4th Grade - Gateway 1

The materials reviewed for Everyday Mathematics 4, Grade 4 meet expectations for assessing grade-level content and, if applicable, content from earlier grades.

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

Materials assess grade-level standards. Examples include:

• Unit 2 Cumulative Assessment, Item 8, “In gym class students were doing the standing long jump. Lance’s jump measured 5 feet. He thinks that he jumped 50 inches. Is he correct? Explain how you know.” (4.NBT.5, 4.MD.1, 4.MD.2) 

• Unit 3 Assessment, Item 5, “a. Using your fraction circles to help you, find and name 2 fractions that are equivalent to \frac{1}{3}. b. Using your fraction circles to help you, find and name 2 fractions that are equivalent to \frac{2}{5}.” (4.NF.1)

• Unit 4 Cumulative Assessment, Item 1, “a. List the first 6 multiples of 9. b. Name two factors of 9. c. Is 9 a multiple of those numbers? Explain.” (4.OA.4)

• Unit 6 Assessment, Item 5, “For each angle, circle the type. Then use a protractor to measure each angle, and record your measurement.” (4.MD.6)

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

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

• Lesson 1-4, Introduction to the Student Reference Book, Warm Up: Mental Math and Fluency, students identify and write the place value of an indicated digit, “Display numbers using a place-value tool. Have students write the value of the indicated digit on their slates. Leveled exercises: What is the value of the 3 in 39? The 8 in 98? The 6 in 602? What is the value of the 7 in 3750? The 2 in 2,006? The 1 in 6,615? What is the value of the 4 in 13,407? The 5 in 15,247? The 1 in 104,539?” Focus, Extending Place Value, Math Journal 1, students read and compare populations. “Use the information in the table to solve the problems. 1. Name two cities that have a 2010 population in the hundred-thousands. 2. Name two cities that have a 2010 population in the millions. 3. Boston’s population in 2010 was 617,594. What is the value of the digit . . . 1? ___ 7? ___ 6? ___ 4. Philadelphia’s population in 2010 was 1,547,607. What is the value of the digit . . . 4? ___ 1? ___ 5? ___5. Round the 2010 population of Houston to the nearest million. 6. Did Boston’s population increase from 2000 to 2010? 7. Record the population for Norman in 2000 and 2010. Use <, >, or = to compare.” Students engage in extensive work with grade-level problems for 4.NBT.2, “Read and write multi-digit whole numbers using base-ten numerals, number names, and expanded form. Compare two multi-digit numbers based on meanings of the digits in each place, using >, =, and < symbols to record the results of comparisons.”

• Lesson 5-5, Adding Tenths and Hundredths, Focus: Solving Fractions Addition Problems with Denominators of 10 and 100, Math Journal 2, students add unlike fractions with tenths and hundredths, “Use what you know about equivalent fractions to add. Write an equation to show your work. 3. \frac{8}{100}+\frac{6}{10} Equation: ___ 4. \frac{47}{100}+\frac{9}{10} Equation: ___ 5. \frac{3}{10}+\frac{50}{100} Equation: ___ 6. \frac{1}{10}+\frac{5}{100}+\frac{20}{10}+\frac{55}{100} Equation: ___ 7. 1\frac{2}{10}+6\frac{35}{100}.” Practice, Math Masters, “Use what you know about equivalent fractions to add. Write an equation to show your work. 1. 2 tenths + 15 hundredths. 2. \frac{68}{100}+\frac{3}{10} Equation: ___ 3. \frac{1}{10}+\frac{50}{100} Equation: ___Equation: ___ 4. \frac{4}{10}+\frac{60}{100}+\frac{3}{10}+\frac{81}{100}. Equation: ___ 5. 1\frac{3}{10}+5\frac{64}{100}” Students engage in extensive work with grade-level problems for 4.NF.6, “Use decimal notation for fractions with denominators 10 or 100. For example, rewrite 0.62 as 62/100; describe a length as 0.62 meters; locate 0.62 on a number line diagram.”

