrator Support section includes a Family Welcome Letter Template, which gives an overview of what children will experience in class and at home, and suggestions and resources for what a family can do to help their student with mathematics. “What will your child experience at home? You and your child can access Reveal Math online from home. Your child will receive an online account that will give you access to the following:

• Family letters for each unit

• Homework assignments

• Interactive Student Edition

• Math Replay videos that review key concepts from the lesson

• eToolkit with digital tools and virtual manipulatives

• STEM Career Kid and Math in Action videos that help your child see how the math he or she is learning now applies to real-world projects and careers.”

Also included in the Administrator Support section is the Family Welcome Presentation. This is a PowerPoint presentation that directs families and caregivers with the resources provided within the materials, slide 8,  “Reveal Math Is… At Home”,  shows examples that may be used specifically at home to help if students are having trouble. These resources can also be found under the “Resources” tab on the “Course” page.

The Digital Teacher Center, Unit Resources, also provides a family letter for each unit that gives specific information about what students will be learning, for example, Unit 8, Measurement: Money and Time, “In this unit, Measurement: Money and Time, we will be learning how to find the value of a given collection of money, tell time to the nearest 5 minutes, and determine whether the time an activity takes place is labeled as a.m. or p.m.” The family is given a list of math terms and student understandings along with a Math@Home Activity, “What can your child do at home? Have your child practice finding the value of coins and telling time to the nearest 5 minutes. For example, keep a bag of change handy. When time permits, give your child a collection of coins. Then have him or her find the value of the coins.”

Reveal Math provides materials in both English and Spanish. Student materials in Spanish include, in print, Student edition and Student Practice Book, and in the Digital Teacher Center, Student eBook, Math Replay Videos, eGlossary, and Family Letter. In the Digital Teacher Center, materials can be found in each unit under the Spanish Edition and Resources section.

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Materials provide explanations of the instructional approaches of the program and identification of the research-based strategies.

The materials reviewed for Reveal Math Grade 2 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 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, 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.”

• 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 researched 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.”

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Materials provide a comprehensive list of supplies needed to support instructional activities.

The materials reviewed for Reveal Math Grade 2 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 2, specifies the comprehensive materials list for the grade. The document specifies classroom materials (e.g., classroom objects to measure, index cards, straightedge, etc.), materials from a manipulative kit (e.g., color tiles, pennies, nickels, dimes and quarters, base-ten blocks, etc.), non-consumable teaching resources (e.g., place value chart, blank open number lines, meter measuring tape, etc.), and consumable teaching resources (coin value cards, time cards, line plot, etc).

In the Teacher Edition, each Unit Planner page lists materials needed for each lesson in the unit, for example, Unit 3, Patterns within Numbers, Materials to Gather, each Lesson’s materials are given:

• Lesson 3-1 - counters, Number Cards 0-10 Teaching Resource, Number Chart 201-300 Teaching Resource, Number Chart 401-500 Teaching Resource

• Lesson 3-2 - Number Chart 1-100 Teaching Resource

• Lesson 3-3 - Number Chart 1-100 Teaching Resource, number cubes

• Lesson 3-4 - counters, Number Cards 0-10 Teaching Resource

• Lesson 3-5 - connecting cubes

• Lesson 3-6 - counters, paper clips

• Lesson 3-7 - connecting cubes, counters.

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

• Lesson 4-7, Meanings of Addition and Subtraction, Materials, “The materials may be for any part of the lesson, Bar Diagram Teaching Resource, number cubes 0-5 and 5-10, Word Problem Cards Teaching Resource.” In Explore & Develop, Activity-Based Exploration, “Materials: Bar Diagram Teaching Resource (1 per group), number cubes 0-5 (1 per group), Word Problem Cards Teaching Resource (1 per group).”

• Lesson 11-4, Collect Measurement Data, Materials, “The materials may be for any part of the lesson, base-ten rods, connecting cubes, inch rulers, measuring tape, Tally Chart Teaching Resource.” In Explore & Develop, Activity-Based Exploration, “Materials: inch ruler (4 per group), Tally Chart Teaching Resource (1 per group).”

