## Everyday Mathematics 4

##### v1.5
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Our Review Process

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 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 meet expectations for practice-content connections.

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

### Focus & Coherence

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5 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 5 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, “How many cubes would it take to fill this prism? ____ cubes; What is the volume of this prism? ____ cubic units.” A rectangular prism partially filled with cubes is shown. (5.MD.3, 5.MD.4)

• Unit 2 Assessment, Item 3, “a. Jesse collects cans for recycling. When he has 1,500 cans, the recycling center will pick them up from his house. Jesse has 120 bags with about 35 cans in each bag. Should he call the recycling center to arrange a pick-up? Explain how you know. b. Did you have to find an exact answer to solve Problem 3a? Explain why or why not.” (5.NBT.5)

• Unit 4 Assessment, Item 19, “Gina is donating money to her neighborhood food pantry. Her aunt agreed to donate two dollars more than Gina donates. The table below shows some of the possible amounts of money they may donate. a. Write the data in the table above as ordered pairs. b. Plot the ordered pairs as points and use a straightedge to connect them.” A table of values is shown. (5.G.2)

• End-Of-Year Assessment, Item 12, “Reed’s class is painting a giant chessboard on the playground. A chessboard consists of 64 squares arranged in 8 rows and 8 columns. His class is making each square \frac{1}{3} m by \frac{1}{3} m. a. What will be the length and width of the chessboard in meters? Show your work. b. What will be the area of the completed chessboard? Show your work. Give your answer in square meters. c. How could you use the number of squares on the chessboard to find the area of the chessboard in square meters?” (5.NF.4b)

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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 5 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards.

Instructional 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 1-10, Visualizing Volume Units, Focus: Converting Volume Units, Math Journal 1, Problem 3, students convert between cubic units, ”a. How many cubic inches do you think are in a cubic foot? b. How many inches are in a foot? c. How many square inches are in a square foot? How did you find your answer? d. How many cubic inches are in a cubic foot? How did you find your answer?” Lesson 2-6, Application: Unit Conversions, Teacher’s Lesson Guide, Focus, Converting Miles to Feet, students convert miles to feet using a provided chart, “Display a two-column table labeled Miles and Feet. Fill in the numbers 1-5 in the Miles Column and complete the first two rows of the Feet column. How many feet of fencing would the rangers need for a 3-mile section of path?” The Table Chart shows Miles 1, 2, 3, 4, 5 and Feet 5,280, 10,560, ?, ?, ?. Students engage in extensive work with grade-level problems for 5.MD.1, “Convert like measurement units within a given measurement system.”

• Lesson 2-12, Strategies for Choosing Partial Quotients, Focus: Using Partial-Quotients Division with Lists of Multiples, Math Journal 1, students use lists of multiples to find partial quotients and use area models, “For Problems 1-4, make an estimate. Then use partial-quotients division to solve. Show your work. You make a list of multiples on Math Masters, page TA10 to help you. 1. 1,647 / 28 ? Estimate: ___ Answer: ___. 2. 4,319 / 42 ? Estimate: ___ Answer: ___. 3. 2,628 / 36 ? Estimate: ___ Answer: ___. 4. 9,236 / 41 ? Estimate: ___ Answer: ___. 5. Paul drew the area model at the right for his solution to Problem 1. What partial quotients did he use to solve the problem?” Lesson 4-4, Comparing and Ordering Decimals, Practice, Interpreting Real-World Remainders, Math Journal 1, students interpret remainders, “Solve each number story. Show your work. Explain what you decided to do with the remainder. 1. Bre earned 189 tickets playing different games at the fair. If each prize cost 15 tickets, how many prizes can Bre get? Number Model: ___. Quotient: ___. Answer: Bre can get ___ prizes. Circle what you did with the remainder. Ignored it, Reported it as a fraction, Rounded the quotient up. Why? ___.” Students engage in extensive work with grade-level problems for 5.NBT.6, “Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division. Illustrate and explain the calculation by using equations, rectangular arrays, and/or area models.”

• Lesson 5-9, Understanding an Algorithm for Fraction Multiplication, Focus: Multiplying Fractions, Math Journal 2, students practicing using a fraction multiplication algorithm, “1. In your own words, describe a method for multiplying fractions discovered in class. Use the fraction multiplication algorithm described above to solve Problems 2-7. 2. \frac{1}{2}\star\frac{3}{6}. 3. \frac{2}{3}\star\frac{1}{4}. 4. \frac{3}{5}\star\frac{1}{6}. 5. \frac{3}{4}\star\frac{3}{8}. 6. \frac{2}{5}\star\frac{4}{10}. 7. \frac{7}{9}\star\frac{2}{12}. For Problems 9 and 10, write a number model. Then solve. 9. Sheila had \frac{3}{4} pound of blueberries. She used \frac{1}{3} of them in a fruit salad. How many pounds of blueberries did she use? Number model: ___. Answer: ___ pound. 10. the mirror in a dollhouse is \frac{2}{4} inch wide and \frac{3}{4} inch tall. What is the area of the mirror in square inches? Number model: ___. Answer: ___ square inch.” Students engage in extensive work with grade-level problems for 5.NF.4, Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.”

The instructional materials provide opportunities for all students to engage with the full intent of Grade 5 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 1-9, Two Formulas for Volume, Focus: Find a Second Volume Formula, Practice: Math Journal 1, students use multiplication to solve for volume, “Use a formula to find the volume of each prism. Record the formula you used. 1. A rectangular prism is shown with 8 cubes in length, 5 cubes for width, and 4 cubes to show height. Volume: ____. Formula: ____.” Lesson 1-11, Volume Exploration, Focus, Estimating Volumes of Musical Instrument Cases, Math Journal 1, students find the volume of figures composed of rectangular prisms by adding the volumes of prisms, “In Problems 1-3, use the mathematical models to estimate the volume of the instrument cases. 1. Trombone case. The volume of the trombone case is about ___ in^3.” The measurements are 8 in., 4 in., 10 in., 9 in., 4 in., and 31 in. Try This, Problem 4, “Asher needs to take the xylophone, the trombone, and the French horn with him to a band concert. His trunk has 13 cubic feet of cargo space. Can he fit all three cases in his trunk? Explain how you know.” Students engage in the full intent of 5.MD.5, Relate volume to the operations of multiplication and addition and solve real-world and mathematical problems involving volume.”

• Lesson 4-1, Decimal Place Value, Reading and Writing Decimals, Practice: Math Journal 1, students read and write decimals to thousands using place value, “Write the following decimals in words. Use the place-value chart on journal page 112 to help you. 1. 0.67, 2. 3.8, 3. 3.622, 4. 0.804. Write each decimal using numbers. Record them on the place-value chart on page 112. Then write the value of 4 in each decimal. 5 a. four and eight tenths. b. 4 is worth ___. 6 a. forty-eight hundredths. b. 4 is worth. 7. a. forty-eight thousandths. b. 4 is worth. 8. a. six and four hundred eight thousandths. b. 4 is worth.” Lesson 4, Comparing and Ordering Decimals, Practice, Math Masters, students practice comparing decimals to thousandths, “Darryl and Charity are playing Decimal Top-It. Their record sheet is shown below. 1. Compare their decimals for each round and write >, <, or = in the middle column. Use the place-value chart above to help you. Round 1, Player 1- Darryl 0.378 ___ Player 2- Charity 0.860. Problem 3a. Put Darryl’s decimals in order from least to greatest. 0.378, 0.9, 0.804, 0.547, and 0.72. 3b. Put Charity’s decimals in order from least to greatest. 0.860, 0.59, 0.92, 0.6, and 0.098.” Students engage in the full intent of 5.NBT.3, “Read, write, and compare decimals to thousandths.”

• Lesson 7-5, A Hierarchy of Triangles, Focus: Making a Triangle Hierarchy, Practice: Math Journal 2, students define a triangle hierarchy to classify triangle cards, “On the left, write the categories and subcategories from the triangle hierarchy you created in class. Use the hierarchy to classify your triangle cards. When you are finished, glue or tape the cards in place.” Students have Triangles, Isosceles triangles, and Equilateral triangles as their triangle hierarchy. Problem 4, “a. All ___ have three sides and three angles. b. All ___ have at least two sides of the same length. c. All ___ have a line of symmetry.” Lesson 7-6, A Hierarchy of Quadrilaterals, Practice, students use the quadrilateral hierarchy to answer questions. Math Masters, “1. Fill in the blanks. a. All ___ are ___, but not all ____ are ____. b. All ____ are ____, but not all ___ are ___. c. All ___ are ____ but not all ____ are ___. 2. a. All parallelograms have two pairs of parallel sides. Does this mean that all rectangles have two pairs of parallel sides? Explain how you can tell by looking at the hierarchy. b. All trapezoids have at least one pair of parallel sides. Explain how you can tell by looking at the hierarchy.” Students engage in the full intent of 5.G.4, “Classify two-dimensional figures in a hierarchy based on properties.”

#### Criterion 1.2: Coherence

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

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• There are 8 instructional units, of which 6 units address major work of the grade or supporting work connected to major work of the grade, approximately 75%.

• There are 113 lessons, of which 88.5 address major work of the grade or supporting work connected to the major work of the grade, approximately 78%.

• In total, there are 170 days of instruction (113 lessons, 37 flex days, and 20 days for assessment), of which 95.5 days address major work of the grade or supporting work connected to the major work of the grade, approximately 56%.

