Everyday Mathematics 4

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Title ISBN Edition Publisher Year
Comprehensive Student Material Set 9780076952168 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040239 McGraw-Hill Education
Comprehensive Student Material Set 9780076952113 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040215 McGraw-Hill Education
Comprehensive Student Material Set 9780076952151 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040222 McGraw-Hill Education
Comprehensive Student Material Set 9780076951048 McGraw-Hill Education
Comprehensive Student Material Set 9780076952205 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040246 McGraw-Hill Education
Comprehensive Student Material Set 9780076952106 McGraw-Hill Education
Comprehensive Classroom Resource Package 9780077040208 McGraw-Hill Education
Comprehensive Student Material Set 9780076951512 McGraw-Hill Education
Comprehensive Classroom Resource Package Comprehensive Student Material Set McGraw-Hill Education
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Report for 2nd Grade

Overall Summary

The materials reviewed for Everyday Mathematics 4 Grade 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 meet expectations for practice-content connections.

Alignment
Meets Expectations
Usability
Meets Expectations

Focus & Coherence

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for focus and coherence. For focus, the materials assess grade-level content and 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 Everyday Mathematics 4 Grade 2 meet expectations for focus as they assess grade-level content and 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 Everyday Mathematics 4, Grade 2 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year. Unit Assessments found at the end of each unit assess the standards of focus for the unit. Open Response Assessments found at the end of odd-numbered units provide tasks addressing one or more content standards. Cumulative Assessments found at the end of even-numbered units include items addressing standards from prior units.

Materials assess grade-level standards. Examples include:

• Unit 2 Assessment, Item 6, “Take an even number of pennies. How many pennies did you take? How do you know that the number of pennies is even? Write a number model with your pennies as the sum. Use equal addends.” (2.OA.3)

• Unit 2 Cumulative Assessment, Item 6, “How much money?” 5 dimes and 2 pennies are displayed. (2.MD.8)

• Unit 7 Open Response Assessment, Items 1 and 2, “Maria represented the number 349 like this (3 hundreds, 4 tens, and 9 ones are shown). Bill represented the number 349 like this (2 hundreds, 13 tens, and 19 ones are shown). Write whether Maria, Bill, or both of them represented the number 349. Explain your answer. You may include drawings.” (2.NBT.1)

• End-of-Year Assessment, Item 3, “Shawn has 24 crayons. His teacher gave him 24 more, then he lost 8 crayons. How many crayons does he have now?” A line is left blank to provide a number model. (2.OA.1)

Materials assess above-grade assessment items that could be removed or modified without impacting the structure or intent of the materials. Examples include:

• Unit 8 Assessment, Item 3, “Circle the shapes that have parallel sides.” (4.G.2)

• Mid-Year Assessment, Item 10, “Write the rule in the box. Then complete the table.” Students determine the rule and fill in the missing numbers in an in/out table. (4.OA.5)

• End-of-Year Assessment, Item 11a, “Circle the largest number.” The numbers are 3,241; 3,421; 3,204; and 3,021. (4.NBT.2)

• End-of-Year Assessment, Item 12, “Complete the table.” Students are given the rule “Expanded Form” and fill in the missing numbers on an in/out table using standard and expanded form. (4.OA.5)

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

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Materials engage all students in extensive work with grade-level problems. Each lesson provides opportunities during Warm Up, Focus Activities, and Practice. Examples include:

• Lesson 2-2, Addition Number Stories, Focus: Writing Number Stories, Math Journal 1, students look at a picture and write a number story to represent it, “Write an equation to represent the story, and solve, using the terminology “Parts and Total” and “Change-to-More” to describe the problem-solving situations.” Unit 2, Lesson 7, students continue to write number stories and models, “Write a number model for this number story. Jessica has 2 dogs and 8 goldfish. How many pets does she have in all?” In Unit 3, Lesson 2, students share subtraction number stories, “Make up a story for the number sentence 10-3=7.” Lesson 3-8, students use a variety of subtraction strategies while solving number stories for context, “Write a number model for this story: Hayden is riding in the elevator of his apartment building. He gets on the elevator at floor 16. He rides down 7 floors to his aunt’s apartments. On what floor is his aunt’s apartment?” In lesson 6-2, students solve comparison number stories, “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.” Lesson 6-3, students determine the kind of problem-solving situation used to solve a number story; “Change Situation, Comparison Situation, or Parts-and-Total Situation”, “Show children how different diagrams can be used to organize the information in Problem 1 [Rushing Waters now has 26 water slides. That is 9 more than last year. How many water slides were there last year?], which can be interpreted as a change situation, a comparison situation, and a parts-and-total situation?” After the situations are described, “Encourage children to share strategies, making sure to demonstrate how to organize the information in a diagram.” Students engage in extensive work with grade-level problems for 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.”

• Lesson 4-4, Numeration and Place Value, Focus: Matching Numbers to Base-10 Block Representations, students use base-ten blocks to represent 3-digit numbers, “Display 3 flats and 4 cubes and ask children to show the number with number cards on their Place-Value Mats. Some children will leave the Tens column empty. Others will put a 1. Write 34 and 304 on the board. Ask, Which number matches the base-10 blocks? Why? Which digit in 304 shows that there are no longs (or no tens)? Students continue to represent numbers with base-10 blocks in Unit 4, Lessons 5 and 6. In Unit 5, Lessons 4, 5, and 10, students solve problems in their Math Journal to practice representing numbers with place value understanding. Math Journal 2, Problem 1, “In the number 300 there are ___ hundreds, ___ tens, ___ones. Students engage in extensive work with grade-level problems for 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.”

The materials provide opportunities for all students to engage with the full intent of Grade 2 standards through a consistent lesson structure. According to the Teacher’s Lesson Guide, Problem-based Instruction “Everyday Mathematics builds problem-solving into every lesson. Problem-solving is in everything they do. Warm-up Activity- Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines - Reinforce and apply concepts and skills with daily activities. Math Message - Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities - Introduce new content with group problem-solving activities and classroom discussion. Summarize - Discuss and make connections to themes of the focus activity. Practice Activities - Lessons end with spiraled review of content from past lessons.” Examples of full intent include:

• Lesson 1-9, Even and Odd Number Patterns, Focus: Introducing Even and Odd Numbers, students identify even and odd by making pairs, “Discuss the following points: Whenever each child standing can be paired with another child, the total number standing is called an even number. Whenever one child cannot be paired with another child, the total number standing is called an odd number.” Routine 2, Calendar Routine: Using the Calendar Routine, “Determine whether there has been an odd or an even number of days in the month so far. Ask: What happens if we try to break the days that have passed into two equal groups? Does the result tell us whether the number is even or odd?” Students engage in the full intent of 2.OA.3, “Determine whether a group of objects (up to 20) has an odd or even number of members, e.g., by pairing objects or counting them by 2s; write an equation to express an even number as a sum of two equal addends.”

• Lesson 7-9, Exploring Shape Attributes, Graphs, and Measurements, Math Journal 2, students sort shapes by attribute, then trace the shapes, “Trace 3 shapes from a different sort. Write a name that describes the sort.” Lesson 8-2, Core Activities: Focus, Identifying Attributes, students complete sentence frames for students to describe shapes, “This is a _____. It has ____ sides. It has ____ vertices. It has ____ angles.” Students engage in the full intent of 2.G.1, “Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.”

Criterion 1.2: Coherence

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

The materials reviewed for Everyday Mathematics 4 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 Everyday Mathematics 4 Grade 2 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• There are 9 instructional units, of which 7 units address major work of the grade or supporting work connected to major work of the grade, approximately 78%.

• There are 108 lessons, of which 75.5 address major work of the grade or supporting work connected to the major work of the grade, approximately 70%.

• In total, there are 170 days of instruction (108 lessons, 39 flex days, and 23 days for assessment), of which 101 days address major work of the grade or supporting work connected to the major work of the grade, approximately 59%.

• Within the 39 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities do not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

A lesson analysis is most representative of the materials. As a result, approximately 70% of the materials focus on the 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 Everyday Mathematics 4 Grade 2 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Digital materials’ Main Menu links to the “Spiral Tracker” which provides a view of how the standards spiral throughout the curriculum. The Lesson Landing Page contains a Standards section noting standards covered by the lesson. Teacher Edition contains “Correlation to the Standards for Mathematics” listing all grade-level standards and correlating lessons. Examples include:

• Lesson 1-3, Math Tools, Focus: Examining the Nickel, students use skip counting to find the total value of coin combinations, “Ask: If every child in our class had 1 nickel, how much money would we have in all? Record children’s estimates of the total; then count all the nickels together by 5s and record the counts on the board. Discuss with the class what patterns they notice as they count by 5s.” This connects the supporting standard 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies,” to the major work of 2.NBT.2, “Count within 1000; skip count by 5s, 10s, and 100s.”

• Lesson 4-2, Telling Time to the Nearest 5 Minutes, Focus: Telling Time to the Nearest 5 Minutes, students tell time using an analog clock to skip count by fives and report the time as so many minutes past the hour, “Display 9:00 on the clock and ask children what time it shows. Move the minute hand slowly forward, to 9:20, pausing on each number 1 through 4. If needed, adjust the hour hand. At each pause, ask: What time is it now? Say the times with the class: 5 minutes after 9, 10 minutes after 9, 15 minutes after 9, 20 minutes after 9.” This connects the supporting standard 2.MD.7, “Tell and write time from analog and digital clocks to the nearest five minutes,” to the major work of 2.NBT.2, “Count within 1000; skip count by 5s, 10s, and 100s.”

• Lesson 7-7, Representing Data: Standing Jumps, Focus: Making a Class Line Plot, students make a line plot using standing-jump data and answer questions to interpret the data, “Label the shortest and longest lengths on the line plot. Ask children questions about the set of data displayed in the line plot: What does it mean when there are a lot of Xs above a number? How many children have a jump of 42 inches?” This connects the supporting standard 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,” to the major work 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.”

• Lesson 7-8, Representing Data: Arm Span, Focus: Comparing Arm Span Measures, students measure their arm span in inches and use the data to create a frequency chart and then a line plot, “Determine who has the shortest and longest arm spans and what their lengths are. Tape an actual tape measure to the board and mark the longest and shortest arm spans. Draw a comparison diagram on the board, filling in the known quantities and writing a question mark for the difference. With the class, find the difference between the two arm spans. Explain that children will use the class arm span data to make a frequency table and a line plot.” This connects the supporting standard 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,” to the major work 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.”

• Lesson 8-8, Equal-Groups and Array Number Stories, Focus: Solving Equal-Groups and Array Number Stories, students solve array number stories, “Pose number stories involving equal groups or arrays of objects. Tell children to work with their partners and use drawings to model and solve each problem. After each number story, have volunteers share their strategies.” This connects the major work of 2.OA.A, “Represent and solve problems involving addition and subtraction.” to 2.OA.C, “Work with equal groups of objects to gain foundations for multiplication.”

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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 Everyday Mathematics 4 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 Teacher Edition contains a Focus section in each Section Organizer identifying major and supporting clusters covered. Materials do not contain connections of supporting work to supporting work. There are connections from supporting work to supporting work and major work to major work throughout the grade-level materials, when appropriate. Examples include:

• Lesson 1-2, Number Lines and Partnership Principles, Focus: Working with a Partner to Add and Subtract on a Number Line, students work with a partner to solve number stories using the number line in the back of their journal, “Have children solve the following number story using one of the number lines on the inside back cover of their journals: Angela had $14. She earned$5 more. How much money does Angela have now?” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.MD.B, “Relate addition and subtraction to length.”

• Lesson 2-9, Even Numbers and Equal Addends, Warm-Up: Mental Math and Fluency, teachers pose number stories to students, and they share their solutions and strategies, “Pose number stories and have children share their solutions and strategies.” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.OA.A, “Represent and solve problems involving addition and subtraction.”

• Lesson 3-3, Fact Families, Focus: Discussing Fact Families, students use fact triangles to name 3 numbers that make addition and subtraction facts, “Ask a volunteer to name another group of three numbers that are related by addition and subtraction. Write these numbers in the corners of the triangle and have children write the fact family for these numbers on their slates.” This connects the major work of 2.OA.B, “Add and subtract within 20” to the major work of 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.”

• Lesson 6-4, Animal Number Stories, Focus: Silly Animal Stories, students use data from the Animal Heights and Lengths Poster from their journal to make up and solve animal number stories, “Tell the class they will use the data from the Animal Heights and Lengths Poster on journal page 146 to make up and solve their own number stories. Have children share their solution strategies.” This connects the major work of 2.NBT.B, “Use place value understanding and properties of operations to add and subtract.” to the major work of 2.MD.B, “Relate addition and subtraction to length.”