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This is not an assessed indicator in Mathematics.

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This is not an assessed indicator in Mathematics.

#### Criterion 3.2: Assessment

The program includes a system of assessments identifying how materials provide tools, guidance, and support for teachers to collect, interpret, and act on data about student progress towards the standards.

The materials reviewed for Reveal Math Grade 2  meet expectations for Assessment. The materials include an assessment system that provides multiple opportunities throughout the grade to determine students' learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up, and the materials provide assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices. The materials partially include assessment information in the materials to indicate which practices are assessed.

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Assessment information is included in the materials to indicate which standards are assessed.

The materials reviewed for Reveal Math Grade 2 partially meet expectations for having assessment information included in the materials to indicate which standards are assessed.

The materials consistently identify the content standards addressed in formal assessments, however, the mathematical practices are not identified in formative or summative assessments. The mathematical practices are identified at the beginning of each lesson in the “Standards” section and are not linked with a specific activity, task, or item in assessments.

The printed Teacher Edition includes content standards for each item of the assessment in the Item Analysis for the Course Diagnostic, Benchmark, End of the Year (Summative) Assessment, Unit Diagnostic (Readiness Diagnostic), and Unit Assessments. The Exit Ticket identifies content standards for each item in the Exit Skill Tracker. The digital versions of these assessments include an icon to the right of the assessment that can be opened to see the standards assessed, however, they are in list form and not specific to each item. In the Unit Performance Task and Work Together activity, the printed Teacher Edition includes content standards for the entire task, not by item. The Math Probes do not include listed content standards. Examples include:

• In Unit 3, Patterns within Numbers, Readiness Diagnostic, Item 3 identifies 1.NBT.5, “Which number is 10 more than 73? A. 70, B. 74, C. 80, D. 83.”

• In Lesson 7-3, Compare Lengths Using Customary Units, Exit Ticket, Exercise 1 identifies 2.MD.4, “How can you compare the lengths? Fill in the equation. Abby’s hair is 15 inches long. Val’s hair is 8 inches long. ___ - ___ = ___.”

• In Unit 10, Strategies to Subtract 3-Digit Numbers, Unit Assessment (Form A), Item 5 identifies 2.NBT.7, “What is the difference? Use base-ten shorthand to show your work. 439 - 212 = ?”

• Unit 12, Geometric Shapes and Equal Shares, Math Probe, “Students circle yes or no to indicate if a given shape is partitioned into four equal shares, Students justify their answers with words or drawings. Targeted Concept Area models can be used to represent shares of a whole that are of equal size. The probe is designed to assess whether students are able to generalize this concept to shapes other than circles or rectangles.”

Throughout the course materials, all content standards are identified correctly and all content standards for the grade level are assessed. The End of the Year (Summative) Assessment assesses standards covered throughout the year, but not all standards are assessed on the summative assessment.

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Assessment system 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.

The materials reviewed for Reveal Math Grade 2 meet expectations for including an assessment system that provides multiple opportunities throughout the grade 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 4, Meanings of Addition and Subtraction, Unit Assessment (Form A), Item 1 lists “Result Unknown within 50 (Take From)” as the Guided Support Intervention Lesson. This resource can be located in the Digital Teacher Center in the Targeted Intervention section of the Unit.

The Unit Performance Task, only available in print, includes a scoring rubric that evaluates student work for each section on a 2, 1, or 0 point scale. For example:

• In Unit 3, Patterns Within Numbers, Performance Task, Party Planning, “Students draw on their understanding of counting and addition patterns. Use the rubric show to evaluate students’ work.”  Rubric, Part A,  “2 Points Student's work shows proficiency in skip counting by 100s. Student completes the counting patterns and identifies the correct number of marbles. 1 Point Student’s work shows developing proficiency in skip counting by 100s. Student identifies the correct number of marbles but does not accurately complete the counting pattern. 0 Points Student’s work reflects a poor understanding of skip counting by 100s. Student fails to complete the counting pattern and does not identify the correct number of marbles.”

