## Everyday Mathematics 4

##### v1.5
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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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### Overall Summary

The materials reviewed for Everyday Mathematics 4 Grade 3 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 3 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 3 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 3 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 1 Assessment, Item 7, “Round each number to the nearest 10. You may use open number lines to help. 7a: 59 rounded to the nearest 10 is ____. 7b: 73 rounded to the nearest 10 is ____.” (3.NBT.1)

• Mid-Year Assessment, Item 6, “Davis and his friends have 4 packs of balloons with 4 balloons in each pack. They inflate all of their balloons. Then 3 balloons pop. How many inflated balloons are left? a. Use pictures, numbers, or words to solve the problem. Write number models to show each step. How do you know your answer makes sense?” (3.OA.8)

• Unit 5, Item 6, “Divide the circle below into 4 equal-size parts. Shade and label one part with a fraction.” A circle is provided for students to partition. (3.NF.1, 3.G.2)

• Unit 9, Assessment, Item 6, “It starts raining at 6:40 A.M. and stops at 9:15 A.M. How long did it rain? Show your thinking. You may use an open number line, your toolkit clock, or other representations.” (3.MD.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 3 Assessment, Item 2, “Complete the tables. Write your own number pair in the last row of each table.” Students are shown an in/out table to determine the “rule” and fill in the missing numbers. (4.OA.5)

• Mid-Year Assessment, Item 4a, “Find the rule. Complete the table.” Students are shown an in/out table to determine the “rule” and fill in the missing numbers. (4.OA.5)

• Unit 6 Assessment, Item 7, “Andy used the order of operations to solve this number sentence. 3+6\times5=33. Explain Andy’s steps for solving the number sentence.” A box titled “Rules for the Order of Operations” is shown. (5.OA.1)

• End-of-Year Assessment, Item 7, “a. Use the order of operations to solve these number sentences. 45-12\times0= ____, (45-12)\times0= ____. b. Explain why the two number sentences have different answers.” (5.OA.1)

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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 3 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 3-4, Column Addition, Focus: Introducing Column Addition, students learn column addition and compare it to partial-sums addition, “Display 47+68=? vertically. With the class, solve additional problems using column addition. 78+65=?, 439+171=?.” Student Math Journal 1, students practice column addition with multi-digit numbers, “Problem 1. 67+25=? Estimate: Problem 2. 227+386=? Estimate: Problem 3. 481+239=? Estimate:” Students engage in extensive work with grade-level problems for 3.NBT.2, “Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.”

• Lesson 5-2, Representing Fractions, Focus: Representing Fractions, students represent fractions in different ways, “Display the Representing Fractions chart to help children connect fraction words, standard notion, and pictures.” A chart is provided for students to fill in with the teacher. Student Math Journal 2, “Use your fraction circle pieces to help you complete the table. Pay attention to the whole in each problem. 1. The whole is the orange piece. 2. The whole is the yellow piece. 3. The whole is the pink piece. 4. The whole is the red circle.” Students engage in extensive work with grade-level problems for 3.NF.1, “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size \frac{1}{b}.”

• Lesson 8-1, Measuring to the Nearest \frac{1}{4} Inch, Practice: Matching Fractions on a Number Line, Math Journal 2, Problem 1, students match fractions to their position on a number line, “Think about where each of the fractions below belong on the number line. Then write one of the fractions in each box for A, B, C, and D on the number line. \frac{1}{2}, \frac{1}{3}, \frac{1}{4}, \frac{3}{4}. Explain how you figured out the location of \frac{3}{4} on the number line. What is another fraction for the point you labeled \frac{1}{2}?” Student Math Journal 2, Students engage in extensive work with grade-level problems for 3.NF.2, “Understand a fraction as a number on the number line; represent fractions on a number line diagram” and 3.NF.3, “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

The materials provide opportunities for all students to engage with the full intent of Grade 3 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 a spiraled review of content from past lessons.” Examples of meeting the full intent include:

• Lesson 1-3, Tools for Mathematics, Focus: Reviewing Length Measurement, Math Journal 1, students tell and write time to the nearest minute, “For Problems 1 and 2, record the times shown on the clocks. For Problem 3, draw the minute and hour hands to show the time.” Three clock images are provided. 1. 8:30, 2. 2:45, 3. 6:10. Lesson 5, Time, Focus, Telling Time to the Nearest Minute, Math Journal 1, Problems 1-6, students tell and record time to the nearest minute, “Write the time shown on each clock.” Six clock images are provided. Lesson 6, How Long Is a Morning?, Focus, Math Message, Math Journal 1, students make sense of the solution to an elapsed-time problem that uses an open number line, “Sheena’s math class began at 9:55 A.M. and ended at 11:10 A.M. She started to figure out how long the class lasted. She used a number line. Use Sheena’s number line to complete the problem. Tell the length of time in hours and minutes. Math class lasted ___ hour and ___ minutes. Explain Sheena’s strategy to your partner.” Students engage in the full intent of 3.MD.1, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.”

• Lesson 4-7, Area and Perimeter, Focus: Comparing Perimeter and Area, Math Journal 2, students use squares to compare perimeter and area, “For Problems 1-3, find the perimeter and the area of the rectangle.” The figure in Problem 1 has an area of 14 square feet and a perimeter of 18 feet. The figure in Problem 2 has an area of 24 square meters and a perimeter of 20 meters. The figure in Problem 3 has an area of 24 square miles and a perimeter of 22 miles. Try This, “Find the perimeter and the area of this shape.” The Figure has an area of 15 square centimeters and a perimeter of 18 centimeters. Lesson 4-8, Area and Composite Units, Focus, Distinguishing Area and Perimeter, Math Journal 1, Problem 1, students compare finding the area and perimeter of rectangles, “Use the shaded composite unit to find the area of each rectangle.” The Figure shown has an area of 8 square units. Lesson 5-1, Focus, Exploration B: Finding All Possible Shapes, Activity Card 63, students explore different shapes with the same area and then find the perimeter, “Connect five 1-inch pattern-block squares so at least one side of each block touches another side. Keep track of each shape you make. Lightly shade the square inches on grid paper. Help each other find all the possible shapes using five pattern blocks. Check that each shape cannot be turned or flipped to match a shape that was already recorded.” Students engage in full intent of 3.MD.6, “Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.”

#### Criterion 1.2: Coherence

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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 3 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 6.5 units address major work of the grade or supporting work connected to major work of the grade, approximately 72%.

• There are 108 lessons, of which 73 address the major work of the grade or supporting work connected to the major work of the grade, approximately 68%.

• In total, there are 169 days of instruction (108 lessons, 37 flex days, and 24 days for assessment), of which 88.75 days address major work of the grade or supporting work connected to the major work of the grade, approximately 53%.

• Within the 37 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 68% 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 3 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 1-12, Exploring Mass, Equal Shares, and Equal Groups, Activity Card 16, students partition shapes into parts with equal areas (3.G.2) to understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (3.NF.1). Problem 1 states, “Share 3 pancakes equally among 6 people. Draw a picture to show part of the 3 pancakes that each person gets. Write your answer next to your picture.”

• Lesson 2-4, Multistep Number Stories, Part I, Math Message, students fluently add and subtract within 1000 (3.NBT.2) to solve two-step word problems (3.OA.8). Teachers present students with a picture of a vending machine that contains snacks ranging from 25 cents to 75 cents. The teacher prompt states, “You have 80 cents in your pocket. Estimate. Do you have enough money to buy two packages of the same snack? Which snack? Write your answer on your slate.” In the Student Math Journal, Problem 1, “A package of rice cakes contains 6 rice cakes. You buy 2 packages of rice cakes and then eat 4 rice cakes. How many rice cakes are left?”

• Lesson 3-7, Exploring Bar Graphs, Area, and Partitioning Rectangles, Focus: Exploration C: Partitioning Rectangles, students partition shapes into parts with equal areas (3.G.2) to understand the concepts of area and relate area to multiplication (3.MD.6). In the Math Masters, Problem 3, “Draw lines to partition the rectangle into 5 rows with 6 same-size squares in each row. You may use a square pattern block to help. How many squares cover the rectangle? Talk to a partner.” Problem 4, “How did you figure out the total number of squares?” Problem 5, “How are the rectangles in Problems 2 and 3 like arrays?”

• Lesson 4-6, Perimeter, Math Journal 1, students measure the sides of rectangles and triangles (3.MD.D) and write number sentences to determine the perimeter (3.OA.D). Problems 1-4 include 2 rectangles and 2 triangles, “Measure the sides of each polygon to the nearest half inch. Use the side lengths to find the perimeters. Write a number sentence to show how you found the perimeter.”

