2nd 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 2 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 2 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 2 meet the expectations for assessing grade-level content.
Examples of assessment items aligned to above grade-level standards include:
- Chapter 9, Test A, Question 6, 8, and 10, and chapter 9, Test B, Item Numbers 6, 8, and 10, students solve a word problem within 1000. Second grade word problems do not go beyond 100 (2.OA.1 Use addition and subtraction within 100).
- Chapter 10, Test A, Question 5, 6, 9, and 10, and Chapter 10, Test B, Item Numbers 5, 6, 9 and 10, students must solve a word problem within 1000. Second grade word problems do not go beyond 100 (2.OA.1 Use addition and subtraction within 100).
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 aligned to grade-level standards include:
- Chapter 1, Tests A and B, Question 4, “You have 4 bags. There are 2 soccer balls in each bag. How many soccer balls are there in all?” (2.OA.C)
- Chapter 1, Test A and B, Question 1, students determine if a given amount of fish is odd or even. (2.OA.3)
- Chapter 2, Test A and B, Question 10 states, “13 kids are at the library. 5 of them leave. 6 more kids come to the library. How many kids are at the library now?” (2.OA.1)
- Chapter 4, Test A and B, Question 4, add “27 + 17 + 48”. (2.NBT.6)
- Chapter 7, Test A and B, Question 5, students count the markers shown. The markers are organized into groups of hundreds, tens, and ones. (2.NBT.1)
- Chapter 8, Test A and B, Question 2, students count by hundreds: “200, 300, 400, ___, ___, ___, ___”. (2.NBT.2)
- Chapter 9, Test A and B, Question 3, add “354 + 257= ___”. (2.NBT.7)
- Chapter 11, Test A and B, Question 4 states, “The top rectangle is about 13 centimeters long. What is the best estimate of the length of the bottom rectangle?" (2.MD.4)
- Chapter 14, Test A and B, Question 4, students read the time on analog clock and write it on the digital clock. (2.MD.7)
- Chapter 14, Test A and B, Question 9 states, “You have $9 and your friend has $12. You find a $10 bill and your friend loses $5. How much money do you and your friend have together now?” (2.MD.8)
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 2 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 84% 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 2 meet the expectation for spending the majority of class time on the major clusters of each grade. For Grade 2, this includes all clusters within 2.NBT along with 2.OA.A and 2.OA.B, and 2.MD.A and 2.MD.B.
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 weeks 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 15, which is approximately 67% 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 88 out of 110 lessons, which is approximately 80% of the instructional time.
- The number of days devoted to major work (including assessments and supporting work connected to the major work) is 143 out of 170 days, which is approximately 84% of the instructional time.
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 84% 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 2 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, above grade-level content is present and not identified.
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 2 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 13, Lesson 1, Show and Grow, Problem 4, connects supporting standard 2.MD.9 to major work 2.OA.2 as students use a chart to determine “How many more students need to choose sneakers so that the number of students who choose sneakers and sandals are equal?”
- Chapter 13, Lesson 4, Think and Grow, connects supporting standards 2.MD.10 to major work of 2.OA.2 when students use horizontal and vertical bar graphs with up to four categories. Students answer, “A student chooses an activity that has the same number of votes as crafts and hiking combined. Which activity does the student choose?”
- Chapter 14, Lesson 1, Think and Grow, supporting standard 2.MD.8 connects to major work 2.NBT.2 when students count coins and skip-count to count-on in increments. This connection is repeated in Lessons 2, 3, and 4.
- Chapter 14, Lesson 5, Think and Grow, connects supporting standard 2.MD.8 to major work 2.NBT.5 when students subtract from 100 to make change for a dollar. Two strategies are outlined: students can count back from 100 by skip-counting the coins backward, or by using a compensation strategy to subtract from 99 instead of 100.
- Chapter 14, Lesson 8, Think and Grow, connects supporting standard 2.MD.7 to supporting standard 2.MD.2 when students skip count by 5s to tell time to the nearest five minutes on an analog clock.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
Instructional materials for Big Ideas Math: Modeling Real Life Grade 2 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 170 days with each lesson counting as 1 day. The minimum time per class period is 45 minutes, with the recommended time of 60-70 minutes. A pacing guide can be found in the Teachers Guide. Grade Two is divided into 15 Chapters. The 170 days include the following:
- 110 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.
- 15 days for Chapter Assessments - Each chapter has a final chapter assessment.
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 reviewed for Big Ideas Math: Modeling Real Life Grade 2 partially meets expectations for being consistent with the progressions in the Standards. The presence of above grade-level content distracts from all students engaging with extensive work of the grade.
The Teacher Edition includes a “Progression Through the Grades” chart which outlines each domain and its accompanying clusters, and which chapters address each cluster. Additionally, tables are provided to identify which lessons address specific standards. The beginning of each chapter includes an overview table “Progressions Through the Grades” that shows the content from the previous and future grade levels, and “Laurie’s Overview” where the math in the chapter is explained and connected to prior and future work of the grade. For example:
- The "Progression Through the Grades chart" states: Grade 1 “Use properties of addition and subtraction as strategies. Fluently add and subtract within 10. Determine the unknown number to complete addition and subtraction equations.” Grade 2 “Determine whether the number of objects in a group is even or odd. Write an addition equation to model even numbers. Fluently add and subtract within 20. Use repeated addition to count the number of objects. “ Grade 3 “Identify addition and multiplication patterns. Use strategies to fluently add and subtract within 1000. Fluently multiply and divide within 100. Understand that factors show the number of equal groups and the size of equal groups.”