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 to use to remediate. 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:

Exit Tickets are provided at the end of each lesson and evaluates students’ understanding of the lesson concepts and provides 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 5-8, Exit Ticket, “If students score 3 out of 3, Then have students do Additional Practice or any of the B or E activities.” The Build Proficiency (B) activities include Practice It! Game Station, Adjusting Addends Task Cards, Own It! Digital Station games, and Interactive Additional Practice. The Extend Thinking (E) activities include Use It! Application Station, Picture Collage, and STEM Adventure.

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Assessments include opportunities for students to demonstrate the full intent of grade-level/course-level standards and practices across the series.

The materials reviewed for Reveal Math Grade 2 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 5-5, Decompose Two Addends to Add, Assess, Exit Ticket, supports the full intent of 2.NBT.5 (Fluently add and subtract within 100) and MP7 (Look for and make use of structure) as students decompose addends into tens and ones. Exercise 2, “Decompose both addends by place value. 56 + 23 = ?” In this exercise, students are given the equation 56 + 23 = ? with blanks under each addend to indicate that each addend can be split into two numbers ___ + ___ .

• Unit 5, Strategies to Add Fluently to 100, Unit Assessment, Form A, supports the full intent  of 2.OA.2 (Fluently add and subtract within 20 using mental strategies) and MP1 (Make sense of problems and persevere in solving them) as students use their knowledge of doubles facts to help them solve a word problem. Item 16, “Henry has 5 apple slices and 7 orange slices. Use a doubles fact to help you find the total number of fruit slices Henry has. Show your work and explain your answer.”

• Benchmark Assessment 3, supports the full intent  of and 2.OA.1 (Use addition and subtraction within 100 to solve one- and two-step word problems) and MP2 (Reason abstractly and quantitatively) as students solve a comparison problem and represent it with equations. Item 18, “Arnold has 8 more stickers than Hector. Arnold has 27 stickers. How many stickers does Hector have?” Students see a bar diagram with Arnold having 27 stickers and Hector showing 8 stickers and a blank bar for the rest of Hector’s stickers. “Which equations match the word problem? Choose all the correct answers. A. 35 - 27 = 8, B. 19 + 8 = 27, C. 27 - 8 = 19, D. 27 + 8 = 25”. [B, C]

• In Lesson 11-6, Show Data on a Line Plot, Assess, Exit Ticket, is aligned to DOK 2 and supports the full intent  of 2.MD.9 (Show the measurements by making a line plot) and MP 4 (Model with mathematics) as students create a line plot to represent data. Exercise 1, “How can you represent the data using a line plot? Use the data to make a line plot. Mila measured the lengths of the bracelets she made.” Students are shown a list of eight measurements ranging from 14 to 18 centimeters.

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Assessments offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The materials reviewed for Reveal Math Grade 2 partially provide assessments which offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

The instructional materials reviewed for Reveal Math Kindergarten include some accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment. While teachers are provided with limited guidance as to how to employ the accommodations, the Digital Student Center provides teachers with a variety of embedded accommodations that can be accessed by students to demonstrate their knowledge. The Reveal Math printed materials include downloadable files of all assessments in Spanish.

The Reveal Math digital materials have some accommodations which do not change the content of the online assessments. Examples include:

• Text to speech is available for these online assessments: Benchmark Assessments, End of Year (Summative) Assessment, Unit Readiness Diagnostic, Unit Assessments, and Exit Tickets.

• The math probes include read aloud (text to speech) and the ability to change font size.

• Embedded eTools are available for students to use throughout the materials and assessments. These enable students to draw or type while answering questions. There are also several different types of virtual manipulatives to choose from to use.