• Lesson 5-3, Equivalent Fractions, Math Message, students partition shapes into parts with equal areas (3.G.2) to compare two fractions with the same numerator or the same denominator by reasoning about their size (3.NF.3d). Students are presented with a problem that depicts two circular, but different-sized pizzas, “Quan ate 1-fourth of this pizza. Aiden ate 1-fourth of this pizza. Partition and shade each pizza to show how much pizza each boy ate. Quan said they ate the same amount because they both ate 1-fourth of a pizza. Do you agree with Quan? Explain.”

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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 3 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. 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 2-6, Equal Groups, Math Journal 1, Problem 1, students solve equal group number story problems. “Shanna buys 3 boxes of mini stock cars to share with her classmates. How many cars does she have all together? Answer: ___. Number model: ___. How much do 3 boxes of cars cost? Answer: ___ Number model: ___.” This connects the major work of 3.OA.A, “Represent and solve problems involving multiplication and division,” to the major work of 3.OA.C, “Multiply and divide within 100.”

• Lesson 4-6, Perimeter, Focus: Math Message, students trace pattern blocks and discuss ways to measure the distance around them. “Take a pattern block. Trace the shape of the block on a piece of paper. What shape did you draw? How do you know? Talk to a partner about how you might measure the distance all the way around the shape you drew.” This connects the supporting work of 3.MD.B, “Represent and interpret data,” to the supporting work of 3.G.A, “Reason with shapes and their attributes.”

• Lesson 4-7, Area and Perimeter, Math Masters, Problem 1, students fluently add numbers to find the perimeter, “Dale said the perimeter of this rectangle is 16 feet and the area is 12 square feet. Do you agree? Explain.” This connects the supporting work of 3.MD.D, “Recognize perimeter as an Attribute of Plane figures and distinguish between linear and area measures” to the supporting work of 3.NBT.A, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”

• Lesson 5-6, Multiplication Fact Strategies: Doubling Part 2, Math Journal 2, problem 4, students use doubling and halving strategies to solve number stories involving area. “Your friend is planning a rectangular garden that is 6 feet wide and 7 feet long. To buy the correct amount of fertilizer, she needs to find the area of the garden, but she does not know how to solve 6 x 7. Show how your friend could use doubling to figure out the area.” This connects the major work of 3.OA.B, “Understand properties of multiplication and the relationship between multiplication and division” to the major work of 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and to addition.”

• Lesson 7-12, Fractions of Collections, Focus: Identifying Fractions of Collections, students name fractions for a set of objects. “Jules has a stamp collection with 12 stamps. She puts \frac{1}{2} of her stamps on one page and the other \frac{1}{2} on another page. How many stamps are on each page? You may use counters or drawings to help.” This connects the major work of 3.NF.A, “Develop understanding of fractions as numbers” to the major work of 3.OA.A, “Represent and solve problems involving multiplication and division.”

• Lesson 8-7, Exploring Number Lines, Fractions, and Area, Activity Card 91, students create rectangles using given area measures. “You and your partner make rectangles with the areas given in the table on journal page 268. For each rectangle you make, record the lengths of two sides that touch.” Students then answer 3 questions in their journals relating to the squares they made during the activity. In the Student Math Journal, Problem 1, “Study your table. What pattern or rule do you see?” This connects the major work of 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and to addition” to the major work of 3.OA.B, “Understand properties of multiplication and the relationship between multiplication and division.”

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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 3 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:

• Unit 4, Measurement and Geometry, Teacher’s Lesson Guide, Links to the Past, “3.MD.5, 3.MD.5b: In Grade 2, children partitioned rectangles into rows and columns of squares of the same size and counted them to find the total in preparation for understanding area.”

• Unit 6, More Operations, Teacher’s Lesson Guide, Links to the Past, “3.NBT.2: In Unit 2, children used extended addition/subtraction facts to solve real-world and mathematical problems. In Unit 3, children were introduced to algorithms. In Grade 2, children added and subtracted within 1,000 using concrete models or drawings, partial-sums addition, and expand-and-trade subtraction.”

• Unit 8, Multiplication and Division, Teacher’s Lesson Guide, Links to the Past, ”3.MD.4: In Unit 4, children measured lengths to the nearest \frac{1}{2} inch and whole centimeter and represented the data in line plots. In Grade 2, children measured length to the nearest whole unit and represented the data in line plots.”

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:

• Unit 4, Measurement and Geometry, Teacher’s Lesson Guide, Links to the Future, “3.G.1: In Grade 4, children will begin more formal geometry work with angles.”

• Unit 6, More Operations, Teacher’s Lesson Guide, Links to the Future, “3.NBT.2: Throughout Grade 3, children will use strategies and algorithms to solve addition and subtraction number stories and problems within 1,000. In Grade 4, children will add and subtract multidigit whole numbers using the standard algorithm.”

• Unit 8, Multiplication and Division, Teacher’s Lesson Guide, Links to the Future, “3.MD.4: In Grade 3, children will measure lengths using rulers marked with \frac{1}{2} and  \frac{1}{4} of an inch and represent the data in line plots. In Grade 4, children will review line plots and create line plots that include smaller fractional units of length and weight.”

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

• Lesson 2-9, Modeling Division, Focus: Modeling with Division, “Children divide to solve number stories and learn about remainders, (3.OA.2, 3.OA.3).” For example, “3 children share 13 pennies. How many pennies will each child get? What is the dividend in this problem? What is the divisor in this problem? What is the quotient in this problem? What is the remainder?” Division with remainders is aligned to 4.NBT.6, “Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.” Division with remainders continues in Lesson 2-10.

• Lesson 8-3, Factors of Counting Numbers, Focus: Finding Factors, “Children relate factors and fact families and identify factor pairs for products, (3.OA.4, 3.OA.6, 3.OA.7, and 3.NBT.3).” For example, “How could you use 3\times4=12 to find factor pairs for 120? How many tens are in 180? What basic facts have 18 as a product?” This aligns to 4.OA.4 (“Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number”).

• Lesson 8-6, Sharing Money, Focus: Making Sense of Remainders, “Children solve a sharing problem involving a remainder, (3.OA.2, 3.OA.3, 3.OA.7, and 3.NF.1).” For example, “Have partnerships use their bills to make $49 and then solve the first Try This problem. Look for children to model sharing$49 equally among 4 people in the following ways: Each person gets $12 and there is a dollar remaining. Each person gets$12 whole dollars and \frac{1}{4} of a dollar. Each person gets $12 and 1 quarter. Each person gets$12 and 25 cents or 12.25.” Solving multi-step word problems posed with whole numbers and having whole-number answers using the four operations in which remainders must be interpreted aligns to 5.NBT.7. ##### Indicator {{'1g' | indicatorName}} In order to foster coherence between grades, materials can be completed within a regular school year with little to no modification. The materials reviewed for Everyday Mathematics 4 Grade 3 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 169 days, however, the Pacing Guide states 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 37 Flex Days that can be used for lesson extension, journal fix-up, differentiation, or games; however, explicit teacher instructions are not provided. • There are 24 days for assessment which include Progress Checks, Open Response Lessons, Beginning-of-the-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: 5-10 minutes; Core Activity: Focus: 35-40 minutes; and Core Activity: Practice: 20-25 minutes. ###### Overview of Gateway 2 ### Rigor & the Mathematical Practices The materials reviewed for Everyday Mathematics 4 Grade 3 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 3 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. ##### Indicator {{'2a' | indicatorName}} Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. The materials reviewed for Everyday Mathematics 4 Grade 3 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 2-12, Exploring Fraction Circles, Liquid Volume, and Area, Practice: Playing Division Arrays, Student Reference Book, students play Division Arrays to practice division by grouping counters equally. “Players take turns. When it is your turn, draw a card and take the number of counters shown on the card. You will use the counters to make an array. Roll the die. The number on the die is the number of equal rows you must have in your array.” Students develop a conceptual understanding of 3.OA.2, “Interpret whole-number quotients of whole numbers.” • Lesson 4-9, Number Sentences for Area of Rectangles, Focus: Math Message, students find the area of a rectangle. “A cloud is partly covering this rectangle. Find the area of the whole rectangle. Tell a partner how you found the area. Then listen to how your partner found the area. Be ready to share your partner’s ideas.” Students develop conceptual understanding of 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and to addition.” • Lesson 5-11, Multiplication Facts Strategies: Break-Apart Strategy, Focus: Breaking Apart Factors to Solve Facts, Math Journal 1, Problem 1, students decompose factors to solve multiplication problems. “You have a rectangular garden that is 7 feet wide and 8 feet long. You decide to plant flowers in one section and vegetables in another. Sketch at least two different ways you can partition, or divide your garden into two rectangular sections. Label the side lengths of each of your new rectangles. Write a number model using easier helper facts for one of your ways. 7\times8= ___ \times ___ + ___ \times ___.” Students develop a conceptual understanding of 3.OA.1, “Interpret products of whole numbers.” • Lesson 7-5, Fractions on a Number Line, Part 1, Focus: Math Journal 1, Problem 4, students identify fractions greater than one on a number line. “Circle all the fractions greater than 1 on the number lines on pages 232 and 233. What do you notice about fractions greater than 1?” Students develop conceptual understanding of 3.NF, “Develop an understanding of fractions as numbers.” • Lesson 7-12, Fraction of Collection, Focus: Naming Fraction of Collections, students name fractions of collections using counters. “Direct children to make collections and name fractions of those collections. For example: There are 4 pennies in \frac{1}{2} of the pile. Show me the whole pile. There are 8 crayons in 1 box. How many crayons are in 2 boxes? In 1\frac{1}{2} boxes?” Students develop a conceptual understanding of 3.OA.2, “Interpret whole-number quotients of whole numbers.” Home Links, Math Boxes, and Practice provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include: • Lesson 2-6, Equal Groups, Home Link, students solve problems involving multiples of equal groups by using strategies like repeated addition and skip counting. “Solve. Show your thinking using drawings, words, or number models. A pack of Brilliant Color Markers contains 5 markers. Each pack costs2. 1. If you buy 6 packs, how many markers will you have?” Students independently demonstrate conceptual understanding of 3.OA.1, “Interpret products of whole numbers.”