• 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 instructional materials. As a result, approximately 78% of the instructional 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 5 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 2-7, U.S, Traditional Multiplication, Part 3, Focus: Estimating and Multipying, students write simple expressions that record calculations with numbers and interpret numerical expressions without evaluating them (5.OA.2) and fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5). Teachers guide students through this problem, “Display the work shown to the right. Ask: Do you think 384 is the correct answer for 64 x 15? How do you know? Interpret the expression 64 x 15 without evaluating it. 64 x 15 is equivalent to a number that is 15 times as large as 64. Ten times as much as 64 is 640, so that means that 64 x 15 is greater than 640. Since 384 is less than 640, it cannot be the correct answer.”

• Lesson 3-8, Renaming Fractions and Mixed Numbers, Math Journal 1, students write and interpret numerical expressions (5.OA.A) and apply and extend previous understandings of multiplication and division (5.NF.B). Students use an equal-grouping interpretation of division to explore connections between fractions and division. Problem 1 states, “Write a division expression to model each story, then solve. You can use fraction circles or draw pictures to help. Olivia is running a 3-mile relay race with 3 friends. If the 4 of them each run the same distance, how many miles will each person run?”

• Lesson 6-4, Line Plots, Focus: Creating and Interpreting a Line Plot with Fractional Pencil-Length Data, students make a line plot to display a data set of measurements in fractions of a unit (5.MD.2) and add and subtract fractions with unlike denominators (including mixed numbers) (5.NF.1). Students measure the length of their pencils to the nearest 1/4 inch and collect data about the lengths of their peers’ pencils. Then students use this data to make a line plot and answer questions about the data. Teacher prompt states, “What is the difference in length between the longest pencil and the shortest pencil?”

• Lesson 8-1, Planning an Athletic Center, Focus: Finding Areas of Playing Surfaces, Math Journal 2, students convert like measurements within a given measurement system (5.MD.1) and fluently multiply multi-digit whole numbers using the standard algorithm (5.NBT.5). Problem 2 states, “The town has 4 acres of land to use for an athletic center. The land is a rectangle with a length of 160 yards and a width of 121 yards. The town wants the athletic center to have a variety of sports playing surfaces. You have been asked to help decide which playing surfaces should be included and how the surfaces should be arranged. Explain how you and your group created your plan.”

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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 5 Grade 5 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 4-11, Addition and Subtraction of Decimals with Hundredths Grid, Math Journal 1, Problems 1 and 2, students use grids to solve decimal addition and subtraction problems, “Shade the grid in one color to show the first addend. Shade more of the grid in a second color to show the second addend. Write the sum to complete the number sentence.” 1. “$$0.6+0.22=$$ ____? 2. 0.18+0.35= ____?” This connects the major work of 5.NBT.A, “Understand the place value system” to the major work of 5.NBT.B, “Perform operations with multi-digit whole numbers and with decimals to hundredths.”

• Lesson 5-10, Identifying and Visualizing Patterns, Math Journal 2, Problem 2, students compare rules from different problems and determine how the rules affect the graph, “a. A rule is given at the top of each column in the table below. Use the rules to fill in the columns. In (x) Rule: +6: 0, ?, ?, ?, ?. Out (y) Rule +2: 0, ?, ?, ?, ?. b. What rule relates each in number to its corresponding out number? 3. Think about the rules you used to fill in the in and out columns. Why did the rule you found in Part b make sense? d. Write the numbers from the table as ordered pairs. Then graph them. Draw a line to connect the points.” This connects the supporting work of 5.OA.B, “Analyze patterns and relationships” to the supporting work of 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.”

• Lesson 6-2, Playing Exponent Ball: Focus: Exponent Ball, students learn to play a game to multiply and divide decimals by powers of 10, and compare decimals and whole numbers. students learn the game. Directions from the game include, “If the card is black, multiply your starting number by the power of 10. If the card is red or blue, divide your starting number by the power of 10. Write an expression to show how to multiply or divide your number. Then find the value of the expression.” This connects the major work of 5.NBT.A “Understand the place value system” to the major work of 5.NBT.B, “Perform operations with multi-digit whole numbers with decimals to hundredths.”

• Lesson 7-11, Rules, Tables, and Graphs, Part 1, Focus: Displaying Data on a Graph, students relate operations with fractions to operations with whole numbers. Teachers use the following example with students, “$$4\frac{2}{3}\star7=4\star7+\frac{2}{3}\star7$$.” This connects the major work of 5.NBT.B, “Perform operations with multi-digit whole numbers” to the major work of 5.NF.B, “Apply and extend previous understandings of multiplication and division.”

• Lesson 8-1, Planning an Athletic Center, Math Message, students perform operations with multi-digit whole numbers and apply and extend previous understandings of multiplication and division to multiply and divide fractions. Students convert measurements to find the area of an Olympic beach volleyball court, “The dimensions of an official Olympic volleyball court are 52 feet 6 inches by 26 feet 3 inches. Find the area of the court in square feet.” This connects the major work of 5.NBT.B, “Perform operations with multi-digit whole numbers and with decimals to hundredths” to the major work of 5.NF.B, “Apply and extend previous understandings of multiplication and division to multiply and divide fractions.”

• Lesson 8-2, Applying the Rectangle Method for Area, Math Journal 2, Problems 3-6, students create a table, rule, and graph to model a situation, “Write the numbers from the table in Problem 1 as ordered pairs. Remember to use parentheses and a comma in each ordered pair. Then graph the ordered pairs on the coordinate grid. Draw a line to connect the points. 4. Use the table. How much will 3 pounds of supplies cost? 5. Use the rule from 2a. How much will 10 pounds of apples cost? 6. Use the graph. How much will 6 pounds of apples cost?” This connects the supporting work of 5.OA.B, “Analyze patterns and relationships” to the supporting work of 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.”

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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 5 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 1, Area and Volume, Teacher’s Lesson Guide, Links to the Past, “5.OA.1: In Grade 3, students inserted parentheses into number sentences and solved number sentences containing parentheses.”

• Unit 5, Operations with Fractions, Teacher’s Lesson Guide, Links to the Past,”5.NF.5, 5.NF.5a: In Unit 4, students made conjectures about how an image on a coordinate grid would change based on multiplying one or more of the coordinates. In Grade 4, students interpreted multiplication equations as comparisons.”

• Unit 7, Multiplication of Mixed Numbers; Geometry; Graphs, Teacher’s Lesson Guide, Links to the Past, “5.NF.4, 5.NF.4b: In Unit 1, students used informal strategies to find areas of rectangles with fractional side lengths. In Unit 5, students represented products as rectangular areas as they learned procedures for fraction multiplication. In Grade 4, students applied the area formula for rectangles to solve problems.”

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 2, Whole Number Place Value and Operations, Teacher’s Lesson Guide, Links to the Future, “5.OA.1: In Unit 7, students will use grouping symbols in an expression to model how to solve a multistep problem about gauging reaction time. In Grade 6, students will evaluate expressions and perform operations according to the Order of Operations.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Teacher’s Lesson Guide, Links to the Future, “5.NBT.2: In Unit 8, students will multiply and divide numbers by powers of 10 to help them solve rich, real-world problems. In Grade 6, students will write and evaluate numerical expressions with whole-number exponents.”

• Unit 8, Application of Measurement, Computation, and Graphing, Teacher’s Lesson Guide, Links to the Future, “5.MD.1: In Grade 6, students will use ratio reasoning to convert measurement units.”

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

• Lesson 4-13, Decimal Subtraction Algorithms, Math Masters, Decimal Subtraction Algorithms, Focus, Extending Whole-Number Subtraction Algorithms to Decimals, “Students practice using decimal subtraction algorithms and use estimates to check the reasonableness of their answers (5.NBT.7).” Problem 2, “Find the page in your Student Reference Book that shows how to use your algorithm to subtract decimals. Write the page number below. Read the example. Then use your algorithm to solve 9.48-7.291. Record your work in the space at the right.” Since one of the numbers includes the thousandths place, this problem aligns to 6.NS.3, fluently adding, subtracting, multiplying, and dividing multi-digit decimals using the standard algorithm for each operation.

• Lesson 8-3, Planning an Aquarium, Focus: Choosing a Fish Tank, Math Journal 2, “Students use area and volume guidelines to choose a tank (5.MD.5).” The image provided shows two fish tanks, and students find the volume of each fish tank. Fish Tank B provides fractional side lengths. Problem 1, “Choose the fish tank that you want for your aquarium. Fish Tank B: Side lengths include 16 in., 6\frac{1}{2} in., 10 in., 10\frac{1}{2} in., 8 in., 20 in.” Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism aligns to 6.G.2.

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

The materials reviewed for Everyday Mathematics 4 Grade 5 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 instructional materials can be completed in 170 days:

• There are 8 instructional units with 113 lessons. Open Response/Re-engagement lessons require 2 days of instruction adding 8 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 20 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.

### Rigor & the Mathematical Practices

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5 meet expectations for rigor. The materials develop conceptual understanding of key mathematical concepts, give attention throughout the year to procedural skill and fluency, and spend sufficient time working with engaging applications of mathematics. There is a balance of the three aspects of rigor within the grade.