• Lesson 7-3, A Fraction as a Multiple of a Unit Fraction, Focus: Multiplying Unit Fractions by Whole Numbers, Math Journal 2, students multiply unit fractions by whole numbers, “Write an addition equation and a multiplication equation to describe each picture. 1. a. Addition equation: ____ b. Multiplication equation: ____ c. What is the second multiple of \frac{1}{5}? Draw a picture to represent the equations. 3. Addition equation: \frac{1}{6}+\frac{1}{6}+\frac{1}{6}=\frac{3}{6}. Multiplication equation: 3\star\frac{1}{6}=\frac{3}{6}. 4. Addition equation: \frac{1}{10}+\frac{1}{10}+\frac{1}{10}+\frac{1}{10}=\frac{4}{10}. Multiplication equation: 4\star\frac{1}{10}=\frac{4}{10}. 5. Use a unit fraction to write an addition equation and an equivalent multiplication equation. Draw a picture to represent the equations.” Practice, Math Masters, “Write a multiplication equation to describe each picture or story. 1. Multiplication equation is 4\star\frac{1}{5}=\frac{4}{5}. What is the fourth multiple of \frac{1}{5}? 3. Demitri fixed a snack for 5 friends. Each friend got \frac{1}{2} of an avocado. How many avocados did Demitri use?” Students engage in extensive work with grade-level problems for 4.NF.4, “Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.”

The materials provide opportunities for all students to engage with the full intent of Grade 4 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 2-6, Little and Big, Focus: Math Message, Math Journal 1, students determine if a given rule is correct, “Mr. Cheng’s class is trying to figure out the rule for the table below. For the rule to be correct, the rule must work for all the rows. In the table below, the first column shows educated guesses, or conjectures, for rules that Mr. Cheng’s students made. Some rules are correct and some are not. Circle Yes or No to tell whether the rule is correct. Then write an explanation, or argument, for why you think the rule is correct or not. The conjecture for Rule. Multiply by 1. Add 3. Double the number you put in and subtract 1.” An in and out table shows, in- 1, 2, 4; out- 1, 3, 7. Lesson 13, Finding the Pattern, Focus, Exploring Shape Patterns, Math Journal 1, Problem 3, students explore shape patterns, “Study the pattern. a. Draw the next step in the pattern. b. What patterns do you notice? c. How many squares will be in the 6th step? In the 100th? d. How did you figure out how many squares will be in the 10th step?” Students engage in the full intent of 4.OA.5, “Generate a number or shape pattern that follows a given rule. Identify apparent features of the pattern that were not explicit in the rule itself.”

• Lesson 4-3, Partitioning Rectangles, Warm Up: Math Message, Math Journal 1, students solve a real-world area problem to determine the amount of tile needed, “Maya wants to lay tile on a floor that is 8 feet wide by 24 feet long. The tiles she wants to use are 1 square foot each. How many tiles will Maya need?” Lesson 11, Area Models for Rectangles and Rectilinear Figures, Focus, Finding the Area of Rectilinear Figures, Math Journal 1, Problem 3, students find area and perimeter by subdividing rectilinear figures. Focus, “Study the figure below. It is a plan for the new computer lab at Pond Cove School. The school’s principal needs to determine how much carpet will be needed to cover the floor. a. Find the area of the room. Show your work below. b. Find the perimeter. Show your work below.” Students engage in the full intent of 4.MD.3, “Apply the area and perimeter formulas for rectangles in real-world and mathematical problems.”

• Lesson 5-2, The Whole for Fractions, Focus: Solving “What is the Whole?”, Math Journal 2, students find the whole, given a fractional part, “Use fraction circle pieces to help you name the whole. Record the name in the whole box. Then write an addition equation to represent the problem. Problem 1. If (yellow fraction circle) is \frac{1}{2}, what is the whole?” Lesson 7, Subtracting Fractions, Focus, Solving More Fraction Subtraction Number Stories, Math Journal 2, Problem 2, students subtract fractions in number stories, “A vegetable lasagna recipe called for \frac{3}{4} teaspoon of pepper. Caleb used \frac{1}{4} teaspoon when he grilled the vegetables. He added the rest to the cheese mix. How much pepper did Caleb add to the cheese mix? a. Fill in the whole box. b. Number model with unknown.___ c. A different way to solve a fraction subtraction problem: d. Answer (with unit): ___.” Students engage in full intent of 4.NF.3a, “Understand addition and subtraction of fractions as joining and separating parts referring to the same whole.”