• Lesson 7-4, Fraction Strips, Home Link, Problem 1, students shade fraction strips to represent given fractions. “Shade each rectangle to match the fraction below it. ‘$$\frac{2}{3}$$’” Students independently demonstrate conceptual understanding of 3.NF.3, “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

• Lesson 8-4, Setting Up Chairs, Home Link, Problem 1, students make conjectures and arguments to explain why an arrangement of marching band members is best. “There are 24 members in the school band. The band director wants them to march in rows with the same number of band members in each row. Find two different ways that the band members can be arranged. Draw a sketch that shows each arrangement.” Students independently demonstrate conceptual understanding of 3.OA.2, “Interpret whole-number quotients of whole numbers.”

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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 2-11, Framers and Arrows, Warm-Up: Mental Math and Fluency, students focus on basic fact families. “Pose each basic fact without an answer. Have children write out the rest of the fact family, including the answers, on their slates: 6+4, 2\times8, 8+5, 5\times4, 9+7, 5\times9.” Students develop procedural skills and fluency of 3.OA.7, “Fluently multiply and divide within 100,” and 3.NBT.2, “Fluently add and subtract within 1,000.”

• Lesson 3-3, Partial-Sums Addition, Focus: Adding with Partial Sums, students add by expanding addends. “Display 145+322 in the vertical form. Ask: What is the expanded form of each addend?” Students develop procedural skills and fluency of 3.NBT.2, “Fluently add and subtract within 1,000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.”

• Lesson 5-9, Multiplication Facts Strategies: Near Squares, Focus: Math Message, students multiply and divide within 100. “Kali knows 7\times7=49. How could she use 7\times7 as a helper fact to figure out 8\times7?” Students develop procedural skills and fluency of 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”

• Lesson 6-2, Playing Baseball Multiplication, Focus: Introducing Baseball Multiplication, students are introduced to the game to build multiplication fact fluency. “Tell children that they will practice multiplication facts while playing Baseball Multiplication. Players solve multiplication facts to move counters around the bases and score runs.” Students develop procedural skills and fluency of 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”

Math Boxes, Home Links, Games, and Daily Routines provide opportunities for students to independently demonstrate procedural skill and fluency throughout the grade. Examples include:

• Lesson 2-8, Picturing Division, Practice: Math Journal 1, Problem 1, students add fluently using strategies or the standard algorithm. “Scientists counted 91 eggs in 2 clutches of python eggs. If 1 python clutch has 52 eggs, how many are in the other clutch? You may draw a diagram or picture.” Students independently demonstrate procedural skill and fluency of 3.NBT.2, “Fluently add and subtract within 1000.”

• Lesson 7-6, Fractions on a Number Line, Part 2, Practice: Student Reference Book, students practice multiplication facts by playing Baseball Multiplication. “Pitching and Batting: Members of the team not at bat take turns ‘pitching’. They roll the dice to get two factors. Players on the ‘batting’ team take turns multiplying the two factors and saying the product.” Students independently demonstrate procedural skill and fluency of 3.OA.7, “Fluently multiply and divide within 100.”

• Facts Workshop, online game, students add and subtract to create fact families. Students are shown a domino that has 2 dots on one side and 3 dots on the other side. Students are asked to select facts that are part of that fact family (i.e. 5-3=2, 5-2=3, 3+2=5). Students independently demonstrate procedural skill and fluency of 3.NBT.2, “Fluently add and subtract within 1000.”

• Division Arrays, online game, students multiply and divide and interpret whole-number quotients. Students can play with a partner or against the computer, “Players take turns making arrays. During each turn, a player is given a total number of counters and numbers of rows, then uses them to build an array. The player earns points equal to the number of counters in one row of the array.” Students develop procedural skills and fluency of 3.OA.7, “Fluently multiply and divide within 100” and 3.OA.2, “Interpret whole-number quotients of whole numbers.”

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

The materials reviewed for 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 4-7, Area and Perimeter, Home-Link, Problem 2, students solve problems involving perimeter. “Your pace is the length of one of your steps. Find the perimeter, in paces, of your bedroom. Walk along each side and count the number of paces. The perimeter of my bedroom is about ___ paces.” Problem 3, “Which room in your home has the largest perimeter? Use your estimating skills to help you decide. The ___ has the largest perimeter. Its perimeter is about ___ paces.” This activity provides the opportunity for students to apply their understanding of 3.MD.8, “Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.”

• Lesson 6-9, Writing Number Stories, Focus: Solving the Open Response Problem, students use the four operations to write and solve real-world problems. “Write a two-step number story to fit the number sentence below. 12-(4\times2)=4.” This activity provides the opportunity for students to apply their understanding of 3.OA.8, “Solve two-step word problems using the four operations.”

• Lesson 7-3, Number Stories with Measures, Focus: Solving Number Stories with Measures, Problem 3, students solve number stories that involve time in a real-world problem. “Lena has a doctor’s appointment at 8:45 A.M. It takes her 25 minutes to drive to her doctor’s office. How many minutes early will Lena be if she leaves at 8:00 A.M.?” This activity provides the opportunity for students to apply their understanding of 3.MD.1, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.”

• Lesson 7-8, Finding Rules for Comparing Fractions, Focus: Solving the Open Response Problem, Problem 1, students write rules for ordering fractions. “Think about these fractions: \frac{1}{6}, \frac{1}{8}, \frac{1}{10}, \frac{1}{3}, \frac{1}{4}, \frac{1}{2}, \frac{1}{5}. Write the fractions in order from least to greatest: What Patterns do you notice? How are these fractions the same or different?” Problem 3, “Write a rule for ordering fractions with the same numerator.” This activity provides the opportunity for students to apply their understanding of 3.NF.3, “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

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 1-8”, Problem 2, students write their own number story problems and represent their story in their own way. “Write a number story about this number sentence: ?=2\times7. Then draw a picture that represents your number story and show how you solved it.” This activity provides the opportunity for students to independently demonstrate understanding of  3.OA.3, “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.”

• Independent Problem Solving 2b, “to be used after Lesson 2-9”, Problem 1, students use multiplication and division to determine the rows of apples. “a. Maria picked 18 apples for her aunt’s fruit market. She wants to display her apples in an array that has 3 rows. Show how Maria can display the apples. How many apples are in each row? Write a number model to describe Maria’s array. b. Her aunt asked Maria to change her display so that the array has 9 apples in each row. Show Maria’s new array. How many rows of apples are in Maria’s new display? Write a number model to describe this array.” This activity provides the opportunity for students to independently demonstrate understanding of  3.OA.3, “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.”

• Independent Problem Solving 4b, “to be used after Lesson 4-10”, Problem 1, students use multiplication and addition strategies to find an area. “For a school project, Keisha has to figure out the area of her back porch. She sketched this model of her porch on grid paper, but her baby brother spilled juice that covered part of her model. Help Keisha figure out the area of her back porch. The area of Keisha’s back porch is ___ square feet. Explain how you figured out the area of Keisha’s back porch.” This activity provides the opportunity for students to independently demonstrate understanding of 3.MD.7, “Relate area to the operation of multiplication and addition.”

• Independent Problem Solving 5b, “to be used after Lesson 5-11”, Problem 1, students create and write situations for area problems. “Kim is helping his dad tile the floor of the bathroom. The floor is 7 feet by 9 feet. Kim’s dad said that each box of tile will cover 10 square feet. To figure out how much tile they need, Kim sketched this rectangle. Use words and numbers to explain how Kim can use this sketch to figure out how many boxes of tile he and his dad need for the bathroom floor. Kim and his dad need to buy ___ boxes of tile.” This activity provides the opportunity for students to independently demonstrate understanding of 3.MD.7, “Relate area to the operation of multiplication and addition.”

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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 3 meet expectations in that the three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the three aspects of rigor within the grade.

