The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for assessing grade-level content. Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year. Above-grade-level assessment items are present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials.

Examples of aligned assessment items include but are not limited to:

• 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)

There are some above-grade-level assessment items that can be omitted or modified. These 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 x 5 = 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 x 0 = _____, (45 - 12) x 0 = ______. b. Explain why the two number sentences have different answers.” (5.OA.1)

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for spending a majority of instructional time on major work of the grade. For example:

• 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 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.

The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 68% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of supporting standards/clusters connected to the major standards/clusters of the grade include but are not limited to:

• In Lesson 1-12, Teacher’s Lesson Guide, 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.”  
• In Lesson 2-4, Teacher’s Lesson Guide, 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. 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?” 
• In Lesson 3-7, Teacher’s Lesson Guide, 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?” 
• In Lesson 4-6, Student Math Journal, students measure 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.”
• In Lesson 5-3, Teacher’s Lesson Guide, 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). In the Math Message, 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.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations that the amount of content designated for one grade level is viable for one year. 

Recommended pacing information is found on page xxii of the Teacher’s Lesson Guide and online in the Instructional Pacing Recommendations. As designed, the instructional materials can be completed in 169 days, however the Pacing Guide states 170 days:

• There are 9 instructional units with 108 lessons. Open Response/Reengagement 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.

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for being consistent with the progressions in the Standards. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades and present extensive work with grade-level problems. The instructional materials relate grade-level concepts with work in future grades, but there are a few lessons that contain content from future grades that is not clearly identified as such.

The instructional materials relate grade-level concepts to prior knowledge from earlier grades. Each Unit Organizer contains a Coherence section with “Links to the Past”. This section describes “how standards addressed in the Focus parts of the lessons link to the mathematics that children have done in the past.” Examples include:

• Unit 4, 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, 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, Teacher’s Lesson Guide, Links to the Past,”3.MD.4: In Unit 4, children measured lengths to the nearest 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.”  

The instructional materials relate grade-level concepts with work in future grades. Each Unit Organizer contains a Coherence section with “Links to the Future”. This section identifies what students “will do in the future.” Examples include:

• Unit 4, Teacher’s Lesson Guide, Links to the Future, “3.MD.6: In Unit 5, children will explore using square units to make the different shapes with the same area.”
• Unit 6, 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, 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.”

In some lessons, the instructional materials contain content from future grades that is not clearly identified as such. Examples include:

• In Lesson 2-9, Teacher’s Lesson Guide, 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.
• In Lesson 8-3, Teacher’s Lesson Guide, 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 x 4 = 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”).
• In Lesson 8-6, Teachers Lesson Guide, 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 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.

Examples of the materials giving all students extensive work with grade-level problems include:

• In Lesson 3-4, Math Journal 1, Column Addition, “Estimate. Then use column addition to solve Problems 1 and 2. Use any strategy to solve Problem 3. Use your estimates to check whether your answers make sense. Problem 1, 67 + 25 = ? Estimate:  ” (3.OA.8, 3.NBT.2)
• In Lesson 8-1, Math Journal 2, Problem 1. “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 name for the point you labeled $$\frac{1}{2}$$?.” (3.NF.2,3)

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

Materials include learning objectives that are visibly shaped by CCSSM cluster headings. Focus and Supporting Clusters addressed in each section are found in the Table of Contents, the Focus portion of each Section Organizer, and in the Focus portion of each lesson. Examples include:

• The Lesson Overview for Lesson 3-3, “Children use partial-sums addition to add 2- and 3-digit numbers,” is shaped by 3.NBT.A, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”
• The Lesson Overview for Lesson 4-6, “Children identify and measure perimeters of rectangles and other polygons,” is shaped by cluster heading 3.MD.B, “Represent and interpret data.”
• The Lesson Overview of Lesson 6-4, “Children self-assess their automaticity with multiplication facts,” is shaped by 3.OA.A and 3.OA.C, “Represent and solve problems involving multiplication and division, and multiply and divide within 100.”
• The Lesson Overview for Lesson 7-6. “Children identify fractions greater than, less than, and equal to one on a number line,” is shaped by 3.NF.A, “Develop understanding of fractions as numbers.”