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

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 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 instructional materials include problems that develop conceptual understanding throughout the grade level, especially where called for in the standards. Examples include:

• Lesson 2-7, U.S. Traditional Multiplication, Part 3, Focus: Introducing U.S. Traditional Multiplication with 2-Digit Factors, Math Journal 1, Problem 5, students use the U.S. traditional multiplication to multiply 2-digit numbers by 2-digit numbers and estimation to determine whether their products make sense. “Complete the area model. Explain how it relates to your work for Problem 3. Area model.” Students create an area model for 87\times46 by breaking 46 into 40 and 6. Students develop a conceptual understanding of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 4-11, Addition and Subtraction of Decimals with Hundredths Grids, Focus: Subtracting Decimals with Grids, Math Journal 1, students discuss strategies for using grids to solve decimal subtraction problems. “Problem 4, “ 0.74-0.36=? Problem 5, Choose one of the problems above. Clearly explain how you solved it.” Students develop a conceptual understanding of 5.NBT.7, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.”

• Lesson 5-4, Subtraction of Fractions and Mixed Numbers, Practice: Math Journal 2, Problem 1, students compare decimals and shade grids to represent the decimals. “Shade the first grid to represent one-tenth. Shade the second grid to represent ninety-nine thousandths. Write <, >, or = to make a true number sentence. 0.1 ___ 0.099.” Students develop a conceptual understanding of 5.NBT.3, “Read, write, and compare decimals to thousandths.”

• Lesson 5-9, Understanding an Algorithm for Fraction Multiplication, Focus: Math Message, Math Journal 2, Problem 8, students find how many total parts and how many shaded parts in an area model while using patterns to derive a fraction multiplication algorithm. “Choose one of the above problems. Draw an area model for the problem. Explain how it shows that your answer is correct.” Students can choose from these problems: \frac{1}{2}\star\frac{3}{6}, \frac{2}{3}\star\frac{1}{4}, \frac{3}{5}\star\frac{1}{6}, \frac{3}{4}\star\frac{3}{8}, \frac{2}{5}\star\frac{4}{10}, or \frac{7}{4}\star\frac{2}{12}.” Students develop conceptual understanding of 5.NF.4 “Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.”

Home Links, Math Boxes, and Practice provide opportunities for students to independently demonstrate conceptual understanding throughout the grade. Examples include:

• Lesson 3-9, Introduction to Adding and Subtracting Fractions and Mixed Numbers, Home Link, Problem 2, students draw pictures and use number lines to solve mixed-number addition and subtraction number stories. “Ethel had 4 feet of ribbon. She used 1\frac{1}{2} feet for a craft project. How many feet of ribbon does she have left?” Students independently demonstrate conceptual understanding of 5.NF.2, “Solve word problems involving addition and subtraction of fractions referring to the same whole, including cases of unlike denominators .”

• Lesson 5-11, Explaining the Equivalent Fraction Rule, Home Link, Problem 3, students use the multiplication rule to find equivalent fractions. “Addison wanted to find a fraction equivalent to \frac{3}{8} with 16 in the denominator. He thought: “$$8\star2=16$$, so I need to multiply \frac{3}{8} by 2.” He got an answer of \frac{3}{16}. a. Is \frac{3}{16} equivalent to \frac{3}{8}? How do you know? b. What mistake did Addison make?” Students independently demonstrate a conceptual understanding of 5.FN.4a, “Interpret the product (\frac{a}{b})\timesq as a part of a partition of q into b equal parts.”

• Lesson 7-7, Playing Property Pandemonium, Practice: Math Boxes, Math Journal 2, Problems 4 and 5, “Problem 4, Which expressions have a value equal to 6? Check all that apply. 6\star\frac{2}{2}, 6\star\frac{8}{7}, \frac{3}{2}\star\frac{6}{1}, 6\star\frac{9}{10}, 6\star1. Problem 5, Explain how you solved Problem 4 without multiplying.” Students independently demonstrate conceptual understanding of 5.NF.5, “Interpret multiplication as scaling.”

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

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 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 2-8, U.S. Traditional Multiplication, Part 4, Focus: Extending U.S. Traditional Multiplication to Larger Numbers, students learn how to solve 2-digit numbers multiplied by 2-digit numbers. “Display the problem 417\star99. Have students work independently or in partnerships to solve it in two ways: using partial-products multiplication and using US traditional multiplication ” Students develop procedural skill and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 3-13, Fraction-Of Problems, Part 1, Practice: Student Reference Book, students practice multiplying fractions and whole numbers by playing the game Fraction Of, “Players take turns. On your turn, draw 1 card from each deck. Place the cards on your gameboard to create a fraction-of problem. The fraction card shows what fraction of the whole you must find. The whole card offers 3 possible choices. Choose a whole that will result in a fraction-of problem with a whole-number answer.” Students develop procedural skills and fluency of 5.NF.4, “Apply and extend previous understandings of multiplication to multiply a fraction or whole number by a fraction.”

• Lesson 4-7, Playing Hidden Treasure, Practice: Math Journal 1, Problem 6, students estimate and solve problems using U.S. traditional multiplication, “$$511\star219$$.” Students develop procedural skills and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 6-9, Multiplication of Decimals, Focus: Using Estimation as a Strategy for Decimal Multiplication, students multiply decimals as if they were whole numbers and use estimation to place decimal points in the products. “Display the following problems: 1.2\star0.8=?; 1.2\star8=?; 12\star8=? What do you notice about the factors in all three problems? Do you think this pattern is true for all multiplication problems with factors that have the same digits in the same order?” Students develop procedural skills and fluency of 5.NBT.7, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used,” and 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

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

• Lesson 3-1, Connecting Fractions and Division, Part 1, Home Link, Problem 4, students make an estimate and solve problems using the standard algorithm of multiplication, “$$2,598\times3$$” and Problem 5, “$$417\times63$$.” Students independently demonstrate procedural skill and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 4-7, Playing Hidden Treasure, Practice: Math Journal 1, Problem 1, students solve problems using the standard algorithm for multiplication, “$$25\times11$$” and Problem 4, “Another student estimated and began solving problems 4-6 using U.S. traditional multiplication. Finish solving the problems.” Students independently demonstrate procedural skill and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 5-5, Connecting Fraction-Of Problems to Multiplication, Practice; Math Boxes, Math Journal 2, Problem 6, students use the standard algorithm of multiplication to solve problems involving multi-digit numbers. “Estimate and solve. 912\times87=?” Students independently demonstrate procedural skill and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Multiplication Top It, online game, students multiply 2-digit numbers by 2 or 3-digit numbers and compare the products. “Directions: Players multiply the numbers shown on gems, then compare the products. The player with the greater product takes all of the gems. Players earn points for correctly multiplying the numbers on their gems, comparing the products, and having the greater product.” Students independently demonstrate procedural skill and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

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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 6 meet expectations for being designed so that teachers and students spend sufficient time working with engaging applications of the mathematics.

Materials include multiple routine and non-routine applications of mathematics throughout the grade level. Focus activities introduce new content, provide routine exercises, review recent learning, and provide challenging problem-solving tasks that help build conceptual understanding, procedural skill and fluency, and application of mathematics. Open Response lessons provide challenging problems that involve more than one strategy or solution. Home-Links relate to the Focus activity and provide informal mathematics activities for students to do at home. Examples of routine and non-routine applications of the mathematics include:

• Lesson 3-5, Game Strategies, Focus: Solving the Open Response Problem, Problem 2, students create a rule for making the largest possible fraction. “Write a rule you can use to make the largest possible fraction with any 3 number cards. Explain why your rule works.” This activity provides the opportunity for students to apply their understanding of 5.NF.3, “Interpret a fraction as division of the numerator by the denominator.”

• Lesson 5-5, Connecting Fraction of Problems to Multiplication, Home-Link, Problem 4, students match number models to fraction-division situations. “Erica’s garden has an area of 24 square feet. She will use \frac{3}{4} of the space for vegetables and \frac{1}{4} of the space for flowers. How much space will she use for vegetables?” This activity provides the opportunity for students to apply their understanding of 5.NF.6, “Solve real world problems involving multiplication of fractions and mixed numbers.”

• Lesson 7-10, Identifying and Visualizing Patterns, Focus: Visualizing Patterns and Relationships, Math Journal 2, Problem 3, students form ordered pairs using corresponding terms of two sequences and graph them in a real-world problem. “a. Use the rules to fill in the column. In (x), Rule: - 1, 5, ___, ___, ___, ___. Out (y), Rule: - 3, 15, ___, ___, ___, ___. b. What rule relates each in number to its corresponding out number? c. Write the numbers from the table as ordered pairs. Then graph the ordered pairs. Draw a line to connect the points.” This activity provides the opportunity for students to apply their understanding of 5.G.2, “Represent real world and mathematical problems by graphing points in the first quadrant of the coordinate plane, and interpret coordinate values of points in the context of the situation.”

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 2b, “to be used after Lesson 2-13”, Problem 2, students write division number stories. “Write a number story that can be modeled with the expression 197\div12 that has a different solution than the number story you wrote for Problem 1. Solve your number story. Explain why your solution is different.” This activity provides the opportunity for students to independently demonstrate understanding of 5.NBT.6, “Find whole-number quotients of whole numbers with up to four-digit dividends and two-digit divisors, using strategies based on place value, the properties of operations, and/or the relationship between multiplication and division.”

• Independent Problem Solving 4a, “to be used after Lesson 4-9”, Problem 1, students compare batting averages using place value understanding with decimals to thousandths. “A batting average in softball is calculated by dividing a player’s number of hits by the player’s number of at-bats. A batting average is typically reported as a decimal rounded to the nearest thousandths place. Caroline has 3 hits and 7 at-bats. Vivien has 42 hits and 117 at-bats. Find each player’s batting average. You may use a calculator. Caroline’s batting average: ___. Vivien’s batting average: ___. Make an argument for why Caroline is a better batter than Vivien. Make an argument for why Vivien is a better batter than Caroline.” This activity provides the opportunity for students to independently demonstrate understanding of 5.NBT.3, “Read, write, and compare decimals to thousandths”, and 5.NBT.4, “Use place value understanding to round decimals to any place.”