The materials reviewed for Everyday Mathematics 4 Grade 4 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 5.7 units address major work of the grade or supporting work connected to major work of the grade, approximately 71%.

• There are 112 lessons, of which 82.75 address major work of the grade or supporting work connected to the major work of the grade, approximately 74%.

• In total, there are 170 days of instruction (112 lessons, 38 flex days, and 20 days for assessment), of which 98.75 days address major work of the grade or supporting work connected to the major work of the grade, approximately 58%. 

• Within the 38 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 74% of the instructional materials focus on the major work of the grade.

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

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

• Lesson 1-13, Finding Perimeters of Squares and Rectangles, Math Journal 1, students apply the area and perimeter formulas for rectangles in real-world and mathematical problems (4.MD.3) to fluently add and subtract multi-digit whole numbers using the standard algorithm (4.NBT.4) and multiply a whole number of up to four digits by a one-digit whole number, and multiply two two-digit numbers, using strategies based on place value and the properties of operations (4.NBT.5). Problem 4, “Jerry wants to build a rectangular vegetable garden with a fence around it. He wants the garden to be 8 feet long and 4 feet wide. Sketch his garden. Find the perimeter. Show your work.”

• Lesson 2-3, Factors and Factor Pairs, Math Journal 1, students multiply a whole number of up to four digits by a one-digit whole number and multiply two two-digit numbers, using strategies based on place value and the properties of operations (4.NBT.5) to find factor pairs for a whole number in the range 1-100 (4.OA.4). Problem 1, “Write equations to help you find the factor pairs of each number below. 20, 16, 13, 27, and 32.” 

• Lesson 6-2, Area: Finding Missing Side Lengths, Math Message, students apply area and perimeter formulas (4.MD.3) to find missing side lengths of rectangles (4.NBT.5, 4.NBT.6). The teacher prompt states, “A rectangular garden has an area of 450 square feet. One side is 9 feet long. How long is the other side?” 

• Lesson 6-7, Partial-Quotients Division, Part 2, Math Journal 2, students find all factor pairs for a whole number in the range 1-100 (4.OA.4) to understand finding whole-number quotients and remainders with up to four-digit dividends and one-digit divisors (4.NBT.6). Students use partial-quotients division to divide whole numbers using factors. The teacher poses this problem, “Corey bought 162 stickers to put in gift bags. She wants each gift bag to contain 6 stickers. How many gift bags can she make?” Problem 2, “Carpenters are installing hinges. They have 371 screws. Each hinge needs 3 screws. How many hinges can they install?” 

• Lesson 7-13, Displaying Insect Data, Math Journal 2, students make a line plot to display a data set of measurements in fractions of a unit (4.MD.4) to understand building fractions from unit fractions (4.NF.3). Problem 3, “How many insects are longer than 7/8 inch and shorter than 1 6/8 inch? What is their combined length?”

The materials reviewed for Everyday Mathematics 4 Grade 4 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 3-8, Modeling Tenths with Fraction Circles, Math Journal 2, Problems 1 and 2, students explore tenths with fraction circles and look at visual models of circles divided into tenths to, “Write a fraction and a decimal to match each circle.” This connects the major work of 4.NF.A, “Extend understanding of fraction equivalence and ordering” to the major work of 4.NF.C, “Understand decimal notation for fractions, and compare decimal fractions.”

• Lesson 5-5, Modeling Tenths and Hundredths, Math Journal 2, Problem 1, students use equivalent fractions to write fractions with denominators of 10 as equivalent fractions with denominators of 100 and add fractions with like denominators, “5 tenths + 27 hundredths.” The directions state, “Use what you know about equivalent fractions to add. Write an equation to show your work.” This connects the major work of 4.NF.B, “Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers” to the major work of 4.NF.A, “Extend understanding of fraction equivalence and ordering.”

• Lesson 5-10, Rotations and Iterating Angles, Math Journal 2, Problems 1-5, students use benchmark angles to practice different types of turns, “Describe each angle by the amount of rotation. Use the words full-turn, three-quarter turn, half-turn, and quarter turn.” This connects the supporting work of 4.MD.C, “Understand concepts of angle and measure angles” to the supporting work of 4.G.A, “Draw and identify lines and angles, and classify shapes by properties of their lines and angles.”