The materials include problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important. Examples include:

• Lesson 5-6 connects 3.OA.B with 3.MD.C as students use doubling and halving strategies to solve number stories involving area. In the Student Math Journal, Problem 4, “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.” 
• Lesson 7-12 connects 3.NF.A and 3.OA.A as students name fractions for a set of objects. In the Teacher’s Lesson Guide, “Jules has a stamp collection with 12 stamps. She puts ½ of her stamps on one page and the other ½ on another page. How many stamps are on each page? You may use counters or drawings to help.” 
• Lesson 8-7 connects 3.MD.C with 3.OA.B as students create rectangles using given area measures. In Activity Card 91, students, “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?”

The instructional 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 which includes Planning for Rich Math Instruction. This component indicates where conceptual understanding is emphasized within each lesson of the Unit. Lessons include Focus, “Introduction of New Content”, designed to help teachers build their students’ conceptual understanding. The instructional materials include problems that develop conceptual understanding throughout the grade level, especially where called for in the standards (3.OA.1 and 3.OA.2). Examples include:

• In Teacher’s Lesson Guide, Lesson 1-8, Multiplication Strategies, Focus, students make sense of representations for equal-groups and array number stories. The teacher is directed to address conceptual understanding, “Bring the class together and introduce the Fact Strategy Wall as a place to record strategies for solving multiplication and division problems. Record children’s suggestions on the Fact Strategy Wall under a heading for today’s focus, such as "Strategies for Equal-Groups Problems". For example, draw pictures of equal groups, draw pictures of arrays, use addition, and use skip counting. You may also wish to post children's work directly on the Fact Strategy Wall. Encourage children to refer to the Fact Strategy Wall to help them choose efficient strategies as they complete the problems in the next activity.” (3.OA.1)
• In Teacher’s Lesson Guide, Lesson 2-6, Equal Groups, Focus-Math Message, students solve problems of equal groups. “Use your slate. Solve: You have 4 packages of pencils. There are 6 pencils in each package. How many pencils in all? Show your thinking with drawings, words, or number models.” (3.OA.1)
• In Student Reference Book, Lesson 2-12, Exploring Fraction Circles, Liquid Volume, and Area, 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.” (3.OA.2)
• In Student Math Journal, Lesson 5-11, Multiplication Facts Strategies: Break-Apart Strategy, 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 x 8 = ___ x ____ + ____ x ___.” (3.OA.1)
• In Teacher’s Lesson Guide, 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?” (3.OA.2)

The materials provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. These include problems from Math Boxes, Home Link, and Practice. Examples include:

• In Math Masters, Lesson 1-9, Introducing Division, Home Link, Problems 3 and 4, “3. Think of things at home that could be shared equally by your family. Record them on the back of this page. 4. Write a number story about equally sharing one of the things you wrote for Problem 3. Use the back of this paper. Then solve your number story.” (3.OA.2)
• In Math Masters, Lesson 2-6, Equal Groups, Home Link, students develop conceptual understanding when they 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 costs $2. 1. If you buy 6 packs, how many markers will you have?” (3.OA.1)
• In Math Masters, Lesson 5-3, Equivalent Fractions, Home Link, students develop conceptual understanding of fraction equivalence (3.NF.3). The directions indicate, “The pictures show three kinds of fruit pie. Use a straight edge to do the following: 1. Divide the peach pie into 4 equal pieces. Shade 2 of the pieces. 2. Divide the blueberry pie into 6 equal pieces. Shade 3 of the pieces. 3. Divide the strawberry pie into 8 equal pieces. Shade 4 of the pieces.” Later, students “Explain to someone at home how you know that all of the fractions on this page are equivalent.” 
• In Math Masters, 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. ‘$$\frac{2}{3}$$’” (3.NF.1)
• In Math Masters, 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.” (3.OA.2)

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for attending to those standards that set an expectation of procedural skill and fluency.