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 2-1, Extended Facts: Addition and Subtraction, Focus: Math Message, students solve multi-digit addition and subtraction problems. “Solve. Record your answers on your slate. Think about the patterns that help you solve each set. 9-7=?; 90-70=?; 900-700=?; ?=7+9; ?=70+90; ?=700+900.” Students develop procedural skills and fluency of 3.NBT.2, “Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.”

• Lesson 3-10, The Commutative Property of Multiplication, Focus: Math Message, students solve problems using the commutative property. “You have 8 apples for sale and want to display them in an array. How many different ways can you arrange them? Make sketches on paper to show your thinking.” Students extend their conceptual understanding of 3.OA.1, “Interpret products of whole numbers” and 3.OA.3, “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.”

• Lesson 8-6, Sharing Money, Home-Link, Problem 1, students engage in application as they interpret whole-number quotients by using multiplication and division. “Four friends share $76. They have seven$10 bills and six $1 bills. They can go to the bank to get smaller bills. Use numbers or pictures to show how you solved the problem. Answer: Each friend gets a total of$___.” Students engage in application of 3.OA.2, “Interpret whole-number quotients of whole numbers.”, 3.OA.3, “Use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities.”, and 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”

Multiple aspects of rigor are engaged simultaneously to develop students’ mathematical understanding of a single unit of study throughout the materials. Examples include:

• Lesson 4-6, Perimeter, Focus: Solving Perimeter Number Stories, Math Journal 1, Problem 2, students solve real-world perimeter problems, “Mr. Lopez wants to put a fence around his rectangular vegetable garden. The longer sides are 14 feet long and the shorter sides are 9\frac{1}{2} feet long. How much fencing should Mr. Lopez buy? You may sketch a picture. Number Model: ____. Mr. Lopez should buy ____ feet of fencing.” Students develop all three aspects of rigor simultaneously of 3.MD.8, “Solve real-world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters.”

• Lesson 5-4, Recognize Helper Facts, Practice: Solving Two-Step Number Stories, Math Journal 2, Problem 1, students solve problems involving two steps. “Savannah earns \$5 selling lemonade. Jessica earns double the amount of money that Savannah earns. How much money do they have together?” Students engage with procedural skills and application of 3.OA.8, “Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including rounding.”

• Lesson 7-11, Fractions in Number Stories, Home-Link, Problem 3, students solve number stories with fractions. “Solve these number stories. Show your answer as a fraction. You may draw pictures to show your work. Nora rode her bike \frac{2}{2} of a block. Brady rode his bike \frac{4}{4} of the same block. Compare the distances each child rode. What do you notice? Explain your answer.” Students develop conceptual understanding and procedural skills and fluency of 3.NF.1, “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction \frac{a}{b} as the quantity formed by a parts of size \frac{1}{b}.”

#### 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 3 meet expectations  for practice-content connections. The materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice (MPs).

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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 2-3, More Number Stories, Focus: Organizing Number Story Information, students consider different strategies to solve number stories. “There are 43 children in the soccer club and 25 children in the science club. How many fewer children are in the science club?” The teacher asks, “How will you organize the information from the story? What do you know already?”

• Lesson 4-1, Measuring with a Ruler, Practice: Math Boxes, Problems 3 and 5, students analyze and make sense of subtraction word problems. Problems 3 and 5, “3. An alligator clutch had 82 eggs. 19 eggs did not hatch. How many eggs did hatch? 5. What strategy could you use to check your answer to Problem 3?”

• Lesson 6-6, Multiplication and Division Diagrams, Focus: Representing and Solving Number Stories, Math Journal 2, Problem 2, students reflect on their problem solving strategies. “There are 48 third graders. The gym teacher groups them into teams of 6. How many teams are there? When most children have finished, bring them together to discuss how they used diagrams to organize the information in each problem and write a number model to represent the story.”

• Independent Problem Solving 9a, “to be used after Lesson 9-4”, Problem 1, students analyze and make sense of the information presented in problems that involve adding time intervals. “Alicia and Jeremy will visit the City Aquarium with their grandpa next week. They plan on leaving their house at 8:15 a.m. It will take them 45 minutes to ride the bus to the aquarium. When they leave the aquarium, they plan on going out to lunch for 1 hour and then taking the 45-minute bus ride home. They need to be back home by 2:15 p.m. The rest of their time will be spent at the aquarium. How much time will they spend at the aquarium altogether? Use words or drawings or both to explain how you figured it out.”

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 1-7, Scaled Bar Graphs, Focus: Organizing and Representing Data, Math Journal 1, students consider units involved in a problem and attend to the meaning of quantities as they organize and represent data in bar graphs. “1. How many last names are there? 2. Use the data you collected to make a tally chart for the last names in your class. Add rows as needed. 3. Look at the data in your tally chart. Write at least three things you know from looking at the data.”

• Lesson 5-7, Patterns in Products, Practice: Finding Clock Fractions, students understand the relationships between problem scenarios and mathematical representations as they connect clocks with fraction circle pieces. “Have children connect fractions of circles with fractions of hours by completing journal page 176, make sure toolkit clocks and fraction circle pieces are available for children to model the problems.” Math Journal 2, “Use your fraction circle pieces and toolkit clock to answer the questions. 1. On Monday, Isaac worked on his science project for 30 minutes. Shade 30 minutes on the clock. What time did he start? Draw hour and minute hands on the clock to show the time Isaac stopped working. What time did he stop? 2. What fraction of the clock did you shade? What fraction of an hour is that?”

• Lesson 9-5, Multi-Digit Multiplication, Focus: Math Message, Problems 1 and 2, students consider units involved in a problem and attend to the meaning of quantities as they partition a rectangle garden. “Jonah’s garden is a rectangle with 16 rows of plants. He wants to plant two sections: one with 10 rows of carrots and the other with 6 rows of beans. Partition the rectangle and label the sections with carrots and beans to show how Jonah could plant his garden. Jonah can plant 9 seeds in each row. How many seeds can he plant all together? Show your work.”

• Independent Problem Solving 3b, “to be used after Lesson 3-13”, Problem 1, students understand the relationships between numbers as they find a target number. “Ashley and Tyrese were playing Name That Number. Here are their cards: 6, 2, 9, 3, 10, Target Number 12. They wanted to write as many different equivalent names as they could for the target number 12. In the space below, use the numbers on the cards to write equivalent names for 12 using +, -, , and .”

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

Each 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 6-10, More Operations, Focus: Exploring Order of Operations, Math Journal 2, Problem 5, students construct a viable argument when they explain to their partner why they picked their answer. “Circle the answer that makes the number sentence true. 2\times(4+3\times2)=?. a. 28, b. 20, c. 14. Explain to a partner why you picked your answer.”

• Lesson 8-4, Setting Up Chairs, Focus, Math Message, Math Journal 2, students use clues to construct mathematical arguments. “Ms. Soto is setting up chairs for Math Night. Her room cannot fit more than 35 chairs. She places the same number of chairs in each row. As she sets up the chairs, she makes up a problem for her class with these clues: Clue A: When there are 2 chairs in each row, there is 1 leftover chair. Clue B: When there are 3 chairs in each row, there is 1 leftover chair. Clue C: When there are 4 chairs in each row, there is still 1 leftover chair. Clue D: When there are 5 chairs in each row, there are no leftover chairs. Use the clues to figure out how many chairs Ms. Soto set up. Joi, one of Ms. Soto’s students, makes a conjecture that Ms. Soto set up 13 chairs. Work with your partner and use the clues to make a mathematical argument for or against Joi’s conjecture. You may draw pictures or use counters to show your thinking. Explain your reasoning.”

• Independent Problem Solving 3a, “to be used after Lesson 3-6”, Problem 1, students justify their strategies and thinking as students use estimation strategies to solve problems. “Sarah estimated that the difference between the mass of a soccer ball and the mass of a softball was about 200 grams. How do you think Sarah made her estimate? When Sarah figured out the exact difference, she got 361 grams. How does Sarah’s estimate help her realize that her answer of 361 is not reasonable?”

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:

• Lesson 7-2, Fractions, Home-Link, Problem 1, students critique the reasoning of others as they determine if two fractions are equivalent. “Nash chose these two cards in a round of Fraction Memory.” One card shows \frac{5}{6} shaded and the other card shows \frac{6}{8} shaded. “Nash says that these cards show equivalent fractions. Do you agree or disagree? Explain.”

• Independent Problem Solving 1a, “to be used after Lesson 1-8”, Problem 1, students critique the reasoning of others and construct mathematical arguments as they solve problems using multiplication strategies. “Grayson’s mother had 3 bags of oranges. Each bag had 5 oranges. She asked Grayson to figure out the total number of oranges in her 3 bags. Grayson said she had 11 oranges in all because 3+5+3=11. Do you agree or disagree with Grayson? Use words, drawings, and numbers to show your thinking.”