• Lesson 6-5, Day 1: Fruit Baskets, Math Journal 2, Problems 1 and 2, students solve division story problems and interpret remainders, “Elbert’s Egg Emporium: One morning, Elbert collected 151 eggs. 1. How many cartons did he need for the eggs? Show your work. Be sure to include units with your answer. 2. How many eggs did Elbert eat for breakfast? Show or explain how you know. Be sure to include units with your answer.” This connects the major work of 4.OA.A, “Use the four operations with whole numbers to solve problems” to the major work of 4.NBT.B, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”

• Lesson 6-9, Measuring Angles, Math Journal 2, students use their ability to measure angles to help classify triangles, “Identify each angle as acute, right, straight, or obtuse. Use your angle measure to measure the angles on this page. Record your measurements in the table. Then circle the right angle below.” This connects the supporting work of 4.MD.C, “Understand concepts of angle and measure angles” and the supporting work of 4.G.A, “Draw and identify lines and angles, and classify shapes by properties of their lines and angles.”

• Lesson 7-1, Converting Liquid Measures: U.S. Customary Units, Math Journal 2, Problem 1, students analyze patterns as they convert measurements between cups, pints, gallons, and quarts, “Complete the two-column tables. a. Pints: 1, 2, 3, 5, ?. Cups: ?, ?, ?, ?, 16. b. Quarts: 1, 2, 4, ?, 9, 13. Pints: ?, ? ?, 14, ?, ?. c. Gallons: 1, 2, 3, ?, 15. Quarts: ?, ?, ?, 36, ?. d. Quarts: 1, 3, 5, 6, ?. Cups: ?, ?, ?, ?, 40.” This connects the supporting work of 4.MD.A, “Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit” to the supporting work of 4.OA.C, “Generate and analyze patterns.”

• Lesson 7-7, Multistep Division Number Stories, Math Journal 2, Problem 2, students interpret the reasonableness of remainders in multi-digit division problems, “Anna wants to put 72 baseball cards in an album. A square album fits 4 cards per page and a rectangular album fits 5 cards per page. How many more pages will she need to fit all the cards if she uses the square album rather than the rectangular album?” This connects the major work of 4.OA.A, “Use the four operations with whole numbers to solve problems” and the major work of 4.NBT.B, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”

The materials reviewed for Everyday Mathematics 4 Grade 4 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, Place Value; Multidigit Addition and Subtraction, Teacher’s Lesson Guide, Links to the Past, “4.NBT.4: In Grade 3, students learn a variety of methods for multidigit addition and subtraction, including partial sums addition, column addition, expand-and-trade subtraction, and trade-first subtraction.” These methods have connections to the U.S. traditional algorithms that are introduced in Grade 4.” 

• Unit 5, Fraction and Mixed-Number Computation; Measurement, Teacher’s Lesson Guide, Links to the Past,”4.NF.3, 4.NF.3a: In Grade 3, students use fraction strips, fraction circles, and fraction number lines to determine equivalence and to compare and order fractions.” 

• Unit 7, Multiplication of a Fraction by a Whole Number; Measurement, Teacher’s Lesson Guide, Links to the Past, “4.MD.4: In Unit 5, students review line plots and create line plots that include fractional units of length and weight. In Grade 3, children measured lengths using rulers marked  \frac{1}{2} and  \frac{1}{4} of an inch and represented the data in line plots.”

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

• Unit 2, Multiplication and Geometry, Teacher’s Lesson Guide, Links to the Future, “4.OA.5: In Grade 5, students use rules, tables, and graphs to extend patterns and solve real-world problems.”

• Unit 6, Division; Angles, Teacher’s Lesson Guide, Links to the Future, “4.NBT.5: Throughout Grade 4, students solve multiplication problems involving varied contexts. In Grade 5, students learn U.S. traditional multiplication and use it to solve problems involving whole numbers.”

• Unit 8, Fraction Operations; Applications, Teacher’s Lesson Guide, LInks to the Future, “4.MD.2: In Grade 5, measurement continues to serve as a context for problem solving and for applying computational skills.”