3rd Grade - Gateway 1

The materials reviewed for Reveal Math Grade 3 meet expectations for assessing grade-level content, and if applicable, content from earlier grades. Each unit contains a Performance Task, two Summative Assessments, and editable auto-scored assessments in the digital library. The summative assessments, found in the Assessment Resource Book, include two forms (Form A and B) for each Unit Assessment. The Assessment Resource Book also includes three Benchmark Assessments and a Summative Assessment at the end of the book. There is no Unit 1 Assessment or Performance Task.

Examples of grade-level assessment items include:

• Unit 2, Use Place Value to Fluently Add and Subtract within 1,000, Performance Task, Parts A, B, and C, students have number cards from 0-9 that they use to make 3-digit numbers. “Round your numbers to the nearest hundred and the nearest ten.” (3.NBT.1) “Use the number cards. What is the greatest possible sum of two 3-digit numbers?” (3.NBT.2) “Use the number cards. What is the greatest possible difference of two 3-digit numbers?” (3.NBT.2) 

• Benchmark Assessment 1, Item 13, “Which expression is equal to 89? A. 9 + 8, B.9 - 8, C. 98, D. 98.” (3.OA.5)

• Unit 5, Use Properties to Multiply by 3, 4, 6, 7, 8, and 9, Unit Assessment, Form B, Item 11, “What completes the equation 3 x ___= 15? A. 4, B. 5, C. 6, D. 7.” (3.OA.4) 

• Unit 7, Fractions, Unit Assessment, Form A, Item 12, “Kira says she ran \frac{5}{1} miles. How many miles did Kira run? Explain.” (3.NF.3c)

• Unit 11, Perimeter, Unit Assessment, Form A, Item 7, “What is the perimeter of this figure?” (3.MD.8)

• Summative Assessment, Item 10, “Elena has 4 bags of dog food. Each bag has a mass of 7 kilograms. What is the total mass, in kilograms, of the bags?” (3.MD.2)

Reveal Math does assess students with fractions that have denominators other than the grade level expectation of 2, 3, 4, 6, and 8. These items could be modified or omitted without impacting the structure of the materials. Examples include:

• Benchmark Assessment 3, Item 11, “Decide whether each comparison is true or false. Choose True or False for each comparison.  \frac{3}{5} < \frac{2}{5}\frac{2}{5}.” Although the fractions being compared have the same denominator, fractions with a denominator of 5 are a Grade 4 expectation, (4.NF.2). Grade 3 fractions are limited to denominators of 2, 3, 4, 6, and 8. 

• Benchmark Assessment 3, Item 18, “Match each fraction to an equivalent fraction. Not all fractions will be used. \frac{1}{4}, \frac{3}{3}, \frac{8}{12}, \frac{2}{8}, \frac{1}{6},  \frac{2}{3}, \frac{4}{5}, frac{4}{4}.” Equivalent fractions are part of the Grade 3 standard, however, \frac{8}{12} has a denominator of 12 which is a Grade 4 expectation, (4.NF.1).  Grade 3 fractions are limited to denominators of 2, 3, 4, 6, and 8. 

• Unit 13, Describe and Analyze 2-Dimensional Shapes, Unit Assessment, Form A, Item 4, “How can you describe the quadrilaterals using the number of parallel sides, side lengths, and angles? ___ pair(s) of parallel lines. ___ pairs of equal sides. ___ right angle(s).” Parallel lines are not introduced to students until Grade 4, (4.G.1). Right angles are not introduced to students until Grade 4, (4.G.2)

The materials reviewed for Reveal Math Grade 3 meet expectations for giving all students extensive work with grade-level problems to meet the full intent of grade-level standards. Within the materials, all standards are represented, and all meet the full intent of the grade-level standard.

Examples where the materials engage all students in extensive work with grade-level problems to meet the full intent of the standard include:

• In Lesson 2-9, Use Addition to Subtract, Reinforce Understanding, Exercise 4, students add and subtract within 1000 using the relationship between addition and subtraction. “Write a related addition equation for each subtraction equation. 1. 845 - 193 = ?, 2. 679 - 291 = ?, 3. 712 - 436 = ?, 4. 363 - 192 = ?” This exercise engages students with the full intent of 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.