The instructional materials develop procedural skill and fluency throughout the grade level. Each Unit begins with Planning for Rich Math Instruction where procedural skills and development activities are identified throughout the unit. Each lesson includes Warm-Up problem(s) called Mental Math Fluency. These provide students with a variety of leveled problems to practice procedural skills. The Practice portion of each lesson provides students with a variety of spiral review problems to practice procedural skills from earlier lessons. Additional procedural skill and fluency practice is found in the Math Journal, Home Links, Math Boxes, and various games. Examples include:

• In Teacher's Lesson Guide, Lesson 2-11, Framers and Arrows, Mental Math and Fluency focuses 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 x 8, 8 + 5, 5 x 4, 9 + 7, 5 x 9.” This activity provides an opportunity for students to develop fluency of 3.OA.7, “Fluently multiply and divide within 100,” and 3.NBT.2, “Fluently add and subtract within 1,000.”
• In Teacher’s Lesson Guide, Lesson 3-3, Partial-Sums Addition, Focus, students develop procedural skill with addition by expanding addends. “Display 145 + 322 in the vertical form. Ask: What is the expanded form of each addend?” This activity provides an opportunity for students to develop 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.”
• In Teacher’s Lesson Guide, Lesson 3-9, Exploring Multiplication Squares, Focus, students solve multiplication squares and record products. “Have children practice multiplication squares as they complete the Rolling and Recording Squares activity. For example, if you roll a 4, think aloud: 4 x 4 = what number? I can count by 4’s: 4, 8, 12, 16. 4 x 4 =16.” This activity provides an opportunity for students to develop fluency of 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”
• In Teacher’s Lesson Guide, Lesson 5-9, Multiplication Facts Strategies: Near Squares, Math Message, students solve problems to build fluency with multiplying and dividing within 100. “Kali knows 7 x 7 = 49. How could she use 7 x 7 as a helper fact to figure out 8 x 7?” This activity provides an opportunity for students to develop fluency of 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”
• In Teacher’s Lesson Guide, Lesson 6-2, Playing Baseball Multiplication, is devoted to building multiplication fact fluency as students learn how to play the game Baseball Multiplication. “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.” This activity provides an opportunity for students to develop fluency of 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division.”

The instructional materials provide opportunities to independently demonstrate procedural skill and fluency throughout the grade level as identified in 3.OA.7, “Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division,” and 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.” Examples include:

• In Student Math Journal, Lesson 2-4, Multistep Number Stories, Part 2, Student Math Journal, students solve multi-step number stories using multiplication. Problem 2, “A package of rice cakes contains 6 rice cakes. You buy 5 packages of rice cakes. You give 15 rice cakes away. How many rice cakes do you have now?” (3.OA.7,8)
• In Student Math Journal, Lesson 2-8, Picturing Division, students add fluently using strategies or the standard algorithm. 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.” (3.NBT.2)
• In Teacher’s Lesson Guide, Lesson 7-6, Fractions on a Number Line, Part 2, Practice, students practice multiplication facts by playing Baseball Multiplication. The directions in the Student Reference book include, “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.” (3.OA.7)
• An online game, Facts Workshop, focuses on building fluency with addition and subtraction (3.NBT.2). For example, 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). 
• An online game, Division Arrays, builds fluency with multiplication and division within 100 (3.OA.7) and interpreting whole-number quotients of whole numbers (3.OA.2). 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.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 partially meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied. The materials do not provide opportunities for students to independently engage in non-routine applications of mathematics throughout the grade level.

