3rd Grade - Gateway 1

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

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

• Unit 1 Assessment, Item 7, “Round each number to the nearest 10. You may use open number lines to help. 7a: 59 rounded to the nearest 10 is ____. 7b: 73 rounded to the nearest 10 is ____.” (3.NBT.1)
• Mid-Year Assessment, Item 6, “Davis and his friends have 4 packs of balloons with 4 balloons in each pack. They inflate all of their balloons. Then 3 balloons pop. How many inflated balloons are left? a. Use pictures, numbers, or words to solve the problem. Write number models to show each step. How do you know your answer makes sense?” (3.OA.8)
• Unit 5, Item 6, “Divide the circle below into 4 equal-size parts. Shade and label one part with a fraction.” A circle is provided for students to partition. (3.NF.1, 3.G.2)
• Unit 9, Assessment, Item 6, “It starts raining at 6:40 A.M. and stops at 9:15 A.M. How long did it rain? Show your thinking. You may use an open number line, your toolkit clock, or other representations.” (3.MD.1)

There are some above-grade-level assessment items that can be omitted or modified. These include: 

• Unit 3 Assessment, Item 2, “Complete the tables. Write your own number pair in the last row of each table.” Students are shown an in/out table to determine the “rule” and fill in the missing numbers. (4.OA.5)
• Mid-Year Assessment, Item 4a, “Find the rule. Complete the table.” Students are shown an in/out table to determine the “rule” and fill in the missing numbers. (4.OA.5)

• Unit 6 Assessment, Item 7, “Andy used the order of operations to solve this number sentence. 3 + 6 x 5 = 33. Explain Andy’s steps for solving the number sentence.” A box titled “Rules for the Order of Operations” is shown. (5.OA.1)
• End-of-Year Assessment, Item 7, “a. Use the order of operations to solve these number sentences. 45 - 12 x 0 = _____, (45 - 12) x 0 = ______. b. Explain why the two number sentences have different answers.” (5.OA.1)

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

• There are 9 instructional units, of which 6.5 units address major work of the grade or supporting work connected to major work of the grade, approximately 72%.
• There are 108 lessons, of which 73 address major work of the grade or supporting work connected to the major work of the grade, approximately 68%.
• In total, there are 169 days of instruction (108 lessons, 37 flex days, and 24 days for assessment), of which 88.75 days address major work of the grade or supporting work connected to the major work of the grade, approximately 53%. 
• Within the 37 Flex days, the percentage of major work or supporting work connected to major work could not be calculated because the materials suggested list of differentiated activities do not include explicit instructions. Therefore, it cannot be determined if all students would be working on major work of the grade.

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

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

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

• In Lesson 1-12, Teacher’s Lesson Guide, Activity Card 16, students partition shapes into parts with equal areas (3.G.2) to understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts (3.NF.1). Problem 1 states, “Share 3 pancakes equally among 6 people. Draw a picture to show part of the 3 pancakes that each person gets. Write your answer next to your picture.”  
• In Lesson 2-4, Teacher’s Lesson Guide, Math Message, students fluently add and subtract within 1000 (3.NBT.2) to solve two-step word problems (3.OA.8). Teachers present students with a picture of a vending machine that contains snacks ranging from 25 cents to 75 cents. Teacher prompt states, “You have 80 cents in your pocket. Estimate. Do you have enough money to buy two packages of the same snack? Which snack? Write your answer on your slate.” In the Student Math Journal, Problem 1, “A package of rice cakes contains 6 rice cakes. You buy 2 packages of rice cakes and then eat 4 rice cakes. How many rice cakes are left?” 
• In Lesson 3-7, Teacher’s Lesson Guide, Focus: Exploration C: Partitioning Rectangles, students partition shapes into parts with equal areas (3.G.2) to understand the concepts of area and relate area to multiplication (3.MD.6). In the Math Masters, Problem 3, “Draw lines to partition the rectangle into 5 rows with 6 same-size squares in each row. You may use a square pattern block to help. How many squares cover the rectangle? Talk to a partner.” Problem 4, “How did you figure out the total number of squares?” Problem 5, “How are the rectangles in Problems 2 and 3 like arrays?” 
• In Lesson 4-6, Student Math Journal, students measure sides of rectangles and triangles (3.MD.D) and write number sentences to determine the perimeter (3.OA.D). Problems 1-4 include 2 rectangles and 2 triangles, “Measure the sides of each polygon to the nearest half inch. Use the side lengths to find the perimeters. Write a number sentence to show how you found the perimeter.”
• In Lesson 5-3, Teacher’s Lesson Guide, students partition shapes into parts with equal areas (3.G.2) to compare two fractions with the same numerator or the same denominator by reasoning about their size (3.NF.3d). In the Math Message, students are presented with a problem that depicts two circular, but different-sized pizzas, “Quan ate 1-fourth of this pizza.  Aiden ate 1-fourth of this pizza. Partition and shade each pizza to show how much pizza each boy ate. Quan said they ate the same amount because they both ate 1-fourth of a pizza. Do you agree with Quan? Explain.”

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

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

• There are 9 instructional units with 108 lessons. Open Response/Reengagement lessons require 2 days of instruction adding 9 additional lesson days.
• There are 37 Flex Days that can be used for lesson extension, journal fix-up, differentiation, or games; however, explicit teacher instructions are not provided.
• There are 24 days for assessment which include Progress Checks, Open Response Lessons, Beginning-of-the-Year Assessment, Mid-Year Assessment, and End-of-Year Assessment.   

The materials note lessons are 60-75 minutes and consist of 3 components: Warm-Up: 5-10 minutes; Core Activity: Focus: 35-40 minutes; and Core Activity: Practice: 20-25 minutes.