• Independent Problem Solving 5a, “to be used after Lesson 5-4”, Problem 1, students construct mathematical arguments and critique the reasoning of others as they reason about equivalent fractions. “Alia’s mom baked 2 same-sized pizzas. She gave Alia \frac{4}{8} of one pizza. She gave Alia’s friend, Blanca, \frac{3}{6}of the other pizza. Alia said she got more than Blanca because 4 slices are more than 3 slices. Do you agree? Show your thinking with words or drawings.”

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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 3 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 6-11, Number Models for Two-Step Number Stories, Focus: Writing Number Models, Math Journal 2, Problem 1, students use the math they know to solve problems and everyday situations as they represent multistep number stories using drawings and number models with unknowns. “Ronald bought 2 packs of crackers. There are 5 crackers in each pack. He ate some crackers. Now Ronald has 7 crackers. How many crackers did he eat?”

• Independent Problem Solving 2a, “to be used after Lesson 2-5”, Problem 1, students model with mathematics as they multiply and divide to solve number stories. “Use information from the poster below to solve each problem. Show your work and write number models to keep track of your thinking. Carter bought 3 boxes of mini-stock cars. He shared half of his cars with his brother. How many cars did Carter give to his brother?”

• Independent Problem Solving 8b, “to be used after Lesson 8-6”, Problem 2, students model the situation with an appropriate representation and use an appropriate strategy as they write their own equal sharing money story. “Write your own equal sharing money number story. Write a number model with a letter for the unknown quantity to model the problem. Solve your story. Use words, numbers, or drawings to show your thinking.”

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

• Lesson 7-11, Fractions in Number Stories, Focus: Solving Fraction Number Stories, Math Journal 2, Problem 2, students solve fraction number stories as they choose appropriate tools and strategies. “Use fraction circles, fraction strips, number lines, or pictures to help solve the number stories. Make sketches to show how you solved. Kaden makes 2 cups of salsa for the party. The 6 guests share the salsa equally. Write a fraction that shows how much each guest eats.”

• Independent Problem Solving 1b, “to be used after Lesson 1-13”, Problem 2, students choose appropriate tools and strategies as they add numbers. “Look at Terry’s and Justin’s record sheets from Problem 1. The person with the larger total sum of rounded numbers wins. Is Terry or Justin in the lead after 3 turns? Show how you know. Explain what you could do to make the other person the winner after 3 turns.”

• Independent Problem Solving 9b, “to be used after Lesson 9-6”, Problem 2, students use tools and strategies to solve problems using multiplication of 10s. “Jaloni’s grandma and the other 3rd grade room parents planned an end-of-year party for the primary grade classrooms. They baked 240 blueberry muffins and had to pack them into boxes that each held 16 muffins. Jaloni’s grandma asked him to figure out how many boxes the room parents need to equally pack all the muffins. He wants to use his calculator to solve, but the + and the keys are both broken. Help Jaloni find a way to use his broken calculator to solve the problem. a. Show or tell how to use Jaloni’s broken calculator to find the number of boxes the room parents need to pack the muffins. b. Show or tell another way for Jaloni to use his broken calculator to solve the problem.”

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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 3 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 1-5, Time, Practice: Introducing the Math Boxes Routine, Math Journal 1, Problem 5, students attend to precision as they use place value, addition, and subtraction strategies to find 10 more and 10 less. “Explain how you found the numbers that were 10 more and 10 less in Problem 1.”

• Independent Problem Solving 6a, “to be used after Lesson 6-1”, Problem 1, students calculate accurately and efficiently as they add and subtract numbers within 1,000, “This summer, Keiko’s family will visit the Statue of Liberty and climb the 354 stairs to the top. To prepare for their visit, Keiko wants to practice stair climbing for 30 minutes each day. She made a chart to record the number of stairs she climbed for one week. This is Keiko’s chart: Day of Week: Mon, Tues, Wed, Thurs, Fri, Sat, Sun. Number of Stairs Keiko Climbed: 102, 114, 147, 181, 215, 231, 0. For each problem, show how you figured it out. a. Did Keiko climb more or less stairs during the week than are in the Statue of Liberty? b. How many more or less?”

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

• Lesson 2-8, (Day 1): Picturing Division, Practice, Math Boxes, Math Journal 1, Problem 5, students formulate clear explanations as they explain how they solved a problem using subtraction. “Explain how you solved Problem 1, (Scientists counted 91 eggs in 2 clutches of python eggs. If 1 python clutch has 52 eggs, how many are in the other clutch? You may draw a diagram or picture.).”

• Independent Problem Solving 4b, “to be used after Lesson 4-10”, Problem 2, students use the specialized language of mathematics as they explain how to find different perimeters with the same area. “Max wanted to build a rectangular pen for his dog with an area of 20 square feet. Show 2 different ways he can design his pen. Then, find and record the perimeter for each pen. c. Explain how the pens you designed can have the same areas but different perimeters.”

• Independent Problem Solving 7a, “to be used after Lesson 7-6”, Problem 2, students use the specialized language of mathematics as they explain how to place fractions on a number line. “Mrs. Rivera asked her class to think of ways this number line could be useful in real life. a. Jude said a number line could be a way to keep track of his bike rides. He knew that the distance from his home to school was \frac{5}{8} mile. From his home to the playground was \frac{11}{8} miles. On this number line, show where Jude should mark the fractions that represent his bike ride distances. b. Clearly explain how you knew where to place the fractions. c. Write a different way fraction number lines could be useful in real life.”

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:

• Student Reference Book, “A function machine, is an imaginary machine. The machine is given a rule for changing numbers. You drop a number into the machine. The machine uses the rule to change the number. The changed number comes out of the machine.”

• Student Reference Book, “Another method you can use to subtract is called trade-first subtraction. To use trade-first subtraction, look at the digits in each place: If a digit in the top number is greater than or equal to the digit below it, you do not need to make a trade. If any digit in the top number is less than the digit below it, make a trade with the digit to the left. After making all necessary trades, subtract in each column.”

• Student Reference Book, “The turn-around rule says you can add two numbers in either order. Sometimes changing the order makes it easier to solve problems. Example: 4+17=? If you don’t know what 4+17 is, you can use the turn-around rule to help you, and solve 17 + 4 instead. 17+4 is easy to solve by counting on.”

• Student Reference Book, “A Frames-and-Arrows diagram, is one way to show a number pattern. This type of diagram has three parts: a set of frames that contains numbers; arrows that show the path from one frame to the next frame; and a rule box with an arrow below it. The rule tells how to change the number in one frame to get the number in the next frame.”

• Lesson 3-6, Expand-and-Trade Subtraction, Focus: Reviewing Expand-and-Trade Subtraction, “Next review expand-and-trade subtraction. The lesson reviews expand-and-trade subtraction, which was introduced late in Second Grade Everyday Mathematics. Expand-and-trade subtraction relies on place-value understanding. Exposing children to multiple strategies allows them to think flexibly and choose the most efficient strategy for them.”

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

Each 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 2-1, Extended Facts: Addition and Subtraction, Focus: Extending Combinations, Math Journal 1, Problem 4, students make use of the structure as they analyze how to solve addition and subtraction problems. “14-9=?, 24-9=?, 54-9=?” Problem 5, “Explain how you used a basic fact to help you solve Problem 4.”

• Lesson 6-10, Order of Operations, Focus: Exploring Order of Operations, Math Journal 2, Problem 4, students look for patterns or structures to make generalizations and solve problems using the order of operations. “Use the order of operations to solve each number sentence below. Show your work. To check your work, use a calculator that follows the order of operations. Rules for the Order of Operations. 1. Do operations inside parentheses first. Follow rules 2 and 3 when computing inside parentheses. 2. Then multiply or divide. In order, from left to right. 3. Finally add or subtract, in order, from left to right. 6+4\div2= ___.” Teacher’s Lesson Guide, “Ask each group to figure out how each calculator solved the problem.”

• Independent Problem Solving 5b, “to be used after Lesson 5-11”, Problem 2, students look for and explain the structure within rectilinear figures by decomposing them to find the area. “Abdul and Isabella are painting a wall mural that is 8 feet by 6 feet. They need to find the area of the mural so they can buy enough white paint to cover the background of the entire mural. Abdul said he could find the area by sketching an 8-by-6 rectangle and breaking 8 into easier-to-multiply factors 4 and 4. Isabella said she could sketch the same rectangle, but break 6 into 5 and 1. Abdul said that both strategies will work. Do you agree? Explain your thinking using words, numbers, and drawings.”

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 3-10, The Commutative Property of Multiplication, Focus: Introducing the Turn-Around Rule for Multiplication, Math Journal 1, Problem 1, students notice repeated calculations to understand algorithms and look for patterns when they generate pairs of facts and arrays. “Roll a die twice to get 2 factors. Sketch an array using those 2 factors and record a number sentence to match. Switch the factors and record an array and number sentence to match. What do you notice about each pair of arrays?” Teacher’s Lesson Guide, “Bring the class together to share their examples. Demonstrate or have a child turn an array pair for the class to see. Ask: What do you notice when you turn the arrays? Point to the number sentences and ask, If you switch the factors, will you always get the same product? Explain.”