• Lesson 7-1, Playing Hit the Target, Practice: Bamboo Plant Number Stories, students solve problems in Math Journal 2, p. 166-167. Students are given a chart of bamboo growth each day for a week measured in inches, ranging from 12 inches to 99 inches. “Use the information above to solve the following number stories.” Problem 1, “How many inches did the bamboo plant grow from Tuesday to Friday? Number Model: ______ Answer: ____ inches.” This 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.”

• Lesson 9-6, Expand-And-Trade Subtraction Part 1, Focus: Representing Subtraction with Trades, students represent numbers using base-ten blocks and sketches of place value, then use to subtract, “Tell children they will now use their base-10 blocks to solve 53-37. Ask children to represent 53 with base-10 blocks. When they have finished, record a sketch of 5 longs and 3 cubes. Ask: Are there enough longs and cubes for me to remove 3 longs and 7 cubes? How can I get more cubes so I can remove 7 cubes? Have the children make the trade with their base-10 blocks. Represent this trade on your sketch by crossing out 1 long and adding 10 cubes.” This connects the major work of 2.NBT.A, “Understand place value,” to the major work of 2.NBT.B “Use place value understanding and properties of operations to add and subtract.”

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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 Everyday Mathematics 4 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.

Materials relate grade-level concepts to prior knowledge from earlier grades. Each Section Organizer contains a Coherence section with “Links to the Past” containing information about how focus standards developed in prior units and grades. Examples include:

• Teacher’s Lesson Guide, Section 2 Organizer, Coherence, “Links to the Past” for 2.OA.3, “In Unit 1, children explored even and odd numbers using concrete and visual models. In Grade 1, children wrote number models to represent pictures of real-world items with paired features.”

• Teacher’s Lesson Guide, Section 5 Organizer, Coherence, “Links to the Past” for 2.MD.6, “In Unit 2, children used number lines to add 2-digit numbers to 10. In Grade 1, children used number lines to count and add.”

• Teacher’s Lesson Guide, Section 8 Organizer, Coherence, “Links to the Past” for 2.G.2, “Children begin their informal exploration of area in Grade 2. In Unit 1, children determined that squares are the best shape for covering a rectangle. In Unit 3, they used 1- and 2-inch squares to explore how measurement relates to the size of the unit.”

Materials relate grade-level concepts to future work. Each Section Organizer contains a Coherence section with “Links to the Future” containing information about how focus standards lay the foundation for future lessons. Examples include:

• Teacher’s Lesson Guide, Section 3 Organizer, Coherence, “Links to the Future” for 2.NBT.5, “Throughout Grade 2, children will represent and solve problems involving addition and subtraction within 100. In Unit 6, children will be introduced to partial-sums addition. In Unit 9, they will be introduced to expand-and-trade subtraction. In Grade 3, children will add and subtract within 1,000 using strategies and algorithms.”

• Teacher’s Lesson Guide, Section 6 Organizer, Coherence, “Links to the Future” for 2.MD.5, “Throughout Grade 2, children will solve number stories involving lengths. In Grade 3, children will solve number stories involving real-world situations including time intervals and masses or volumes.”

• Teacher’s Lesson Guide, Section 8 Organizer, Coherence, “Links to the Future” for 2.G.2, “In Grade 2, children will informally explore area by partitioning rectangles into rows and columns and counting to find the total. In Grade 3, children will apply their understanding of square units to find the area of plane figures in a variety of contexts.”

Materials contain content from future grades in some lessons that is not clearly identified. Examples include:

• Lesson 1-10, Skip-Counting Patterns, Focus: Skip Counting with a Calculator, “Children use calculators to skip count.” “Children practice programming their calculators by setting them to count up by 1’s. Next, the students try group counts by numbers other than 2, 5, and 10, such as by 3, 4, and 9. Children press the appropriate keys on their calculators as they count in unison. Suggestions: Count from 22 by 3s. Count from 22 by 4s. Count from 80 by 6s. Count from 180 by 9s.” This lesson is labeled 2.NBT.2, “Count within 1000; skip-count by 5s, 10s, and 100s.” Identifying arithmetic patterns, including patterns in the addition table or multiplication table, is aligned to a Grade 3 standard [3.OA.9, “Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties of operations”].

• Lesson 7-7, Representing Data: Standing Jumps, Warm Up: Mental Math and Fluency, “Dictate pairs of numbers for children to write on their slates and compare, recording the results with >, <, and =. Ask children to explain their answers in terms of place value. 1,054 and 1,154, 1,243 and 1,233, and 1,522 and 1,622.” This lesson is labeled 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.” Comparing two multi-digit numbers based on the meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons is aligned to a Grade 4 standard (4.NBT.2, “Read and write multi-digit whole numbers using base-10 numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons”).

• Lesson 9-4, Fractional Units of Length, Focus: Introducing Half-Inches, “Explain that measuring in half-inches, rather than inches or feet, produces more-precise measurements.” Students then practice measuring to the \frac{1}{2} inch throughout the lesson and on page 227 f their Math Journal. This lesson is labeled 2.MD.1, “Measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes” and 2.MD.4, “Measure to determine how much longer one object is than another, expressing the length difference in terms of a standard length unit.” Measuring to the ½ inch is a Grade 3 standard (3.MD.4, “Generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch”).

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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 Everyday Mathematics 4 Grade 2 can be completed within a regular school year with little to no modification to foster coherence between grades.

Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. As designed, the materials can be completed in 170 days:

• There are 9 instructional units with 108 lessons. Open Response/Re-engagement lessons require 2 days of instruction adding 9 additional lesson days.

• There are 39 Flex Days that can be used for lesson extension, journal fix-up, differentiation, or games; however, explicit teacher instructions are not provided.

• There are 23 days for assessment which include Progress Checks, Open Response Lessons, Beginning-of-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment.

The materials note lessons are 60-75 minutes and consist of 3 components: Warm-Up: 10-15 minutes; Core Activity: Focus: 30-35 minutes; and Core Activity: Practice: 15-20 minutes.

Rigor & the Mathematical Practices

The materials reviewed for Everyday Mathematics 4 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 Everyday Mathematics 4 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, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for developing conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where conceptual understanding is emphasized within each lesson of the Unit. The Focus portion of each lesson introduces new content, designed to help teachers build their students’ conceptual understanding through exploration, engagement, and discussion. The materials include problems that develop conceptual understanding throughout the grade level, especially where called for in the standards. Examples include:

• Lesson 1-4, Class Number Scroll, Focus: Exploring Patterns on the Number Grid, students describe and explore patterns on a number grid. Students are expected to observe such things as every other number on the grid is odd and all of the numbers in the far right column end in a 0. Next, the teacher leads the students in using the chart to skip count by 2s, 5s, and 10s. “Lead children in counting by 2s in unison starting at 0. Point to the numbers on the Number-Grid Poster as you count. Ask: What patterns do the count-by-2 numbers make on the grid?” This activity supports conceptual understanding of 2.NBT.2, “Count within 1000, skip-count by 5s, 10s, and 100s.”

• Lesson 2-5, The Near-Doubles Strategy, Focus: Discussing the Near-Doubles Strategy, the teacher leads a discussion about how using a near-doubles fact can help find the answer to a more difficult problem. “Display problems 5+7=? and 6+4=? and tell partners to use their knowledge of doubles facts to solve them. After a few minutes, invite volunteers to share their strategies. These may include adding or subtracting 2 from a double (for example, 5 + 7 = 5 + 5 + 2 = 12) or ‘sharing’ (for example, taking 1 from 7 and giving it to 5 to make the double 6 + 6).” This activity supports the conceptual understanding of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”

• Lesson 4-4, Numeration and Place Value, Focus: Reviewing Values of Digits, students examine base-10 blocks. “Display a cube, a long, and a flat. Remind children that these are called base-10 blocks. Hold up a cube. Say: This is a base-10 cube. It represents 1. Then hold up a long and say: This is a long. It represents 10. Ask children to explain why a long represents 10. Hold up a flat and say: This is a flat. It represents 100. Ask children to explain why a flat represents 100.” This class discussion supports students in developing a conceptual understanding of 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones.”

• Lesson 5-5, Exploring Arrays, Time, and Shapes, Focus: Introducing Arrays, students make arrays and write number models to represent them. “Explain that the arrangement of dots in rows and columns, as shown in the Math Message, is called an array. All of the rows have the same number of dots, and all of the columns have the same number of dots. Ask: How many rows of dots are there? How many dots are in each row? How many dots are there in all?” This activity supports conceptual understanding of 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.”

• Lesson 9-5, Reviewing Place Value, Focus: Comparing Multi-digit Numbers, the teacher leads a discussion about expanding three-digit numbers. “How can we use the expanded form of each number to help us compare them? Sample answer: First we can look at the hundreds. Both numbers have 2 hundreds, or 200, so next, we look at the tens. We see that 292 has 9 tens, or 90, but 289 has 8 tens, or 80. So we know 292 is larger.” Then the teacher asks, “Do we need to look at the ones?” Students may answer, “No. The tens told us that 292 is larger.” The teacher repeats this activity with other pairs of 3-digit numbers as needed. This activity supports conceptual understanding of 2.NBT.4, “Compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >, =, and < symbols to record results of comparisons.”

Home Links and Games provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Lesson 1-8, My Reference Book, Quarters and Math Boxes, Math Journal 1, Problem 3, students make multiple representations of 25 cents. “Show two ways to make 25 cents. Use [circle with a P inside, circle with an N inside, circle with a D inside].” This practice activity supports conceptual understanding of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies using $and ¢ symbols appropriately.” • Lesson 2-8, Exploring Addition Tools, Odd and Even Patterns, and Shapes, Math Journal 1, Problem 1, students use number lines provided to find sums. “Show 62 + 10 on the number line below.” Then students record their answers. This practice activity supports the conceptual understanding of 2.NBT.1, “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.” • Lesson 4-5, Using Place Value to Compare Numbers, Math Journal 1, Problem 2, students write numbers in expanded form to compare them. “Write each number in expanded form. Then write < or > in the box to compare the two numbers.” Students compare 42 and 48, then write 40+2 and 40+8 so they can use the ones to make a comparison. This practice activity supports conceptual understanding of 2.NBT.3, “Read and write numbers to 1000 using base-10 numerals, number names, and expanded form.” Indicator {{'2b' | indicatorName}} Materials give attention throughout the year to individual standards that set an expectation for procedural skill and fluency. The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for giving attention throughout the year to individual standards that set an expectation of procedural skill and fluency. All units begin with a Unit Organizer, Planning for Rich Math Instruction. This component indicates where procedural skill and fluency exercises are identified within each lesson of the Unit. The Mental Math Fluency exercises found at the beginning of each lesson develop fluency with basic facts and other skills that need to be automatic while engaging learners. The Practice portion of the lesson provides ongoing practice of skills from past lessons and units through activities and games. Examples include: • Lesson 2-3, Doubles and Combinations of 10, Focus: Using Double Ten Frames, students explore strategies to find dot totals on double ten frames. “Flash each Quick Look Card for 2 to 3 seconds before removing it from view or covering it. Always allow a second look and follow up by asking children both what they saw and how they saw it. Asking such questions will allow a variety of strategies to emerge. Encourage children to share multiple strategies but focus attention on those that involve doubles and combinations of 10.” This activity provides an opportunity for students to develop fluency in 2.OA.2, “Fluently add and subtract within 20 using mental strategies.” • Lesson 5-7, Open Number Lines, Focus: Using Open Number Lines, students use mental strategies to solve addition number stories and record their thinking on open number lines. “Pose the following number story and have children draw open number lines on their slates to record their thinking: Peter has 64 blocks in his toy box and 30 blocks on the table. How many blocks does he have in all?” This activity provides an opportunity for students to develop 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.” • Lesson 7-3, Playing Basketball Addition, Focus: Introducing Basketball Addition, students are introduced to a new game. “Basketball Addition is played by two teams of 3 to 5 players each. The number of points scored by each player in each half is determined by rolling one 20-sided polyhedral die or by rolling three 6-sided dice and using their sum. The team that scores the most points wins the game.” This activity provides an opportunity for students to develop 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.” • Routine 3: Attendance Routine, students use data from the attendance chart to tell number stories. “Today, 23 children are here. If 2 more children arrive, how many will be present? There are 24 children here today. If 6 go to the library, how many are left?” This activity provides continuous opportunities for students to develop 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.” Math Boxes, Home Links, Games, and Daily Routines provide opportunities for students to independently demonstrate procedural skills and fluency throughout the grade. Examples include: • Lesson 2-4, The Making-10 Strategy, Practice: Math Journal 1, students apply the making 10 strategy. “Use the double ten frames to make 10. Then find the sum. Write the combination of 10 that helped.” In Question 1, students are shown 9 and 5. The suggested answer is, “The combination of 10 that helped: 9+1=10 and fact 9+5=10.” This activity provides an opportunity for students to independently demonstrate the procedural skill of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.” • Lesson 4-11, Matching Facts with Strategies, Measuring a Path, Exploring Arrays, Practice: Math Journal 1, students match subtraction facts to strategies used to solve. “In small groups children discuss their reasoning for their pairings, focusing especially on differences in how they matched facts and strategies.” This activity provides an opportunity for students to independently demonstrate the procedural skill 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.” • Lesson 5-7, Open Number Lines, Practice: Math Journal 2, Problem 2, students use Open Number Lines to record their thinking when adding two 2-digit numbers. “You build the second tower with 37 red blocks and 32 blue blocks. How many blocks did you use?” This activity provides an opportunity for students to independently demonstrate the procedural skill 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.” • Lesson 9-7, Expand-And-Trade Subtraction, Part 2, Practice; Math Journal 2, Problem 3, students are given a subtraction problem and find a ballpark estimate, write each number in expanded form, and solve, “$$72-49=?$$” This activity provides an opportunity for students to independently demonstrate the procedural skill 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.” Indicator {{'2c' | indicatorName}} Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Focus activities introduce new content, provide routine exercises, review recent learning, and provide challenging problem-solving tasks that help build conceptual understanding, procedural skill and fluency, and application of mathematics. Open Response lessons provide challenging problems that involve more than one strategy or solution. Home-Links relate to the Focus activity and provide informal mathematics activities for students to do at home. Examples of routine and non-routine applications of the mathematics include: • Lesson 3-9, Going-Back-Through-10 Strategy for Subtraction, Focus: Going Back Through 10, Math Journal 1, Problem 4, students use a subtraction strategy to solve problems. “Make up and solve your own subtraction story.” Students apply their understanding 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.” • Lesson 5-3, Counting Up With Money, Focus: Making Change, Math Journal 2, students count up from the cost of an item to the amount paid using Pine School’s Fruit and Vegetable Sale. “I am buying an orange. I give the clerk two dimes. How much change should the clerk give back?” Students apply their understanding of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using$ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”