Examples of students engaging in routine application of mathematics include:

• In Teacher’s Lesson Guide, Lesson 3-11, Adding a Group, Focus, Math Message, students use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities. For example, “Suppose you are arranging chairs for a class show. On a half-sheet of paper, sketch 5 rows with 4 chairs in each row. Write a number model that shows the total number of chairs.” (3.OA.3)
• In Student Math Journal, Lesson 5-10, Button Dolls: Solving a Number Story, students interpret whole-number quotients of whole numbers (3.OA.2) and multiply and divide within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (3.OA.3) as they apply division. For example, “There are 10 children on Maurice’s baseball team. The coach gives each child 2 granola bars from a package of 24 bars. The coach gets the leftover granola bars. How many granola bars does Maurice’s coach get? What do you need to find out? Use words or pictures to show what you know about the problem and how to solve it.” 
• In Student Math Journal, Lesson 6-6, Multiplication and Division Diagram, students use multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities as they write equations and solve number stories. Problem 3, “There are 7 boxes of golf balls. Each box has the same number of balls. There are 63 total golf balls. How many golf balls are in each box?” (3.OA.4,6,7)
• In Student Math Journal, Lesson 6-9, Writing Number Stories, students solve a two-step word problem and represent the problem using equations with a letter standing for the unknown quantity. For example, “Quincy played 3 soccer games. In each game, he scored 2 goals. How many more goals does Quincy need to score a total of 10 goals? 10 - (3 x 2) = G Explain to a partner how the number model fits the number story.” (3.OA.8)

The instructional materials provide opportunities for students to independently demonstrate the use of mathematics flexibly in a variety of contexts. Examples include:

• In Math Masters, Lesson 2-6, Equal Groups, Home Link 2-6, students interpret products of whole numbers. Problem 3, “Make up a number story to match the number sentence below: 1 x 5 = 5.” (3.OA.1)
• In Assessment Handbook, Unit 2 Assessment, students solve two-step word problems using the four operations. Problem 7, “Jeremiah read the number story below. Then he drew a picture and wrote two number models to help keep track of his thinking. ‘Mr. Riley has 2 packs of pencils with 5 pencils in each pack.  He gives 4 of the pencils to his students. How many pencils does he still have?’ Do Jeremiah’s number models fit the story? Explain your answer.” (3.OA.8).
• In Math Masters, Lesson 7-1, Liquid Volume, Home Link 7-1, students measure and estimate liquid volumes and masses of objects using standard units of grams (g), kilograms (kg), and liters (l). Students add, subtract, multiply, or divide to solve one-step word problems involving masses or volumes that are given in the same units. For example, “Estimate the liquid volume of a clean dinner plate: about ___mL. If you have a measuring tool marked with milliliters, find the liquid volume of your dinner plate by measuring how much water it holds before spilling over the edges: about ___ mL. On the back of this page, explain how you found the liquid volume of the dinner plate.” (3.MD.2)
• In Math Masters, Lesson 8-6, Sharing Money, Home Link 8-6, students interpret whole-number quotients of whole numbers and use multiplication and division within 100 to solve word problems involving money. For example, “1. 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 $___.”  (3.OA.2,3,7)

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the instructional materials. Student practice includes all three aspects of rigor, though there are fewer questions for conceptual understanding. 

There are instances where conceptual understanding, procedural skill and fluency, and application are addressed independently throughout the instructional materials. Examples include:

• In Teacher’s Lesson Guide, Lesson 2-1, Extended Facts: Addition and Subtraction, Math Message, students use basic addition and subtraction facts to solve multi-digit problems, emphasizing procedural skills. “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.” (3.NBT.2)
• In Math Masters, Lesson 3-4, Column Addition, students apply what they learned about column addition to solve mileage problems. Problem 2, “Tony drives from Washington, D.C., to Cleveland on Friday. He drives back on Sunday. How many miles did Tony drive all together?” (3.NBT.2)
• In Teacher’s Lesson Guide, Lesson 3-10, The Commutative Property of Multiplication, Math Message, students develop conceptual understanding of the Commutative Property of Multiplication as students sketch arrays. “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.” (3.OA.1, 3.OA.3)