• In Lesson 4-5, Multiply Fluently by 0, 1, 2, 5 and 10, On my Own, Exercise 6, students multiply and divide within 100. “How can you complete the equation? 2 x 7 = ?” In Exercise 9, “How can you complete the equation? ___ = 5 x 6.” Then in Lesson 9-3, Use Multiplication to Divide, On my Own, Exercise 11, students divide within 100. “Leon has 60 tickets. He wants to use all of his tickets, but is only allowed to get 6 prizes. How can he use all his tickets to buy only 6 prizes?” These exercises engage students with the full intent of 3.OA.7, fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division or properties of operations. 

• In the Interactive Student Edition, Lesson 6-1, Exercise 3, students “Draw to complete the tiling. Then find the area.” Students are provided with an irregular polygon to calculate the area. This exercise engages students with the full intent of 3.MD.7a, find the area of a rectangle with whole-number side lengths by tiling it, and show that the area is the same as would be found by multiplying the side lengths. 

• In Lesson 8-6, Teacher Edition, Compare Fractions with the Same Numerator, Develop the Math, Activity-Based Exploration, students create two fractions with the same numerators, compare the fractions, and discuss conclusions based on their results. “Divide students into pairs. Provide a number cube, spinner and the Spinner Numbers to each pair. Instruct the pair to spin the spinner to identify the numerator both partners will use. Then each partner rolls the number cube to identify the denominator each partner will use for their fraction. The partners decide which of their fractions is greater and record the comparison with a symbol. Students may need fraction tiles or fractions circles for support.” Support Productive Struggle: Ask students, “How is comparing fractions with the same numerator like comparing fractions with the same denominator? How is it different? What do you know about the parts of each whole in the fraction? How can you use the fraction models to help you compare?” This exercise engages students with the full intent of 3.NF.3, explain equivalence of fractions in special cases, and compare fractions by reasoning about their size.

• In Lesson 13-2, Digital Interactive Student Edition, Describe Quadrilaterals, Exercise 7, “Choose the correct answer. I am a quadrilateral with 0 pairs of parallel sides, 0 pairs of equal sides, and 0 right angles. What shape am I?” This provides students with the opportunity to identify the attributes of a quadrilateral, and recognize the specific example of a quadrilateral for this exercise. This exercise engages students with the full intent of 3.G.1, understand that shapes in different categories (e.g., rhombuses, rectangles, and others) may share attributes (e.g., having four sides), and that the shared attributes can define a larger category (e.g., quadrilaterals). Recognize rhombuses, rectangles, and squares as examples of quadrilaterals, and draw examples of quadrilaterals that do not belong to any of these subcategories.

The materials reviewed for Reveal Math Grade 3 meet expectations that, when implemented as designed, the majority of the materials address the major clusters of each grade. 

Within the materials, at least 65% of instructional materials address the major work of the grade, or supporting work is connected to the major work of the grade. For example: 

• There are 13 Units, of which 8.5 address major work, or supporting work connected to major work of the grade, approximately 65%.

• There are 92 lessons, of which 68.5 address major work, or supporting work connected to major work, approximately 74%.

• There are 154 days of instruction, 101 of which address major work, or supporting work connected to major work, approximately 66%.

The materials contained discrepancies with the number of days per unit, and guidance was not given as to how those days were accounted for; therefore, a lesson level analysis is most representative of the materials. As a result, approximately 74% of the instructional materials focus on major work of the grade.

The materials reviewed for Reveal Math Grade 3 meet expectations that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Some supporting standards (Rounding 3.NBT.1, use place value understanding to round whole numbers to the nearest 10 or 100) are taught in isolation, but the separation is mathematically reasonable. 

Examples of supporting work engaging simultaneously with major work of the grade when appropriate include:

• In Lesson 2-4, Use Addition Properties to Add, Practice & Reflect, On My Own, Exercise 12, connects the supporting work of 3.NBT.2, fluently add and subtract within 1000 to the major work of 3.OA.8, solve two-step word problems using the four operations. “Mrs. Ruiz is checking her receipt. The three items cost $305, $350, and $195. How can she use both properties of addition to add more efficiently?”

• In Lesson 7-2, Understand Fractions, Extend Thinking, Differentiation Resource Book, connects the supporting work of 3.G.2, partition shapes into parts with equal areas to the major work of 3.NF.1, understand a fraction \frac{1}{b} as the quantity formed by 1 part when a whole is partitioned into b equal parts. “Ravi says \frac{1}{2} of this figure is shaded? What would you say to Ravi? How else can the rectangle be divided evenly with the same amount shaded? What fraction represents that amount. Show your work.”