• Lesson 6-4, Animal Number Stories, Focus: Drawing a Bar Graph, Math Journal 2, Problem 4, students draw a bar graph and use the information to write their own number story. “Use the data in the bar graph to write your own number story.” Students apply their understanding 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. Solve simple put-together, take-apart, and compare problems using information presented in a bar graph.”

• Lesson 8-8, Equal-Groups and Array Number Stories, Home Link, Problem 2, “Find the total number of objects in each picture. Then write a number model.” Students are shown a picture of a muffin tin. “There are ____ muffin cups. Number Model ____.” This activity provides the opportunity for students to apply their understanding of 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.”

Materials provide opportunities for students to independently demonstrate multiple routine and non-routine applications of the mathematics throughout the grade level. Independent Problem Solving provides “additional opportunities for children to apply the content they have learned during the section to solve non-routine problems independently. These problems often feature: applying math in the real world, multiple representations, drawing information or data from pictures, tables, or graphs, and opportunities for children to choose tools to support their problem solving.” Examples of independent demonstration of routine and non-routine applications of the mathematics include:

• Independent Problem Solving 1a, “to be used after Lesson 1-6”, Problem 1, students use mental strategies to add and subtract. “a. Sarah used a calculator to check her brother’s math homework. When she tried to enter 15 into the calculator she found that the 5 key was broken. Write at least 3 number sentences that show how Sarah can show 15 on the calculator without using the 5 key.” This activity provides the opportunity for students to independently demonstrate an understanding of 2.OA.2, “Fluently add and subtract within 20 using mental strategies.”

• Independent Problem Solving 1b, “to be used after Lesson 1-11”, Problem 1, students draw combinations of coins to show 35 cents. “Juan’s mom gave him and his sister Maria each 35¢. They noticed they each had a different combination of coins. Use P, N, D, Q. Draw possible coins for Juan and Maria.” This activity provides the opportunity for students to independently demonstrate understanding of 2.MD.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $and ¢ symbols appropriately.” • Independent Problem Solving 5b, “to be used after Lesson 5-10”, Problem 1, students use a table with temperatures of 3 cities at 6:00 am and 6:00 pm to write and solve number stories. “Use the information in the table above to write a number story about the temperature change in one of the cities/towns. Solve your number story. Show your work below.” This activity provides the opportunity for students to independently demonstrate an understanding 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.” • Independent Problem Solving 7a, “to be used after Lesson 7-1”, Problem 1, students draw possible combinations of coins to show 35 cents. “a. Ellen has saved 26. She needs 80 to buy a new gaming headset. Ellen knows she could subtract to find out how much more money she needs, but the subtraction key on her calculator is broken. How might she use her broken calculator to get from 26 to 80? b. Ellen needs ___ more to buy the headset. c. What other tool(s) could Ellen use to start at 26 and end at 80? d. Explain how Ellen might use the tool(s) you list above.” This activity provides the opportunity for students to independently demonstrate an understanding 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.” Indicator {{'2d' | indicatorName}} The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade. All three aspects of rigor are present independently throughout the grade. Examples where materials attend to conceptual understanding, procedural skill and fluency, or application include: • Lesson 2-2, Addition Number Stories, Focus: Creating and Solving Addition Number Stories, students make up and solve number stories, “1. Display the story or draw a picture that illustrates the story but doesn't suggest a solution strategy. 2. Draw an empty unit box below the story. 3. Have children write a label in the unit box and share how they would answer the question in the story. 4. Ask a volunteer to write a number model for the story. 5. Ask another volunteer to explain how the numbers in the number model connect to the story.” This activity develops a conceptual understanding 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.” • Lesson 3-2, Subtraction From Addition: Think Addition, Focus: Generating Related Addition and Subtraction Facts, students generate related addition and subtraction facts based on dominoes, “Display a domino with 5 dots on one side and 4 dots on the other, Help children discover the addition facts and subtraction facts it shows. Ask: Which addition facts describe the domino? If needed, remind children about using the turn-around rule to generate related addition facts. Which subtraction facts describe this domino?” Students repeat the activity with other dominos. This activity develops the procedural skill 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.” • Lesson 7-8, Representing Data: Arm Spans, Focus: Making a Line Plot of Arm Span Data, students measure their arm spans, enter the data in a frequency table, and draw a line plot. “Discuss children’s completed line plots. Ask: What does it mean when there are a lot of Xs above a number? Which arm span is the most common? What do you know about the numbers that have no Xs above them? How many children have an arm span of 51 inches? Of 46 inches?” This activity provides an opportunity for students to apply their understanding 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.” Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Examples include: • Lesson 4-7, Playing Target, Focus: Playing Target to 50, students add and subtract using base-10 blocks, “Players take turns. When it is your turn, do the following: Turn over 2 cards. You may either use one card to make a 1-digit number or both cards to make a 2-digit number. Model your number with base-10 blocks. Put these blocks just below your Target Game Mat but not on the mat. You now have two choices: Choice 1: Add all of the base-10 blocks below the mat to the blocks already on your Target Game Mat. Choice 2: Subtract all of the blocks below the mat from the blocks already on your Target Game Mat. If you decide to subtract, you may first have to make exchanges on the mat.” The first player to have a mat with a value of exactly 50 wins. Students develop conceptual understanding of 2.NBT.1, “Understand that the three digits of a three-digit number represent amounts of hundreds, tens, and ones,” and procedural skills with 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.” • Lesson 4-11, Matching Facts with Strategies, Measuring a Path, Exploring Arrays, Focus: Exploration A: Matching Facts with Strategies, students match subtraction facts to possible solution strategies. “Children independently match subtraction facts from Math Masters, page 110 to strategies they could use to solve them on journal page 89. In small groups children discuss their reasoning for their pairings, focusing especially on differences in how they matched facts and strategies.” Students develop procedural skills with 2.OA.2, “Fluently add and subtract within 20 using mental strategies,” and conceptual understanding 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.” • Lesson 6-4, Animal Number Stories, Focus: Solving Silly Animal Stories and Writing Silly Animal Stories, students solve number stories comparing the heights and lengths of various animals. “Have children share the names and lengths of the longest animal and the shortest animal.” Then students write and solve their own number stories, “Children write two number stories. In each story, they compare or add the lengths in feet of two animals from journal page 146.” Students develop procedural skills with 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 application 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.” Criterion 2.2: Math Practices Materials meaningfully connect the Standards for Mathematical Content and Standards for Mathematical Practice (MPs). The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs). Indicator {{'2e' | indicatorName}} Materials support the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for supporting the intentional development of MP1: Make sense of problems and persevere in solving them; and MP2: Reason abstractly and quantitatively, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards. Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice). Materials provide intentional development of MP1 to meet its full intent in connection to grade-level content. Students make sense of problems and persevere in solving them as they work with the support of the teacher and independently throughout the units. Examples include: • Lesson 3-2, Subtraction From Addition: Think Addition, Focus: Summarizing Subtraction Strategies, students consider different strategies to solve problems involving subtraction. “Have partners discuss the following questions: If you want to solve a subtraction fact that you don’t know, what strategies could you use? Pose a few subtraction facts to provide a context, such as 12-6, 15-8, and 16-7. Encourage children to refer to their My Subtraction Fact Strategies Table on journal page 48. As volunteers share their ideas, record their strategies on the Class Data Pad and lead a class discussion about the similarities and the differences between the strategies.” • Lesson 3-4, Playing Salute! Focus: Introducing and Playing Salute! students use various addition strategies and determine if answers make sense while playing a game to practice adding and finding missing addends. “Circulate among the groups as they play. Whenever possible, encourage children to reflect on and discuss strategies they think would have been more efficient for a given round. Have them resolve any discrepancies between their answers.” • Lesson 5-2, Using Coins to Buy Things, Focus: Reviewing Money Equivalencies, students analyze and make sense of money problems and as they find equivalent coin combinations. “Display a nickel. Ask: What is this called? How much is it worth? Write nickel and 5 cents on the Class Data Pad. Ask: How much are 2 nickels worth? Repeat with a penny, a dime, a quarter, and a$1 bill.”

• Independent Problem Solving 5b, “to be used after Lesson 5-10”, Problem 2, students solve a word problem in two different ways. “Hai had some action figures. His friend Amalia gave him 9 more. Now Hai has 24 action figures. How many action figures did Hai have to start with? a) Solve the problem in two different ways. Use drawings, words, or both to show your thinking in the space below.”

Materials provide intentional development of MP2 to meet its full intent in connection to grade-level content. Students reason abstractly and quantitatively as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 2-4, The Making-10 Strategy, Focus: Exploring the Making-10 Strategy, students use the making-10 strategy to determine the number of dots in ten frames and record symbolically.  “Remind children that Quick Look activities help us think about addition strategies. Flash Quick Look cards 95 and 98 in sequence. Have children write words or number sentences on their slates to record how they figured out the total number of dots on each card.”

• Lesson 8-7, Partitioning Rectangles, Part 2, Focus: Partitioning Strategies, students explain number representations when partitioning rectangles into same-size squares and discuss connections between rows and columns. “Ask children to share their strategies for determining how many squares are needed to cover the rectangle. Some children may have visually estimated how many squares will fit in one row and one column, while others may have used their fingers or marks on paper to help them estimate. Ask: How were you able to make sure that your squares were the same size?”

• Lesson 9-5, Reviewing Place Value, Focus: Comparing Multi-Digit Numbers, Math Journal 2, students attend to the meaning of quantities as they compare numbers after writing in expanded form, “Write each number in expanded form. Then write < or > in the box to compare the two numbers.” For example, in Problem 5, students compare the numbers 1,583 and 1,221.

• Independent Problem Solving 3a, “to be used after Lesson 3-4”, Problem 2, students write a word problem to go with an equation. “Write a number story for the number sentence 4=8-4.”

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Materials support the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for supporting the intentional development of MP3: Construct viable arguments and critique the reasoning of others, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide support for the intentional development of MP3 by providing opportunities for students to construct viable arguments in connection to grade-level content. Examples include:

• Lesson 3-8, Using Doubles to Subtract, Home Link, students construct viable arguments as they explain their strategy to someone at home. “Look at the missing addend in each Fact Triangle. Tell someone at home how to use doubles to help find it. Explain how you found the missing addend.”