• Lesson 7-7, Comparing Fractions, Focus: Using Benchmarks to Compare Fractions, Math Journal 2, Problem 2, students evaluate the reasonableness of their answers and thinking to develop a general rule for comparing fractions. “Choose two fractions that are less than \frac{1}{2}. Of these two fractions, which one is closer to 0? How do you know? Write a number sentence that compares your two fractions. Use <, >, or =.”

• Lesson 8-3, Factors of Counting Numbers, Focus: Recognizing Factor Pairs, Math Journal 2, Problem 6, students use repeated reasoning and make generalizations about factors and multiples. “The Kim family is serving dinner for 24 people. Mrs. Kim could have 1 table with 24 people or 2 tables with 12 people at each. What are some other ways Mrs. Kim could seat 24 people in equal groups at different numbers of tables? Is 1 in a factor pair for every counting number?”

### Usability

The materials reviewed for Everyday Mathematics 4 Grade 3 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 3 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 3 meet expectations for providing teacher guidance with useful annotations and suggestions for how to enact the student materials and ancillary materials, with specific attention to engaging students in order to guide their mathematical development.

Materials provide comprehensive guidance that assists 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 3, Operations, Organizer, Coherence, provides an overview of content and expectations for the unit. “In Unit 2, children represented multiplication number stories with arrays and recorded a number model to match. In Grade 2, children used addition to find the total number of objects arranged in rectangular arrays with up to 5 rows and up to 5 columns. They wrote an equation to express the total as a sum of equal addends. In Unit 5, children will use helper facts, doubling, and near-squares to solve for unknown products. In Grade 4, children will use multiplicative comparison statements to interpret a multiplication equation.”

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 2-2, Number Stories, Focus: Assessment Check-In, teacher guidance supports students in writing number stories. “Expect most children to make sense of and solve Problems 1-4 and to write number models with question marks for the unknowns. For children who struggle to make sense of and solve the problems, ask the guiding questions from the lesson. If children struggle to write a number model, suggest that they use a situation diagram or draw a picture to help organize the information from the story.”

• Lesson 4-3, Exploring Measures of Distance and Comparisons of Mass, Focus: Measuring Around Objects, Math Message, teacher guidance connects students' prior knowledge to new concepts. “Have children compare their measurements with a partner and think about whether they make sense. Invite volunteers to share how they measured and how they know whether their measures make sense. Expect responses to include that the distance around someone’s head is more than the distance around someone’s wrist because a head is bigger around than a wrist. Ask: Which measuring tools did you choose and why? When might it be useful to know these measurements?”

• Lesson 7-8, (Day 2): Finding Rules for Comparing Fractions, Common Misconception, teacher guidance addresses common misconceptions as students write rules for ordering fractions. “Watch for children who assume fractions with smaller denominators are smaller in size (or that fractions with larger denominators are larger in size). Encourage them to model two fractions, such as \frac{1}{3} and \frac{1}{4} using fraction circles. Ask: Would you get more pizza if you shared a pizza with three friends or four friends? Why?”

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

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 3 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 1-4, Number Lines and Rounding, Professional Development, explains connections between rounding and estimating. “Rounding can help with estimation. This lesson introduces a common rounding method that involves rounding to the nearest 10 or 100. The traditional version of this algorithm involves rounding up if the digit to the right of the target place is 5 or greater, and rounding down if the digit is less than 5.”

• Unit 3, Operations, Unit 3 Organizer, 3.G.1, supports teachers with concepts for work beyond the grade. “Links to the Future: In Grade 4, children will solve multistep number stories using all four operations and interpret the remainders in division number stories. They will explore different estimation strategies.”

• Unit 4, Measurement and Geometry, Unit 4 Organizer, 3.OA.8, provides support with explanations and examples of the more complex grade/course-level concepts. “Links to the Past: In Grade 2, children focused on specific attributes such as the number of sides, angles, and faces. They explored parallel sides.”

• Lesson 5-1, Exploring Equal Parts, Fractions of Different Wholes, and Area, Professional Development, explains concepts for work beyond the grade. “When working with fraction circles, many children may incorrectly think that the red circle is always the whole. For example, a pink piece may be the whole with a yellow piece representing 1-half. Children worked with other pieces as the whole in Lesson 2-12, Exploration A. Flexibility with the whole is important for solving real-world problems in which the size of the whole varies. It also lays a foundation for more complicated computation in later grades.”

• Lesson 6-4, Fact Power and Beat the Calculator, Professional Development, explains connections between multiplication and fluency. “The first five units of Third Grade Everyday Mathematics include many fact strategies to help children develop fluency with multiplication facts. By now, many children will already be automatic with beginning facts, such as 2s, 5s, and 10s, and squares- that is, they are able to recall these facts from memory or use a strategy automatically and instantaneously. For the rest of the year, meaningful practice through games, activities, and fact-extensions exercises will encourage children to progress beyond fluency to automaticity with basic multiplication facts.”

• Lesson 7-1, Liquid Volume, Professional Development, supports teachers with concepts for work beyond the grade. “In Everyday Mathematics, children begin by comparing liquid volume informally, followed by estimating in liters and finally estimating and measuring using liters and milliliters. As with other forms of measurement, such as length and mass, the need for more precise measurement motivates children's use of small, standard units. This progression done interactively, helps children understand volume concretely before exploring more abstract volume concepts in later grades.”

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

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 3 meet expectations for including standards correlation information that explains the role of the standards in the context of the overall series.

Correlation information is present for the mathematics standards addressed throughout the grade level/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:

• 3rd Grade 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.

• 3rd Grade Math, Unit 2, Number Stories and Arrays, Organizer, Contents Lesson Map outlines lessons, aligned standards, and the lesson overview for each lesson. This is present for all units and allows teachers to identify targeted standards for any lesson.

• Lesson 6-3, Taking Inventory of Known Fact Strategies, Core Standards identified are 3.OA.1, 3.OA.5, and 3.OA.7. Lessons contain a consistent structure that includes an Overview, Before You Begin, Vocabulary, Warm-Up, Focus, Assessment Check-In, Practice, Minute Math, Math Boxes, and Home-Link. This provides an additional place to reference standards, and language of the standard, within each lesson.

• Mastery Expectations, 3.OA.1, “First Quarter: Represent multiplication as equal groups with concrete objects and drawings. Second Quarter: Represent multiplication as equal groups with arrays. Third Quarter: Interpret products of whole numbers, e.g., interpret 5 x 7 as the total number of objects in 5 groups of 7 objects each. For example, describe a context in which a total number of objects can be expressed as 5 x 7. Fourth Quarter: Ongoing practice and application.” Mastery is expected in the Third Quarter.

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 1, Math Tools, Time, and Multiplication, Organizer, Coherence, includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children partitioned shapes into equal shares and described the whole as two-halves, three-thirds, or four-fourths. In Grade 4, children will extend the use of equal-sharing strategies to help develop an understanding of fraction equivalence. In Grade 5, children will interpret fraction and mixed-number quotients of whole numbers and will solve number stories that lead to quotients in the form of fractions or mixed numbers.”

• Unit 4, Measurement and Geometry, Organizer, Coherence, includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children focused on specific attributes such as the number of sides, angles, and faces. They explored parallel sides. In Grade 4, children will begin more formal geometry work with angles.”

• Unit 9, Multidigit Operations, Organizer, Coherence includes an overview of how the content in 3rd grade builds from previous grades and extends to future grades. “In Grade 2, children used Commutative and Associative properties of operations to add and subtract. In Grade 4, children will solve larger whole-number problems using strategies based on place value and the properties of operations.”

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

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 3 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 3-14, (Day 1): Unit 3 Progress Check, Home-Link, Family Letter, “In this unit children learn to make more precise measurements as they measure lengths, including perimeters, to the nearest half inch. Children will generate measurement data by measuring their shoe lengths and body parts, and they will represent the data on line plots. Building on their experiences from second grade, they will further explore attributes of polygons that help define shape categories such as quadrilaterals. Children develop an understanding of the area of rectangles and square units. They find areas by counting unit squares, repeatedly adding composite units, and multiplying side lengths. Through solving real-world and abstract problems, children will explore ways to find the perimeters of polygons and calculate the areas of rectilinear figures. In Unit 4 children will: Measure to the nearest centimeter and \frac{1}{2} inch. Generate and represent measurement data on a line plot. Review characteristics of polygons, Sort quadrilaterals into categories based on defining attributes. Measure perimeters of rectangles. Distinguish between perimeter as a measure of distance around the area as a measure of the amount of surface within the boundaries of a 2-dimensional shape. Find the areas of rectangles using composite units. Write multiplication number sentences that show how to find areas of rectangles. Develop strategies for finding area and perimeter. Find the areas of real-world rectilinear figures by partitioning figures.”

