5th Grade - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
Gateway 1 - Meets Expectations | 92% |
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials for Big Ideas Math: Modeling Real Life Grade 5 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. Students and teachers using the materials as designed would 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 5 meet the expectations that the materials do not assess topics from future grade levels. The instructional materials do contain assessment items that assess above grade-level content, but these can be modified or omitted.
Indicator 1a
The instructional materials reviewed for Big Ideas Math: Modeling Real Life Grade 5 meet expectations for assessing grade-level content. 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 6, “Round 4.822 to the nearest hundredth.” (5.NBT.4)
- Chapter 2, Test B, Assessment Book, Item 4, “Evaluate [17 + (15 x 20)] - 58.” (5.OA.2)
- Chapter 3, Test A, Assessment Book, Item 3, “Evaluate 22.16 - 8.5 + 46.83 = ______”. (5.NBT.7)
- Course Benchmark 1, Assessment Book, Item 4, “Round 2.369 to the nearest tenth.” (5.NBT.4)
- Chapter 9, Test B, Assessment Book, Item 4, “Find the area of the rectangle. Write your answer in simplest form.” [The dimension of the rectangle is 7/9 by 1/4.] (5.NF.4b)
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. In the Dynamic Classroom, assessments can be downloaded as an editable document. Examples of assessment items that assess above grade-level content include:
- Assessment Book, Chapter 3, Test A, Item 13; and Test B, Item 13, “Order the expressions from least to greatest.” Two of the expressions include fractions with a denominator of 1,000 (“510/1,000 + 46/1,000 and 689/1,000-136-1,000”), a third expression includes decimals to the thousandths (“1.79 - 1.26”), and the fourth includes adding and subtracting decimals to the thousandths (“2.186 - (1.6 + 0.034”). The fourth expression is aligned to 6.NS.3.
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 5 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 70% 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 5 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 evaluated: 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 out of 14, which is approximately 71% 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 82 out of 93, which is approximately 88% of the instructional time.
- The number of days devoted to major work (including assessments and supporting work connected to the major work) is 104 out of 149 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.
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 5 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, and the materials describe how the lessons connect with the grade-level standards. However, the materials do not meet the full intent of the standards because off-grade level content is present.
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 5 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 4, Lesson 3, connects the supporting work of writing and interpreting numerical expressions (5.OA.1) with the major work of fluently multiplying multi-digit whole numbers (5.NBT.5). For example, Think and Grow: Modeling Real Life states, “A Cuvier’s beaked whale can dive 1,324 feet deeper than 4 times the depth a beluga whale can dive (2,123 feet). How deep can a Cuvier’s beaked whale dive? Write and solve an equation to find the depth.”
- Chapter 7, Lesson 9, connects the supporting work of writing and interpreting numerical expressions (5.OA.2) with the major work of performing operations with multi-digit whole numbers with decimals to hundredths (5.NBT.7). For example, Think and Grow: Problem Solving: Decimal Operations states, “You spend $67.45 on the video game controller, the gaming headset, and 3 video games. The video games each cost the same amount. How much does each video game cost?” Students are given a scaffolded “Plan” including writing an equation to solve the problem.
- Chapter 11, Lesson 6, connects the supporting work of representing and interpreting data (5.MD.2) with the major work of multiplying fractions (5.NF.4). For example, Think and Grow: Make Line Plots, students multiply fractions in order to create fractions with the same denominator (eighths) and place the fractions on a line plot that has been divided into eighths.
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 5 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 149 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 5 is divided into 14 Chapters. The 149 instructional days include the following:
- 93 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 5 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 the standards because off-grade level content is present.
The Grade 5 materials develop according to the grade-by-grade progressions with content from prior or future grades clearly identified and related to grade-level work.
- 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. However, the progression ends at Grade 5, so the progression for Grade 6 is not noted.
- Each chapter contains a chapter overview with a “Through the Grades” chart. The chart shows the chapter learning skills with the Progression from Grade 4 through Grade 6.
- 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 “Place Value Concepts” (pages T-1C and T-1D): “The first two sections of this chapter begin with a review of the place value ideas for multi-digit whole numbers... Understanding tenths and hundredths was developed in Grade 4 using manipulatives and relating to fraction equivalents... A major strand in Grade 5 is expanding students’ understanding of operations of the base ten system to decimals through thousandths.”
- Cluster 5.NBT.B “Perform operations with multi-digit whole numbers and with decimals to hundredths” is developed in the following chapters: In Chapter 3, Add and Subtract Decimals, Lessons 1-7, students use rounding or compatible numbers to estimate sums and differences in decimals (Lesson 1), use models to add or subtract decimals (Lesson 2), add decimals and check whether the sum is reasonable (Lesson 3), subtract decimals and check answers (Lesson 4), use addition and subtraction to evaluate expressions involving decimals (Lesson 5), use mental math to add or subtract decimals (Lesson 6), and solve multi-step word problems involving money (Lesson 7). In Chapter 4, Lessons 3-5, students multiply multi-digit numbers by one-digit numbers (Lesson 3), multiply multi-digit numbers by two-digit numbers (Lesson 4), and multiply multi-digit whole numbers (Lesson 5). Students continue to work with 5.NBT.B in multiple lessons within Chapters 5, 6, 7, 10, 11, and 13.