• Lesson 8-4, (Day 2): Drawing and Reasoning About Quadrilaterals, Focus: Setting Expectations, students construct viable arguments as they discuss solutions to the Open Response Problem. “Review the open response problem from Day 1. Ask: What do you think a complete answer to this problem needs to include? Sample answer: It needs drawings of gardens for Juan and Linda and an explanation for why the circled shape has the attributes for Linda’s plan.”

• Independent Problem Solving 2b, “to be used after Lesson 2-10”, Problem 2, students construct viable arguments as they look for patterns in the sums of even and odd numbers. “Alice wonders if the sum of dots on a domino with an even number of dots on one side and an odd number of dots on the other side will always be even, odd, or could be either. a) Draw at least 1 different even/odd domino and see if you can help Alice figure this out. Use drawings or words or both to show Alice what you think and why.”

Materials provide support for the intentional development of MP3 by providing opportunities for students to critique the reasoning of others in connection to grade-level content. Examples include:

• Unit 3, More Fact Strategies, Open Response Assessment, A Subtraction Strategy, students critique the reasoning of others as they explain and use subtraction strategies. “Grace solved 12-7 this way: ‘I started at 12 and took away 2 to get to 10. Then I took away 5 more. I ended up at 5. So 12-7=5.’ Grace solved 13-4 this way: ‘I started at 13 and took away 3 to get to 10. Then I took away 1 more. I ended up at 9. So 13-4=9.’ Show and explain how to use Grace’s subtraction strategy to solve 14-8.”

• Lesson 4-7, Playing Target, Practice: Practicing Place-Value Concepts, Math Journal 1, Problem 8, students critique the reasoning of others as they analyze a provided student strategy. “Marta wrote 24 to describe the number shown by these base-10 blocks: Do you agree with Marta? Explain your answer.”

• Independent Problem Solving 6b, “to be used after Lesson 6-8”, Problem 2, students critique the reasoning of another student’s addition strategy. “Louisa is checking supplies for a party. She counts 27 small cups and 34 large cups. She wants to know how many cups she has in all. Her strategy to solve 27+34= ___ is: 24+30=57, 57+4=61, 27+34=61. Do you agree that Louisa’s strategy works? Use drawings or words or both to explain why or why not.”

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Materials support the intentional development of MP4: Model with mathematics; and MP5: Choose tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for supporting the intentional development of MP4: Model with mathematics; and MP5: Use appropriate tools strategically, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide intentional development of MP4 to meet its full intent in connection to grade-level content. Students model with mathematics to solve real-world problems, identify important quantities to make sense of relationships, and represent them mathematically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 9-3, Focus: Solving the Open Response Problem, students use the math they know to divide muffins equally among two and four children, describing each child’s share. “Distribute Math Masters, pages 254-255 to all children. Read the problem as a class and ask partners to discuss what the problem asks them to do. Encourage children to refer to the Equal Shares posters and use fraction vocabulary like that on the poster as they talk about and write responses to the problem. Review the terms one-half, two-halves, one-fourth, and four-fourths. Tell children that an important part of the task is to write how much muffin is in one child’s share. Circulate as children work. Ask children to explain their drawings and descriptions of one child’s share and encourage them to add details to clarify their responses. You may also want to make notes about children’s strategies. Ask: How did you show your work and thinking for this problem? Did you use words, symbols, or anything else?”

• Independent Problem Solving 6a, “to be used after Lesson 6-5”, Problems 1 and 2, students model the situation with an appropriate representation as they solve word problems involving addition. “1. Asia has 24 tickets. She was happy to have 4 more tickets than last year. She wants to get a bracelet, a whistle, and a pencil. How many tickets will Asia have left over? Use drawings or words or both to show your thinking. 2. Mario has 2 tickets fewer than Asia. He wants to use all his tickets. What items could he buy at the carnival?”

• Independent Problem Solving 8b, “to be used after Lesson 8-7”, Problems 1 and 2, students use the math they know to solve problems and everyday situations to find the total number of objects arranged in an array. “1. The principal asked Koke to set up the gym for the science fair. Each student needs the same amount of space for their project. Koke drew a picture of the gym floor and partitioned it into same-sized squares. Each square can hold one project. Before he counted the total number of squares, he accidentally spilled milk on his drawing. Look at Koke’s drawing. Help him figure out how many squares there are in all. 2. Use words to explain how you found the total number of squares in Koke’s drawing.”

Materials provide intentional development of MP5 to meet its full intent in connection to grade-level content. Students use appropriate tools strategically as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 9-11, Multiples of 10 and 5, Focus: Math Message, students choose and use appropriate tools and strategies as they solve a word problem. “You have 6 boxes of markers with 10 markers in each box. How many markers do you have in all? Talk to a partner about how you could solve this problem using each of the following tools: a number line, a number grid, and base-10 blocks. Then solve the problem.”

• Independent Problem Solving 7b, “to be used after Lesson 7-7”, Problem 1, students solve problems that involve measuring and estimating lengths using any tool or strategy. “Two partnerships are each measuring the length of a wall. Jack and Tessa used two yardsticks. Tessa placed the edge of one yardstick at the beginning of the wall. Jack placed the second yardstick at the end of the Tessa’s yardstick. Then Tessa picked up her yardstick and placed it at the end of Jack’s yardstick. They did this over and over until they reached the end of the wall. Does Jack and Tessa’s measuring strategy work? Why or why not?”

• Independent Problem Solving 8b, “to be used after Lesson 8-7”, Problem 3, students choose tools and strategies to solve a word problem. “Mike’s mom told him to clean his closet. He wants to neatly arrange his shoes in his closet. He has 8 pairs of shoes. (Think: How many shoes are in a pair?) Show 2 ways Mike can arrange his pairs of shoes in equal rows. Use counters, drawings, or any other tool to help.”

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Materials attend to the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Everyday Mathematics 4 Grade 2 partially meet expectations for supporting the intentional development of MP6: Attend to precision; and attend to the specialized language of mathematics, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

MP6 is explicitly identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Students attend to precision in connection to grade-level content as they work with the support of the teacher and independently throughout the units. Examples include:

• Lesson 4-1, Clocks and Telling Time, Focus: Estimating Time with the Hour and Minute Hands, students attend to precision as they discuss how to use the hour and minute hands to estimate time. “Ask questions such as the following: If you don’t need to know the exact time, which hand is more important? Could you tell time if your clock had only a minute hand? Explain. What if your clock had only an hour hand? Could you estimate the time? Explain. Which hand helps you tell the time to the nearest minute?”

• Lesson 9-1, Creating and Naming Equal Parts, Focus: Naming 2, 4, and 3 Equal Shares, students attend to precision when solving word problems. “Begin a 2 Equal Shares poster on the Class Datapad or chart paper. Have children refer to their paper squares from the previous activity. Ask the following questions. Record children’s answers on the poster. (See margin). How can you name one child’s share? Sample answers: half; one-half; 1-half; 1 out of 2 equal parts. How can you name both shares together? Sample answers: two-halves; 2-halves; 2 out of 2 equal parts; whole.”

• Independent Problem Solving 4b, “to be used after Lesson 4-10”, Problem 2, students attend to precision when measuring. “Anna measured the pencil above and said that it was about 6 inches long. Howard measured the same pencil and said that it was about 15 centimeters long. a) Use tools to find out who is correct. b) Use words to explain your answer.”

Materials attend to the specialized language of mathematics in connection to grade-level content. Examples include:

• Lesson 2-3, Doubles and Combinations of 10, Focus: Naming Doubles and Combinations of 10, students attend to the specialized language of mathematics when they sort facts into two groups, “doubles” and “combinations of 10”, and record their strategies. “Tell children that combinations of 10 have a sum of 10. If needed, remind children that the sum is the answer to an addition problem.”

• Lesson 5-9, Parts-and-Total Number Stories, Focus: Introducing the Parts-and-Total Diagram, students attend to the specialized language of mathematics when they use parts-and-total diagrams to find the total number of dots on a domino. “Draw a unit box with the label dots. Display a parts-and-total diagram. Write 8 and 9 in the two boxes labeled Part. Write 17 in the box labeled Total. Tell children that the diagram is a convenient way to represent the domino in the Math Message. The Part boxes show the number of dots on each side of the domino, and the Total box shows the total number of dots on the domino.”

• Lesson 7-5, Measuring with Meters, Focus: Introducing the Meter, students attend to the specialized language of mathematics when they compare a meter stick to a tape measure and a yardstick. “Remind children that inches, feet, and yards are part of the U.S. customary system and centimeters are part of the metric system. In the metric system, the meter is another commonly used standard unit of length. Tell children that the abbreviation for meter is m. Show the class a meterstick. On the Class Data Pad, write ‘A meter stick is 100 centimeters long.”

While the materials do attend to precision and the specialized language of mathematics, there are several instances of mathematical language that are not precise or grade level appropriate. Examples include:

• Lesson 2-6, The Turn-Around Rule for Addition, Focus: Exploring the Turn-Around Rule for Addition, students write 2 related addition facts using dominoes. “Label this the turn-around rule and instruct children to add it to their My Addition Fact Strategies list on journal page 22.”

• Lesson 3-7, “What’s My Rule?” Focus: Introducing “What’s My Rule?”, students fill in a rule for a given table of numbers. “Use children’s answers to fill in the rule box for Table 1. Explain that children will use tables like this to solve problems.” The materials later state, “Explain that these tables are called “What’s My Rule?” tables.”

• Lesson 9-7, Expand-and-Trade Subtraction, Part 2, Focus: Introducing Expand-and-Trade Subtraction, students use expanded form to subtract 2 and 3 digit numbers with and without regrouping. “Tell children that today they will use the expanded form to help them think about making trades.” The materials later state, “Tell children that this subtraction method is called expand-and-trade subtraction because children use expanded form to think about whether they need to make trades.”

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Materials support the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to the grade-level content standards, as expected by the mathematical practice standards.

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for supporting the intentional development of MP7: Look for and make use of structure; and MP8: Look for and express regularity in repeated reasoning, for students, in connection to grade-level content standards, as expected by the mathematical practice standards.

Each lesson targets one to three MPs. Math Practices are identified for teachers in several places: Pathway to Mastery Correlation to the Mathematical Processes and Practices, Focus, Student Math Journals, Student Reference Book, Independent Problem Solving Masters, and Practice. Materials refer to the Mathematical Practices as GMPs (Goals for Mathematical Practice).

Materials provide intentional development of MP7 to meet its full intent in connection to grade-level content. Students look for and make use of structure throughout the units as they describe, and make use of patterns within problem-solving as they work with the support of the teacher and independently throughout the units. Examples include

• Lesson 7-2, Four of More Addends, Focus: Counting Pencils, students look for and explain the structure within mathematical representations as they discuss strategies for solving a number story with three addends. “Were any of the three ways easier for you to find the sum? Why? Does it make a difference in what order the three numbers are added? Why? If no child mentions the turn-around rule, ask: How do you think this is related to the turn-around rule for addition?”

• Independent Problem Solving 2a, “to be used after Lesson 2-3”, Problem 2, students analyze a problem and look for more than one approach as they fluently add and subtract within 20. “Jamal said he could always tell how many pennies Jason had in his fist by looking at the number of pennies on the plate. He said he could use a chart to write all the combinations of 15. Help Jamal complete the chart he started. a. Do you agree that Jason’s chart will help him with all the combinations? b. Explain your thinking.”

