5th Grade - Gateway 1

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations for assessing grade-level content. Summative Interim Assessments include Beginning-of-Year, Mid-Year, and End-of-Year.

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

• 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.4.b)

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations for spending a majority of instructional time on major work of the 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.

The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 78% of the instructional materials focus on major work of the grade.

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

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

• In Lesson 2-7, Teacher’s Lesson Guide, 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). In the Focus portion of the lesson, 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.” 
• In Lesson 3-8, Student Math Journal, 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?”
• In Lesson 6-4, Teacher’s Lesson Guide, 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?”  
• In Lesson 8-1, Student Math Journal, 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.”

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations that the amount of content designated for one grade level is viable for one year. 

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

• There are 8 instructional units with 113 lessons. Open Response/Reengagement 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.

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations for being consistent with the progressions in the Standards. The instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades and present extensive work with grade-level problems. The instructional materials relate grade-level concepts with work in future grades, but there are a few lessons that contain content from future grades that is not clearly identified as such. 

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

• Unit 1, 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, 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, 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.” 

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

• Unit 2, 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, 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, Teacher’s Lesson Guide, Links to the Future, “5.MD.1: In Grade 6, students will use ratio reasoning to convert measurement units.”

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

• In Lesson 4-12, Math Masters, Decimal Addition Algorithms, Focus, Extending Whole-Number Addition Algorithms to Decimals, “Students practice using decimal addition algorithms and use estimates to check the reasonableness of their answers (5.NBT.7).” Problem 3, “Find the page in your Student Reference Book that shows how to use your algorithm to add decimals. Write the page number below. Read the example. Then use your algorithm to solve 2.965 + 7.47. 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.
• In Lesson 4-13, 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.
• In Lesson 8-3, Student Math Journal, Planning an Aquarium, Focus, Choosing a Fish Tank, “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.

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

• In Lesson 4-4, Student Math Journal, Comparing and Ordering Decimals, “Darryl and Charity are playing Decimal Top-It. Their record sheet is shown below. Problem 1, Compare their decimals for each round and write >, <, or = in the column. Use the place-value charge above to help you.” (5.NBT.6, 5.NF.3, 5.MD.1)
• In Lesson 5-2, Teacher Lesson Guide, More Strategies for Finding Common Denominators, Focus, Using Factors and Multiples to Find Common Denominators, “Students learn strategies for finding a common denominator for a pair of fractions (5.NF.1).” Have students give factors and multiples of additional numbers. Teachers display the factors and multiples that students name (call out). Suggestions: 12: Factors: 1, 2, 3, 4, 6, 12 Multiples: 12, 24, 36, 48.” Finding factors and multiples is a part of adding and subtracting fractions with unlike denominators. (5.NF.1)

• In Lesson 8-2, Math Journal 2, Problem 3, “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.” (5.G.1,2)

The instructional materials reviewed for Everyday Mathematics 4 Grade 5 meet expectations for fostering coherence through connections at a single grade, where appropriate and required by the Standards.

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

• The Lesson Overview for Lesson 1-8, “Students relate volume to multiplication and addition by thinking about iterating layers to find the volumes of prisms,” is shaped by 5.MD.C, “Geometric measurement: understand concepts of volume” and “Relate volume to multiplication and to addition.”
• The Lesson Overview for Lesson 3-7, “Students use benchmarks to estimate sums and differences of fractions,” is shaped by 5.NF.A, “Use equivalent fractions as a strategy to add and subtract fractions.”
• The Lesson Overview for Lesson 4-6, “Students are introduced to the coordinate grid and use ordered pairs to plot and identify points,” is shaped by cluster heading for 5.G.A, “Graph points on the coordinate plane to solve real-world and mathematical problems.”
• The Lesson Overview for Lesson 6-9, “Students learn two strategies for solving decimal multiplication problems,” is shaped by 5.NBT.A, “Understand the place value system” and 5.NBT.B, “Perform operations with multi-digit whole numbers and with decimals to hundredths.”

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

• Lesson 4-11 connects 5.NBT.A and 5.NBT.B as students use grids to solve decimal addition and subtraction problems. In the Student Math Journal, Problems 1 and 2, “Shade the grid in one color to show the first addend. Shade more of the grid in a second color to show the second addended. Write the sum to complete the number sentence.” 1. “0.6 + 0.22 = ____?  2. 0.18 + 0.35 = ____?”
• Lesson 6-2 connects 5.NBT.A and 5.NBT.B as students multiply and divide decimals by powers of 10, and compare decimals and whole numbers. In the Focus portion of the lesson, students learn the game “Exponent Ball”. 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.”
• Lesson 7-1 connects 5.NBT.B and 5.NF.B as students relate operations with fractions to operations with whole numbers. Teachers use the following example with students, “4 $$\frac{2}{3}$$ * 7 = 4 * 7 + $$\frac{2}{3}$$ * 7.”
• Lesson 8-1 connects 5.NBT.B with 5.NF.B as students perform operations with multi-digit whole numbers and apply and extend previous understandings of multiplication and division to multiply and divide fractions. In the Math Message, 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.”