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 5, 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 3, Add and Subtract Decimals, Lessons 3-7 includes the mathematics of adding and subtracting decimals using the standard algorithm (6.NS.3). For example, in Lesson 3, “Find the sum, check whether your answers are reasonable." Problem 1: “1.3 + 7.5”; Problem 2: “601.58 + 82.31”; Problem 3: “19.73 + 7.16”; Problem 4: “84.6 + 44.7.” Four of the seven lessons in this chapter require the standard algorithm and do not use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
- Chapter 5, Multiply Decimals, Lesson 8 uses the standard algorithm to multiply decimals. (6.NS.3) The standard algorithm is demonstrated extensively throughout the lesson, and most multiplication problems have the directions, “Find the Product.” For example, Problem 10: “46.5 x 0.73=______”; Problem 11: “14.8 x 9.3 = _______”; Problem 12: “1.54 x 2.6 =_____.” In the Dynamic Classroom for the above problems, students can select a “?” and see how the problem is solved. In all of these examples, the video demonstrates solving the problems using the standard algorithm.
- In Chapter 6, Divide Whole Numbers, Lessons 4 and Lessons 7 - 9, students divide whole numbers using the standard algorithm for division of up to four-digit dividends and two-digit divisors (6.NS.2). For example, Lesson 7 (Homework and Practice) includes the following: Problem 1 "21⟌735"; Problem 2: "64⟌802"; and Problem 3: "40⟌901”. The example problem is solved using the standard algorithm. Four of the nine lessons in the chapter require the use of the standard algorithm and do not use concrete models or drawings and strategies based on place value, properties of operations, and/or the relationship between addition and subtraction.
Prior knowledge from earlier grades is explicitly related to grade-level concepts. For example:
- Chapter 2, Numerical Expressions, (5.OA.1, 5.OA.2) builds on Grade 4 work in using all four operations to solve multi-step word problems and using variable to represent unknown numbers (4.OA.3). For example, Lesson 3, “Newton has $20. He spends $4 on lunch and $13 at the store. Write an expression to represent the situation.”
- Chapter 5, Multiplying Whole Numbers, (5.NBT.2, 5.NBT.5) builds on Grade 4 work of fluently adding and subtracting multi-digit numbers (4.NBT.4), and using properties and strategies to multiply up to a four-digit number by a one digit number and two two-digit numbers (4.NBT.5). For example, Lesson 3, “You build the card tower shown. Each row is 0.08 meter tall. Your friend’s card tower is 0.3 meter tall. Whose tower is taller? Because your card tower has 4 rows, multiply by 0.08 to find the height of your tower. Use a model. Shade 4 groups of 0.08. Compare the height of your tower to the height of your friend’s tower. So, ________ tower is taller.” A 10 x 10 grid is provided in the problem for students.
- Chapter 8, Add and Subtract Fractions, (5.NF.1, 5.NF.2) builds on the Grade 4 work of comparing two fractions with different numerators and denominators (4.NF.2), and adding and subtracting mixed numbers with like denominators (4.NF.3.C). For example, Lesson 4, Problem 13: “The George Washington Bridge links Manhattan, NY, to Fort Lee, NJ. The part of the bridge in New Jersey is about 1/2 mile long. The part in New York is about 2/5 mile long. About how long is the George Washington Bridge?"
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 5 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 5, Lesson 3, the Learning Target “Use models to multiply decimals and whole numbers” is shaped by 5.NBT.B, Perform operations with multi-digit whole numbers and with decimals to hundredths.
- In Chapter 13, Lesson 3, the Learning Target “Use a formula to find volumes of rectangular prisms” is shaped by 5.MD.C, Geometric measurement: understand concepts of volume and relate volume to multiplication and to addition.
- In Chapter 11, Lesson 6, the Learning Target “Make line plots and use them to solve problems” is shaped by 5.MD.B, Represent and interpret data.
- In Chapter 12, Lesson 2, the Learning Target “Relate Points and find distances in a coordinate plane” are shaped by 5.G.A, Graph points on the coordinate plane to solve real-world and mathematical problems.
Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:
- Chapter 13, Lesson 3 connects 5.MD.C and 5.NBT.B when students need to understand volume and perform operations with multi-digit whole numbers. For example, Homework & Practice, Problem 8, “A sandbox is a rectangular prism. The area of the base is 3,600 square inches. The height is 11 inches. You add 38,000 cubic inches of sand to the box. Do you fill the sandbox to the top? Explain.”
- Chapter 12, Lesson 7, connects 5.G.A with 5.OA.B when students graph relationships on a coordinate plane and analyze these relationships. For example, Think and Grow: Modeling Real Life states, “Some friends plan to go to a trampoline park for 2 hours. They want to go to the park that costs less money. Which park should they choose? What is the cost for each person? Graph the relationship between time and cost at both parks.”