• Independent Problem Solving 9b, “to be used after Lesson 9-9”, Problem 1, students analyze a problem and look for more than one approach as they solve a money problem in two different ways. “Maya purchased items from Moran’s Market. She spent exactly $50. Show two different combinations of items she might have bought. Show your work below.” Students are given a picture of a table with items and their prices. Materials provide intentional development of MP8 to meet its full intent in connection to grade-level content. Students look for and express regularity in repeated reasoning throughout the units to make generalizations and build a deeper understanding of grade level math concepts as they work with the support of the teacher and independently throughout the units. Examples include: • Lesson 3-6, -0 and -1 Fact Strategies and Subtraction Top-It, Focus: Discussing the -0 and -1 Strategies, students create methods for solving -0 and -1 facts. “Ask children to copy the facts onto their slates and solve. Prompt them to describe how to find the answers to -0 facts and -1 facts. Encourage children to look at the facts to find patterns and determine rules for solving these types of facts. Sample answers: If 0 is subtracted from any number, that number does not change. If 1 is subtracted from any number, the result is the next smaller number.” • Lesson 9-10, Connecting Doubles Facts, Even Numbers, and Equal Groups, Focus: Connecting Doubles and Equal Groups, students notice repeated calculations as they use doubles facts to solve equal-groups stories. “After all 10 possible arrays have been recorded, have children examine the list. Ask: What patterns do you notice? Referring to the two lists of possible number models, discuss the idea that when children need to find the total number of objects in 2 equal groups (or multiply by 2), they can use addition doubles. Ask: How can we use doubles facts to help us solve number stories about 2 equal groups?” • Independent Problem Solving 3a, “to be used after Lesson 3-4”, Problem 1, students evaluate the reasonableness of answers and thinking as they add and subtract. “a. Mrs. Foy asked her class to share anything they noticed about 4+3 and 3+4. Akilah noticed that both number sentences equal 7 and figured out that the order of the addends does not matter. Dakota said that this also works for subtraction: If 4-3 is 1, then 3-4 is 1 as well. Do you agree with Dakota? b. Use drawings or words or both to show how you know.” Overview of Gateway 3 Usability The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for Usability. The materials meet expectations for Criterion 1, Teacher Supports; partially meet expectations for Criterion 2, Assessment; and meet expectations for Criterion 3, Student Supports. Gateway 3 Meets Expectations Criterion 3.1: Teacher Supports The program includes opportunities for teachers to effectively plan and utilize materials with integrity and to further develop their own understanding of the content. The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for Teacher Supports. The materials: provide teacher guidance with useful annotations and suggestions for enacting the student and ancillary materials; contain adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject; include standards correlation information that explains the role of the standards in the context of the overall series; provide explanations of the instructional approaches of the program and identification of the research-based strategies; and provide a comprehensive list of supplies needed to support instructional activities. Indicator {{'3a' | indicatorName}} Materials provide teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development. Materials provide comprehensive guidance that will assist teachers in presenting the student and ancillary materials. Examples include: • Teacher's Lesson Guide, Welcome to Everyday Mathematics, explains how the program is presented. “Throughout Everyday Mathematics, emphasis is placed on problem solving in everyday situations and mathematical contexts; an instructional design that revisits topics regularly to ensure depth of knowledge and long-term learning; distributed practice through games and other daily activities; teaching that supports “productive struggle” and maintains high cognitive demand; and lessons and activities that engage all children and make mathematics fun!” • Implementation Guide, Guiding Principles for the Design and Development of Everyday Mathematics, explains the foundational principles. “The foundational principles that guide Everyday Mathematics development address what children know when they come to school, how they learn best, what they should learn, and the role of problem-solving and assessment in the curriculum.” • Unit 7, Whole Number Operations and Measurement and Data, Lesson Organizer, Coherence, 2.NBT.6, provides an overview of content and expectations for the unit. “In Grade 1, children applied their knowledge of addition strategies to solve number stories involving three whole numbers whose sum is less than 20. In Unit 9, children will choose at least three items to purchase for$100. In Grade 3, children will add and subtract numbers using strategies and algorithms.”

Materials include sufficient and useful annotations and suggestions that are presented within the context of the specific learning objectives. Examples include:

• Implementation Guide, Everyday Mathematics Instructional Design, “Lesson Structure and Features include; Lesson Opener, Mental Math and Fluency, Daily Routines, Math Message, Math Message Follow-Up, Assessment Check-In, Summarize, Practice, Math Boxes, and Home-Links.”

• Lesson 1-6, Equivalent Names for Numbers, Focus: Assessment Check-in, teacher guidance supports students to find equivalent number names. “Expect that most children will find at least one equivalent name each for Problems 1-5 on journal page 4. Some children may find more than one name for each; others may use more than one operation. For children who struggle to find one name for each problem, have them count out the number of counters that is the same as the ‘show’ number, divide the counters into two groups, and write an addition number model to represent the groups. Be sure that the number model does not contain the number of the broken key.”

• Lesson 4-7, Playing Target, Focus: Making Exchanges, Adjusting the Activity, teacher guidance supports struggling students. “For children who struggle to remember the values of the base-10 blocks, provide a card showing pictures of the base-10 blocks and their values.”

• Lesson 8-10, Playing Array Concentration, Focus: Math Message Follow-Up, teacher guidance connects students' prior knowledge to new concepts. “Remind children that when they arrange things in equal rows, they are making arrays. Ask volunteers to share their arrays and number models. If children wrote multiplication number models, ask them to suggest addition models as well.”

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Materials contain adult-level explanations and examples of the more complex grade-level/course-level concepts and concepts beyond the current course so that teachers can improve their own knowledge of the subject.

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

Each Unit Organizer Coherence table provides adult-level explanations and examples of complex grade/course-level concepts so teachers can improve their content knowledge. Professional Development side notes within Lessons support teachers in building knowledge of key mathematical concepts. Examples include:

• Lesson 1-9, Even and Odd Number Patterns, Focus: Identifying Even and Odd Numbers, Professional Development, teacher guidance clarifies the pairing strategy for even numbers. “The pairing definition for even numbers does not apply to the number 0 because 0 objects cannot be paired. In later grades, children will learn that a number is even if dividing it by 2 yields a remainder of 0. Using this definition, 0 is an even number because 0\div2 has a remainder of 0.”

• Lesson 4-9, The Inch, Focus: Sharing Strategies, Professional Development, teacher guidance explains the transition from iterating units to standard measurement. “The 12-inch (foot-long) ruler is introduced in this lesson. Some children may not yet see the ruler as composed of a series of inch-long intervals. The activities in this lesson are designed to show children that the length of an object must be the same number of inches, whether it is measured with 1-inch long blocks or with a ruler-a potentially unfamiliar concept to children.”

• Lesson 5-8, Change-to-More Number Stories, Focus: Introducing the Change Diagram, Professional Development, teacher guidance explains how number models are used beyond the grade. “In Everyday Mathematics, children use number models to represent situations and summarize relationships among quantities. In first through fifth grade, number models are used to clarify the quantitative relationships in a problem. Writing number models may help some children decide how to solve a problem, but more importantly, doing so helps them learn the mathematical-symbol system. Translating a word problem into a number model that can be manipulated to find an answer comes later when children begin to learn formal algebra.”

• Lesson 6-3, Interpreting Number Stories, Focus: Sharing Strategies, Professional Development, explains the connection between previous lessons and this lesson. “Until now, lessons have focused on one type of number story at a time. For example, all the problems in Lesson 6-2 were comparison stories, and the comparison diagram was the only diagram used. In this lesson, children are asked to categorize addition and subtraction number stories and then solve them. Do not force any number story into a particular mold. There may be several ways to interpret a problem.”

• Lesson 8-7, Partitioning Rectangles, Part 2, Focus: Partitioning Strategies, Professional Development, supports teachers with concepts for work beyond the grade. “Work with partitioning in Grade 2 lays the foundation for area measurement in Grade 3. In Grade 2 children develop the ability to visualize a rectangle as a collection of squares arranged in a row-by-column structure. This structure is important because it allows children to see the one-to-one correspondence between the number of squares in a row or a column and the number of units of measurement in the rectangle’s sides.”

• Lesson 9-10, Connecting Doubles Facts, Even Numbers, and Equal Groups, Focus: Connecting Doubles and Equal Groups, Professional Development, supports teachers with concepts for work beyond the grade. “This lesson focuses on finding the total number of objects in two equal groups and expressing an even number of objects as the sum of the number of objects in two equal groups. These are expectations for second grade but also build an understanding of how doubles addition facts relate to multiplying by 2. Children are exposed to multiplication number models in this lesson to build readiness for solving 2s multiplication facts early in third grade.”

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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 Everyday Mathematics 4 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/series and can be found in several places, including the Correlations to the Standards for Mathematics, Unit Organizers, Pathway to Mastery, and within each lesson. Examples include:

• Grade 2 Math, Correlation to the Standards for Mathematics Chart includes a table with each lesson and aligned grade-level standards. Teachers can easily identify a lesson when each grade-level standard will be addressed.

• Mastery Expectations, 2.NBT.2, “First Quarter: Count by 1s to at least 120; skip count by 5s using a calculator, and skip count by 10s to at least 200. Second Quarter: Count by 1s within 500; skip count by 5s and 10s past 200; count by 100 to 900. Third Quarter: Count within 1000; skip-count by 5s, 10s, and 100s. Fourth Quarter; Ongoing practice and application.”

• Lesson 3-6, -0 and -1 Fact Strategies and Subtraction Top-It, standards identified in the Focus are 2.OA.2, 2.NBT.5, 2.NBT.9, and standards identified in the Practice are 2.OA.2, 2.NBT.3, and 2.NBT.5. Lessons contain a consistent structure that includes an Overview, Before You Begin, Vocabulary, Warm-Up, Focus, Assessment Check-In, Practice, Math Boxes, and Home-Link. This provides an additional place to reference standards within each lesson.

Each Unit Organizer Coherence table includes an overview of content standards addressed within the unit as well as a narrative outlining relevant prior and future content connections for teachers. Examples include:

• Unit 4, Place Value Measurement, Unit 4 Organizer, Coherence, 2.NBT.1a, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Grade 1, children used base-10 blocks to learn about place value of 2-digit numbers through a variety of hands-on activities. In Grade 3, children will use place value understanding to round whole numbers to the nearest 10 or 100.”

• Unit 6, Whole Number Operations and Number Stories, Unit 6 Organizer, Coherence, 2.OA.1, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. In Grade 1, children modeled and solved number stories within 20 of all different types, with the position of the unknown varying. In Grade 3, children will solve one-and two-step number stories using all operations.”

• Unit 8, Geometry and Arrays, Unit 8 Organizer, Coherence, 2.G.1, includes an overview of how the content in Kindergarten builds from previous grades and extends to future grades. “In Grade 1, children began to differentiate between defining and non-defining attributes as they sorted attribute blocks and defined a rectangle by its attributes. Such work extended informal Kindergarten discussions of attributes and activities that involved building and drawing shapes. In Grade 3, children will compare and classify polygons based on attributes and will explore the relationships between categories of quadrilaterals.”

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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 Everyday Mathematics 4 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.

Home Connection Handbooks can be shared with stakeholders through digital or print copies. The Implementation guide suggests, “These handbooks outline articles, explanatory material about Everyday Mathematics philosophy and program, and provide suggestions for parents regarding how to become involved in their children’s mathematics education.” Each unit also has a corresponding Family Letter available in both English and Spanish, providing a variety of support for families including the core focus for each unit, ideas for practice at home, key vocabulary terms, building skills through games, and solutions to the homework from each lesson. Examples include:

• Lesson 3-12, Progress Check (Day 2), Home Link, Family Letter, “In Unit 4 your child will tell and write time using analog and digital clocks and discuss how to use a.m and p.m. to specify the time of day. Children will read, write, and compare numbers from 0 through 999, building on concepts and skills explored in Everyday Mathematics for Kindergarten and first grade. They will also review and extend their understanding of place value, which is the system that gives each digit a value according to its position in a number. In the number 52, for example, the 5 represents 5 tens (or 50), and the 2 represents 2 ones (or 2). Unit 4 also focuses on estimating and measuring lengths using inches, centimeters, and feet. Children will learn that measurements are not exact, and they will use terms such as close to, a little more than, a little less than, between, and about when describing measurements.”

• Lesson 9-5, Reviewing Place Value, Home Link, Family Note, “In this lesson your child reviewed place value and how it is used to determine the value of digits in numbers. For example, the 5 in 503 is worth 5 hundreds, or 500, because it is in the hundreds place. The 5 in 258 is worth 5 tens, or 50, because it is in the tens place. Your child also used place value to compare numbers. For example, to compare 571 and 528, your child might think, “Both numbers have 5 hundreds. But 571 has 7 tens and 528 has only 2 tens. So 571 is the larger number.”

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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 Everyday Mathematics 4 Grade 2 meet expectations for providing explanations of the instructional approaches of the program and identification of the research-based strategies.

Instructional approaches to the program are described within the Teacher’s Lesson Guide. Examples include:

• Teacher’s Lesson Guide, Welcome to Everyday Mathematics, The University of Chicago School Mathematics Project (UCSMP) describes the five areas of the Everyday Mathematics 4 classroom. “Problem solving in everyday situations and mathematical contexts; an instructional design that revisits topics regularly to ensure depth of knowledge and long-term learning; distributed practice through routines, games, and other activities; teaching that supports ‘productive struggle’ and maintains high cognitive demand; and lessons and activities that engage all children and make mathematics fun!”

• Teacher’s Lesson Guide, About Everyday Mathematics, An Investment in How Your Children Learn, The Everyday Mathematics Difference, includes the mission of the program as well as a description of the core beliefs. “Decades of research show that children who use Everyday Mathematics develop deeper conceptual understanding and greater depth of knowledge than students using other programs. They develop powerful, life-long habits of mind such as perseverance, creative thinking, and the ability to express and defend their reasoning.”