The instructional materials develop according to the grade-by-grade progressions. For example, in the Teacher Edition, Chapter 9, Lesson 6 addresses 2.NBT.7:
- Explore and Grow: “Model to solve. Make a quick sketch of your model. 327+458= ?”
- Think and Grow and Apply and Grow: “272+154 = ?” includes a place value chart to model drawings of base ten blocks and includes a problem written vertically with place value identified and a box to show regrouping.
- Practice: additional practice problems are included.
Throughout the instructional materials, above grade-level content is present. This content is not identified as above grade-level, and distracts students from engaging with extensive work with grade-level mathematics to meet the full intent of grade-level standards. For example:
- Chapter 4, Lessons 4 -7, Think and Grow, students use the standard algorithm (without tools or drawings) to solve 2-digit addition problems. (4.NBT.4)
- Chapter 4, students solve 3-step word problems throughout the chapter. (4.OA.3)
- Chapter 10, students use the standard algorithm for subtraction to subtract 3-digit numbers throughout the chapter. (4.NBT.4)
There are some standards which are addressed in a small number of lessons, and may not present students with opportunities to meet the full intent of the standard. For example:
- Chapter 9, Lesson 9, (Add Numbers within 1000), and Chapter 10, Lesson 9, (Subtract Numbers within 1000), students “explain why addition and subtraction strategies work, using place value and the properties of operations.” (2.NBT.9)
- Chapter 15, Lesson 5, “Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.” (2.G.2) There are 3 lessons (Chapter 15, Lessons 6, 7, and 8) that students “Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.” (2.G.3)
- Chapter 12, Lesson 1, students connect the ruler they have just practiced with to the number line to solve addition, subtraction, and compare problems. (2.MD.6) In Lesson 2, students practice with bar models. This is a missed opportunity to help students build a mental model of number lines to add and subtract which is key to working with number lines in grade 3. (3.NF.2)
The portion of the lessons titled “Connect and Extend Learning” includes a section “Prior Skills” that clearly identifies prior-grade content. For example,
- Teacher Edition, Chapter 4, Prior Skills, Exercise 8-11: Grade 1, Using Mental Math: Ten More, Using Mental Math: Ten Less
- Teacher Edition, Chapter 9, Prior Skills, Exercise 10: Grade 1, Sorting Two-Dimensional Shapes
- Teacher Edition, Chapter 10, Prior Skills, Exercise 7: Grade 1, Reading and Interpreting Bar Graphs
Materials relate grade-level concepts explicitly to prior knowledge from earlier grades:
- Teacher Edition, Chapter 3, Laurie’s Notes, Preparing to Teach, “In this lesson, students work with the familiar hundreds chart to add groups of ten. In Grade 1, students used the chart to count on from a decade number, now we expand to a starting addend that is not a decade number. Students will transfer between working on the hundreds chart to representing their counting on an open number line.”
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 2 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:
- Chapter 1, Lesson 3, Apply and Grow, “Determine the total number of objects in equal groups.” Students look at circled items and fill in blanks (ex. ____ groups of ____). Then the student writes the repeated addition equation to match the pictures and solve the equation. (2.OA.C)
- Chapter 3, Lesson 3, Explore and Grow, the Learning Target is visibly shaped by the cluster heading 2.NBT.B. The directions state, “How can you use a model to solve 37+15 (problem is written vertically).” The problem has a place value chart labeled tens and ones for the student to use to model the problem with base-ten blocks.
- Chapter 4, Lesson 4, Explore and Grow, the Learning Target states, “Use regrouping when needed to add.” Students make a sketch of base-ten blocks in a place value chart to find “38 + 24”. (2.NBT.C)
- Chapter 7, Lesson 1, Explore and Grow, the Learning Target states, “Identify groups of tens as hundreds.” Students identify how many unit cubes and rods are in a flat. (2.NBT.B)
- Chapter 7, Lesson 5, Explore and Grow, the Learning Target states, “Represent numbers in different ways.” Show and Grow students “show 261 two ways”, and “show 345 two ways”. (2.NBT.A)
- Chapter 11, Lesson 3, Show and Grow, students draw an object based on the estimated measurement of another object. For example, “The piece of celery is about 10 centimeters long. Draw a carrot that is about 5 centimeters long.” (2.MD.A)
Examples of problems and activities connecting two or more clusters in a domain, or two or more domains in a grade, include:
- Chapter 2, Lesson 1, Show and Grow, connects representing and solving problems involving addition and subtraction (2.OA.A) with adding and subtracting within 20 (2.OA.B). For example, Question 11, “There are 13 race cars. 6 of them have numbers. The rest do not. How many race cars do not have numbers?”
- Chapter 3, Lesson 1, Think and Grow, relates addition and subtraction to length as a strategy (2.MD.B) with using place value understanding and properties of operations to add and subtract (2.NBT.B) For example, “Write an equation that matches the number line.” The number line shows starting at 43 and counting by tens three times in order to reach 73.
- In Chapter 9, Lesson 2, Explore and Grow, students “Show how to skip count by tens five time on the number line.” The number line starts with the number 154. Students make 5 hops of 10 on the number line. Then students finish an equation “154 + ____ = ____ (154 + 50 = 204)”. This connects understanding place value (2.NBT.A) with using place value understanding and properties of operations to add and subtract (2.NBT.B).