• Independent Problem Solving 5b, “to be used after Lesson 5-14”, Problem 1, students use division of fractions by whole numbers to solve problems. “The librarian, Mr. Gates, received a shipment of new books. He put half the books on the shelves in the library. He put \frac{2}{3} of the other half on a book display in the hallway. The remaining books were split equally among the 6 fifth-grade teachers. What fraction of the entire shipment of books did each fifth-grade teacher receive? Show your work and explain your thinking.” This activity provides the opportunity for students to independently demonstrate understanding of 5.NF.7, “Apply and extend previous understandings of division to divide unit fractions by whole numbers and whole numbers by unit fractions.”

• Independent Problem Solving 7b, “to be used after Lesson 7-12”, Problem 1, students use multiplication strategies to solve fraction problems. “The Smith School student council is collaborating with a local artist to create a tile mosaic. The space they have for the mosaic is 6\frac{1}{2}feet long and 4\frac{1}{2}feet in height. The student council has to select the tiles they are going to use. They have narrowed it down to 2 choices described in the table below. The student council would prefer to choose the tile that costs less so that they have money left over for other projects. Which tile should the student council choose? Explain your answer.” This activity provides the opportunity for students to independently demonstrate understanding of 5.NF.6, “Solve real world problems involving multiplication of fractions and mixed numbers.”

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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 5 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 Grade 7. Examples where instructional materials attend to conceptual understanding, procedural skill, and fluency, or application include:

• Lesson 2-6, Application: Unit Conversions, Home-Link, Problem 6, students practice multiplying multi-digit whole numbers. “$$377\star4=?$$” Students develop procedural skills and fluency of 5.NBT.5, “Fluently multiply multi-digit whole numbers using the standard algorithm.”

• Lesson 3-1, Connecting Fractions and Division, Focus: Creating Other Models for Fair Share Stories, Math Journal 1, Problem 3, “A school received a shipment of 4 boxes of paper. The school wants to split the paper equally among its 3 printers. How much paper should go to each printer?” Students extend their conceptual understanding of 5.NF.3, “Interpret a fraction as division of the numerator by the denominator ($$\frac{a}{b}=a\div b$$). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.”

• Lesson 4-6, Introduction to the Coordinate System, Home-Link, Problem 4, students use addition to solve number stories involving decimals. “At the 2012 Summer Olympics in London, Usain Bolt won the men’s 100-meter race with a time of 9.63 seconds and the men’s 200-meter race with a time of 19.32 seconds. How long did it take the sprinter to run the two races combined?” Students engage in the application of 5.NBT.7, “Add, subtract, multiply, and divide decimals to hundredths, using concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction; relate the strategy to a written method and explain the reasoning used.”

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

• Lesson 2-3, Applying Powers of 10, Focus: Estimating with Powers of 10, Math Journal 1, Problem 1, students estimate with powers of 10 to solve multiplication problems while checking the reasonableness of products. “A hardware store sells ladders that extend up to 12 feet. The store’s advertising says: Largest inventory in the country? If you put all our ladders end to end, you could climb to the top of the Empire State Building! The company has 295 ladders in stock. The Empire State Building is 1,453 feet tall. Is it true the ladders would reach the top of the building? Explain how you solved the problem.” Students engage with conceptual understanding and application of 5.NBT.2, “Explain patterns in the number of zeros of the product when multiplying a number by powers of 10, and explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.”

• Lesson 4-4, Comparing and Ordering Decimals, Interpreting Real-World Remainders, Math Journal 1, Problem 2, students solve division number stories and interpret the remainders, “Elisabeth is 58 inches tall. What is her height in feet? Number model: Quotient: Remainder: Answer: Elisabeth is ___ feet tall. Circle what you did with the remainder. Ignored it, Reported it as a fraction, Rounded the quotient up; Why?” Students engage with procedural skill and application of 5.NF.3, “Interpret a fraction as division of the numerator by the denominator ($$\frac{a}{b}=a\div b$$). Solve word problems involving division of whole numbers leading to answers in the form of fractions or mixed numbers.”

• Lesson 5-7, Fractions of Fractions, Focus: Finding Fractions of Fractions, students find fractions of whole numbers and fractions of fractions as they make sense of and solve problems, “Larry has \frac{1}{2} of a fruit bar. He wants to give \frac{1}{2} of what he has to his brother. What part of a whole fruit bar will Larry give to his brother? Tell students they will use a sheet of paper to represent Larry’s fruit bar. Have them fold it in half vertically and then unfold it. Demonstrate to students how to orient their sheet so that the fold line is vertical, and ask them to shade in \frac{1}{2}. Ask: If the paper is an entire fruit bar, what does the shaded part of the paper model represent? What part of the \frac{1}{2} fruit bar are we trying to find? Have students fold their sheets in half in the opposite direction, unfold them, and orient the sheets so that the new fold is horizontal...” Teachers finish the activity by having students shade in the \frac{1}{2} of a \frac{1}{2} to demonstrate how much of the whole Larry is giving his brother.” Students engage with procedural skill and conceptual understanding of 5.NF.4a, “Interpret the product (a/b) × q as a parts of a partition of q into b equal parts; equivalently, as the result of a sequence of operations a × q ÷ b.”, 5.NF.4b, “Find the area of a rectangle with fractional side lengths by tiling it with unit squares of the appropriate unit fraction side lengths, and show that the area is the same as would be found by multiplying the side lengths. Multiply fractional side lengths to find areas of rectangles, and represent fraction products as rectangular areas.”, and 5.NF.6, “Solve real-world problems involving multiplication of fractions and mixed numbers, e.g., by using visual fraction models or equations to represent the problem.”

#### 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 5 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 5 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 2-1, Understanding Place Value, Home-Link, Problem 2, students analyze and make sense of place value problems to solve number riddles. “I have 5 digits. My 9 is worth 9+10,000. My 2 is worth 2 thousand. One of my 7s is worth 70. The other is worth 10 times as much. My other digit is a 6. What number am I?”

• Lesson 3-6, Fraction Estimation with Number Sense, Home-Link, Problem 2, students utilize fraction number sense to determine if their answers make sense. “Renee calculated \frac{3}{6}+\frac{2}{4} and said the answer was \frac{5}{10}. Josie solved the same problem and said the answer was 1. Whose answer is more reasonable? Explain how you know.”

• Lesson 6-3, Application: Converting Measurement in the Metric System, Focus: Converting Metric Units, Math Journal 2, Problem 4, students make sense of information in different problems to make metric unit conversions. “There are 43 milligrams of caffeine in a bottle of ice tea. How many grams of caffeine is that? Answer the questions below to solve. a. What units do you need to convert? b. How are those units related? c. Write your answers to Parts a and b in the “What’s My Rule?” table. Fill in the rule. d. How many grams is 43 milligrams?” Teacher’s Lesson Guide, “Draw students’ attention to Problem 4. Point out how this problem required them to convert a measurement to solve a real-world problem. Ask: How did you decide which units you needed to convert?”

• Independent Problem Solving 8a, “to be used after Lesson 8-7”, Problem 1, students analyze and make sense of problems as they use estimation strategies. “Plastic pollution is considered a pressing environmental issue. Some scientists estimate that plastic waste makes up 80% of the pollution in the oceans. One source of plastic waste is bottled water. One estimate is that in the United States alone, 1,500 bottles of water are consumed each second! Another estimate is that only about 2 out of every 10 water bottles are recycled. The rest are thrown away. Use this information to estimate how many bottles of water are thrown away in the United States every month. Assume that 1 month has 30 days. Show your work and explain your thinking. You may use a calculator to help you.”

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 1-5, Introduction to Volume, Practice: Math Boxes, Math Journal 1, Problem 3, students consider units involved in a problem and attend to the meaning of quantities as they find the area of a rectangle. “Jo’s closet is 6 ft wide and 1\frac{1}{2} ft deep. Find the area of the closet floor.” Problem 5, “Explain how you found the area of Jo's closet floor in Problem 3.”

• Lesson 4-1, Decimal Place Value, Focus: Extending Place-Value Patterns to the Thousandths Place, students make sense of representations to model decimal numbers. “Students consider a picture of a large square (representing 1) and then 10 strips or 100 small squares that compose the large square, using language like 10 times and \frac{1}{10} of to describe the relative sizes of the squares and strips. Abstracting from these ideas, they represent decimals on a place-value chart and with numerals. What might \frac{1}{10} of the small square look like?”

• Lesson 5-8, Area Models for Fraction Multiplication, Focus: Math Message, students represent situations symbolically as they solve fraction-of problems by using folding paper strategies. “Fold and shade a sheet of paper to find \frac{2}{3} of \frac{2}{3}.” Focus, Making Sense of Area Models, Teacher’s Lesson Guide, “How should we label the other tick marks? Why? How does this area model show the product of \frac{2}{3} and \frac{2}{3}?”

• Lesson 7-1, Multiplication of Mixed Numbers, Part 1, Focus: Solving Mixed-Number Multiplication Problems, Math Journal 2, Problem 2, students understand the relationships between problem scenarios and mathematical representations as they multiply fractions and mixed numbers. “Use the rectangle to make an area model. Label the sides. Find and list partial products. Label the partial products in the area model. Add the partial products to find your answer. you may need to rename fractions with a common denominator. 2\frac{3}{5}\star\frac{1}{4}=?