• Teacher’s Lesson Guide, About Everyday Mathematics, A Commitment to Educational Equality, outlines the student learning experience. “Everyday Mathematics was founded on the principle that every child can and should learn challenging, interesting, and useful mathematics. The program is designed to ensure that each of your children develops positive attitudes about math and powerful habits of mind that will carry them through college, career, and beyond. Provide Multiple Pathways to Learning, Create a System for Differentiation in Your Classroom, Access Quality Materials, Use Data to Drive Your Instruction, and Build and Maintain Strong Home-School Connections.”

• Teacher’s Lesson Guide, About Everyday Mathematics, Problem-based Instruction, approach to teaching skills helps to outline how to teach a lesson. “Everyday Mathematics builds problem solving into every lesson. Problem solving is in everything they do. Warm-up Activity: Lessons begin with a quick, scaffolded Mental Math and Fluency exercise. Daily Routines: Reinforce and apply concepts and skills with daily activities. Math Message: Engage in high cognitive demand problem-solving activities that encourage productive struggle. Focus Activities: Introduce new content with group problem solving activities and classroom discussion. Summarize: Discuss and make connections to the themes of the focus activity. Practice Activities: Lessons end with a spiraled review of content from past lessons.”

• Teacher’s Lesson Guide, Everyday Mathematics in Your Classroom, The Everyday Mathematics Lesson, outlines the design of lessons. “Lessons are designed to help teachers facilitate instruction and engineered to accommodate flexible group models. The three-part, activity-driven lesson structure helps you easily incorporate research-based instructional methods into your daily instruction. Embedded Rigor and Spiraled Instruction: Each lesson weaves new content with the practice of content introduced in earlier lessons. The structure of the lessons ensures that your instruction includes all elements of rigor in equal measure with problem solving at the heart of everything you do.”

Preparing for the Module provides a Research into Practice section citing and describing research-based strategies in each unit. Examples include:

• Implementation Guide, Everyday Mathematics & the Common Core State Standards, 1.1.1 Rigor, “The Publishers’ Criteria, a companion document to the Common Core State Standards, defines rigor as the pursuit, with equal intensity, of conceptual understanding, procedural skill and fluency, and applications (National Governors Association [NGA] Center for Best Practices & Council of Chief State School Officers [CCSSO], 2013, p. 3).

• Implementation Guide, Differentiating Instruction with Everyday Mathematics, Differentiation Strategies in Everyday Mathematics, 10.3.3, Effective Differentiation Maintains the Cognitive Demand of the Mathematics, “Researchers broadly categorize mathematical tasks into two categories; low cognitive demand tasks, and high cognitive demand tasks. While the discussion of cognitive demand in mathematics lessons is discussed widely, see Sten, M.K., Grover, B.W. & Henningsen, M. (1996) for an introduction to the concept of high and low cognitive demand tasks.”

• Implementation Guide, Open Response and Re-Engagement, 6.1 Overview, “Research conducted by the Mathematics Assessment Collaborative has demonstrated that the use of complex open response problems “significantly enhances student achievement both on standardized multiple-choice achievement tests and on more complex performance-based assessments” (Paek & Foster, 2012, p. 11).”

• The University of Chicago School Mathematics Project provides Efficient Research on third party studies. For example:

• Use of Student Constructed Number Stories in a Reform-Based Curriculum.

• An Action-Based Research Study on How Using Manipulatives Will Increase Student’s Achievement in Mathematics.

• Differentiating Instruction to Close the Achievement Gap for Special Education Students Using Everyday Math.

• Implementing a Curriculum Innovation with Sustainability: A Case Study from Upstate New York.

• Mental Computation of Students in a Reform-Based Mathematics Curriculum.

• ARC Center Tri-State Achievement Study.

• Teacher-Initiated Differentiation.

• The Impact of Two Standards-Based Mathematics Curricula on Student Achievement in Massachusetts.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for providing a comprehensive list of supplies needed to support instructional activities.

A year-long list of materials needed is provided in the Teacher’s Lesson Guide, Getting to Know Your Classroom Resource Package, Manipulative Kits, and eToolkit. “The table below lists the materials that are used on a regular basis throughout Second Grade Everyday Mathematics.” Each unit includes a Materials Overview section outlining supplies needed for each lesson within the unit. Additionally, specific lessons include notes about supplies needed to support instructional activities, found in the overview of the lesson under Materials. Examples include:

• Lesson 2-1, Grouping by 10s, Overview, Materials, Math Message, “Math Masters, pp. G11-G13; scissors; envelope, paper clip, or rubber band”

• Lesson 4-1, Clocks and Telling Time, Focus: Math Message, “Display two clock faces as shown in the margin. Which clock shows 4:30? Explain to a partner how you know. Use the words minute hand and hour hand.”

• Unit 5, Addition and Subtraction, Unit 5 Organizer, Unit 5 Materials, each lesson has materials under the following categories: Math Master, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 5-3, materials listed, Math Masters: “pp.121; 123-125”, Activity Card: “66-67”, Manipulative Kit; “toolkit coins; per group: 4 each of number cards 0-10; per partnership: two 6-sided dice”, Other Materials: “slate; scissors.”

• Unit 7, Whole Number Operations and Measurement and Data, Unit 7 Organizer, Unit 7 Materials, each lesson has materials under the following categories: Math Master, Activity Cards, Manipulative Kit, and Other Materials. For example, Lesson 7-8, materials listed, Math Masters: “pp.155 (1 copy per partnership); 202-206”, Activity Card: “94-95”, Manipulative Kit; “tape measure; per partnership; on 6-sided die”, Other Materials: “slate; stick-on notes; stick-on notes from Math Message.”

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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 Everyday Mathematics 4 Grade 2 partially meet expectations for Assessment. The materials identify the standards and the mathematical practices assessed in formal assessments. The materials provide multiple opportunities to determine students' learning and sufficient guidance to teachers for interpreting student performance but do not provide suggestions for follow-up. The materials include opportunities for students to demonstrate the full intent of grade-level standards and mathematical practices across the series.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

Beginning-of-Year Assessment, Unit Assessments, Open Response Assessments, Cumulative Assessments, Mid-Year Assessment and End-of-Year Assessment consistently and accurately identify grade-level content standards along with the mathematical practices within each Unit. Examples from formal assessments include:

• Unit 3, More Fact Strategies, Unit Assessment, denotes standards and mathematical practices addressed for each problem. Problem 6, “Martin made a 10 to figure out the sum for 8 + 4. Explain Martin’s thinking.” (2.OA.2, SMP6)

• Unit 5, Addition and Subtraction, Open Response Assessment, denotes standards addressed for the open response. “Carlos wants to buy chocolate milk from the vending machine. The milk cost 75 cents. Carlos has 2 quarters, 5 dimes, and 5 nickels. Show at least four possible coin combinations Carolos could use to pay for the milk. Use N, D, and Q to record your answers.” (2.MD.8)

• Mid-Year Assessment, denotes the aligned grade-level standard and mathematical practices. Problem 13, “Farid says the clock at the right reads 9:15. Yasmin says the clock reads 3:45. Who is correct? How do you know? Explain the other child’s mistake.” (2.MD.7, SMP3)

• Unit 8 Cumulative Assessment, denotes standards and mathematical practices addressed for each problem. Problem 3, “Solve. Try to make friendly numbers. 23+17+10+12= __, 16+31+14+19= ____ Pick one of the problems above. Explain how you added the numbers.” (2.NBT.6, 2.NBT.9, SMP6)

• End-of-Year Assessment, denotes the aligned mathematical practice. Problem 3, “Shawn has 24 crayons. His teacher gave him 24 more. Then he lost 8 crayons. How many crayons does he have now? Number model(s): ___.” (SMP4)

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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 Everyday Mathematics 4 Grade 2 partially meet expectations for including an assessment system that provides multiple opportunities throughout the grade, course, and/or series to determine students’ learning and sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.

In the Everyday Mathematics 4 materials, the assessment system consists of Ongoing and Periodic Assessments. Ongoing Assessments provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up through Assessment Check-Ins. Periodic Assessments provide sufficient guidance to teachers for interpreting student performance; however, they do not provide suggestions to teachers for follow-up with students.

Summative Assessments, such as Unit Assessments, Cumulative Assessments, Mid-Year Assessment, and End-of-Year Assessment, provide an answer key with aligned standards. Open Response Assessments, include an answer key and generic rubric for evaluating the Goal for Mathematical Process and Practice and provide examples of student responses and how they would score on the rubric (such as Exceeding Expectations, Meeting Expectations, Partially Meeting Expectations, and Not Meeting Expectations). A student achievement recording spreadsheet for each unit learning target is available that includes: Individual Profile of Progress in Unit Assessment Check-Ins, Individual Profile of Progress in Unit Progress Check, Whole-Class Progress Check, Individual Profile of Progress Mathematical Process and Practice for Units, and Whole Class Record of Mathematical Process and Practice Opportunities. While some scoring guidance is included within the materials, there is no guidance or suggestions for teachers to follow up with students. Examples include:

• Unit 1, Establishing Routines, Unit Assessment, Problem 8, “Beth is playing Fishing for 10. She has a 5 in her hand. a) What card should she fish for?____ b) Complete the number model to show her total after she gets the card she fished for. 5 + ___ + 10.” The answer is, “a. 5, b. 5.” This problem aligns with 2.OA.2.

• Unit 3, More Fact Strategies, Open Response Assessment, “Grace solved 12-7 this way: I started at 12 and took away 2 to get to 10. Then I took away 5 more. I ended up at 5. So, 12-7=5.” Grace solved 13-4 this way: “I started with 13 and took away 3 to get to 10. Then I took away 1 more. I ended up at 9. So, 13-4=9.” Show and explain how to use Grace’s subtraction strategy to solve 14-8.” The Goal for Mathematical Process and Practice, “Not Meeting Expectations: Provides no evidence of using Grace’s subtraction strategy. Partially Meeting Expectations: Provides limited evidence in words, drawings, or number models, of using Grace’s strategy by decomposing 8 into parts to subtract, but does not go through 10 OR Subtract 4 to reach 10, but decomposes the wrong number (e.g., 6 into 4 and 2) to reach 8. Meeting Expectations: Provides evidence, in words, drawings or number models, of using Grace’s strategy by decomposing 8 into parts in order to subtract 4 to reach 10, and then to subtract 4 more (totaling 8) to reach 6. Exceeding Expectations: Meets expectations and provides evidence in two or three forms (words, drawings, or number models), each of which represents adequate evidence of using Grace’s strategy.” This question is aligned to 2.OA.2 and SMP3.

• Unit 4, Place Value and Measurement, Cumulative Assessment, Problem 2, “Solve. a) 0+9= ____ b) 5 + ___ = 5 c) 7 - 0 = ___ d) For Problems 2a-2c, what patterns do you notice?” The answer options are, “a. 9, b. 0, c. 7, d. When you add 0 to or subtract 0 from a number, the answer is that number.” This problem aligns with 2.OA.2.

• Mid-Year, Assessments, Problem 7, “Place the number 10 in the correct spot on this number line.” A number line shows a starting number of 0 and an ending number of 25. The answer is, “Ten is placed between 0 and 25 closer to 0.” This question is aligned to 2.NBT.2.

• End-Of-Year Assessment, Problem 25, “Circle the tool that you would use to measure the length of a bus. a six-inch ruler, a yardstick, a tape measure, a meter stick. Explain why you chose that tool. Answers vary. Sample answer: I would use the tape measure because it is the longest and I would only need to move it a couple of times.” This question is aligned to 2.MD.1.

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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 Everyday Mathematics 4 Grade 2  meet expectations for providing assessments that include opportunities for students to demonstrate the full intent of grade-level standards and practices across the series.

Formative Assessments include Beginning-of-Year Assessment and Preview Math Boxes. Summative Assessments include Mid-Year Assessment, End-of-Year Assessment, Unit Assessments, Open Response Assessment/Cumulative Assessments. All assessments regularly demonstrate the full intent of grade-level content and practice standards through a variety of item types: multiple choice, short answer, and constructed response. Examples include:

• Mid-Year Assessment, develops the full intent of standard 2.OA.2, fluently add and subtract within 20 using mental strategies. Problems 1, “a. 1 + 5 = ___. b. 9 + ___= 10. c. 4 - 1 = ___. d. 7 - ___ = 6.” Problem 2, “a. 7 + 7 = ___. b. 2 + 9 = ___. c. 10 + ___ = 20. d. 8 + 8 = ___. e. For problems 2a-2d, which fact does not fit the pattern? How is it different?”