• Unit 6, More Operations, Home-Link, Family Letter, Vocabulary, “Important lesson components and terms in Unit 6: fact power- In Everyday Mathematics automaticity with basic arithmetic facts. Automatically knowing the facts is as important to arithmetic as knowing words by sight is to reading. multiplication/division diagram- A diagram used in Everyday Mathematics to model situations in which a total number is made up of equal-size groups. The diagram contains a number of groups, a number in each group, and a total number. Order of operations- Rules that specify the order in which operations in a number sentence should be carried out. In Third Grade Everyday Mathematics, the order of operations is described as: 1. Do operations inside parentheses first. Follow rules 2 and 3 when computing inside parentheses. 2. Then multiply or divide, in order, from left to right. 3. Finally, add or subtract in order, left to right. parentheses- () Grouping symbols used to indicate which pairs of a number sentence should be done first. Trade-first subtraction- One method for solving subtraction problems in which all trades are made before subtracting.”

• Unit 9, Multidigit Operations, Home-Link, Family Newsletter, Do-Anytime Activities, “The following activities provide practice for concepts taught in this unit and previous units. 1. Continue to work toward automaticity with all multiplication facts using Fact Triangles or by playing games such as Product Pile-Up, Multiplication Top-It, and Salute! 2. Practice using basic facts to solve extended-multiplication and division facts, such as using 3\times7=21 to solve 3\times70=210 or 18\div6=3 to solve 180\div6=30. 3. Calculate how long daily activities take.”

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

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 3 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, a distributed practice through 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 students 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 student can and should learn challenging, interesting, and useful mathematics. The program is designed to ensure that each of your students 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:

• A Study to Explore How Gardner’s Multiple Intelligences Are Represented in Fourth Grade Everyday Mathematics Curriculum in the State of Texas.

• 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.

• Achievement Results for Second and Third Graders Using the Standards-Based Curriculum Everyday Mathematics.

• The Relationship between Third and Fourth Grade Everyday Mathematics Assessment and Performance on the New Jersey Assessment of Skills and Knowledge in Fourth Grade (NJASK/4).

• The Impact of a Reform-Based Elementary Mathematics Textbook on Students’ Fractional Number Sense.

• A Study of the Effects of Everyday Mathematics on Student Achievement of Third, Fourth, and Fifth-grade students in a Large North Texas Urban School District.

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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 Third 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:

• Unit 3, Operations, Unit 3 Organizer, Unit 3 Materials, teachers need, “pattern blocks; 25 centimeter cubes; number cards 1-9 (4 of each), slate; 1-foot square cardboard templates; colored paper; scissors; straightedge (optional); masking tape (optional); collection of objects (optional) in lesson 7.”

• Lesson 5-5, Multiplication Facts Strategies, Doubling, Part 1, Overview, Materials, “Math Masters, p. TA19; centimeter cubes (50 per partnership); rectangles; Class Data Pad; slate; Math Journal 2, pp. 164-165; Minute Math; Math Journal 2, p. 167; Math Masters, p. 167.” Math Message, “Use centimeter cubes and grid paper to show your thinking.”

• Unit 7, Fractions, Unit 7 Organizer, Unit 7 Materials, teachers need, “Quick Look Cards 164, 165, 174; fraction circles; Class Fraction Number-Line Poster; fraction strips; straightedge; Fact Strategy Logs (optional); slate; fraction cards; comparison-symbol cards; paper (optional); scissors (optional); The Area and Perimeter Game Action Deck, Deck B. in lesson 10.”

• Lesson 7-10, Justifying Fraction Comparisons, Math Message, “Use your fraction circles to solve this problem.” Focus: Modeling Fraction Comparisons, “Have children use their fraction strips and the Fraction Number-Line Post on journal page 229 (or the Class Fraction Number-Line Poster) to show that \frac{1}{6}>\frac{1}{8} with other tools.”

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

This is not an assessed indicator in Mathematics.

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

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 3 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.

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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 include:

• Unit 2, Number Stories and Arrays, Unit Assessment, denotes standards addressed for each problem. Problem 5, “Maria swam a total of 56 minutes over the weekend. She swam for 20 minutes on Saturday. How many minutes did she swim on Sunday?” (3.OA.3)

• Unit 3, Operations, Open Response Assessment, denotes mathematical practices for the open response. Open Response, “Mia wants to solve this problem: 552-153=? She begins by making an estimate. Estimate: 550-150=400. Then she uses the expand-and-trade subtraction to find an exact answer, but her answer is not close to her estimate. ‘Oops,’ said Mia, ‘I didn’t cross out 500 and write 400.’ Explain why not changing 500 to 400 is a mistake.” (SMP3)

• Mid-Year Assessment, denotes standards addressed for each problem. Problem 2, “A brown bear has a mass of about 318 kilograms. A grizzly bear has a mass of about 363 kilograms. About how much more mass does the grizzly bear have than the brown bear? Solve. Show your work.” (3.MD.2)

• Unit 6, More Operations, Cumulative Assessment, denotes mathematical practices addressed for each problem. Problem 7, “Draw a picture and use words to explain why 2\times8=8\times2.” (SMP8)

• End-of-Year Assessment, denotes standards addressed for each problem. Problem 9, “A collection of 6 movie tickets is shared equally among 3 families. How many tickets does each family get? What fractions of the collection of movie tickets does each family get?” (3.NF.1)

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

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.

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

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 3 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:

• Unit 1, Math Tools, Time, and Multiplication, Open Response Assessment, supports the full intent of MP4, model with mathematics, as students use addition and subtraction strategies to figure out time. Problem 2, “Carols leaves for school at 8:00 A.M. Cheryl leaves 5 minutes later. a. Who gets to school first? b. Explain how you figured it out.”

• Mid-Year Assessment, develops the full intent of standard 3.OA.1, interpret products of whole numbers. Problem 1, “Explain how 2\times9=18 matches the array. Payton wants to use 2\times9=18 as a helper fact to solve 3\times9=? Use the helper fact and the above array to help Payton. Explain your thinking.”

• Unit 7, Fractions, Unit Assessment, problems support the full intent of MP2, reason abstractly and quantitatively, as students make sense of quantities and their relationships as they partition a number line with increments of \frac{1}{4}. Problem 6, “Partition the number line into fourths and label each tick mark. You may use the fraction strip to help.” A fraction strip shows \frac{0}{4} to \frac{?}{4} on a number line.

• End-of-Year Assessment, develops the full intent of 3.G,1, understand that shapes in different categories), and that the shared attributes can define a larger category. Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories. Problem 21, “Circle all the rectangles, mark an X on all squares, and sade all the rhombuses. Explain why the shapes you circled are rectangles. Draw another quadrilateral that is not a rectangle, a square, or a rhombus.”

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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 3 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, Number Stories and Arrays, Unit Assessment, Adjusting the Assessment, Item 6, “To scaffold Item 6, have children draw comparison diagrams to help organize the story information. Discuss what is known and unknown.”

• Unit 5, Fractions and Multiplication Strategies, Open Response Problem, Adjusting the Activity, “For children who have difficulty, help them use counters to model the doubling or near-squares multiplication strategies.”

• Unit 8, Multiplication and Division, Cumulative  Assessment, Adjusting the Assessment, Item 6, “To scaffold Item 6, have children provide a completed multiplication/division diagram to help. To extend Item 6, have children make up a number story that fits one of the other number models.”

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

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for providing strategies and supports for students in special populations to support their regular and active participation in learning grade-level mathematics.

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 6, More Operations, Lesson 4, include:

• Readiness, “To prepare children for playing Beat the Calculator, have them use calculators to solve missing-factor problems. As needed, remind children how to enter numbers and clear calculators. Pose problems verbally or display them in a table. Explain that they should use multiplication to find the answers. For example: Start with 3. Change to 6. How? Start with 5. Change to 30. How? Allow children to experiment with their calculators to find the missing factors, including using guess-and-check. If needed, rephrase and display problems as 3 times what equals 6? 3\times ___ = 6? Have children explain their thinking to the group.”

• Enrichment, “To apply children’s understanding of multiplication and division, have them complete two-rule Frames-and-Arrows puzzles on Math Masters, page 196. Note the rules will not always alternate ABAB. Have children color-code their arrows with crayons to distinguish one rule from another. When children finish, have them discuss their solution strategies and explain any useful patterns they identified while solving.”

• Extra Practice, “To provide additional practice with multiplication and division facts, have children generate sets of multiplication facts and compare strategies used to solve them. Some children may benefit from a small strip of tape to secure the fact wheel to their slate.”

• English Language Learner, Beginning ELL, “Use gestures to scaffold the terms Caller, Calculator, and Brain from Beat the Calculator. Point to your mouth and a multiplication fact and say: I am the Caller. I will call out a fact. I will not say the answer. Point to a child’s head and say: You are the Brain. You will solve the problem in your head. Point to the calculator and demonstrate entering the multiplication fact as you point to another child and say: You are the Calculator. You will solve the multiplication fact on the calculator.”

