3rd Grade - Gateway 1

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 meet expectations for assessing grade-level content.

Examples of assessment items aligned to grade-level standards include:

• Chapter 1, Test A, Assessment Book, Item 7, “You want to play as many games as possible with 18 tokens. Each game costs 3 tokens. Which model can you use to find how many games you can play?” Students determine which of 3 models represent $$18\div3$$. (3.OA.2)
• Chapter 3, Test A, Assessment Book, Items 1-6, “Find the product. [9 x 3, 4 x 5, 6 x 6, 10 x 7, 8 x 4, 7 x 9]”. (3.OA.7)
• Chapter 7, Test A, Assessment Book, Items 1-4, “1. Round 54 to the nearest 10; 2. Round 770 to the nearest hundred; 3. Round 44 to the nearest ten; 4. Round 550 to the nearest hundred.” (3.NBT.1)
• Chapter 9, Test A, Assessment Book, Item 11, “Find 8 x 50. How many hundreds are in the product? How many tens?” (3.NBT.3)

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 assessment items that assess above grade-level content include:

• Chapter 2, Test B, Assessment Book, Item 12, “Tell whether the number 15 is a multiple of 2, 5, or both.” (4.OA.4)
• Chapter 3, Test A, Assessment Book, Item 9, “Which are not multiples of 9? 18, 24, 71, 81, 27, 35”. (4.OA.4)

The instructional materials reviewed for Big Ideas Math: Modeling  Real Life Grade 3 meet expectations for spending a majority of instructional time on major work of the grade. 

To determine the focus on major work, three perspectives were examined: the number of chapters devoted to major work, the number of lessons devoted to major work, and the number of days devoted to major work. 

• The approximate number of chapters devoted to major work of the grade (including assessments and supporting work connected to the major work) is 10.5 out of 15 chapters, which is approximately 70% of the instructional time.
• The number of lessons devoted to major work of the grade (including assessments and supporting work connected to the major work) is 83 out of 98 lessons, which is approximately 85% of the instructional time.
• The number of days devoted to major work (including assessments and supporting work connected to the major work) is 111 out of 158 days or 70%.

A day-level analysis is most representative of the instructional materials because the number of days is not consistent within chapters and lessons.  As a result, approximately 70% of the instructional materials focus on the major work of the grade.

The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 3 meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade.

Examples of the connections between supporting work and major work include the following:

• Chapter 7, Lesson 5, connects the supporting work of understanding place value to perform multi-digit arithmetic (3.NBT.2) with the major work of solving two-step word problems (3.OA.8). In the Think and Grow section, Problems 20 and 21, students add two 3-digit numbers and then subtract in order to find "about how many more" in a two-step word problem.
• Chapter 10, Lesson 2, connects the supporting work of partitioning shapes with equal areas (3.G.2) to the major work of understanding a fraction 1/b as the quantity formed by one part when the whole is partitioned into b equal parts (3.NF.1). For example, Problem 14 states, “You paint a plate that has 4 equal parts. You paint two parts orange and one part red. You paint the rest of the plate yellow. What fraction of the plate is yellow?”
• Chapter 14, Lesson 6, connects the supporting work of making a line plot using measurement data from measuring lengths (3.MD.4) with the major work of representing a fraction on a number line (3.NF.2). In the Think and Grow section, students are provided a two-inch ruler compared to a number line with the fractions labeled 0/2 through 4/2 to show the correspondence between the number line and a ruler. Students "Measure the length of each line to the nearest half inch. Then record each length on the line plot." Students are provided four different length lines and are asked to fill in the missing numbers on the line plot, then mark the correct length on the line plot.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 meet expectations that the amount of content designated for one grade-level is viable for one year. 