• Unit 5, Addition and Subtraction, Unit Assessment, develops the full intent 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. Problem 6, “Use an open number line to help you solve the story. Mrs. Peters had 22 pencils to give to her students. She bought 35 more. How many does she have now? ___ pencils.” (An open number line is pictured below the problem.)

• Unit 7, Whole Number Operations and Measurement and Data, Open Response Assessment, develops the full intent of MP2, reason abstractly and quantitatively as students determine if two sets of base-10 blocks represent the same number. Problems 1 and 2 “1.) Maria represented the number 349 like this (three flats, four longs, and nine units). Bill represented the number 349 like this (two flats, thirteen longs, and nineteen units). Write whether Maria, Bill, or both of them represented the number 349. 2) Explain your answer. You may include drawings.”

• End-of-Year Assessment, develops the full intent of MP3, construct viable arguments and critique the reasoning of others as students explain their strategy. Problem 10g, “Below, Marsha explained how she solved Problem 10d. I counted up from 178 to 200. I knew that was 22. I know that from 200 to 256 is 56 so I added 22 and 56 and got 78. Does Marha’s strategy work? ___ Explain.”

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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 Everyday Mathematics 4 Grade 2 provide assessments that offer accommodations that allow students to demonstrate their knowledge and skills without changing the content of the assessment.

According to the Implementation Guide, Assessments in Everyday Mathematics, Assessment Opportunities, 9.3.2 Progress Check Lessons, “For each item in the Unit Assessment, modifications are provided in an Adjusting the Assessment table. Modifications to scaffolded items may suggest providing students a tool (such as a number line or counters), providing strategic hints, or administering the item or response in a different format. Modifications to extended items provide extra challenge related to the problem.” In addition to technology-enhanced items, the digital assessments include the ability to highlight items, magnify the screen, utilize a line reader for text to speech, cross out answers, and provide a calculator, protractor, and reference sheets. Examples include:

• Unit 2, Fact Strategies, Cumulative Assessment, Adjusting the Assessment, Item 6, “To extend item 6, have children count a collection of coins that include pennies, nickels, dimes, and quarters.”

• Unit 5, Addition and Subtraction, Unit Assessment, Adjusting the Assessment, Item 5, “To extend item 5, have children explain how they used mental strategies to solve Problems 5a-5h.”

• Unit 8, Geometry and Arrays, Unit Assessment, Adjusting the Assessment, Item 4, “To scaffold item 4, provide a shapes poster with labels identifying the angles and sides on each of the shapes.”

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 Everyday Mathematics 4 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.

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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 Everyday Mathematics 4 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.

Materials regularly provide strategies, supports, and resources for students in special populations to help them access grade-level mathematics. Implementation Guide, Differentiating Instruction with Everyday Mathematics, 10.1 Differentiating Instruction in Everyday Mathematics: For Whom?, “Everyday Mathematics lessons offer specific differentiation advice for four groups of learners. Students Who Need More Scaffolding, Advance Learners, Beginning English Language Learners, and Intermediate and Advanced English Language Learners.” Differentiation Lesson Activities notes in each lesson provide extended suggestions for working with diverse learners. Supplementary Activities in each lesson include Readiness, Enrichment, Extra Practice, and English Language Learner.

For example, the supplementary activities of Unit 1, Establishing Routines, Lesson 1, include:

• Readiness, “For experience reading and comparing numbers, children put number cards in order. Write a sequence of numbers (such as 0-10) on index cards. Children work together to put the cards in order.”

• Enrichment, “To explore whole numbers represented as lengths from 0 on a number line, children complete number-line puzzles.”

• Extra Practice, “For additional practice with counting, children fill in missing numbers on a number line. Depending on children’s ability to read and order numbers, write one or more 1-, 2-, or 3-digit numbers on the number lines on Math Masters, page 3. Children review their work with a partner and explain how they found the missing numbers.”

• English Language Learner, Beginning ELL, “The Total Physical Response (TPR) technique allows beginning English language learners to participate in lesson activities even with minimal English language proficiency. To teach children actions they can use to demonstrate understanding, display a number line and then model actions as you say the following: Point to the number that comes before 5. Circle the number that comes after 6. Use your finger to hop on the number line from 7 to 10. After demonstrating several times with other numbers, have children respond to the same directions without your modeling.”

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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 Everyday Mathematics 4 Grade 2 meet expectations for providing extensions and/or opportunities for students to engage with grade-level mathematics at higher levels of complexity.

Materials provide multiple opportunities for advanced students to investigate the grade-level content at a higher level of complexity rather than doing more assignments. The Implementation Guide, Differentiation Instructions with Everyday Mathematics, 10.4 Working with Advanced Learners, “Nearly all Everyday Mathematics lessons include a set of high cognitive demand tasks with mathematical challenges that can be extended. Every regular lesson includes recommended enrichment activities related to the lesson content on the Differentiation Options page opposite the Lesson Opener Everyday Mathematics lessons incorporate varied grouping configurations which enables the kind of flexibility that is helpful when advanced learners in heterogeneous classrooms. Progress Check lessons include suggestions for extending assessment items for advanced learners and additional Challenge problems.” The 2-day Open Response and Re-Engagement lesson rubrics provide guidance for students in Exceeding Expectations. Examples include:

• Lesson 3-5, Subtraction Strategies: Counting Up and Counting Back, Enrichment, “To extend their understanding of subtraction, partners find differences between two 2-digit numbers by playing The Number-Grid Difference Game. On each turn, players mark two numbers on a number grid with counters and then find the difference.”

• Unit 4, Place Value and Measurement, Challenge, Problem 2, an analog clock is pictured with the time 12:10,“Simon thinks the time says 2:00. Is he correct? Explain how you know.”

• Lesson 7-2, Four or More Addends (Day 1), Focus: Solving the Open Response Problem, Adjusting the Activity, “If children quickly solve the problem and write a complete explanation, ask them to check their work by using a second strategy to solve the problem.”

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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 Everyday Mathematics 4 Grade 2 provide various approaches to learning tasks over time and variety in how students are expected to demonstrate their learning and provide opportunities for students to monitor their learning.

Students engage with problem-solving in a variety of ways: Student Math Journals, Math Masters, and Open Response and Re-Engagement Lessons, a key component of the program. Examples of varied approaches include:

• Lesson 2-4, The Making-10 Strategy, Home Link, Problem 1, students write addition facts for 10., “Write all the addition facts that have a sum of 10. Hint: There are 11 different facts.”

• Lesson 4-4, Numeration and Place Value, Focus: Matching Numbers to Base-10 Block Representations, students use base-10 blocks to represent numbers on a place-value mat. “Continue showing different representations and asking children to represent numbers in different ways. For example: Display 200 + 40 + 8. Ask children to show the number using base-10 blocks. Ask: What number did you make? What digit is in the hundreds place?

• Lesson 8-4, Drawing and Reasoning About Quadrilaterals (Day 1), Focus: Solving the Open Response Problem, Problem 1, students draw shapes on dot paper to solve a number story. “Juan wants a quadrilateral with four right angles. Try drawing shapes on a sheet of dot paper that will work for Juan’s plan. Circle the one you think Juan should use for the garden.”

Opportunities for students to monitor their learning are found in the Assessment Handbook. These reflection masters can be copied and used to analyze the work from any lesson or unit. Each unit also contains a self assessment for students to reflect on how they are doing with the unit’s focus content. Examples include:

• Assessment Handbook Unit 7, Whole Number Operations and Measurement and Data, Self Assessment, students answer reflection questions by putting a check in the box to denote they can do it by themselves and explain how to do it, can do it by themselves, or need help, “Play Hit the Target. Add 3 or more numbers. Measure objects to the nearest inch and centimeter. Complete a line plot. Use personal references to help estimate length. Use measuring tools correctly.”

• Assessment Handbook, Good Work!, students reflect on the work they have completed and fill out the following sheet and attach it to their work, “I have chosen this work because _______.”

• Assessment Handbook, My Work, students reflect on work they have completed and fill out the following sheet to attach to their work, “This work shows I can _______. I am still learning to _______.”

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

The materials reviewed for Everyday Mathematics 4 Grade 2 provide opportunities for teachers to use a variety of grouping strategies.

Everyday Mathematics provides suggestions for whole class, small group, partner, and independent work. Implementation Guide, 5.2.1 Collaborative Groupings, explicitly directs teachers in establishing collaborative groupings, “Because Everyday Mathematics provides activities for various groupings, teachers may want to plan seating arrangements that allow students to transition between whole-class, small-group, and independent work efficiently and with minimal disruption. Flexible grouping allows students to work with many other students in class and keep their interests high. Mixed ability, heterogenous group allows students to learn from each other by having opportunities to hear the thoughts and ideas of their peers. Homogenous groups allow the work to be differentiated to meet the needs of all in the group.” Examples include:

• Lesson 2-1, Grouping by 10s, Focus: Making Exchanges, students work with partners to make money exchanges. “Have partners make exchanges by trading either ten 1 bills for one 10 bill or ten 10 bills for one 100 bill. Both children count the money again to check that they still have the same total.”

• Lesson 4-10, The Centimeter, Focus: Measuring with the 12-Inch and 10-Centimeter Rulers, students independently measure objects around the room. “Have children use their tape measures or their 12-inch and 10-centimeter rulers to measure the lengths of the pictures in Problems 1 and 2 on journal page 87. When most children are finished, bring the class together to share their measurement strategies and results.”

• Lesson 6-10, Exploring Arrays, Length, and Shapes, Focus: Discussing Arrays, students are given explanations for the 3 explorations, and put into 3 small groups, Exploration A: Making Geoboard Arrays, Exploration B: Comparing Lengths, and Exploration C: Making Shapes, “After explaining the Explorations activities, assign groups to each one. Plan to spend most of your time with children working on Exploration A.”

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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 Everyday Mathematics 4 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 Teacher’s Lesson Guide and ConnectED Teacher Center include guidance for the teacher in meeting the needs of English Language Learners. There are specific suggestions for making anchor charts or explaining new vocabulary. The Implementation Guide, English Language Learners, Everyday Mathematics addresses the needs of three groups of ELL based on their English language proficiency (beginning, emerging, and advanced), “Beginning English language learners fall into Entering (level 1) and Emerging (level 2) proficiencies. This group is typically within the first year of learning English; students' basic communication skills with everyday language are in their early development. These students require the most intensive language-related accommodations in order to access the mathematics in most lessons. Intermediate and Advanced English learners represent Levels 3, 4, and 5 (Developing, Expanding, and Bridging) in the English language proficiencies identified above. Students in this category are typically in their second to fourth year of learning English. They may be proficient with basic communications skills in English and able to carry on everyday conversations, but they are still developing proficiency with more cognitively demanding academic language of the mathematics class.” The ConnectED Teacher Center offers extended suggestions for working with diverse learners including English Language Learners. The Teacher’s Lesson Guide provides supplementary activities for beginning English Language Learners, Intermediate, and Advanced English Language Learners. In every lesson, there are Differentiation Support suggestions, English Language Learner for Beginning ELL located on the Differentiation Options Page and Focus section. Examples include:

• Lesson 1-4, Class Number Scroll, Differentiation Options, English Language Learner, Beginning ELL, “Introduce the work pattern by showing examples of simple patterns and examples that are not patterns, using materials such as pattern blocks, classroom objects, and strings of numbers. Point to examples of a pattern and say: This is a pattern. Point to the non-examples and say: This is not a pattern. As you point to examples and non-examples, ask yes/no questions. For example: Is this a pattern?

• Lesson 6-6, Recording Addition Strategies, Differentiation Options, English Language Learner, Beginning ELL, “The expression ballpark estimate is a familiar usage in American English. Provide context for this term for English language learners by displaying visuals of a ballpark. Introduce the expressions in the ballpark and out of the ballpark. Gesture to one of the visuals to demonstrate what happens when a home run is hit out of the ballpark. Connect that to an estimate that is far away from the actual answer, or out of the ballpark. Estimates close to the actual answer are in the ballpark (such as a ground ball hit in the infield) and are therefore called ballpark estimates.”

• Lesson 9-7, Expand-and-Trade Subtractions, Part 2, Differentiation Options, English Language Learner, Beginning ELL, “Use role play to review the term trade. Give a child 10 pennies and place a dime in front of you on the table. Say: I need to trade. Please give me your 10 pennies, and I will give you my dime. Have children practice with equivalent amounts in pennies, nickels and dimes. As they trade, encourage them to use sentence frames like the following: I need to trade. Please give me ___, and I will give you ____.