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

• In Math Masters, Lesson 4-7, Area and Perimeter, Home Link, students apply their knowledge of finding the perimeter of their bedroom while demonstrating conceptual understanding. “Your pace is the length of one of your steps. 2. 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. 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.” (3.MD.5a,7a,8)
• In Student Math Journal, Lesson 5-4, Recognizing Helper Facts, students use procedural skills and fluency to solve an application problem. Problem 1, “Savannah earns $5 selling lemonade. Jessica earns double the amount of money that Savannah earns. How much money do they have together?” (3.OA.8)
• In Teacher’s Lesson Guide, Lesson 6-6, Multiplication and Division, Focus, Introducing Multiplication/Division Diagrams, “Students will use a multiplication/division diagram to organize the number of groups, the number in each group, and the total in each number story.” Students use conceptual understanding and procedural skill and fluency as they solve real-world application problems. “Anna has 8 bags of rubber bands. Each bag has the same number of rubber bands. Anna has 56 rubber bands in all. How many rubber bands are in each bag? Record an equation to match the story and then solve. What do you understand from reading the story? What do we know? What do we need to find out?” (3.OA.2,3,4,6,7)

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for identifying the Standards for Mathematical Practice and using them to enrich mathematics content within and throughout the grade level.

The Implementation Guide states, “The SMPs (Standards for Mathematical Practice) are a great fit with Everyday Mathematics. The SMPs and Everyday Mathematics both emphasize reasoning, problem-solving, use of multiple representations, mathematical modeling, tool use, communication, and other ways of making sense of mathematics. To help teachers build the SMPs into their everyday instruction and recognize the practices when they emerge in Everyday Mathematics lessons, the authors have developed Goals for Mathematical Practice (GMP). These goals unpack each SMP, operationalizing each standard in ways that are appropriate for elementary students.”  

All MPs are clearly identified throughout the materials, with few or no exceptions. Examples include:

• In the Teacher’s Lesson Guide, Unit Organizer, Mathematical Background: Process and Practice, provides descriptions on how the Standards for Mathematical Practices are addressed in the unit and what mathematically proficient students should do. 
• The Unit 6 Organizer identifies MP1, “Make sense of problems and persevere in solving them.” “In order to make sense of a problem, children must learn to decipher the information that is given in the problem. They must determine what is known and what the problem is asking them to find out. Situation diagrams provide a framework to guide children as they make sense of the roles different numbers play in the number stories.” 
• Lessons identify the Math Practices within the Warm Up, Focus, and Practice sections.

The MPs are used to enrich the mathematical content. Examples include:

• MP1 is connected to mathematical content in Lesson 6-6, More Operations, as students write a number story that matches a number model with a letter. In the Student Math Journal, Problem 2, “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.”
• MP2 is connected to mathematical content in Lesson 3-5, Counting-Up Subtraction, as students reason about numbers represented on number lines and in number sentences. In the Teacher’s Lesson Guide, Unit 3 Organizer, “In Lesson 3-5 children represent counting-up subtraction as a series of ‘jumps’ on open number lines and with a string of number sentences. In Lessons, 3-9 through 3-12 children represent multiplication facts as arrays. When working to derive multiplication facts, children connect number models with the array representation. Providing opportunities to make connections among different representations can enable children to make sense of an unfamiliar representation by explicitly relating it to familiar ones.”
• MP4 is connected to mathematical content in Lesson 9-7, The Length-Of-Day Project, as students use information from a scaled bar graph. In the Teacher’s Lesson Guide, Unit 9 Organizer, “In Lesson 9-7 children revisit the Length-of-Day Graph showing data they have collected throughout the year. Children use the information on the scaled bar graph to compare the lengths of days throughout the school year. Children also interpret length-of-day graphs with data from cities in different parts of the world. They connect the data with the location of the cities on maps to draw conclusions about the lengths of day in regions in the Northern and Southern Hemisphere and closer to the Equator.”
• MP7 is connected to mathematical content in Lesson 3-10, The Commutative Property of Multiplication, as students develop a rule, “turn-around rule”, for multiplication. In the Teacher’s Lesson Guide, Unit 3 Organizer, “In Lesson 3-10 children explore their array representations of multiplication facts to discover the Commutative Property of Multiplication (the turn-around rule). Later in this lesson, children look for patterns in the multiplication facts table, and connect these patterns with square numbers and facts related by the turn-around rule.”
• MP8 is connected to mathematical content in Lesson 8-3, Multiplication and Division, as students look for and discuss generalizations about factors and multiples. In the Student Math Journal, Problem 6, “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?”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 partially meet expectations for carefully attending to the full meaning of each practice standard. The materials attend to the full meaning of most of the MPs, but they do not attend to the full meaning of MP5 as students do not get to choose tools strategically.