As designed, the instructional materials can be completed in 158 days. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide is found on pages xl and xli in the Teacher’s Guide (Volumes 1 and 2). Grade 3 is divided into 15 Chapters. The 158 instructional days include the following:

• 98 days of Lessons
• 15 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.
• 30 days for “Connect and Grow” Activities - Two days per chapter are dedicated to these activities which include a performance task and chapter practice on one day and centers on the other day. The STEAM performance tasks are designated to be administered the same day as the cumulative practice - following chapters 4, 8, 12, and 15. 
• 15 days for Chapter Assessments - Each chapter has a final chapter assessment.

Three days are set aside for Benchmark Assessments to be used formatively, however the series does not identify when these should be administered.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 meet expectations for being consistent with the progressions in the Standards. The Grade 3 materials develop according to the grade-by-grade progressions with content from prior and future grades clearly identified and related to grade-level work. Materials give students extensive work with grade-level problems and the materials relate grade-level concepts explicitly to prior knowledge from earlier grades.  

Materials develop according to the grade-by-grade progression in the Standards. In addition, Grade 3 standards progress across the grade level. For example:

• The Teacher Edition contains a “Progressions Through the Grades” section (pages xxxiv-xxxv). This contains the vertical progressions and identifies the domain and chapters in which they are found in each grade level. 
• Each chapter contains a chapter overview with a “Through the Grades” chart. The chart shows the chapter learning skills with the progression from Grade 2 through Grade 4.  For example, in Chapter 6, the “Through the Grades” identifies the Grade 2 skill: “Find the total number of squares in a rectangle;” the Grade 3 skill: “Use addition and multiplication to find the area of a shape;” and the Grade 4 skill: “Use area and perimeter formulas to solve word problems.”  The manual does not give specific references to standards. 
• In each chapter, there is a written summarization (Laurie’s Overview/Preparing to Teach) about prior teaching that informs teachers of the conceptual progression of the upcoming chapter/lesson. For example, in Laurie’s Overview for Chapter 1 (pages T-1C and T-1D): “This chapter develops an understanding of multiplication and division through multiple representations: equal groups, equal-sized groups, number lines, skip counting, and writing equations. This understanding builds the foundation for future use with multi-digit whole numbers, integers, fractions, and decimals. Students begin to build connections between prior knowledge of repeated addition and subtraction to see how this knowledge can be applied to a new concept. This interconnectedness of mathematics is important for understanding the progression of numbers and operations, rather than compartmentalizing mathematics as a set of non-related topics.”  
• “Multiply and divide within 100” (3.OA.C) is developed across several chapters. For example, in Chapter 1, the first four lessons develop an understanding of multiplication. These lessons include identifying equal groups, writing a repeated addition equation for equal groups, using a number line to skip count, identifying the number of rows and columns in an array, writing a multiplication equation for an array, and using arrays to show the Commutative Property of Multiplication. The final three lessons develop an understanding of division. These lessons include using division to find the size of equal groups, writing a division equation, using division to find the number of equal groups, using a number line to skip count backward, and writing repeated subtraction equations and a division equation. Chapter 2 includes multiplying by 2, 5, and 10, using properties to multiply by 0 or 2, using the Distributive Property to multiply, and using the problem-solving plan to solve word problems involving multiplication. In Chapter 3, the first six lessons address multiplying by 3, 4, 6, 7, 8, and 9, respectively. Each lesson uses models, develops fact fluency, and includes practice in finding products. Lesson 7 addresses multiplication strategies for multiplying two factors. Lesson 8 introduces the Associative Property of multiplication and multiplying three factors to find a product. The last lesson in the chapter focuses on solving problems involving multiplication. Additional lessons in Chapters 4, 5, 6, 12, 14, and 15 continue work with this standard. 