• The online Student Center and Student Reference Book use sound to reduce language barriers to support English language learners. Students click on the audio icon, and the sound is provided. Questions are read aloud, visual models are provided, and examples and sound definitions of mathematical terms are provided.

• The Differentiation Support ebook available online contains Meeting Language Demands providing suggestions addressing student language demands for each lesson. Vocabulary for the lesson and suggested strategies for assessing English language learners’ understanding of particularly important words needed for accessing the lesson are provided.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 provide a balance of images or information about people, representing various demographic and physical characteristics.

The characters in the student-facing materials represent different races and portray people from many ethnicities in a positive, respectful manner, with no demographic bias for who achieves success in the context of problems. Names include multi-cultural references such as Johan, Leli, Kalani, and Faustina and problem settings vary from rural, urban, and international locations.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 provide guidance to encourage teachers to draw upon student home language to facilitate learning.

The Implementation Guide, “This edition of Everyday Mathematics incorporates a variety of strategies to increase the accessibility of the lessons to English language learners. A fundamental principle of Everyday Mathematics is that students learn mathematics best when they use it to solve problems in meaningful contexts. Similarly, languages are acquired more effectively when learned in conjunction with meaningful content and purposeful communication. Thus, instruction with Everyday Mathematics can serve two purposes for English language learners: helping them learn mathematics and helping them develop English language proficiency. English language learners enter mathematics classrooms with many similarities and differences in the language spoken at home, previous school preparation, and academic background in English as well as in their first language. Grade level does not dictate English proficiency. For example, English language learners in higher grade levels may be at beginning English proficiency levels. Conversely, students in the early grades may be at higher levels of English proficiency. Some English language learners have extensive educational backgrounds, which include the study of English. Others may have very limited formal school experiences, which may mean they lack literacy skills in their home language and English. Moreover, English proficiency does not determine mathematical proficiency.”

English Language Learner notes provide activities to support students with different English language proficiency. Examples include:

• Lesson 3-4, Playing Salute¡, Focus: Introducing and Playing Salute¡, Differentiation Options, and English Language Learner Support, Beginning ELL, “Introduce the roles played by the dealer and the players in the game Salute¡ by modeling the actions each role requires as you name the role and display the word in writing. Then use TPR prompts to give children opportunities for oral practice naming the roles and pantomiming players’ actions.”

• Implementation Guide, 10.5.3 Developing and Reinforcing Vocabulary: Selected Accessibility Strategies for English Language Learners, Using Reference Materials, “Encourage English learners to use the Everyday Mathematics My Reference Book in Grades 1 and 2 and the Students Reference Books in Grades 3-6 along with other reference materials in print and online, such as encyclopedias, almanacs, and dictionaries (including bilingual dictionaries). For Spanish speakers, note that technical terms used in Everyday Mathematics may be similar to the Spanish words, which may enhance Spanish speakers’ retention of new terminology. In the appropriate context, list English and Spanish words for students to build meaning, but do not assume that students understand the meanings of that Spanish word. Some examples are: angle/angulo, circle/circulo, parallel/paralelo, interior/interior, and polygon/poligono.”

The Implementation Guide, “Increasing English language learner’s accessibility to lesson content involves a variety of strategies with the same basic principle: consider the language demands of a lesson and incorporate language-related strategies for helping students access the core mathematics of the lesson. In other words, provide students with enough language support so that their time with the lesson can focus on the mathematical ideas rather than interpreting the language.” Examples include:

• Role Playing: “An excellent way to deepen understanding of concepts is to give students the opportunity to apply what they have learned to a familiar situation. In one lesson, students simulate a shopping trip using mock Sale Posters as visual references and play with money as a manipulative to practice making change. In this example, English learners can take turns being the shopkeeper and the customer. This role play helps students learn and practice the phrases and vocabulary they need in real shopping situations while gaining familiarity with the language needed to access the mathematics content of the lesson.”

• Tapping Prior Knowledge: “English learners sometimes feel that they must rely on others to help them understand the instruction and practice in school each day. However, English learners bring unique knowledge and experience that they should be encouraged to contribute to the classroom community. For example, working with metric measurement and alternative algorithms present excellent opportunities for English learners to share their expertise with the group. Those who have gone to school outside the United States may know the metric system or other algorithms well.”

• Sheltered Instruction: “The Sheltered Instruction Observation Protocol (SIOP) Model was developed at the Center for Applied Linguistics (CAL) specifically to help teachers plan for the learning needs of English language learners. The model is based on the sheltered instruction approach, an approach for teaching content to English language learners in strategic ways that make the content comprehensible, while promoting English language development.” Components and Features of the SIOP Model include: Lesson Preparation, Building Background, Comprehensible Input, Strategies, Interaction, Practice and Application, Lesson Delivery, and Review and Assessment.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 provide guidance to encourage teachers to draw upon student cultural and social backgrounds to facilitate learning.

Materials include some cultural connections within student reference books, activities, or games. Examples include:

• My Reference Book, Measures All Around: Animals and Tools, Page 118, students examine images of different animals when zoologists use measurements. “Lemurs are found in the world only on the island of Madagascar. Sloths live in trees in the rainforest of Central and South America.”

• Lesson 1-9, Exploring Math Materials, Focus: Exploring with Pattern Blocks, Base-10 Blocks, and Geoboards, Home-Link, students learn about exploring with new mathematical tools like Christopher Columbus did when he arrived in America. “Ask children whether they know who Christopher Columbus was. Explain that Columbus was an explorer who was trying to find a new way to sail to the East Indies but instead arrived in America. Explorers are people who try to discover things they did not know before.”

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

The materials reviewed for Everyday Mathematics 4 Grade 2 partially provide supports for different reading levels to ensure accessibility for students.

• Lesson 1-11, Comparing Numbers and Home Links, Focus: Reviewing Relation Symbols: Is Less Than (<), Is Greater Than (>), and Is Equal To (=), Academic Language Development, “Discuss the word symbol and explain that a symbol is an image or a character that stands for something specific. Show examples of symbols that children may see in everyday use. For example, show the symbol for no parking, the symbol for wheelchair accessible, and the symbol for number (#).”

• Lesson 2-11, Playing Name that Number, Focus: Demonstrating Name That Number, Academic Language Development, “Use game examples and visuals - such as bull’s-eye, a goal post, or a basketball hoop - to explain the term target as something children aim for.”

• Lesson 6-10, Exploring Arrays, Length, and Shapes, Focus: Exploration A: Making Geoboard Arrays, Academic Language Development, “To explain that enclose means ‘to surround something,’ build on children’s knowledge of the word close, which means ‘to shut’. Open the classroom door and then close it. Explain that when the door is open, children can move in and out of the room, but when the door is closed, the room is totally enclosed (or surrounded) by the four walls. Make similar connections to other real-life examples, such as a fence enclosing a yard when the gate is closed.”

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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 Everyday Mathematics 4 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.

The materials consistently include suggestions and/or links, within the lesson notes, for virtual and physical manipulatives that support the understanding of grade-level math concepts. Examples include:

• Lesson 4-4, Numeration and Place Value, Focus: Matching Numbers to Base-10 Block Representations, materials reference use of base-10 blocks. “Display 200 + 40 + 8. Ask children to show the number using base-10 blocks.”

• Lesson 8-5, Attributes of 3-Dimensional Shapes, Focus: Describing Cubes, materials reference use of 3-Dimensional shapes. “Distribute a centimeter cube to each partnership. Have children share with their partners what they notice about the cube. After a few minutes, bring the class together to discuss children’s observations.”

• Lesson 9-1, Creating and Naming Equal Parts, Focus: Math Message, materials reference use of fraction squares. “Take 8 paper squares. Two children want to share a sandwich equally. Fold a paper square to show how to divide the sandwich into 2 equal shares. Draw a line on the fold. Talk with a partner. Did you both fold the square the same way?”

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 Everyday Mathematics 4 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. The materials 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. The materials provide teacher guidance for the use of embedded technology to support and enhance student learning.

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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 Everyday Mathematics 4 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/series standards, when applicable.

Materials include a visual design that is engaging and references/integrates digital technology. Examples include:

• Materials accessible online only: eToolKit, ePresentations, Assessment Reporting Tools, Spiral Tracker, Implementation Guide, Virtual Learning Community, Home Connection Handbook, Student Learning Centers, EM Games Online, and Facts Workshop Games.

• Teacher’s Lesson Guide, “eToolkit contains online tools and virtual manipulations for dynamic instruction. ePresentations are ready-made interactive whiteboard lesson content to support daily instruction.”

• Interactive Student Journal, available for each lesson provides access to virtual manipulatives and text and drawing tools, that allow students to show work virtually. This resource includes the Student Math Journal, Student Reference Book, eToolkit, Activity Cards, and other resources, which allow students to receive immediate feedback on selected problems and is available in English or Spanish.

• Digital Student Assessments, provide progress monitoring. The assessment tools create student, class, or district reports. Data is provided in real-time and allows teachers to make informed instructional decisions that include differentiating instruction.

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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 Everyday Mathematics 4 Grade 2 include or reference digital technology that provides opportunities for teachers and/or students to collaborate with each other, when applicable.

Teachers can provide feedback to students through the Student Learning Center. The Implementation Guide, “If students complete their work in the Student Learning Center using a digital device, the teacher can see that work by selecting ‘Digital Activity.’ As the teacher reviews student work, he or she can select a writing tool and add feedback. When students go to the activity screen in their Student Learning Center, they see any notes from their teacher.”

Teachers can collaborate with other teachers through the Virtual Learning Community. The Implementation Guide, “Many Everyday Mathematics teachers have found support through the Virtual Learning Community, or the VLC, hosted by the University of Chicago. This online resource provides professional resources, demonstration lessons, the ability to join or form groups, and so much more. Having colleagues to share Everyday Mathematics experiences with enriches the program experience.”

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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 Everyday Mathematics 4 Grade 2 provide a visual design (whether in print or digital) that supports students in engaging thoughtfully with the subject, and is neither distracting nor chaotic.

There is a consistent design within units and lessons that supports student understanding of the mathematics. Examples include:

• Each unit begins with an organizer that displays the content, focus, coherence, rigor, necessary materials, spiral toward mastery, and mathematical background.

• Each lesson follows a common format with the following components: Before You Begin, Vocabulary, Warm-Up (Mental Math and Fluency), Focus (Math Message and Activities), Assessment Check-In, and Practice (Math Minute, Math Boxes, and Home-Link). The layout for each lesson is user-friendly and each component is included in order from top to bottom on the page.

• The Teacher’s Lesson Guide follows a consistent format, including visuals of student-facing materials and answer keys within the lesson.

• Student Math Journal pages, Math Boxes, and Home Links follow a consistent pattern and work pages provide enough space for students to record work and explain their reasoning.

• The font size, amount of text, and placement of directions and print within student materials are appropriate.

• The digital format is easy to navigate and engaging. There is ample space in the Student Math Journal and Assessments for students to capture calculations and record answers.

• The Student Center is engaging and houses all student resources in one area.

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

The materials reviewed for Everyday Mathematics 4 Grade 2 provide teacher guidance for the use of embedded technology to support and enhance student learning, when applicable.

The Teacher’s Lesson Guide includes a description of embedded tools, how they should be incorporated, and when they can be accessed to enhance student understanding. Examples include:

• Lesson 8-2, Playing Shape Capture, Focus: Identifying Attributes, Adjusting the Activity, Differentiate, “Go Online, Differentiation Support.” Lessons provide this icon to show when and where differentiation strategies are suggested.

• Teacher’s Lesson Guide, Planning for Rich Math Instruction, “Go Online: Evaluation Quick Entry- Use this tool to record student’s performance on assessment tasks. Data: Use the Data Dashboard to view student’s progress reports.”

• Teacher’s Lesson Guide, Getting Ready to Teach Second Grade Everyday Mathematics, Lesson Parts, and Features, Part 3: Practice, “Go Online to the Implementation Guide for tips to ensure that all children have ample game time.”

Report Overview

Summary of Alignment & Usability for Everyday Mathematics 4 | Math

Math K-2

The materials reviewed for Everyday Mathematics 4 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 including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.

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 Everyday Mathematics 4 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 including Teacher Supports and Student Supports; the materials partially meet expectations for Assessment.

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

Math 6-8

The materials reviewed for Everyday Mathematics 4 Grade 6 partially meet expectations for Alignment to the CCSSM. In Gateway 1, the materials partially meet expectations for focus and coherence. In Gateway 2, the materials meet expectations for rigor and practice-content connections.

Alignment
Partially Meets Expectations
Not Rated

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Overall Summary

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Usability
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