Examples of the materials attending to the full meaning of most MPs include:

• MP1: In Lesson 2-3, More Number Stories, Teacher’s Lesson Guide, students make sense of strategies used when solving 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?”
• MP2: In Lesson 5-3, Equivalent Fraction, students generate equivalent fractions. Student Math Journal, Problem 1, “Partition each circle in the name-collection box to show different ways to represent $$\frac{1}{2}$$. Then add other equivalent fraction names.” Students reason quantitatively about equivalent fractions, then draw representations to show what they look like.
• MP4: In Lesson 1-8, Multiplication Strategies, students solve equal group number stories using different strategies. Student Math Journal, Problem 2, “For other number stories, draw sketches to show your solutions and write number models.” For example, Teacher’s Lesson Guide, “There are 6 bicycles at the park. Each bicycle has 2 wheels. How many wheels are there in all?” Students model real-world situations by using a sketch and a number model to illustrate understanding.  
• MP6: In Lesson 4-10, Playing The Area and Perimeter Game, students use precise language as they find the area and perimeter of a rectangle. Student Math Journal, “Talk to a partner about this rectangle. List all the ways you could find the area. List all the ways you could find the perimeter.” Students attend to precision by discussing the different strategies they could use to find perimeter and area. 
• MP7: In Lesson 2-1, Extended Facts: Addition and Subtraction, students look for and use structure to solve addition and subtraction problems. In Student Math Journal, Problem 5, “Explain how you used a basic fact to help you solve Problem 4.” Problem 4 states, “14 - 9 = ?, 24 - 9 = ?, 54 - 9 = ?”
• MP8: In Lesson 7-8, Finding Rules for Comparing Fractions, students write a rule to determine where a fraction is greater or less than $$\frac{1}{2}$$. In Student Math Journal, Problem 2, “With a partner, write a rule that Steve can use to check where a fraction is greater or less than $$\frac{1}{2}$$.” Students recognize patterns in sets of fractions.

Examples of the materials not attending to the full meaning of MP5 because students do not get to choose tools strategically include:

• In Lesson 2-12, Focus: Introducing Fraction Circles, students compare liquid volumes of containers, “Have children follow directions on Activity Card 33 and explain how the 1-liter breaker helps them compare the liquid volume different containers can hold.” 
• In Lesson 6-4, Focus: Introducing Beat the Calculator, students play a game to learn their multiplication facts, “Review how to find products using a calculator. Display a multiplication fact, such as 4 x 6 =____. Tell children to press 4 x 6 = to find the answer.”
• In Lesson 8-2, Practice: Measuring Book Heights, students use a tape measure or ruler to measure book heights, “Have children choose three books from the classroom. Then have them use their toolkit tape measure or ruler to measure the heights of their books to the nearest $$\frac{1}{4}$$ inch and complete journal page 257. Have them decide where the books will fit on a new classroom bookcase.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for prompting students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. 