In the Digital Teacher Center, Assessments Settings tab, teachers are able to select settings and choose from the following available accommodations to implement in digital format with students:

• Feedback and Resources: Available Learning Aids, Student Can Check Answers: One Time or Up to Three Times.

• Display Options: Allow Students to Cross Out Answers, Hide Question Navigation Bar, Hide Answer Choice Letters, Randomize Question Order, Allow Students to Access Available Rubrics.

Also included in the Digital Teacher Center, Assessments, teachers are able to alter assessments by adding their own questions. As a result, these items have the potential to alter grade-level expectations due to the fact that these are teacher-created items. The printed version does not allow this accommodation.

#### Criterion 3.3: Student Supports

The program includes materials designed for each child’s regular and active participation in grade-level/grade-band/series content.

The materials reviewed for Reveal Math Grade 2 meet expectations for Student Supports. The materials provide: strategies and supports for students in special populations and for students who read, write, and/or speak in a language other than English to support their regular and active participation in learning grade-level mathematics; multiple extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity; and manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

##### Indicator {{'3m' | indicatorName}}

Materials provide strategies and supports for students in special populations to support their regular and active participation in learning grade-level/series mathematics.

The materials reviewed for Reveal Math Grade 2 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, and therefore are 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.

##### Indicator {{'3n' | indicatorName}}

Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity.

The materials reviewed for Reveal Math Grade 2 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.

##### Indicator {{'3o' | indicatorName}}

Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The materials reviewed for Reveal Math Grade 2 provide varied approaches to learning tasks over time, and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning.

The Reveal Math materials include multi-modal opportunities for students to question, investigate, sense-make, and problem solve using a variety of formats and methods. Reveal Math lessons can be delivered by the teacher while students use pencil and paper to solve problems in a workbook or can be delivered digitally in the Interactive Student Edition. There are a variety of types of questions and answer formats used such as; multiple choice, drop down menus, drawing, or writing out your thinking.

Throughout the lesson components, students have opportunities to share their thinking, compare their thinking with other students, adjust and change their thinking, and to apply their understanding in new contexts. Students can share their thinking verbally in Think-Pair-Share activities, group activities, or in a class discussion during Ignite!, Number Routine, Notice & Wonder, and Math Language Routines. Students have opportunities to compare and adjust their thinking with classmates during Work Together practice or Activity-Based or Guided Explorations. Students can also show their learning and apply their understanding of lesson concepts independently in the On My Own section of the lesson, and through assessments such as Exit Tickets, Math Probes, and Performance Tasks.

Throughout the lesson there are opportunities for students to practice and review concepts and receive feedback from peers, teachers, or self-reflect on their own learning. Teachers provide oral feedback throughout the Launch, Explore & Develop, and Practice & Reflect sections of the lessons. Teachers can also provide oral or written feedback after students complete independent work or an assessment such as a Math Probe or Exit Ticket, or Unit Review. Teachers can then assign differentiation activities based on students’ needs. Each of these opportunities allows teachers to give students feedback, and allows students to develop their learning prior to taking a unit assessment. Students are also given the opportunity to self-reflect on their learning on Math Probes and Exit Tickets in Reflect on Your Learning. Students reflect on their learning and score themselves on a scale of 1 to 3 with 3 being the highest confidence or by circling thumbs up, thumb to the side, or thumbs down.

##### Indicator {{'3p' | indicatorName}}

Materials provide opportunities for teachers to use a variety of grouping strategies.

The materials reviewed for Reveal Math Grade 2 provide opportunities for teachers to use a variety of grouping strategies.

The materials provide opportunities for different grouping strategies based on the needs of the students and give guidance for teachers on how and when to use those strategies.

• Unit Resources At-A Glance, Workstations, “Reveal Math offers rich and varied resources that teachers can use to differentiate and enrich students’ instructional experiences with the unit content.” At the beginning of each unit is a table that presents an overview of the resources available for the unit with recommendations for when to use.” The provided table includes the activity, activity description, and which lesson to use the activity after. These activities can be partner or small group games, digital games, or application activities such as STEM Project Cards or Real World Cards where students apply concepts to real world scenarios.

