3rd Grade - Gateway 1

The materials reviewed for Everyday Mathematics 4, Grade 3 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, “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)

Materials assess above-grade assessment items that could be removed or modified without impacting the structure or intent of the materials. Examples 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\times5=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\times0= ____, (45-12)\times0= ____. b. Explain why the two number sentences have different answers.” (5.OA.1)

The materials reviewed for Everyday Mathematics 4 Grade 3 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 3-4, Column Addition, Focus: Introducing Column Addition, students learn column addition and compare it to partial-sums addition, “Display 47+68=? vertically. With the class, solve additional problems using column addition. 78+65=?, 439+171=?.” Student Math Journal 1, students practice column addition with multi-digit numbers, “Problem 1. 67+25=? Estimate: Problem 2. 227+386=? Estimate: Problem 3. 481+239=? Estimate:” Students engage in extensive work with grade-level problems for 3.NBT.2, “Fluently add and subtract within 1000 using strategies and algorithms based on place value, properties of operations, and/or the relationship between addition and subtraction.”

• Lesson 5-2, Representing Fractions, Focus: Representing Fractions, students represent fractions in different ways, “Display the Representing Fractions chart to help children connect fraction words, standard notion, and pictures.” A chart is provided for students to fill in with the teacher. Student Math Journal 2, “Use your fraction circle pieces to help you complete the table. Pay attention to the whole in each problem. 1. The whole is the orange piece. 2. The whole is the yellow piece. 3. The whole is the pink piece. 4. The whole is the red circle.” Students engage in extensive work with grade-level problems for 3.NF.1, “Understand a fraction 1/b as the quantity formed by 1 part when a whole is partitioned into b equal parts; understand a fraction a/b as the quantity formed by a parts of size \frac{1}{b}.”

• Lesson 8-1, Measuring to the Nearest \frac{1}{4} Inch, Practice: Matching Fractions on a Number Line, Math Journal 2, Problem 1, students match fractions to their position on a number line, “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 for the point you labeled \frac{1}{2}?” Student Math Journal 2, Students engage in extensive work with grade-level problems for 3.NF.2, “Understand a fraction as a number on the number line; represent fractions on a number line diagram” and 3.NF.3, “Explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.”

The materials provide opportunities for all students to engage with the full intent of Grade 3 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 1-3, Tools for Mathematics, Focus: Reviewing Length Measurement, Math Journal 1, students tell and write time to the nearest minute, “For Problems 1 and 2, record the times shown on the clocks. For Problem 3, draw the minute and hour hands to show the time.” Three clock images are provided. 1. 8:30, 2. 2:45, 3. 6:10. Lesson 5, Time, Focus, Telling Time to the Nearest Minute, Math Journal 1, Problems 1-6, students tell and record time to the nearest minute, “Write the time shown on each clock.” Six clock images are provided. Lesson 6, How Long Is a Morning?, Focus, Math Message, Math Journal 1, students make sense of the solution to an elapsed-time problem that uses an open number line, “Sheena’s math class began at 9:55 A.M. and ended at 11:10 A.M. She started to figure out how long the class lasted. She used a number line. Use Sheena’s number line to complete the problem. Tell the length of time in hours and minutes. Math class lasted ___ hour and ___ minutes. Explain Sheena’s strategy to your partner.” Students engage in the full intent of 3.MD.1, “Tell and write time to the nearest minute and measure time intervals in minutes. Solve word problems involving addition and subtraction of time intervals in minutes, e.g., by representing the problem on a number line diagram.”

• Lesson 4-7, Area and Perimeter, Focus: Comparing Perimeter and Area, Math Journal 2, students use squares to compare perimeter and area, “For Problems 1-3, find the perimeter and the area of the rectangle.” The figure in Problem 1 has an area of 14 square feet and a perimeter of 18 feet. The figure in Problem 2 has an area of 24 square meters and a perimeter of 20 meters. The figure in Problem 3 has an area of 24 square miles and a perimeter of 22 miles. Try This, “Find the perimeter and the area of this shape.” The Figure has an area of 15 square centimeters and a perimeter of 18 centimeters. Lesson 4-8, Area and Composite Units, Focus, Distinguishing Area and Perimeter, Math Journal 1, Problem 1, students compare finding the area and perimeter of rectangles, “Use the shaded composite unit to find the area of each rectangle.” The Figure shown has an area of 8 square units. Lesson 5-1, Focus, Exploration B: Finding All Possible Shapes, Activity Card 63, students explore different shapes with the same area and then find the perimeter, “Connect five 1-inch pattern-block squares so at least one side of each block touches another side. Keep track of each shape you make. Lightly shade the square inches on grid paper. Help each other find all the possible shapes using five pattern blocks. Check that each shape cannot be turned or flipped to match a shape that was already recorded.” Students engage in full intent of 3.MD.6, “Measure areas by counting unit squares (square cm, square m, square in, square ft, and improvised units.” 

