4th Grade - Gateway 1

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

The number of lessons devoted to major work is most representative of the instructional materials. As a result, approximately 74% of the instructional materials focus on major work of the grade.

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

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

• In Lesson 1-13, Student Math Journal, 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.”
• In Lesson 2-3, Student Math Journal, 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.” 
• In Lesson 6-7, Teacher’s Lesson Guide, 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?” The Student Math Journal, Problem 2, “Carpenters are installing hinges. They have 371 screws. Each hinge needs 3 screws. How many hinges can they install?” 
• In Lesson 6-2, Teacher’s lesson Guide, 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?” 
• In Lesson 7-13, Math Journal, 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 instructional materials reviewed for Everyday Mathematics 4 Grade 4 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 112 lessons. Open Response/Reengagement lessons require 2 days of instruction adding 8 additional lesson days.
• There are 38 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 4 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 with work in future grades, and the materials present extensive work with grade-level problems.

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, “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, 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, 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.”  

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, “4.OA.5: In Grade 5, students use rules, tables, and graphs to extend patterns and solve real-world problems.”
• Unit 6, 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, 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.”

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

• In Lesson 1-4, Teacher’s Lesson Guide Volume 1, Warm Up, students identify and write the place value of an indicated digit. For example, “Display numbers using a place-value tool. Have students write their 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?” (4.NBT.2)
• In Lesson 5-5, Teacher’s Lesson Guide, Adding Tenths and Hundredths, Focus, Solving Fractions Addition Problems with Denominators of 10 and 100, “Students add unlike fractions with tenths and hundredths.” For example, Student Math Journal, “Problem 7, ‘1 $$\frac{2}{10}$$ + 6 $$\frac{35}{100}$$’.” (4.NF.6)
• In Lesson 7-3, Math Journal 2, Problem 3, “Draw a picture to represent the equations. Addition equation: $$\frac{1}{6}$$ + $$\frac{1}{6}$$ + $$\frac{1}{6}$$ = $$\frac{3}{6}$$; Multiplication equation; 3 * $$\frac{1}{6}$$ = $$\frac{3}{6}$$.” (4.NF.4)

The instructional materials reviewed for Everyday Mathematics 4 Grade 4 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 2-3, “Students work with factor pairs, arrays, and corresponding equations,” is shaped by 4.OA.B, “Gain familiarity with factors and multiples.”
• The Lesson Overview for Lesson 2-7, “Students convert units of time to smaller units of time and solve number stories involving time,” is shaped by 4.MD.A, “Solve problems involving measurement and conversion of measurements from a larger unit to a smaller unit.”
• The Lesson Overview for Lesson 3-2, “Students use an area model to recognize and generate equivalent fractions,” is shaped by cluster heading, 4.NF.A, “Extend understanding of fraction equivalence and ordering.”
• The Lesson Overview for Lesson 7-10, “Students solve multistep number stories involving fractions,” is shaped by 4.NF.A, “Extend understanding of fraction equivalence and ordering” and 4.NF.B, “Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.”

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

• Lesson 3-8 connects 4.NF.A and 4.NF.C as students explore tenths with fraction circles. In the Student Math Journal, Problems 1 and 2, students look at visual models of circles divided into tenths and “Write a fraction and a decimal to match each circle.”
• Lesson 5-5 connects 4.NF.B with 4.NF.A as students use equivalent fractions to write fractions with denominators of 10 as equivalent fractions with denominators of 100 and add fractions with like denominators. In the Student Math Journal, Problem 1, “5 tenths + 27 hundredths.” The directions state, “Use what you know about equivalent fractions to add. Write an equation to show your work.”
• Lesson 6-5 connects 4.OA.A and 4.NBT.B as students solve division story problems and interpret remainders. In the Student Math Journal, Problems 1 and 2, students solve “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.”
• Lesson 7-7 connects 4.OA.A and 4.NBT.B as students interpret the reasonableness of remainders in multi-digit division problems. In the Student Math Journal, Problem 2, “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?”