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

The materials reviewed for Everyday Mathematics 4 Grade 5 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 6-8, Estimating Decimal Products and Quotients, Focus, Math Message, students justify their strategies and thinking as they make conjectures about the relative size of a decimal product based on the factors. “You know that 2.4\star1=2.4. Will 2.4\star1.8 be greater than or less than 2.4? How do you know? Share your conjecture and argument with a partner.”

• Independent Problem Solving 3a, “to be used after Lesson 3-7”, Problem 2, students construct mathematical arguments as they divide fractions. “Keiko has a goal of running 10 miles this month. She plans to run on Mondays, Wednesdays, and Fridays. On Mondays she will run \frac{3}{4} mile, on Wednesdays she will run \frac{1}{2} mile, and on Fridays she will run \frac{2}{3} mile. Keiko thinks she will meet her goal of running 10 miles in a month on this training schedule. Do you agree with Keiko? Use words and a drawing to explain why you agree or disagree.”

• Independent Problem Solving 8a, “to be used after Lesson 8-7”, Problem 2, students construct viable arguments as they use place value strategies to multiply. “There are approximately 330 million people in the United States. Problem 1 told you that it is estimated that 1,500 bottles of water are consumed every second in the United States. Does that estimate seem reasonable? Show your work and explain your thinking. You may use a calculator to help you.”

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 1-3, Area and Volume, Focus: Solving the Open Response Problem, Problem 1, students critique the reasoning of others when they use the area to compare. “Allyson and Justin are working together to sew a quilt. Justin wrote down the length and width of the quilt and started to sketch a plan for the design. He showed Allyson his sketch and told her they will use 54 square feet of fabric. Allyson disagrees and says they will only use 13\frac{1}{2} square feet of fabric. Why might Justin think they will use 54 square feet of fabric? Do you agree or disagree with Justin's answer? Why?” Problem 2, “Why might Allyson think they will use 13\frac{1}{2} square feet of fabric? Do you agree or disagree with Allyson’s answer? Why?”

• Lesson 5-9, Operations with Fractions, Focus: Multiplying Fractions, Math Journal 2, Problem 11, students critique the reasoning of others as they multiply fractions. “Ben tried to solve Problem 9 and got the answer \frac{4}{7}. He said, “That can’t be right because \frac{1}{3} is less than \frac{4}{7}.” Do you agree with Ben? Explain.”

• Independent Problem Solving 4b, “to be used after Lesson 4-14”, Problem 2, students critique the reasoning of others as they perform operations with decimals. “Jamella is helping her brother mix green paint to repaint the car he is restoring. They must mix 39.5 pounds of white paint with 0.593 pounds of yellow paint and 0.593 pounds of blue paint. Jamella is trying to figure out how much more white paint she needs than yellow and blue paint together. Her work is below. What was Jamella’s mistake? How would you explain it to Jamella so that she understands how to solve this kind of problem in the future? Use drawings, tools, or pictures in your explanation.”

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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 5 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 5-7, Focus, Finding Fractions of Fractions, students model fractions of fractions by folding paper and using shading to illustrate understanding. Student Math Journal, Problem 2, “Fold paper to help you solve this number story. Carolyn had \frac{1}{3} liter of water. She drank \frac{3}{4} of the water. What part of a liter did she drink? Fold and shade paper to show \frac{1}{3}. Then fold and double-shade it to show \frac{1}{4} of \frac{1}{3}. Add double-shading to your paper to show \frac{3}{4} of \frac{1}{3}. What part of a liter of water did Carolyn drink?”

• Independent Problem Solving 1a, “to be used after Lesson 1-4”, students use the math they know to solve problems and everyday situations as they find areas of rectangles with fractional sides. Independent Problem Solving Masters, Problem 2, “A mosaic is a piece of art created by covering a surface with small pieces of colorful material. Kha-Minh has a box of 36 square tiles with a side length of \frac{1}{3} inch that she would like to use to make a mosaic. She wants the mosaic to be a rectangle and she wants to use all the tiles. Draw and label two different rectangles that Kha-Minh could make. Are the areas of each rectangle the same? Why or why not?”

• Independent Problem Solving 4a, “to be used after Lesson 4-9”, students describe and explain what they do with a model and how it relates to the problem situation. Independent Problem Solving Masters, Problem 2, “Angelo’s mom pays him $5 per hour for doing work in the yard. His mom makes him save half of what he earns in a bank account and lets him spend the other half however he wants. Angelo wants to buy himself a pair of sneakers that cost$75. How many hours will Angelo have to work to earn enough money to buy the sneakers? Use the grid to help you model and solve the problem. Angelo will have to work ___ hours to earn enough money to buy the sneakers. Explain how you used the grid to model the problem.”

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 5-6, Multiplication of Fraction and Whole Numbers, Focus: Discussing Strategies for Multiplying Fractions by Whole Numbers, Math Journal 2, Problem 5, students choose and use appropriate tools as they multiply fractions and whole numbers. “Solve problems 2-5 using any strategy. Show your work. In a classroom, there are 14 cubbies along a wall. Each cubby is \frac{5}{6} foot wide. How long is the line of cubbies?”

• Independent Problem Solving 2a, “to be used after Lesson 2-8”, Problem 2, students recognize both the insight to be gained and limitations of tools and strategies as they convert measurements. “Jamie has a new fitness tracker. Her tracker gives her a goal of taking 10,000 steps each day. Jamie went for a 4-mile run on Saturday. She estimates that when she runs her stride length (the distance from the toe of one foot to the toe of the other foot) is 4 feet. Did Jamie meet her goal of 10,000 steps by running 4 miles? Choose and use an appropriate tool to help you solve the problem. Explain your answer and describe the tool you used.”

• Independent Problem Solving 3b, “to be used after Lesson 3-12”, Problem 1, students recognize both the insight to be gained and limitations of tools and strategies as they solve problems with fractions. “Write a number story to match the following expression. Then solve your number story. Choose and use an appropriate tool to solve your number story. Describe how you used the tool. (3\div4)+2\frac{1}{8}.”

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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 5 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 2-9, (Day 1): One Million Taps, Focus: Solving the Open Response Problem, Problem 1, students attend to precision as they use estimation strategies. “How many seconds do you think it would take to tap your desk 1 million times without any interruptions? Be prepared to tell your partner how you made your guess.” Problem 5, “Estimate the time it would take you to tap your desk 1 million times without any interruptions. Use the time it took you to make 100 taps in your estimate. Use a strategy that is more efficient than Maya’s strategy. Show your strategy on another sheet of paper.” Teacher’s Lesson Guide, “How does your guess for Problem 1 compare to the calculated estimate for Problem 5? Did you calculate the exact time it would take to make 1,000,000,000 taps? Why or why not?”

• Lesson 8-5, Spending 1,000,000, Home-Link, Problem 1, students calculate accurately and efficiently when they use rounding strategies to spend $500 on a camping trip. “You are planning a camping trip for yourself and two friends. After saving money for a few months, you and your friends have$500 to spend on the trip. Use the prices above to plan how you will spend $500. Round each unit cost to find approximate total costs. Write a number sentence in the last column to show how you estimated. Spend as close to$500 as you can.”

• Independent Problem Solving 1a, “to be used after Lesson 1-4”, Problem 1, students attend to precision as they use multiplication strategies to find the area of rectangles that have fractional lengths. “Parnika is helping her father re-tile the wall behind their stovetop, called the backsplash. The backsplash is 2\frac{1}{2} feet wide and 2 feet tall. The tiles they are using are squares with a side length of \frac{1}{4} foot. The tiles are sold in boxes of 15 tiles in each box. a. What is the area of the backsplash? b. How many boxes of tiles should Parnika and her father buy? Show your work and explain your thinking below.”

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

• Lesson 6-6, Applying Volume Concepts, Focus: Comparing Strategies for Finding Volume, Math Journal, Problem 2, students formulate clear explanations as they explain which strategy is more effective when they estimate. “Describe the strategy your group used to estimate the volume of Willis Tower. Explain your strategy as clearly as you can.” Problem 3, “Do you think your group could have used a more efficient strategy? Explain at least one way your strategy could have been more efficient.”

• Independent Problem Solving 2b, “to be used after Lesson 2-13”, Problem 1, students use the specialized language of mathematics as they write a number story using an expression. “Write a number story that can be modeled with the expression 197\div12. Solve your number story and show your work.”

• Independent Problem Solving 8b, “to be used after Lesson 8-10”, Problem 2, students use the specialized language of mathematics as they reason about the volume of a rectangular prism and use precise units in their explanations. “Christopher has the fish tank shown below. When he fills the tank with water, he needs to leave an inch of space at the top. Christopher is trying to decide how many fish he can put in his tank. Remember that for every inch of fish length: The tank must hold at least 230 cubic inches of water. The base of the tank should have an area of at least 30 square inches. Christopher is buying guppies, which grow to a maximum of 2\frac{1}{2} inches in length. What is the greatest number of guppies Christopher should buy? Show your work and explain your thinking.”

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

• Lesson 4-13, Decimal Subtraction Algorithms, Math Journal 1, Problem 7, students must select an algorithm term trade-first subtraction, counting-up subtraction, or the U.S. traditional subtraction and answer questions, “Choose one problem. Think about the algorithm you used. Answer the questions below. How did your choice of algorithm help you get an accurate answer? Was your choice of algorithm the most efficient choice? Why or why not?”

### Usability

The materials reviewed for Everyday Mathematics 4 Grade 5 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 5 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.