The instructional materials give all students extensive work with grade-level problems. For example:

• Each lesson has “Explore and Grow” that provides students a hands-on approach. For example, in Chapter 8, Lesson 1, students “use the addition table to write all of the addition equations that have a sum of 13.” 
• Each lesson has “Think and Grow” that offers teacher-guided instruction. For example, in Chapter 3, Lesson 1, students use an array model and the Distributive Property to multiply by 3. 
• Each lesson has “Show and Grow” that presents students with 2-5 problems and helps teachers to formatively assess student understanding. For example, Chapter 4, Lesson 1 includes 4 problems involving division and arrays. 
• Each lesson has “Apply and Grow” which provides students independent practice. For example, Chapter 5, Lesson 2 includes 17 problems for students to solve independently involving multiplication and division facts.
• Each lesson has “Think and Grow: Modeling Real Life” that brings problem solving and real life situations together for students to apply their learning. For example, Chapter 6, Lesson 3 states “Your rectangular animal poster is 4 feet long and 1 foot wide. Which poster has a greater area, your animal poster or your space poster?” (Space poster and its dimensions are shown on the student page.)
• Each lesson has “Connect and Extend Learning” that includes homework and practice problems as well as Cross-Curricular Connections. For example, Chapter 11, Lesson 7 contains a cross-curricular connection for Language Arts, and 11 Homework and Practice Problems.

Each chapter includes a “Progressions Through The Grades” chart that makes explicit connections to the prior knowledge in relation to the content in the chapter. However, there is not explicit guidance by lesson connecting prior knowledge to the content of the lesson, although connections can be made. For example: 

• Chapter 4, Division Facts and Strategies, builds on students' learning of multiplication strategies (arrays) and division in Chapter 1 as well as learning from previous grades (fact families, place value) to use strategies to divide. The mathematics include interpreting whole-number quotients of whole numbers (3.OA.2), using multiplication and division within 100 to solve word problems in situations involving equal groups, arrays, and measurement quantities (3.OA.3), understanding division as an unknown-factor problem (3.OA.4), fluently multiplying and dividing within 100 (3.OA.7), and applying properties of operations as strategies to multiply and divide (3.OA.5).
• In Chapter 6, Relate Area to Multiplication, students build an understanding of area (3.MD.5), measure area by counting unit squares (3.MD.6), and relate area to the operations of multiplication and addition (3.MD.6).
• In Chapter 13, Classify Two-Dimensional Shapes, students build on previous learning of shapes and attributes to identify, classify, and draw shapes. The mathematics of this chapter focuses on identifying shapes by name and attributes, comparing shapes using their attributes, and identifying examples and non-examples of quadrilaterals (3.G.A.1). This grade-level work is the foundation for future work with points, lines, and angles.

The instructional materials for Big Ideas Math: Modeling Real Life Grade 3 meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the Standards. Overall, the materials include learning objectives that are visibly shaped by CCSSM cluster headings, and they provide problems and activities that connect two or more clusters in a domain or two or more domains where the connections are natural and important.

Examples of learning objectives visibly shaped by CCSSM cluster headings include:

• In Chapter 1, Lesson 1, the Learning Target “Use Equal Groups to Multiply” is shaped by 3.OA.B, Understand properties of multiplication and the relationship between multiplication and division.
• In Chapter 6, Lesson 3, the Learning Target “Use multiplication to find the area of a rectangle” is shaped by 3.MD.C, Geometric measurement: understand concepts of area and relate area to multiplication and to addition.
• In Chapter 10, Lesson 3, the Learning Target “Identify and write a fraction” is shaped by 3.NF.A, Develop understanding of fractions as numbers.
• In Chapter 12, Lesson 8, the Learning Target “Measure masses in grams and kilograms” is shaped by 3.MD.A, Solve problems involving measurement and estimation of intervals of time, liquid volumes, and masses of objects.

Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:

• Chapter 6, Lesson 3, connects understanding concepts of area (3.MD.C) with representing and solving problems involving multiplication and division (3.OA.A) by having students multiply to find the area of rectangles. For example, Problem 8 states, “A city street parking spot has an area of 72 square feet. The parking spot is 9 feet long. How wide is the parking spot?”
• Chapter 5, Lesson 3, connects representing and solving problems involving multiplication and division (3.OA.A) with multiplying and dividing within 100 (3.OA.C). For example, Think and Grow, Problem 11, “You make favor bags for a birthday party. Complete the table to find how many of each item you need for the given numbers of bags.”