4th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 64% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 0 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 partially meet the expectations for Gateway 1, focus and coherence. Assessments represent grade-level work, and items that are above grade level can be modified or omitted. However, students and teachers using the materials as designed would not devote a majority of time to the major work of the grade. The materials are coherent and consistent with the standards.
Criterion 1.1: Focus
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain an assessment item that assesses above grade-level content, but this can be modified or omitted.
Indicator 1a
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 4 meet expectations for assessing grade-level content. One above grade-level assessment item is present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials. Probability, statistical distribution, similarity, transformation, and congruence do not appear in the assessments.
Examples of assessment items aligned to grade-level standards include:
- Chapter 1, Test A, Assessment Book, Item 3, “Compare. 502,956 and
482,956”. (4.NBT.2)
- Chapter 2, Test B, Assessment Book, Item 5, “67,542 + 89,227 = ______”. (4.NBT.4)
- Chapter 3, Test A, Assessment Book, Item 8, “Write the multiplication equation represented by the expression. (2,000 x 7) + (80 x 7) + (6 x 7)”. (4.NBT.5)
- Chapter 5, Test A, Assessment Book, Item 7, “Each table at a banquet seats 8 people. There are 456 people at the banquet. How many tables are there?” (4.NBT.6)
- Chapter 10, Test B, Assessment Book, Item 6, “0.2 + 0.7 = _____”. (4.NF.5
Criterion 1.2: Coherence
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 do not meet the expectations for spending a majority of class time on major work of the grade when using the materials as designed. Time spent on the major work was figured using chapters, lessons, and days. Approximately 56% of the time is spent on the major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 4 do not 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 9 out of 14 chapters, which is approximately 64% 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 66 out of 108, which is approximately 61% of the instructional time.
- The number of days devoted to major work (including assessments and supporting work connected to the major work) is 84 out of 150 days or 56%.
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 56% of the instructional materials focus on the major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 4 meet the expectations that the materials are coherent and consistent with the standards. The materials represent a year of viable content. Teachers using the materials would give their students extensive work in grade-level problems, but the materials do not explicitly connect prior knowledge to lesson content.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 4 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 3, connects the supporting work of factors and multiples (4.OA.4) with the major work of understanding equivalent fractions (4.NF.1). In the Think and Grow section, students find an equivalent fraction for 8/12 using division. Students list the factors of 8 and 12 and circle the factors they have in common and list them. Students divide 8/12 by the common factor 2 in order to create an equivalent fraction. Students also find equivalent fractions, for example Problem 3, “ 4/10 = ▢/5.”
- Chapter 11, Lesson 6, connects the supporting work of making a line plot with a data set (4.MD.4) with the major work of understanding fraction equivalence and ordering (4.NF.A). For example, Think and Grow section, Problem 1, “You survey 10 people about the amount of water each person drinks in 1 day. Make a line plot to display the data. Which amount of water consumed is the most common?” Students are given a table “Amount of Water (gallon)” with 10 fractions and a line plot that is partially created.
- Chapter 12, Lesson 2, connects the supporting work of applying the area and perimeter formulas for rectangles in real world and mathematical problems (4.MD.3) with using the four operations to solve problems (4.OA.1). For example, Homework & Practice, Problem 8, “An interior designer says that a rug under a dining room table should be 4 feet longer and 4 feet wider than the table. What is the area of a rug a customer should buy for under the table?” [The table is 6 ft. by 3 ft.]
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 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 150 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 4 is divided into 14 Chapters. The 150 instructional days include the following:
- 94 days of Lessons
- 14 days of Lesson Opener Activities - Each Chapter begins with a chapter opener.
- 28 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 3, 7, 11, and 14.
- 14 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.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 partially meet expectations for the materials being consistent with the progressions in the Standards. Overall, the materials address the standards for this grade level and provide all students with extensive work on grade-level problems. The materials make connections to content in future grades, but they do not meet the full depth of grade-level standards because off-grade level content is present, and they do not explicitly connect prior knowledge to lesson content.
Materials develop according to the grade-by-grade progression in the Standards. In addition, Grade 4 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 3 through Grade 5.
- 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 One “Place Value Concepts” (pages T-1C and T-1D): “This chapter begins with a review of the place value ideas developed in Grade 3... Students will read and represent numbers with precision, becoming comfortable moving between representations.” Additionally, “A major strand in Grade 4 is developing depth of conceptual place value understanding. This chapter focuses on place value relationships, concept of numbers, and then rounding. These ideas will form a basis for ideas to come; properties of operations and fluency of multi-digit arithmetic.”