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

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

• Teacher's Lesson Guide, Welcome to Everyday Mathematics, explains how the program is presented. “Throughout Everyday Mathematics, emphasis is placed on problem solving in everyday situations and mathematical contexts; an instructional design that revisits topics regularly to ensure depth of knowledge and long-term learning; distributed practice through games and other daily activities; teaching that supports “productive struggle” and maintains high cognitive demand; and lessons and activities that engage all students 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 2, Whole Number Place Value and Operations, Organizer, Coherence, provides an overview of content and expectations for the unit. “In Grade 4, students used partial-products multiplication and lattice multiplication to solve multi-digit multiplication problems. Through Grade 5, students will use U.S. traditional multiplication to solve multiplication problems in mathematical and rich, real-world contexts. In Grade 6, students will use U.S.traditional multiplication to solve multi-digit decimal multiplication problems.”

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 2-5, U.S. Traditional Multiplication, Part 2, Focus: Assessment Check-In, teacher guidance supports students in solving multiplication problems. “Expect most students to be able to solve 423\star3, which does not involve writing any digits above the line, using U.S. traditional multiplication. Some may also be able to solve 2,681\star5, which does involve writing digits above the line and remembering to add them.”

• Lesson 4-3, Representing Decimals in Expanded Form, Focus: Introducing Expanded Form for Decimals, Math Message Follow-Up, teacher guidance connects students' prior knowledge to new concepts. “Ask: What did you notice as you added different colors of shading to your grid? Display a shaded grid for the Math Message problem. Ask: What number do the first 3 columns of shading represent? What number does the 1 square in the second color represent? What number do the 2 tiny rectangles shaded in the third color represent? Point out that the shading shows how 0.3, 0.01, and 0.002 combine to make 0.312. Ask: What operation is used to show combining or putting together? Display the number sentence 0.312=0.3+0.01+0.002. Remind students that this way of writing a number is called expanded form. Highlight how expanded form shows the number broken apart by place value and shows the sum of the value of each digit.”

• Lesson 7-3, Multiplication of Mixed Numbers, Part 2, Common Misconception, teacher guidance addresses common misconceptions as students use tiling to differentiate square foot. “Students may confuse \frac{1}{2} of square foot, as shown in Figure 1, with a \frac{1}{2} foot square (a square that is \frac{1}{2} foot by \frac{1}{2} foot), as shown in Figure 2. When speaking, be sure to differentiate between fractions of a square area and squares with fractional side lengths.”

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

The materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations for containing adult-level explanations and examples of the more complex grade-level concepts and concepts beyond the current grade so that teachers can improve their own knowledge of the subject.

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

• Lesson 1-9, Two Formulas for Volume, Professional Development, explains finding the volume of rectangular prisms. “Counting the cubes that fit into the bottom of a rectangular prism and finding the area of the base of the prism result in the same numerical value, but they are two different measurements. The number of cubes that pack the first layer of a prism is the volume of the first layer, which is a 3-dimensional measurement, while the area of the base is a 2-dimensional measurement. They have the same numerical value because, to find the volume, the area is multiplied by 1 to account for the height of the layer. Multiplying by 1 does not change the numerical value, but it does change the unit of measurement from square units to cubic units, thereby making it a different measurement.”

• Lesson 2-4, U.S. Traditional Multiplication, Part 1, Professional Development, explains the traditional multiplication algorithm. “Everyday Mathematics calls the algorithm introduced in this lesson U.S. traditional multiplication because it is not the standard algorithm in other parts of the world. The Grade 5 standards require students to fluently multiply multi-digit whole numbers using U.S. traditional multiplication, so it is the focus of Fifth Grade Everyday Mathematics lessons. Students should learn this method, but if they prefer a different multiplication strategy, they should be allowed to use it to solve multiplication problems.”

• Unit 3, Fraction Concepts, Addition, and Subtraction, Unit 3 Organizer, 5.NF.5, provides support with explanations and examples of the more complex grade/course-level concepts. “Links to the Past: In Grade 4, students used visual fraction models and other strategies to solve number stories involving multiplication of a fraction by a whole number.”

• Lesson 4-7, Playing Hidden Treasure, Professional Development, supports teachers with concepts for work beyond the grade. “There are two common ways to look at distances in the coordinate plane. One type of distance is practical distance. On a coordinate grid, the practical distance between two points is along horizontal and vertical grid lines. Practical distance is sometimes called taxicab distance because it measures the distance along a route a taxicab might take. The other type of distance is straight line distance. On a coordinate plane, the straight-line distance between two points is the length of the line segment that connects the points. In Grade 5 students explore practical distance only. They will explore straight-line distance in later grades.”

• Lesson 5-13, Fraction Division, Part 1, Professional Development, supports teachers with concepts for work beyond the grade. “Lessons 5-13 and 5-14 build conceptual understanding of fraction division. According to the standards (5.NF.7), fraction division problems in Grade 5 are limited to the division of unit fractions by whole numbers and vice versa. Students are expected to use visual models and informal reasoning to solve them. They are not expected to use a generalized method of fraction division. Students will be introduced to an algorithm for fraction division in Grade 6. To build a conceptual understanding of division, students are asked to write multiple number models. The initial number model with a variable is intended to help students identify problems as division situations. The number models for the summary division sentence and multiplication check are designed to emphasize the relationship between division and multiplication as described in 5.NF.7a.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Unit 6 Organizer, 5.MD.1, supports teachers with concepts for work beyond the grade. “Links to the Future: In Grade 6, students will use ratio reasoning to convert measurement units.”

##### 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 5 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:

• 5th 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.

• 5th Grade Math, Unit 1, Area and Volume, 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 8-4, Extending Line Symmetry, Core Standards identified are 5.NBT.2, 5.MD.3, 5.MD.5, and 5.MD.5b. 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, 5.NBT.4, “First Quarter: No expectations for mastery at this point. Second Quarter: Use grids, number lines, or a rounding shortcut to round decimals to the nearest tenth or hundredth in cases when rounding only affects one digit. Third Quarter: Use place value understanding to round decimals to any place. 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 2, Fraction Concepts, Addition, and Subtraction, Organizer, Coherence, includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students worked with place-value concepts in whole numbers through 1,000,000. In Grade 6, students will extend their understanding of place value by applying their reasoning to make sense of decimal computation.”

• Unit 5, Operations with Fractions, Organizer, Coherence, includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students explored and explained a multiplication rule for producing equivalent fractions. In Grade 6, students will consider the sizes of dividends and divisors to help them make sense of the size of quotients when they divide fractions.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Organizer, Coherence includes an overview of how the content in 5th grade builds from previous grades and extends to future grades. “In Grade 4, students made line plots to display fractional measurement data and answered questions about that data. In Grade 6, students will collect and display data using dot plots, histograms, and box plots.”

##### 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 5 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:

• Unit 1, Area and Volume, Home-Link, Family Letter, “Students begin Unit 1 by exploring the Grade 5 Student Reference Book. They review how to interpret parentheses in mathematical expressions, and they review area and develop strategies for finding the area of rectangles in which the length of one side is a fraction. Students then began to explore the concept of volume. They measure how much a container can hold by packing it with small items, like beans, or popcorn kernels, and then they move to a more standard unit: the unit cube. Students learn to measure volume in increasingly sophisticated ways. They started by counting individual cubes. Then they work with layers of cubes. Finally, students discover two mathematical formulas for volume. They use their understanding of volume measurement to solve real-world problems about the volume of boxes, cases, and other containers. As your child works through, Unit 1, Home Links will provide many opportunities to explore the volume of everyday objects at home. While Unit 1 lessons focus on the volume of rectangular prisms (boxes), it is important to remember that all 3-dimensional objects have volume.”

• Lesson, 5-10, (Day 2): Sharing Breakfast, Home-Link, “Family Note: If your child needs help with the following problems, consider putting up signs in a room in your home to indicate the directions north, south, east, and west. Do the turns with your child. Please return this Home Link to school tomorrow.”

• Unit 6, Investigations in Measurement: Decimal Multiplication and Division, Home-Link, Family Letter, Vocabulary, “Important terms in Unit 6: base- A number that is raised to a power in exponential notation. For example, in 10^3, the base is 10. calibrate- To divide or mark a measuring tool with graduations, such as the degree marks on a thermometer. data point- A single piece of information gathered by counting, measuring, questioning, or observing. data set- A collection of data points. displacement method- A way to measure the volume of an object by submerging it in water and then measuring the volume of the water that is displaced. The method is especially useful for finding the volume of irregularly shaped objects. equivalent problems- Division problems that have different dividends and divisors but the same quotient. exponential notation- A way to show repeated multiplication by the same factor. line plot- A sketch of data in which checkmarks, Xs, stick-on notes, or other marks above a labeled line show the frequency of each value. metric system- A measurement system based on the base-10 numeration system. The metric system is used in most countries around the world. power of 10- A whole number that can be written as a product of 10s. exponent- A number used in exponential notation to tell how many times the base is used as a factor. The exponent is often written as a small, raised number or after a caret. For example, in 10^3, the exponent is 3. AN exponent can also be called the power of a number, as in “10 to the third power.” reaction time- the amount of time it takes to react to a stimulus. scale of a number line- The unit interval on a number line or measuring device.”