• After each Unit Readiness Diagnostic, an Item Analysis provides targeted interventions for a unit based on students’ readiness diagnostic data. Teacher Edition, Readiness Diagnostic, Targeted Intervention, “Use Guided Support intervention lessons available in the Digital Teacher Center to provide targeted intervention.” These intervention lessons can be assigned to students or used for small group instruction.

• Exit Tickets provide opportunities to assign differentiated resources based on students' responses. In the Teacher Edition, Assess, teachers are provided Exit Ticket Recommendations based on, “If students score...Then have students do”.

The materials provide a balance of whole group, small group, and individual instruction throughout lesson components to provide for interaction among students.

##### Indicator {{'3q' | indicatorName}}

Materials provide 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 reviewed for Reveal Math Grade 2 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).

##### Indicator {{'3r' | indicatorName}}

Materials provide a balance of images or information about people, representing various demographic and physical characteristics.

The materials reviewed for Reveal Math Grade 2 provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the STEM In Action videos are from different ethnic groups and portray all ethnicities in a positive and respectful manner. There doesn’t appear to be any demographic bias. Names include multi-cultural references such as “Hugo, Marisol, and Jin” and gender neutral names like “Jordan and Riley.” Within the text, there is a balance of male and females and they have included students from a variety of ethnic groups. Male and female names both have correct and incorrect responses.

##### Indicator {{'3s' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The materials reviewed for Reveal Math Grade 2 do not provide guidance to encourage teachers to draw upon student home language to facilitate learning.

While there are supports in place at the unit and lesson level for teachers to guide students who read, write, and/or speak in a language other than English, there is no evidence of promoting home language knowledge as an asset to engage students in the content material or purposefully utilizing student home language in context with the materials.

##### Indicator {{'3t' | indicatorName}}

Materials provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

The materials reviewed for Reveal Math Grade 2 partially provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Some guidance is given within the Implementation Guide and Unit Overview regarding Social and Emotional Learning. Each lesson also contains a Social and Emotional Learning (SEL) objective.

In the Implementation Guide, Social and Emotional Competencies, Social Awareness, the materials guides you to where SEL objectives can be found for the following Social Awareness topics:

• Appreciate Diversity: “It is important for students to understand that people come from a range of ethnic, cultural, and social backgrounds and have a wide range of abilities and interests.”

• Develop perspective: “Helping students appreciate the diversity of people they are likely to encounter, and understand the value of different viewpoints and perspectives will open students’ minds to creative problem solving.”

• Empathy: “Empathy is the ability to understand and feel what another person is experiencing. Empathy is different from sympathy in that one is able to share the feelings of the other. “

• Respect Others: “When students respect one another they accept others as they are, for who they are, in spite of differences of ideas, viewpoints, or abilities. Respecting others creates mutual feelings of respect and trust, safety, and well-being.”

Materials for all stakeholders are available in Spanish, including videos and communication with parents.

There are discrepancies in the Social Emotional Learning (SEL) statements and prompts between the print Teacher Editions and the Digital Print Teacher Editions.

##### Indicator {{'3u' | indicatorName}}

Materials provide supports for different reading levels to ensure accessibility for students.

The materials reviewed for Reveal Math Grade 2 provide supports for different reading levels to ensure accessibility for students.

The materials provide Math Language Routines (MLR) that are specifically geared directly to different reading levels to ensure accessibility for students. Students practice Sense-Making and Number Routines. These routines allow struggling readers to access and engage with the mathematics without having to rely solely on reading skills.The materials work with students on Math Language Development (MLD) skills in each unit. These focus on one of the four areas of language competence- reading, writing, speaking and/or listening, and provide strategies to build students’ proficiency with language.

##### Indicator {{'3v' | indicatorName}}

Manipulatives, both virtual and physical, are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

The materials reviewed for Reveal Math Grade 2 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.