- Cluster 4.NF.C “Understand decimal notation for fractions, and compare decimal fractions" is developed across the grade level. For example, prerequisite work on understanding fractions (4.NF.A, 4.NF.B) is the focus of Chapter 7 (Understand Fraction and Equivalence and Comparison), Chapter 8 (Add and Subtract Fractions), and Chapter 9 (Multiply Whole Numbers and Fractions). In Chapter 10 - Relate Fractions and Decimals - the focus is on understanding decimal notation for fractions and comparing decimal fractions. Lessons 1 and 2 build an understanding of tenths and hundredths. Lesson 3 focuses on writing tenths and hundredths in both fractions and decimals. Lesson 4 focuses on comparing decimals to the hundredths place. Lesson 5 explores using equivalent fractions to add decimal fractions and decimals. Lesson 6 brings in money and focuses on writing amounts of money in different ways (dollar sign and decimal, fractions or mixed numbers). The last lesson in the Chapter, Lesson 7, asks students to add, subtract, multiply, and divide amounts of money.
The instructional materials do not always attend to the full intent of the grade-level standards by giving all students extensive work with grade-level problems. In Big Ideas Math: Modeling Real Life Grade 4, there are multiple examples where the content extends beyond the grade-level standards, which takes away from the focus of the grade-level mathematics. For example:
- Chapter 4, Lessons 6-8 extend beyond Grade 4 (4.NBT.5) when the standard algorithm for multiplication is used, including regrouping (5.NBT.5). For example, in Lesson 8, students are provided an example problem: “A store receives a shipment of 5 boxes of pretzels. Each box is 50 centimeters high and has 24 bags of pretzels. How many ounces of pretzels does the store receive in the shipment?” Step 1 of the problem is written as a standard algorithm. Additionally, there are two regrouping boxes for students to put the regrouped tens. This example serves as a model to students for the remainder of the lesson. In the Dynamic Classroom, these problems are modeled using only the standard algorithm.
- Chapter 5, Lessons 6-8 extend beyond Grade 4 content when students use the standard algorithm for division (6.NS.2). For example, in Lesson 7, the example problem “Find 3,129 ÷ 4=______.” The examples use the standard algorithm and then students engage in six practice problems. In this chapter, 3 of the 9 lessons focus on the standard algorithm, which takes away the focus on the grade-level standards.
- In Chapter 9, Lesson 4, students multiply a whole number by a mixed number, extending beyond the Grade 4 standard, 4.NF.4 (“Apply and extend previous understandings of multiplication to multiply a fraction by a whole number.”) Example problems include: “2 x 1 1/2 + ______”; “2 x 3 5/6 = ___”; “4 x 3 6/10 = ___”.
Each chapter includes “The Progressions Through The Grades” table 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 2, Add and Subtract Multi-Digit Numbers, (4.NBT.3, 4.NBT.4, 4.OA.3) builds on the Grade 3 work of “Fluently add and subtract within 1,000 (3.NBT.2)” and “Use all operations to solve two-step word problems (3.OA.8).” In Grade 4, students “Round multi-digit numbers to a given place” (in Lesson 1, students round to estimate sums and differences), “Fluently add and subtract multi-digit numbers...” and ”Use comparative relational thinking to determine whether an addition or subtraction equations is true or false.” (In Lesson 6, students use number sense to tell whether an addition equation is true or false, and in Lesson 7, they use number sense to tell whether a subtraction equation is true or false.)
- Chapter 6, Factors, Multiples and Patterns, (4.OA.4) builds on the Grade 3 work of “Fluently multiply and divide within 100. Use multiplication facts to divide. Use properties of addition and multiplication to explain addition and multiplication patterns.” (In Lesson 1, students use models to find factor pairs; in Lesson 2, they use division to find factor pairs; in Lesson 3, they use their understanding of the relationship between factors and multiples.)
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The instructional materials for Big Ideas Math: Modeling Real Life Grade 4 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 when the connections are natural and important.
Examples of learning objectives visibly shaped by CCSSM cluster headings include:
- In Chapter 6, Lesson 5, the Learning Target “Create and describe number patterns” is shaped by 4.OA.C, Generate and analyze patterns.
- In Chapter 14, Lesson 5, the Learning Target “Classify quadrilaterals” is shaped by 4.G.A, Draw and identify lines and angles, and classify shapes by properties of their lines and angles.
- In Chapter 6, Lesson 1, the Learning Target “Use models to find factor pairs” is shaped by 4.OA.B, Gain familiarity with factors and multiples.
- In Chapter 8, Lesson 7, the Learning Target “Add mixed numbers with like denominators” is shaped by 4.NF.B, Build fractions from unit fractions by applying and extending previous understandings of operations on whole numbers.
Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:
- Chapter 16, Lesson 5, connects 4.OA.B with 4.OA.C when students solve problems using multiples and patterns. For example, Think and Grow: Modeling Real Life, Problem 17, “The pattern of animals on a Chinese calendar repeats every 12 years. The year 2000 was the year of the dragon. How many times will the year of the dragon occur between 2001 and 2100?
- Chapter 2, Lesson 1 connects 4.NBT.A with 4.NBT.B when students estimate numbers and add. For example, Think and Grow: Modeling Real Life, Problem 16, “Mount Saint Helens is a volcano that is 8,363 feet tall. Mount Fuji is a volcano that is 4,025 feet taller than Mount Saint Helens. About how tall is Mount Fuji?”