##### 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 5 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 5 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 Fifth Grade Everyday Mathematics.” Each unit includes a Materials Overview section outlining supplies needed for each lesson within the unit. Additionally, specific lessons include notes about supplies needed to support instructional activities, found in the overview of the lesson under Materials. Examples include:

• Lesson 3-2, Connecting Fractions and Division, Part 2, Overview, Materials, “slate; fraction circles; Math Journal 1, pp. 74-75; Student Reference Book p. 318; per partnership: Math Masters p. G11; two 6-sided dice; Math Journal 1, p. 76; Math Masters, p. 82.” Math Message, “Use your fraction circle pieces to help you.”

• Unit 5, Operations with Fractions, Unit 5 Organizer, Unit 5 Materials, teachers need, “fraction circles; per partnership: cards 0-10 (4 of each), 4 counters; slate; per partnership: calculator (optional); coin (optional) in lesson 1.”

• Unit 7, Multiplication of Mixed Numbers; Geometry; Graphs, Unit 7 Organizer, Unit 7 Materials, teachers need, “fraction circles (optional); per partnership: number cards 1-8 (4 of each); Fraction Number Lines Poster; per group: Math Journal 2, Activity Sheet 19 (Spoon Scramble cards); scissors; 3 spoons in lesson 2.”

• Lesson 7-2, Multiplication of Mixed Numbers, Part 2, Math Message, “You may use fraction circle pieces or the Fraction Number Lines Poster to help you.”

##### 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 5 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 and 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 5 meet expectations for having assessment information included in the materials to indicate which standards are assessed.

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

• Unit 3, Fraction Concepts, Addition, and Subtraction, Unit Assessment, denotes standards addressed for each problem. Problem 2, “Three families live in the same apartment building. They decided to share a giant 220-ounce of laundry detergent. If the families split the detergent equally, how many ounces of laundry detergent will each family get?” (5.NBT.6)

• Mid-Year Assessment, denotes standards addressed for each problem. Problem 2, “___ = 180\div{13+17}.” (5.OA.1)

• Unit 5, Operations with Fractions, Open Response Assessment, denotes mathematical practices for the open response. “Fred’s Restaurant is famous for its fresh fruit smoothies. Fred’s recipe calls for \frac{1}{3} of an apple, \frac{1}{4} of a lemon, and \frac{2}{3} of a peach to make a single smoothie. A family of 6 arrives at Fred’s restaurant. How much of each fruit does Fred need to make smoothies for the entire family? Use drawings, numbers, or other models to show your work. Be sure to use units in your answer.” (SMP4)

• Unit 8, Application of Measurement, Computation, and Graphing, Cumulative Assessment, denotes mathematical practices addressed for each problem. Problem 6, “Explain how you solve Problem 5 ($$88.4\div2.6$$).” (SMP6)

• End-of-Year Assessment, denotes standards addressed for each problem. Problem 10, Gary walked 2\fra{1}{3}miles on Monday, 3\frac{1}{2}miles on Tuesday, and 1\frac{3}{4}miles on Wednesday. How many miles did he walk in the three days?” (5.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 5 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 2, Whole Number Place Value and Operations, Cumulative Assessment, Problem 2, “For Problems 1-4, insert grouping symbols to make the number sentences true. 4+6\star8\div2=40. (4+6)\star8\star2=40.” This question is aligned to 5.OA.1.

• Unit 3, Fraction Concepts, Addition, and Subtraction, Open Response Assessment, Problem 1, “Clarre was training for a running race. She decided to run \frac{3}{8} mile from school to the park. Later she left the park and ran \frac{1}{2} mile home. She told her brother the distances she ran. Her brother said, “You ran a total of \frac{2}{5} mile.” Do you agree with Clare’s brother? Use pictures, words, number sentences, or other representations to explain why you agree or disagree. Not Meeting Expectations: Does not attempt to create or use a representation to solve the problem. Partially Meeting Expectations: Creates a partially correct or incomplete representation that shows \frac{1}{2}+\frac{3}{8} is greater than or not equal to \frac{2}{5}, or that \frac{1}{2} is greater than \frac{2}{5}. Meeting Expectations: Creates a correct representation that shows \frac{1}{2}+\frac{3}{8} is great than or not equal to \frac{2}{5}, or that \frac{1}{2} is greater than \frac{2}{5}. Exceeding Expectations: Meets expectations and creates more than one correct representation.” This question is aligned to 5.NF.2 and SMP2.

• Mid-Year Assessment, Problem 8, “Denali is making curtains for her room. She needs 12 feet of fabric for one curtain and 16 feet for the other. The fabric store has 8 yards of fabric she wants to use. Is that enough fabric? Explain your answer. No. Sample explanation: Denali needs 28 feet of fabric. There are 3 feet in 1 yard, so 8 yards of fabric is 24 feet. That is not enough fabric for both curtains.” This question is aligned to 5.MD.1.

• Unit 7, Multiplication of Mixed Numbers; Geometry; Graphs, Unit Assessment, Problem 13, “The graph in Problem 12c models this situation: Alexis saves \frac{1}{5} of the money she earns babysitting to buy a new pair of sneakers. Use the graph to answer the following questions. a. If Alexis has earned $10, how much money has she saved for sneakers? b. If Alexis has earned$18, about how much money has she saved for sneakers? 2 dollars. Between 3 and 4 dollars.” This question is aligned to 5.G.2.

• End-Of-Year Assessments, Problem 16, “Graham has \frac{1}{3} box of food for his iguana that needs to last 6 days. How much food should he give his iguana each day so that it gets the same every day? Number model:___. \frac{1}{3}\div6=i; \frac{1}{18}.” This question is aligned to 5.NF.7.

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

The materials reviewed for Everyday Mathematics 4 Grade 5 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, Area and Volume, Open Response Assessment, supports the full intent of MP6, attend to precision, as students explain calculate the volume of a rectangular prism and soccer balls. Problem 2, “Monica began to fill a box with the soccer balls and then took a break. The picture below shows what the box looked like when she took her break. Will all 30 soccer balls fit in this box? How do you know?”

• Mid-Year Assessment, develops the full intent of standard 5.OA.2, write simple expressions that record calculations with numbers, and interpret numerical expressions without evaluating them. Problem 14, “This week 6 different students paid $2.00 each in fines to the school librarian. The librarian also received a$60.00 donation from a local business. She spent $37.50 to buy books and supplies. Write an expression that shows the amount of money the librarian has at the end of the week. Do not solve the problem.” • Unit 5, Operations with Fractions, Unit Assessment, supports the full intent of MP7, look for and express regularity in repeated reasoning as students look for a strategy to find common denominators. Problem 2, “Describe the strategy you used to find a common denominator for \frac{3}{8} and \frac{2}{5} in problem 1b.” • End-of-Year Assessment, develops the full intent of 5.NBT.1, recognize that in a multi-digit number, a digit in one place represents 10 times as much as it represents in the place to its right and \frac{1}{10} of what it represents in the place to its left. Problem 3, “a. Write the value of 2 in each of the following numbers. 32,048,671 ___. 214.9 ___. 406.972 ___. 0.028 ___. b. Look carefully at your answers to Part a. How does the value of the 2 change as it shifts one place to the left? To the right? c. Use the information in Parts a and b to write a rule about the value of any digit when it moves one place to the left or one place to the right in a number.” ##### Indicator {{'3l' | indicatorName}} 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 5 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 1, Area and Volume, Open Response Problem, Adjusting the Activity, “If students struggle to determine the dimensions of the box, have them recreate the picture with centimeter cubes.” • Unit 5, Operations with Fractions, Unit Assessment, Adjusting the Assessment, Item 10, “To scaffold Item 10, have students answer the question using smaller numbers such as 3\star\frac{1}{2}. Then ask them to use what they noticed in the problem 3\star\frac{1}{2} to solve Item 10.” • Unit 8, Application of Measurement, Computation, and Graphing, Cumulative Assessment, Adjusting the Assessment, Item 5, “To scaffold Item 5, have students write an equivalent problem they could use to solve.” #### 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 5 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 5 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 3, Fraction Concepts, Addition and Subtraction, Lesson 7, include: • Readiness, “To prepare for using benchmarks to estimate, students compare fractions to \frac{1}{2} and locate them on a number line. Have students represent fractions between 0 and 1 with fraction circles. Ask them whether each fraction is less than, equal to, or greater than \frac{1}{2} and have them explain their thinking. They record the fractions in the appropriate box on Math Masters, page 97, and then complete the problems at the bottom of the page. Discuss students’ responses.” • Enrichment, “To further develop fraction number sense and explore using benchmarks, students play Fraction Top-It (Estimation Version). In this version, they apply their knowledge of benchmarks to estimate sums and compare them.” • Extra Practice, “For more practice using benchmarks to estimate sums and differences, students complete Math Masters, page 98. They make sense of number stories and match the stories to estimates shown on a number line.” • English Language Learner, Beginning ELL, “Make think-aloud statements using the term scaffold student’s understanding of the term benchmark as a point of reference, or a standard according to which things are judged. For example, I will use the fraction \frac{1}{2} to help me think about the size of \frac{5}{8}. I will use \frac{1}{2} as a benchmark to help me think about the size of \frac{5}{8}. Students may benefit from seeing how benchmarks can be useful in the same way helper facts are useful for thinking about nearby facts.” ##### Indicator {{'3n' | indicatorName}} Materials provide extensions and/or opportunities for students to engage with grade-level/course-level mathematics at higher levels of complexity. The materials reviewed for Everyday Mathematics 4 Grade 5 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 5, Operations with Fractions, Challenge, Problem 4, “What is \frac{1}{2} of \frac{2}{3} of \frac{3}{4} of 1? Explain how you found your answer.” • Lesson 6-5, Working With Data in Line Plots, Enrichment, “To extend their work using line plots to solve problems, students create line plots showing the scores of two competitive divers. They calculate the divers’ final scores in two ways: first by using all seven judges’ scores and then by following competitive diving rules, where the two highest and two lowest scores are thrown out. Students compare results and consider why using the scoring rule makes sense.” • Lesson 7-12, Rules, Tables, and Graphs, Part 2, Enrichment, “To extend their understanding of constructing graphs from data, students represent race results with multiple graphs. Students conduct two different types of races along a 5-meter course. They graph the results for each participant, then compare and discuss the resulting graphs.” ##### Indicator {{'3o' | indicatorName}} Materials provide varied approaches to learning tasks over time and variety in how students are expected to demonstrate their learning with opportunities for students to monitor their learning. The materials reviewed for Everyday Mathematics 4 Grade 5 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 1-6, Exploring Nonstandard Volume Units, Practice: Home-Link, Problem 1, students circle items that have volume. “Circle each item below that has volume. A wiggly line drawn on paper, a blue rectangle, a bar of soap, a circle, a baseball, an empty crayon box, a drawing of a tree, a bucket, a swimming pool, a drawing of a flower pot, a cereal box, and the kitchen sink.” • Lesson 6-10, (Day 1): Fundraising, Focus: Solving the Open Response Problem, Problem 1, students calculate money donated by two classes. “Two-fifth grade classes raised money for their local animal shelters. There are 20 students in Class A. Each student raised$12. There are 20 students in Class B. Each student in Class B raised 1.5 times as much as each student in Class A. How much money did the students in both classrooms raise all together?”