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

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

• Unit 4, Teacher’s Lesson Guide, Links to the Past, “3.MD.5, 3.MD.5b: In Grade 2, children partitioned rectangles into rows and columns of squares of the same size and counted them to find the total in preparation for understanding area.”  
• Unit 6, Teacher’s Lesson Guide, Links to the Past, “3.NBT.2: In Unit 2, children used extended addition/subtraction facts to solve real-world and mathematical problems. In Unit 3, children were introduced to algorithms. In Grade 2, children added and subtracted within 1,000 using concrete models or drawings, partial-sums addition, and expand-and-trade subtraction.”  
• Unit 8, Teacher’s Lesson Guide, Links to the Past,”3.MD.4: In Unit 4, children measured lengths to the nearest 1/2 inch and whole centimeter and represented the data in line plots. In Grade 2, children measured length to the nearest whole unit and represented the data in line plots.”  

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

• Unit 4, Teacher’s Lesson Guide, Links to the Future, “3.MD.6: In Unit 5, children will explore using square units to make the different shapes with the same area.”
• Unit 6, Teacher’s Lesson Guide, Links to the Future, “3.NBT.2: Throughout Grade 3, children will use strategies and algorithms to solve addition and subtraction number stories and problems within 1,000. In Grade 4, children will add and subtract multidigit whole numbers using the standard algorithm.”
• Unit 8, Teacher’s Lesson Guide, Links to the Future, “3.MD.4: In Grade 3, children will measure lengths using rulers marked with $$\frac{1}{2}$$ and $$\frac{1}{4}$$ of an inch and represent the data in line plots. In Grade 4, children will review line plots and create line plots that include smaller fractional units of length and weight.”

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

• In Lesson 2-9, Teacher’s Lesson Guide, Modeling Division, Focus, Modeling with Division, “Children divide to solve number stories and learn about remainders, (3.OA.2, 3.OA.3).” For example, “3 children share 13 pennies. How many pennies will each child get? What is the dividend in this problem? What is the divisor in this problem? What is the quotient in this problem? What is the remainder?” Division with remainders is aligned to 4.NBT.6, “Find whole-number quotients and remainders with up to four-digit dividends and one-digit divisors.” Division with remainders continues in Lesson 2-10.
• In Lesson 8-3, Teacher’s Lesson Guide, Factors of Counting Numbers, Focus, Finding Factors, “Children relate factors and fact families and identify factor pairs for products, (3.OA.4, 3.OA.6, 3.OA.7, and 3.NBT.3).” For example, “How could you use 3 x 4 = 12 to find factor pairs for 120? How many tens are in 180? What basic facts have 18 as a product?” This aligns to 4.OA.4 (“Gain familiarity with factors and multiples. Find all factor pairs for a whole number in the range 1-100. Recognize that a whole number is a multiple of each of its factors. Determine whether a given whole number in the range 1-100 is a multiple of a given one-digit number”).
• In Lesson 8-6, Teachers Lesson Guide, Sharing Money, Focus, Making Sense of Remainders, “Children solve a sharing problem involving a remainder, (3.OA.2, 3.OA.3, 3.OA.7, and 3.NF.1).” For example, “Have partnerships use their bills to make $49 and then solve the first Try This problem. Look for children to model sharing $49 equally among 4 people in the following ways: Each person gets $12 and there is a dollar remaining. Each person gets 12 whole dollars and 1/4 of a dollar. Each person gets $12 and 1 quarter. Each  person gets $12 and 25 cents or $12.25.” Solving multi-step word problems posed with whole numbers and having whole-number answers using the four operations in which remainders must be interpreted aligns to 5.NBT.7.

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

• In Lesson 3-4, Math Journal 1, Column Addition, “Estimate. Then use column addition to solve Problems 1 and 2. Use any strategy to solve Problem 3. Use your estimates to check whether your answers make sense. Problem 1, 67 + 25 = ? Estimate:  ” (3.OA.8, 3.NBT.2)
• In Lesson 8-1, Math Journal 2, Problem 1. “Think about where each of the fractions below belong on the number line. Then write one of the fractions in each box for A, B, C, and D on the number line. $$\frac{1}{2}$$, $$\frac{1}{3}$$, $$\frac{1}{4}$$, $$\frac{3}{4}$$; Explain how you figured out the location of $$\frac{3}{4}$$ on the number line. What is another fraction name for the point you labeled $$\frac{1}{2}$$?.” (3.NF.2,3)

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

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

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

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

• Lesson 5-6 connects 3.OA.B with 3.MD.C as students use doubling and halving strategies to solve number stories involving area. In the Student Math Journal, Problem 4, “Your friend is planning a rectangular garden that is 6 feet wide and 7 feet long. To buy the correct amount of fertilizer, she needs to find the area of the garden, but she does not know how to solve 6 x 7. Show how your friend could use doubling to figure out the area.” 
• Lesson 7-12 connects 3.NF.A and 3.OA.A as students name fractions for a set of objects. In the Teacher’s Lesson Guide, “Jules has a stamp collection with 12 stamps. She puts ½ of her stamps on one page and the other ½ on another page. How many stamps are on each page? You may use counters or drawings to help.” 
• Lesson 8-7 connects 3.MD.C with 3.OA.B as students create rectangles using given area measures. In Activity Card 91, students, “You and your partner make rectangles with the areas given in the table on journal page 268. For each rectangle you make, record the lengths of two sides that touch.” Students then answer 3 questions in their journals relating to the squares they made during the activity. In the Student Math Journal, Problem 1, “Study your table. What pattern or rule do you see?”