• Lesson 5-3, Equivalent Fractions, Focus: Recognizing Equivalent Fractions, Math Journal 2, Math Message, Problems 1-3, students generate equivalent fraction names for 1-half, “Wait for your teacher to explain these problems. 1. Lara ate 1 piece of her pizza. Nicole ate 2 pieces of her pizza. Shade in the number of pieces of pizza each child ate. 2. Who ate more pizza? How do you know? 3. Write a fraction showing how much pizza each child ate. Lara: ___. Nicole: ___.” Lara’s pizza is shaded 1 of 2, or half. Nicole’s pizza is shaded 2 of 4, or half. Focus, Equivalent Names for Fractions, Math Journal 1, Problem 1, “Partition each circle in the name collection box to show different ways to represent \frac{1}{2}. Then add other equivalent fraction names.” The names are 1-half, 1-fourth, and 1-third. Practice, Math Masters, Problems 1-6, “The pictures show three kinds of fruit pie. Use a straightedge to do the following: 1. Divide the peach pie into 4 equal pieces. Shade 2 of the pieces. 2. Divide the blueberry pie into 6 equal pieces. Shade 3 of the pieces. 3. Divide the strawberry pie into 8 equal pieces. Shade 4 of the pieces. What fraction of each piece did you shade? 4. I shaded ____ of the peach pie. Write another name for this fraction: ___. 5. I shaded ___ of the blueberry pie. Write another name for this fraction: ___. 6. I shaded ___ of the strawberry pie. Write another name for this fraction: ___. Explain to someone at home how you know that all of the fractions on this page are equivalent.” Students engage in the full intent of 3.NF.3b, “Recognize and generate simple equivalent fractions, e.g., \frac{1}{2}=\frac{2}{4}, \frac{4}{6}=\frac{2}{3}. Explain why the fractions are equivalent, e.g., by using a visual fraction model.”

The materials reviewed for Everyday Mathematics 4 Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major work of each grade.

• 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 the 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.

A lesson analysis is most representative of the materials. As a result, approximately 68% of the materials focus on the major work of the grade.

The materials reviewed for Everyday Mathematics 4 Grade 3 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 1-12, Exploring Mass, Equal Shares, and Equal Groups, 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.” 

• Lesson 2-4, Multistep Number Stories, Part I, 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. The 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?” 

• Lesson 3-7, Exploring Bar Graphs, Area, and Partitioning Rectangles, 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?” 

• Lesson 4-6, Perimeter, Math Journal 1, students measure the 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.”

• Lesson 5-3, Equivalent Fractions, Math Message, 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). 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 materials reviewed for Everyday Mathematics 4 Grade 3 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 2-6, Equal Groups, Math Journal 1, Problem 1, students solve equal group number story problems. “Shanna buys 3 boxes of mini stock cars to share with her classmates. How many cars does she have all together? Answer: ___. Number model: ___. How much do 3 boxes of cars cost? Answer: ___ Number model: ___.” This connects the major work of 3.OA.A, “Represent and solve problems involving multiplication and division,” to the major work of 3.OA.C, “Multiply and divide within 100.”

• Lesson 4-6, Perimeter, Focus: Math Message, students trace pattern blocks and discuss ways to measure the distance around them. “Take a pattern block. Trace the shape of the block on a piece of paper. What shape did you draw? How do you know? Talk to a partner about how you might measure the distance all the way around the shape you drew.” This connects the supporting work of 3.MD.B, “Represent and interpret data,” to the supporting work of 3.G.A, “Reason with shapes and their attributes.”

• Lesson 4-7, Area and Perimeter, Math Masters, Problem 1, students fluently add numbers to find the perimeter, “Dale said the perimeter of this rectangle is 16 feet and the area is 12 square feet. Do you agree? Explain.” This connects the supporting work of 3.MD.D, “Recognize perimeter as an Attribute of Plane figures and distinguish between linear and area measures” to the supporting work of 3.NBT.A, “Use place value understanding and properties of operations to perform multi-digit arithmetic.”

• Lesson 5-6, Multiplication Fact Strategies: Doubling Part 2, Math Journal 2, problem 4, students use doubling and halving strategies to solve number stories involving area. “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.” This connects the major work of 3.OA.B, “Understand properties of multiplication and the relationship between multiplication and division” to the major work of 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and to addition.”

• Lesson 7-12, Fractions of Collections, Focus: Identifying Fractions of Collections, students name fractions for a set of objects. “Jules has a stamp collection with 12 stamps. She puts \frac{1}{2} of her stamps on one page and the other \frac{1}{2} on another page. How many stamps are on each page? You may use counters or drawings to help.” This connects the major work of 3.NF.A, “Develop understanding of fractions as numbers” to the major work of 3.OA.A, “Represent and solve problems involving multiplication and division.”

• Lesson 8-7, Exploring Number Lines, Fractions, and Area, Activity Card 91, students create rectangles using given area measures. “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?” This connects the major work of 3.MD.C, “Geometric measurement: understand concepts of area and relate area to multiplication and to addition” to the major work of 3.OA.B, “Understand properties of multiplication and the relationship between multiplication and division.”

The materials reviewed for Everyday Mathematics 4 Grade 3 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 4, Measurement and Geometry, 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, More Operations, 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, Multiplication and Division, Teacher’s Lesson Guide, Links to the Past, ”3.MD.4: In Unit 4, children measured lengths to the nearest \frac{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.” 

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 4, Measurement and Geometry, Teacher’s Lesson Guide, Links to the Future, “3.G.1: In Grade 4, children will begin more formal geometry work with angles.”

• Unit 6, More Operations, 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, Multiplication and Division, 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.”

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

• Lesson 2-9, 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.

• Lesson 8-3, 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\times4=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”).

• Lesson 8-6, 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 \frac{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.