#### Criterion 3.4: Intentional Design

The program includes a visual design that is engaging and references or integrates digital technology, when applicable, with guidance for teachers.

The materials reviewed for Reveal Math Grade 2 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, and the materials partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other. The materials have a visual design that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic, and the materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

##### Indicator {{'3w' | indicatorName}}

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

The materials reviewed for Reveal Math Grade 2 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level standards, when applicable.

The materials reviewed integrate technology such as interactive tools, virtual manipulatives, games, modeling tools, and videos. They engage students in grade-level standards when applicable, however, there is little guidance for the teacher or student on how to use the virtual manipulatives or modeling tools.

There are many technology features available to students that support student engagement in doing mathematics. Examples include:

• Implementation Guide, Digital Experience, “The Interactive Student Edition allows students to interact with the Student Edition as they would in print. If students can mark up or answer a question in print, they can do so digitally as well. Slide numbers align with the print page numbers to allow for easy wayfinding.”

• Implementation Guide, Digital Experience, “Embedded eTools allow students to type or draw as they work out problems and respond to questions. Students can access the eToolkit at any time and use virtual manipulatives to represent and solve problems.” The eToolkit contains virtual manipulatives such as counting sticks, connecting cubes, counters, number paths, and pattern blocks.

• All aspects of the materials can be accessed digitally, however there are some components that are only digital such as the STEM In Action Videos, Expert Insights Videos, Game Stations, and Digital Stations.

• Teachers can select and assign lessons for independent work. The lesson is assigned in its entirety. Implementation Guide, Digital Experience, “Digital Practice, Assigned Interactive Additional Practice and Spiral Review  provide a dynamic experience, complete with learning aids integrated into items at point-of-use, that support students engaged in independent practice.”

• A Digital Station Center is available for all students with specific grade level appropriate games for them to play digitally.

There are also some digital materials available for teachers that are customizable for students or to the grade-level content standards. Examples include:

• Teachers have access to digital manipulatives relative to their specific grade level and standards and can add manipulatives to the students’ eToolkit.

• Student Assessments are available in digital format and can be modified and configured to meet the needs of learners.

• In the Digital Teacher Center, Assignments, Teachers can create online assignments that are customizable. Teachers can choose from several assignment types.

• Online Questions, teachers can select from McGraw-Hill assessments or build their own assignments using questions you select or create.

• Instruction, teachers can create instructions for a gradable offline activity.

• Submission, teachers can create an assignment that allows students to upload files, submit links, or enter their work directly.

• External tool, teachers can create an assignment with content from an external tool.

• Teachers are able to rearrange, add, or remove lesson resources or add their own content to the digital presentations by clicking the “edit” button at the top of a digital lesson landing page and selecting from available resources in the pop up box. It was not found, however, that you could edit the specific content within a resource. Teachers can also upload their own materials in Teacher-added Resources.

##### Indicator {{'3x' | indicatorName}}

Materials include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

The materials reviewed for Reveal Math Grade 2 partially include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Teachers have opportunities to collaborate with each other digitally, as they can share items such as class rosters, assignments, lesson plans, instructional groupings, or teacher-created resources for the purpose of instructional planning or co-teaching. There are opportunities for some collaboration for teachers and students, but they are very limited. Teachers can leave comments for students on submitted assignments, relating to specific questions, but students cannot reply back to those comments. Teachers can also use the Calendar feature to create events that can then be shared and read by students on their digital dashboard. Student to student collaboration is only through in-person, small group activities, not digitally. Students do not have a way to collaborate online.

##### Indicator {{'3y' | indicatorName}}

The visual design (whether in print or digital) supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

The materials reviewed for Reveal Math Grade 2 have a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

Throughout the materials, both in print and online, the visual design supports student learning. The graphics, images and models are clear, consistent and engaging. No visuals distract from student learning.