• In Lesson 10-6, Explain the Reasonableness of a Solution, Additional Practice, Exercise 4  connects the supporting work of 3.NBT.3, multiply one-digit whole numbers by multiples of ten to the major work of 3.OA.8, assessing the reasonableness of answers using estimation strategies. “Find the solution. Then show an estimate to check the reasonableness of your answer. Quentin builds 4 robots with his construction blocks set. He needs 80 construction blocks to build one robot. He has 463 construction blocks. He estimates he will have 130 construction blocks left. Is his estimate reasonable?”

• In Lesson 11-2, Determine Perimeter of Figures, Practice & Reflect, On My Own, Exercise 9, connects the supporting work of 3.MD.8, solve real world and mathematical problems involving perimeters of polygons to the major work of 3.OA.8, solve two-step word problems using the four operations. “How can you determine the perimeter of a rectangle that is 3 cm wide and 5 cm long in two different ways? Which strategy do you think is more efficient?”

• In Lesson 11-4, Solve Problems Involving Area and Perimeter, Assess, Exit Ticket, Exercise 3, connects the supporting work of  3.MD.8, solve real world and mathematical problems involving perimeters of polygons to the major work of 3.MD.7, relate area to the operations of multiplication and addition. “Sara draws two rectangles that have the same area but different perimeters. Which rectangles could be the rectangles she draws?”

• In Lesson 12-11, Show Measurement Data on a Line Plot, Build Proficiency, Student Practice Book, Exercise 3, connects the supporting work of 3.MD.4, generate measurement data by measuring lengths using rulers marked with halves and fourths of an inch to the major work of 3.NF.2, understand a fraction as a number on the number line; represent fractions on a number line diagram. “How can you create a line plot from the data in the table?”

• In Lesson 12-9, Solve Problems Involving Scaled Graphs, Practice & Reflect, On My Own, Exercise 9, connects the supporting work of 3.MD.3, draw scaled picture graphs and scaled bar graphs to represent a data set with several categories to the major work of 3.OA.8, solve two-step word problems using the four operations. “Maya visits a second dig site. She collects 5 fewer samples of each type. How many total samples does she collect at the second dig site? Show your work.”

The materials reviewed for Reveal Math 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 materials contain connections from supporting work to supporting work, and connections from major work to major work throughout the grade-level materials when appropriate.

Connections between major clusters or domains include:

• Lesson 4-5, Multiply Fluently by 0, 1, 2, 5, and 10, On My Own, Extend Your Thinking, Exercise 15, connects the major work of 3.OA.D, Solve problems involving the four operations, and identify and explain patterns in arithmetic, to the major work of 3.OA.C, Multiply and divide within 100. “Dawn spills her drink on her homework and can only see the answers. What multiplication facts could she have been practicing? Explain.” All numbers shown in the exercise are multiples of 10.

• In Interactive Student Edition, Lesson 5-5, On My Own Part 1: Use Properties to Multiply by 8, Exercise 2 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, as students decompose a multiplication equation using an array. Students solve, “Show your answer. Jonathan placed cubes in 8 rows, with 6 cubes in each row. How can you decompose a factor to find the number of cubes he placed?”

• In Lesson 6-2, Count Unit Squares to Determine Area, Differentiate, Extend Thinking, Exercise 2 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.C, multiply and divide within 100, as students use multiplication to calculate area. “Solve each problem. Show your work and explain your answers. Kari made a map of a park that is 16 square inches. Which of these could be the side lengths of the map? 2 in by 8 in, 8 in by 4 in, 4 in by 4 in.”

• In Lesson 9-1, Use Multiplication to Solve Division Equations, Differentiate, Extend Thinking, Differentiation Resource Book, Exercise 1 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.OA.A, Represent and solve problems involving multiplication and division, as students make connections between interpreting products of whole numbers to division as unknown-factor problems. “Mario drew an array and wrote parts of the 4 equations it represents. Complete the equations for his array and explain how it represents 2 multiplication and 2 division equations.  ___ x ___ = 24, 24___ = ___, ___ x ___ = 24, 24 ___ x ___.” This is presented with a 4 by 6 array of stars.        

• In Lesson 12-1, Measure Liquid Volume, Practice & Reflect, On My Own, Exercise 4 connects the major work of 3.MD.A, Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects to the major work of 3.NF.A, Develop understanding of fractions as numbers, as students measure liquid volumes in fractional increments. In Exercise 4, “What is the liquid volume?” Students are presented with a picture of a container with 1\frac{1}{2} liters of red liquid.         