• Lesson 7-9, Collecting and Using Fractional Data, Focus: Collecting and Plotting Fractional Data, Math Journal 2, Problem 5, students plot measurements on a line plot that they collected from classmates. “Use your class measurements to create line plots for the cubit lengths, great-span lengths, and joint lengths.”

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

• Assessment Handbook, Unit 3, Fraction Concepts, Addition, and Subtraction, 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, “Use visual models to solve division number stories with fractional answers. Report the remainder to a division problem. Place a fraction on a number line. Estimate answers to fraction addition and subtraction problems. Rename fractions and mixed numbers using the same denominator. Use visual models to add and subtract fractions and mixed numbers. Use visual models to solve fraction addition and subtraction number stories. Solve fraction-of problems.”

• Assessment Handbook, Sample Math Work, students reflect on work they have completed and fill out the following sheet and attach to their work, “This work is an example of _____, This work shows that I can: _____, This work shows that I still need to improve: _____.”

• Assessment Handbook, Discussion of My Math Work, students reflect on work they have completed and fill out the following sheet to attach to their work, “Tell what you think is important about your sample.”

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

The materials reviewed for Everyday Mathematics 4 Grade 5 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 1-5, Introduction to Volume, Focus: Comparing Volume, Teacher’s Lesson Guide, “Distribute 2 half-sheets of paper to each small group of students. Encourage them to ask questions, making sure they understand the thinking of the other students in their group.”

• Lesson 4-2, Representing Decimals Through Thousandths, Focus: Collecting Names for Decimals, Teacher’s Lesson Guide, “Then have them complete journal page 114 and 115 independently or in partnerships.”

• Lesson 5-14, Fraction Division, Part 2, Practice: Playing Fraction/Whole Number Top It, Teacher’s Lesson Guide, “What strategy did you use to multiply? Compare your strategy with your partner’s strategy. When you multiply a fraction by a whole number, is the product greater than or less than the factors? What if you multiply a fraction by a fraction? Why?

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

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

• Lesson 1-8, Measuring Volume By Iterating Layers, Differentiating Lesson Activities, Using Layers to Solve Cube-Stacking Problems, “Scaffold to help students justify their volume calculations by providing questions-and-response prompts. For example: Can you explain why you ___? If I ___ then we need to ___ because ___ What does that mean? Let me show you what I mean. To paraphrase what you just said you ___.”

• Lesson 3-9, Introduction to Adding and Subtracting Fractions and Mixed Numbers,  English Language Learner Beginning ELL, “Build on students’ understanding of the word remainder as what remains so that they make a connection between the terms remain and remainder. Display a number of objects that do not divide evenly and say: We are going to share these ____ between the 3 of us: 1 for you, 1 for you, and 1 for me…. Point to the remaining objects at the end, saying: These are left over. This is what remains. These are the remainder. Partners do the same using another set of objects, repeating the think-aloud. Ask students to point to the remainder after each round.”

• Lesson 7-9, Collecting and Using Fractional Data, Differentiation Options, English Language Learner Beginning ELL, “In this lesson students work with the word span, which begins with the consonant cluster sp. English language learners may find it difficult to pronounce this sound in the initial position if it does not occur in that position in their home language. Students may add the vowel sound /e/ to the English pronunciation of span to make it easier to pronounce. Point out the correct pronunciation and articulate it carefully. List other words that begin with the sp sound.”

• 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 5 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 Carlos, Viktoriya, Juan, and Termica 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 5 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 7-7, Playing Property Pandemonium, Warm-Up: Mental Math and Fluency, Differentiation and English Learners Support, “Scaffold academic conversation by providing prompt-and-response sentence starters, such as: What is your estimate? Why does your estimate make sense? Is that a reasonable estimate? I used these numbers to make an estimate because___ I think this is where the decimal point goes because ___ I think it’s a reasonable answer because ___ My reason for saying ___ is based on ___.”

• 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.The materials reviewed for Everyday Mathematics 4 Grade 5 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 7-7, Playing Property Pandemonium, Warm-Up: Mental Math and Fluency, Differentiation and English Learners Support, “Scaffold academic conversation by providing prompt-and-response sentence starters, such as: What is your estimate? Why does your estimate make sense? Is that a reasonable estimate? I used these numbers to make an estimate because___ I think this is where the decimal point goes because ___ I think it’s a reasonable answer because ___ My reason for saying ___ is based on ___.”

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

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

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

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

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

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

The materials reviewed for Everyday Mathematics 4 Kindergarten 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, Volume in the Real World, Page 253, students examine the water storage per person in cubic meters from three continents. “Not all places on Earth have the same capacity for water shortage or the same number of people who depend on the water. Water resource professionals calculate the volume of water available to each person in an area by dividing the total amount of available water in cubic meters by the total number of people: water (m^3)/ number of people. This is sometimes called “water storage per capita,” or per person. In North America, water storage per person is about 5,660 cubic meters. In sub-Saharan Africa, water storage per person is about 543 cubic meters due to low levels of rainfall and the lack of large reservoirs to store water. In Asia, water storage per person is about 353 cubic meters because available water reserves must serve an extremely large population.”

• Independent Problem Solving 1a “to be used after Lesson 1-4”, Problem 2, students are introduced to a piece of art called a mosaic. “A mosaic is a piece of art created by covering a surface with small pieces of colorful material. Kha-Minh has a box of 36 square tiles with a side length of \frac{1}{3} inch that she would like to use to make a mosaic. She wants the mosaic to be a rectangle and she wants to use all the tiles. Draw and label two different rectangles that Kha-Minh could make. Are the areas of each rectangle the same? Why or why not?”

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

The materials reviewed for Everyday Mathematics 4 Grade 5 partially provide supports for different reading levels to ensure accessibility for students.

• Lesson 2-1, Understanding Place Value, Focus: Representing Place Value, Academic Language Development, “Contrast numbers written in standard notation and expanded form to help students actively construct the meaning of standard as “that which is normally used.” Ask students which of the two forms- standard or expanded- they are more likely to see in everyday use.”

• Lesson 5-2, More Strategies for Finding Common Denominators, Focus: Using Factors and Multiples to Find Common Denominators, Academic Language Development, “Have partners complete a 4-Square Graphic Organizer (Math Masters, TA2) for the term they read about - factor or multiple- to use as they explain to each other what they learned. The quadrant headings going clockwise can be: Factors of 36/First Six Multiples of 8; One thing I learned about factors/One thing I learned about multiplies; Non-Example of a Factor of 36/Non-Example of a Multiple of 8; My Definition.”

• Lesson 7-6, A Hierarchy of Quadrilaterals, Focus: Classifying Quadrilaterals, Academic Language Development, “Have students work in partnerships to define the term branched hierarchy using the 4-Square Graphic Organizer (Math Masters, p. TA2) with the following headers: Example, Non-example, Definition, and Illustration.”

##### 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 5 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 1-7, Measuring Volume by Counting Cubes, Focus: Math Message, materials reference use of unit cubes. “Cut out and assemble Rectangular Prisms A, B, and C. Take 25 cubes. Estimate how many cubes will fit into each prism. Record your estimates in the second column of the table on Journal page 18.”

• Lesson 3-1, Connecting Fractions and Division, Part 1, Focus: Modeling with Fraction Circle Pieces, materials reference use of fraction circles. “Make the point that fraction circle pieces are being used to model the situation.”

• Lesson 4-14, Addition and Subtraction of Money, Focus: Introducing Spend and Save, materials reference use of coins, bills, and counters. “Then distribute one Spend and Save Record Sheet to each student and 1 coin and 1 counter to each partnership. Make play bills and coins available to students who might need them to play the game.”

#### 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 5 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 5 integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the grade-level/series standards, when applicable.

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

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

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

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

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

##### 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 5 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 5 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 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 5 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 3-12, Solving Fraction Number Stories, 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- 5-6, 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 student’s performance on assessment tasks. Data: Use the Data Dashboard to view student’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

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### Overall Summary

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###### Usability
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