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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 3 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:

• Unit 1, Math Tools, Time, and Multiplication, Challenge, Problem 2, “Don and Molly played Number-Grid Difference. The object of the game is to have the lower sum of 5 scores. Don picked 3 and 5 and made the number 35. Molly picked 8 and 5. What number should Molly make? Explain your answer.”

• Lesson 6-3, Taking Inventory of Know Fact Strategies, Enrichment, “To extend children’s application of multiplication strategies, have them choose strategies and develop rules to multiply 11 by single-digit numbers on Math Masters, page 193.”

• Lesson 7-6, Fractions on a Number Line, Part 2, Enrichment, “To apply children’s understanding of fractions greater than 1, have them locate fractions between whole numbers on a number line. Ask children to defend the placement of their fractions and make changes as needed.”

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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 3 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 4-11, (Day 1): Building a Rabbit Pen, Focus: Solving the Open Response Problem, Problem 1, students draw two rectangles with a given perimeter and different areas for a rabbit pen. “Miguel wants to build a rectangular pen for his rabbit. He has 24 feet of fence that he can use to make the pen. He plans to use all 24 feet of fence to make the best pen he can for his rabbit. Use the grid to draw at least 2 different pens that Miguel could build.” Problem 2, “Find the area of each pen and record it inside the pen.”

• Lesson 6-5, Exploring Geometry Problems, Measurement Data and Polygons, Focus: Exploring with Straws and Twist Ties, Math Journal 2, Problems 1-3, students create quadrilaterals to match descriptions. “For each problem, use straws, and twist ties to make the shape. Then draw a picture of your shape. 1. Make a rhombus that is not a square. 2. Make a quadrilateral that is both a parallelogram and a rhombus. 3. Make a different quadrilateral.”

• Lesson 9-3, Using Mental Math to Multiply, Practice: Home-Link, Problem 1, students use a number model and words to show how to multiply. “Solve each problem in your head. Use number models and words to show your thinking. The mass of one California condor is 9 kilograms. What is the mass of twelve 9-kilogram California condors?”

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 consider how they are doing on the unit’s focus content. Examples include:

• Assessment Handbook, Unit 2, Number Stories and Arrays, 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. “Solve extended facts. Solve number stories by adding or subtracting. Check whether my answer makes sense. Solve equal-group and array number stories. Solve division number stories. Solve Frames-and-Arrows problems.”

• 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 3 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 1-3, Tools for Mathematics, Focus: Reviewing Length Measurement, Teacher’s Lesson Guide, “Have partners discuss how to use rulers to measure the lengths of line segments to the nearest inch or centimeter. Have children independently complete journal page 5 using appropriate math tools.”

• Lesson 4-10, Playing the Area and Perimeter Game, Focus: Playing The Area and Perimeter Game, Teacher’s Lesson Guide, “Have partners play The Area and Perimeter Game. Children should independently record their turns on Math Masters, page G16 and keep track of their calculations on paper.”

• Lesson 6-1, Trade-First Subtraction, Focus: Practicing Trade-First Subtraction, Teacher’s Lesson Guide, “Have children work independently or in partnerships to solve the problems on journal page 190 while you circulate to check their progress.“

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

The 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 3-5, Counting-Up Subtraction, Differentiation Options, English Language Learner Beginning ELL, “Display a number line vertically, with the smaller numbers at the bottom. Demonstrate counting up as you move your hand up along the number line. Orally and with gestures, direct children to count up on a number line. For example, say, Count up from 25, gesturing to 25, then 26, 27, 28, and so on as children count. Once children can count up as you gesture, point to a number and have them count up without gestures. Provide for oral practice by asking children short-response questions, such as: How will you count?”

• Lesson 6-3, Taking Inventory of Known Fact Strategies, Differentiating Lesson Activities, Analyzing Multiplication Facts Strategies, “Scaffold to help partnerships think together about the facts to identify efficient and appropriate strategies for solving them, as well as to plan for using multiple representations to communicate their thinking. Post a menu of questions and response starters. For example: Partner A: Does this fact remind you of other facts we already know? Partner B: It reminds me of ___ Do you agree? Do you think we should try the ___ strategy? Partner A: I think/don’t think that strategy would be appropriate because ___Perhaps we could ___ Partner B: Do you think it would be efficient to use the ___ strategy? Partner A: That strategy would/would not help us get the answer quickly.”

• Lesson 8-5, Playing Factor Bingo, English Language Learner Beginning ELL, “Scaffold the terms factor and product to prepare children to play Factor Bingo. Display a multiplication fact. Circle and label the factors, and then underline and label the product. Draw a square around the multiplication symbol and label it groups of, times, and multiplied by. Point to the labels as you explain the directions for the game.”

• 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 3 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 Cieo, Judi, Sai, and Imani, 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 3 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 3-3, Partial-Sums Addition, Focus: Adding with Partial Sums, Differentiation and English Learners Support, “Prepare an anchor chart, titled Partial-Sums Addition, where children can see each step written numerically and in words. Provide individual copies for children to use as a guide as they solve and talk about problems.”

• 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.

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

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

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

• Student Resource Book, Geometry, Page 211, students examine two flags as they distinguish the prefix in polygon names to determine the number of sides it has. “The flag of Nepal is the only flag in the world with five sides. All other flags have four sides. The flag of Switzerland has a white cross with an edge that is a dodecagon (12 sides).”

• Lesson 9-7, The Length-of-Day Project, Revisited, Focus: Calculating Length of Day Around the World, Math Journal 2, Problem 1, students calculate the lengths of days in world locations. “Find the length of day for Esperanza Base, Antarctica, on June 21, 2016. Show your world. Sunrise time: ___. Sunset time: ___. Elapsed time: ___.”

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 partially provide supports for different reading levels to ensure accessibility for students.

• Lesson 1-4, Number Lines and Rounding, Focus: Using Number Lines to Round, Academic Language Development, “Ask children to demonstrate or restate sentences, such as: I will choose a round shape. Round up your classmates. Let’s play a round of Top-It. Point out to children that they will be learning about the mathematical meaning of the word round, which will add to other meanings they already know for that word.”

• Lesson 5-4, Recognizing Helper Facts, Focus: Identifying Helper Facts, Academic Language Development, “Deepen children’s understanding of the phrase take inventory by role-playing. Direct children to take inventory of items, such as the books they have in their desks, the number and the color of pencil they have, or the items in their math toolkit. Discuss the value of occasionally taking inventory. Extend children’s ideas to taking inventory of the multiplication facts they know.”

• Lesson 8-1, Measuring to the Nearest \frac{1}{4} Inch, Focus: Measuring to the Nearest \frac{1}{4} Inch, Academic Language Development, “Have partnerships use the 4-Square Graphic Organizer (Math Masters, page TA20) to deepen their understanding of the term precisely. Suggest the following quadrant headings: Picture, Non-Example, and My Definition.”

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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 2-8, (Day 1): Picturing Division, Focus: Solving the Open Response Problem, materials reference use of counters and drawings. “Make slates, markers, and counters available so children can act out the problem, but remind them to record drawings and words that describe their thinking on paper.”

• Lesson 5-2, Representing Fractions, Focus: Math Message, materials reference use of fraction circles. “The pink fraction circle piece is the whole. Show 1-third of the pink piece. Explain to your partner how you know it shows 1-third.”

• Lesson 7-4, Fraction Stirps, Focus: Math Message, materials reference use of fraction strips. “Cut out five fraction strips. Each strip is one whole. Fold one strip in half. What fraction names each part of the strip?”

#### 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 3 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.

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for providing manipulatives, both virtual and physical, that are accurate representations of the mathematical objects they represent and, when appropriate, are connected to written methods.

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 2-8, (Day 1): Picturing Division, Focus: Solving the Open Response Problem, materials reference use of counters and drawings. “Make slates, markers, and counters available so children can act out the problem, but remind them to record drawings and words that describe their thinking on paper.”

• Lesson 5-2, Representing Fractions, Focus: Math Message, materials reference use of fraction circles. “The pink fraction circle piece is the whole. Show 1-third of the pink piece. Explain to your partner how you know it shows 1-third.”

• Lesson 7-4, Fraction Stirps, Focus: Math Message, materials reference use of fraction strips. “Cut out five fraction strips. Each strip is one whole. Fold one strip in half. What fraction names each part of the strip?”

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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.”

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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.

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

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

The materials reviewed for Everyday Mathematics 4 Grade 3 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 1-1, Number Grids, 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, Contents, Grades- 3-4, Games Correlation, shows where games are utilized within the lesson.

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

## 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

## Report for {{ report.grade.shortname }}

### Overall Summary

###### Alignment
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###### Usability
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##### Gateway {{ gateway.number }}
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