• In Lesson 12-4, Estimate and Solve Problems with Mass, Own My Own, Exercise 9 connects 3.MD.A, Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects, to the major work of 3.OA.A, Represent and solve problems involving multiplication and division, as students multiply kilograms. “Rakesh bought blueberries, raspberries, blackberries, and strawberries for his bakery. He bought 4 kilograms of each type of berry. How many kilograms of berries did he buy? Show your work.”

Connections between supporting clusters or domains include:

• In Interactive Student Edition, Lesson 11-2, Guided Exploration: Measure Mass, Exercise 2: Develop the Math connects the supporting work of 3.MD.D, Geometric measurement: 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, as students use addition to calculate perimeter. “We can use an addition equation to find the perimeter. What is the perimeter of the square garden?” Students are presented with a square garden that is 2 yards on each side.

The materials reviewed for Reveal Math 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. 

Content from future grades is identified within the chapters, units, and lessons; and is connected to grade-level work. Examples include:

• Lesson 4-3, Use Patterns to Multiply by 10, Coherence, Now, includes 3.OA.7, multiply and divide within 100. “Students use patterns to multiply with 10.” In Coherence, Next, “Students extend their understanding of basic facts by multiplying with other numbers (Unit 4). Students multiply multi-digit numbers by whole numbers (Grade 4).” 4.NBT.5, Multiply a whole number of up to four digits by a one-digit number, and multiply two two-digit numbers…

• Lesson 6-5, Use Distributive Property to Determine Area, Coherence, Now, includes 3.MD.7, relate area to the operations of multiplication and addition. “Students apply the Distributive Property to find area.” In Coherence, Next, “Students solve problems involving area and perimeter (Unit 11). Students use equations to find length and width when given the area in real-world problems (Grade 4).” 4.MD.3, apply the area and perimeter formula for rectangles in real world and mathematical problems.

• Lesson 8-6, Compare Fractions with the Same Numerator, Teacher Edition, Previous, Now, Next, includes 3.NF.2, develop understanding of fractions as numbers, “students use the size of the denominator to compare fractions with the same numerator.” In Next, “students add and subtract fractions (Grade 4)” 4.NF.3, understand a fraction a/b with a>1 as a sum of fractions 1/b.

• Lesson 11-2, Determine Perimeter of Figures, Teacher Edition, Coherence, 3.MD.8, solve real world and mathematical problems involving perimeters of polygons including finding the perimeter given the side lengths... “Now: Students extend their understanding of perimeter by using addition and multiplication to find the perimeter of figures” In Next, “Students solve real-world problems involving perimeter and area (Grade 4).” 4.MD.3, apply the area and perimeter formula for rectangles in real world and mathematical problems.

Examples where the instructional materials relate grade-level concepts explicitly to prior knowledge from earlier grades include: 

• Lesson 2-4, Use Addition Properties to Add, Coherence, Now includes 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. “Students explore addition properties by grouping addends or changing the order of addends to add more efficiently.” In Coherence, Previous, “Students used place value understanding and properties of operations to add and subtract (Grade 2).” 2. NBT.5, use place value understanding and properties of operations to add and subtract.

• Lesson 8-7, Compare Fractions, Teacher Edition, Previous, Now, Next, includes 3.NF.A, develop understanding of fractions as numbers, “Students compare fractions by using the size of the denominator and the size of the numerator.” In Previous, “Students compared numbers using <, >, and = (Grade 2).” 2.NBT.4, compare two three-digit numbers based on meanings of the hundreds, tens, and ones digits, using >,=, and < symbols to record the results of comparisons.

• Lesson 11-3, Determine an Unknown Side Length, Teacher Edition, Coherence, Now, 3.MD.8, solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length... “Students solve real-world problems involving perimeter.” In Previous, “Students measured lengths by choosing correct tools (Grade 2).” 2.MD.1, measure the length of an object by selecting and using appropriate tools such as rulers, yardsticks, meter sticks, and measuring tapes.

• Unit 12 Overview, Measurement and Data, Teacher Edition, Coherence, Now, includes 3.MD.A, solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects as “Students tell time to the nearest minute and measure time intervals in minutes.” In Previous, “Students told time to the nearest 5 minutes (Grade 2).” 2.MD.7, tell and write time from analog and digital clocks to the nearest five minutes, using a.m. and p.m.