Student materials consistently prompt students to construct viable arguments. Examples include:

• In Lesson 3-2, Estimating Costs, Math Message, Student Math Journal, students analyze the thinking of others. In Strategies for Estimation, “Rosa makes an estimate for the addition problem below. She uses numbers that are close to the numbers in the problem but are easier to use. ‘322 + 487 = ?’ Another problem is provided in the thought bubble: ‘320 + 490 = 810’ 1. Explain Rosa’s thinking to a partner. 2. Make a different estimate. What close-but-easier numbers could you use? Write a number sentence in the thought bubble to show your thinking.” 
• In Lesson 6-10, Order of Operations, Student Math Journal, students construct a viable argument when they explain to their partner why they picked their answer. Problem 5, “Circle the answer that makes the number sentence true. 2 x (4 + 3 x 2) = ?. a. 28, b. 20, c. 14. Explain to a partner why you picked your answer.” 
• In Lesson 7-2, Exploring Arrays, Volume, and Equal Shares, Math Masters, students construct a viable argument when they compare two different ways of dividing a room equally. The same size shape is divided in two different ways. The square is divided in half with a vertical line down the middle. The other same size square is divided into half with a diagonal line. “Mariana says that they both get the same amount of space. Use words or drawings to explain how Mariana can prove that both drawings divided the room into the same amount of space. You may cut out the drawings of the two rooms on page 227 and fold or cut apart the pieces to compare the parts of the room.” 
• In Lesson 8-4, Setting Up Chairs, Math Masters, Home Link, Problem 1, students solve “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. Which way do you think is better? Explain your reasoning.” 

Student materials consistently prompt students to analyze the arguments of others. Examples include:

• In Lesson 3-14, Progress Check, Assessment Handbook, “Mia wants to solve this problem: 552 - 153 = ? She begins by making an estimate. 550 - 150 = 440. Then she uses 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.” Students must find and explain the mistake someone made in a subtraction problem. 
• In Lesson 7-2, Exploring Arrays, Volume, and Equal Shares, Home Link, Math Masters, students explain if two fraction cards are equivalent. Problem 1, “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.”
• In Lesson 7-7, Comparing Fractions, Practice, Student Math Journal, “Gail says the liquid volume of container C is less than the liquid volume of Container A. She says that container C holds less water because it is wide and short, and container A holds more because it is taller. Kerod says all three of their containers have the same amount of volume. Do you agree with Gail or Keron? Explain your thinking.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations for assisting teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

The Teacher’s Lesson Guide assists teachers in engaging students in constructing viable arguments and/or analyzing the arguments of others throughout the program. Many of the activities are designed for students to work with partners or small groups where they collaborate and explain their reasoning to each other. Examples include:

• In Lesson 1-10, Foundational Multiplication Facts, Teacher’s Lesson Guide, Focus: Math Message, teachers facilitate a discussion between students regarding how many dots there are without counting. “Focus on helping children make sense of each other’s thinking and strategies with prompts such as: Did everyone understand Rebecca’s strategy? Explain it in your own words. How could you try Rebecca's strategy on the image?”
• In Lesson 2-11, Frames and Arrows, Teacher’s Lesson Guide, teachers are provided with guidance to help students analyze the arguments of their peers. “Select children to share both effective and ineffective strategies during the follow-up discussion. Encourage the class to repeat the strategies in their own words and to ask questions to help them make sense of others’ strategies. You may wish to provide children with sentence stems such as: I notice… I wonder… How did you… Why did you…”.  
• In Lesson 2-12, Exploring Fraction Circles, Liquid Volume, and Area, Teacher’s Lesson Guide, students explore fraction circles. “Encourage children to make and confirm predictions about part-whole relationships between different fraction circle pieces.  Ask: What fraction of a ______ piece is a ______ piece?  How do you know?” 
• In Unit 3 Open Response Assessment, Teachers Lesson Guide,  teachers are provided the following guidance, “This open response problem requires children to apply skills and concepts from Unit 3 to find a mistake in a subtraction problem. The focus of this task is GMP 3.2: Make sense of others’ mathematical thinking. Before starting the problem, tell children that they will make sense of another child’s work on a subtraction problem and find and explain a mistake.”
• In Unit 7, Open Response Assessment, Teacher’s Lesson Guide, teachers support students to reflect on their arguments and the arguments of others. “After children complete their work, discuss their arguments. You may wish to use this as an opportunity to review and discuss conjectures and arguments. The statements or claims that Demitrius and Emma made comparing the amount of pizza they ate are conjectures. The drawings and words that children used to tell how each statement could be correct are arguments. Ask: What was Demitrius’s claim or conjecture? What was your argument that Demitrius was correct? What was Emma’s claim or conjecture? What was your argument to support her conjecture?” 
• In Lesson 7-10, Justifying Fraction Comparisons, Teacher’s Lesson Guide, teachers allow students to work with a partner and use fraction tools to help name equivalent fractions and justify answers with an explanation. “Have children use their fraction strips and the Fraction Number-Line Poster on journal page 229 (or the Class Fraction Number-Line Poster) to show that $$\frac{1}{6}$$ > $$\frac{1}{8}$$ with other tools. Invite volunteers to justify the comparison with each representation. For example: $$\frac{1}{6}$$ is a larger part of the whole strip than $$\frac{1}{8}$$. $$\frac{1}{6}$$ is farther from 0 (or closer to 1) on the number line than $$\frac{1}{8}$$.”  “As they work, ask them to justify their answer by explaining how each fraction tool models the equivalence.”   
• In Lesson 8-4, Setting Up Chairs, Teacher’s Lesson Guide, teachers facilitate a discussion between students regarding which child’s conjecture is correct in regards to their conjectures on how many total chairs there are in the room. The teacher displays a student's work and then begins the discussion. “What is this child’s conjecture? What is this child’s argument? Explain in your own words. Why did this child use only one clue in his or her argument? Do you agree with this argument? What mathematical reasoning did this child use in the argument? How can this argument be improved?”

The instructional materials reviewed for Everyday Mathematics 4 Grade 3 partially meet expectations for explicitly attending to the specialized language of mathematics. The materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols, but there are instances when the materials use mathematical language that is not precise or appropriate for the grade level.

The Section Organizer provides a vocabulary list of words to be used throughout lesson discussions. Each lesson contains a vocabulary list, Terms to Use, and vocabulary words appear in bold print in the teacher notes. Some lessons incorporate an Academic Language Development component that provides extra support for the teacher and students. Additionally, the Teacher’s Lesson Guide contains a detailed glossary with definitions and images where appropriate. Examples of explicit instruction on how to communicate mathematical thinking include:

• In Lesson 2-6, Focus: Equal Groups, Teacher’s Lesson Guide, “Remind children that groups with the same number of objects are called equal groups.”

• In Lesson 4-5, Focus: Special Quadrilaterals, Teacher’s Lesson Guide, “Review the definition of a quadrilateral as a polygon that has four sides. Look for examples of each of the following subcategories, or types of quadrilaterals: squares, rectangles, parallelograms, rhombuses, trapezoids, and kites.”
• In the Student Reference Book, “Fractions that name the same amount or name the same distance from 0 are called equivalent fractions. Equivalent fractions are equal because they name the same number. Example: Eight children go to a party. Two are girls. Six are boys.$$\frac{1}{4}$$ of the children are girls. $$\frac{2}{8}$$ of the children are girls. $$\frac{1}{4}$$ of the children are the same as $$\frac{2}{8}$$ of the children.” 
• In the Student Reference Book, “An array is a group of objects arranged in equal rows and columns. Each row is filled and has the same number of objects. Each column is filled and has the same number of objects.”

Examples of the materials using mathematical language that is not precise or appropriate for the grade level include:

• In the 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.” 
• In the 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.”
• In the 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.”
• In the 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.” 
• In Lesson 3-6, Focus: Reviewing Expand-and-Trade Subtraction, Teacher’s Lesson Guide, “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.”