The printed format is consistent from grade to grade and lesson to lesson. Examples include:

• Units contain a Readiness Diagnostic (beginning in Unit 2), a Unit Opener including a STEM in Action video and Ignite! activity, Lessons, Math Probe (1 or 2 per Unit), Unit Review/Fluency Practice, Unit Assessment (Form A and Form B) and a Performance Task.

• Lessons have six sections: Number Routine, Launch, Explore & Develop, Practice & Reflect, Assess, and Differentiate with the same organizational structure and clear routines.

• The font size, amount of directions, and language in student materials is appropriate in printed materials.

• In print format, the graphics and models are visually appealing and connect with the lesson. Images are colorful; they are not distracting, and they support student learning.

The digital format is consistent from grade to grade and lesson to lesson. Examples include:

• Units contain: Unit Resources, Readiness Diagnostic (beginning in Unit 2), Targeted Intervention, STEM in Action videos, Ignite!, and Spanish Edition and Resources.

• Lessons include: Lesson Resources, Number Routine, Launch, Explore & Develop, Practice & Reflect, Assess, Differentiate, and Spanish Edition and Resources with the same organizational structure and clear routines.

• At the end of every unit, there is a Unit Review & Assess section. This section contains the following:  Unit Resources, Unit Review, Assess, Targeted Intervention, and Spanish Edition and Resources.

• The font size and language in digital student materials is appropriate.

• In digital format, the graphics mirror the print images.

The materials provide images, graphics, and models that clearly communicate information or support student understanding of concepts.

There are minor grammar and/or spelling errors; however they are not distracting or chaotic.

##### Indicator {{'3z' | indicatorName}}

Materials provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The materials reviewed for Reveal Math Grade 2 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Digital Teacher Center, Program Overview: Learning & Support Resources, includes resources that provide guidance on the use of its technology for teachers and students. Examples include:

• Implementation Guide, “This guide supports teachers with overarching program information, design principles, professional development resources, and intended use of the materials.”

• Reveal Math Quick Start “includes focused, concise videos and PDFs that guide teachers step-by-step through implementing the Reveal Math program.”

• Student support includes a Digital Walk-Through: Welcome to Reveal Math, “This video walks students through their Reveal Math digital platform, including how to navigate the lesson screen and locate online resources.”

• Teacher support includes a Digital Walk-Through: Welcome to Reveal Math, “This video walks teachers through their Reveal Math Digital Teacher Center, including how to navigate the course and locate online resources.”

• The Digital Teacher Center also includes several self-paced digital resources and Ready to Teach Workshop Modules that support teachers with implementing Reveal math such as  Expert Insights Videos, Model Lesson Videos, and instructional videos on topics such as Be Curious Sense Making Routines and Math Probes.

The Teacher Edition provides teachers with guidance to access digital tools and technology for students and teacher use at the unit and lesson level. The Unit Resources At a Glance page reviews the print and digital tools available for teachers in a specific unit.

## Report Overview

### Summary of Alignment & Usability for Reveal Math | Math

#### Product Notes

The materials reviewed for Reveal Math Grades K-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability. Within Gateway 3, the materials meet expectations for Teacher Supports (Criterion 1), Assessment (Criterion 2), and Student Supports (Criterion 3).

#### Math K-2

The materials reviewed for Reveal Math Grades K-2 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability. Within Gateway 3, the materials meet expectations for Teacher Supports (Criterion 1), Assessment (Criterion 2), and Student Supports (Criterion 3).

##### Kindergarten
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

#### Math 3-5

The materials reviewed for Reveal Math Grades 3-5 meet expectations for Alignment to the CCSSM. In Gateway 1, the materials meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections. In Gateway 3, the materials meet expectations for Usability. Within Gateway 3, the materials meet expectations for Teacher Supports (Criterion 1), Assessment (Criterion 2), and Student Supports (Criterion 3).

###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations
###### Alignment
Meets Expectations
###### Usability
Meets Expectations

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### Overall Summary

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###### Usability
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