5th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 85% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The materials reviewed for Grade 5 meet the expectations for Gateway 1. These materials do not assess above-grade-level content, and they spend the majority of the time on the major work of the grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. These materials are partially consistent with the mathematical progressions in the standards, and students are offered extensive work with grade-level problems. Connections are made between clusters and domains where appropriate. Overall, the Grade 5 materials are focused and follow a coherent plan.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 5 meet the expectations for assessing grade-level content. Overall, no above-grade-level content was assessed within the summative assessments provided. Summative assessments considered during the review for this indicator include unit post-assessments and Number Corner assessments that require mastery of a skill.
Indicator 1a
The instructional materials reviewed for Grade 5 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessments.
- No above-grade-level content was assessed on summative assessments.
- The summative assessments focus on grade-level or previous grade-level topics.
Summative assessment items reviewed did assess material in alignment with the Grade 5 content standards:
- In unit 3, addition and subtraction of decimals items do not require the standard algorithm (although addition and subtraction problems are sometimes written vertically). Also in unit 3, multi-digit division items do not require the standard algorithm. For example, on the post-assessment, item 10b. says, “Use numbers, words, or labeled sketches to solve the problem.”
- In alignment with standard 5.NBT.5, multi-digit multiplication is assessed using the standard algorithm.
- In Unit 5, multiplication and division of fractions, all division items on all the assessments contain only whole numbers divided by fractions or fractions divided by whole numbers.
- In Unit 6, graphing, geometry, and volume, all items are in the first quadrant of the graph.
- In Unit 7, the multiplication and division of decimals items do not require standard algorithm.
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 reviewed for Grade 5 meet the expectations for focus on the major clusters of each grade. Students and teachers using the materials as designated will devote the majority of class time to major clusters 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 Grade 5 meet the expectations for focus by spending the majority of class time on the major work of the grade. All sessions (lessons), except summative and pre-assessment sessions, were counted and assigned 60 minutes of time. Number Corner activities were counted and assigned 20 minutes of time. When Bridges sessions or Number Corner activities focused on supporting clusters clearly supported major clusters of the grade, they were counted. Reviewers looked individually at each session and Number Corner in order to determine alignment with major clusters and supporting clusters. Standards reported in the teacher materials for sessions and Number Corners were not always found to be accurate or representative of the actual content of the sessions and Number Corners. Reviewers determined standards alignment of the sessions and Number Corner activities based on teacher directions, student activities and work, not standards that the teacher materials claimed. Optional Daily Practice pages and Home Connection pages were not considered for this indicator because they did not appear to be a required component of the sessions.
All calculations, including the number of units, the number of modules (chapters), the number of sessions (lessons), and instructional time, when considering both sessions and Number Corners together, equal more than 65 percent of the time spent on major work of the grade.
- Units: 6.5 out of 8 units spend the majority of the time on major work of the grade, which is approximately 81 percent. Units 1, 2, 3, 4, 5 and 7 spend all or most of the instructional time on major work of the grade. Unit 8 does not spend most of the instructional time on major work of the grade. Units 6 spends instructional time on major work of the grade about half of the time.
- Modules (chapters): 25.5 out of 32 Modules spend the majority of the time on major work of the grade, which is approximately 80 percent. Modules that spend about half the time on major work of the grade are: Unit 1, Modules 1, 2, and 3; and Unit 8, Modules 1 and 2. Modules that do not spend time on major work of the grade are Unit 6, Modules 1 and 2.
- Bridges Sessions (lessons): 115 out of 146 session spend the majority of the time on major work of the grade, which is approximately 79 percent. Approximately 45 percent of Bridges sessions, or 66 out of 146 Bridges Sessions, address operations of fractions, a critical area and major work in Grade 5. For example, in Unit 2 all 18 sessions address concepts related to adding and subtracting fractions and in Unit 5, 17 out of 18 sessions address concepts related to multiplying and dividing fractions. In addition, Unit 6 has 3 sessions which address dividing fractions, and Unit 7 includes an additional 9 sessions related to dividing fractions. Approximately 42 percent of Bridges Sessions, or 62 out of 146, address whole number and decimal operations which is a critical area and major work in Grade 5. For example, in Unit 3, 14 out of 18 sessions address whole number or decimal operations, including adding and subtracting decimals and whole number division using the area model. In Unit 4, 15 out of 18 sessions address multiplying and dividing whole numbers and decimals as students are introduced to strategies for multiplying and dividing whole numbers and decimals with a progression that includes using arrays to eventually introduce the standard algorithm for multi-digit multiplication.
- Instructional Time, including Bridges sessions and Number Corner activities: 9,200 out of 11,960 instructional minutes are spent on the major work of the grade, which is approximately 77 percent. While teaching just sessions alone will ensure the majority of instructional time is spent on major clusters of the grade (6,900 out of 8,760 instructional minutes or approximately 79 percent), the content in Number Corner activities is also an essential component of the curriculum and will additionally support students’ work and practice on major and supporting clusters of the grade (2,260 out of the 3,200 instructional minutes or approximately 72 percent).
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 5 partially meet the expectations for coherence. The materials use supporting content as a way to continue work with the major work of the grade. The materials provide viable content for a school year, including 160 days of lessons and assessments. The materials are partially consistent with the progressions in the standards, with some above, grade-level content unidentified and interfering with grade-level work. All students are given extensive work on grade-level problems, even students who are struggling, and this work progresses in a mathematically, logical way. Knowledge from prior grades is related to grade-level standards. Connections are made between domains and clusters within the grade level, however the materials lack visible learning objectives shaped by CCSSM cluster headings. Overall, the Grade 5 materials partially support coherence and consistency with the progressions in the standards.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Grade 5 meet the expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the materials engaged students in major clusters of the grade while focusing on supporting clusters. For Grade 5, reviewers focused on the use of data and conversion of measurements as methods for supporting operations with whole numbers, fractions, and decimals, as well as understanding the place value system, in both the daily sessions and the Number Corner activities:
- In Unit 3, Module 3, session 1, students are converting megabytes to kilobytes; the teacher direction 8 on page 6 says, “Guide students to see and describe patterns in the placement of the decimal point when a decimal number is multiplied by powers of 10.” Also, the directions suggest use of place value charts to demonstrate the multiplication.
- In Unit 3, Module 3, session 2, the forum (student discussion) is centered on the work from the day before, converting megabytes to kilobytes using place value and operations involving decimals.
- In Unit 3, Module 3, session 3, when students are doing metric conversions, the visual representation shows a table with kilograms (1, 0.5, and 1.5) and grams (1,000, 500, and 1,500). It asks how many grams are equivalent to 1.5 kilograms and suggests showing multiplication by ½.
- In the December Calendar Collector during Number Corner, students are engaging in measurement conversions and working with data with fractions on a line plot, using the context of student heights and foot lengths.
- In the February Calendar Collector during Number Corner, students are working with conversions involving liters, and in the February Solving Problems, students are solving conversion problems, all involving understanding of the place value system as well as whole number and decimal operations.
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 reviewed for Grade 5 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. While reviewers note that there are a minimum of 80 minutes of daily instruction required for all the curriculum components to be completed, including sessions and Number Corner activities, the amount of content, specifically the number of days, is viable for one school year:
- The materials contain 160 sessions (daily lessons) that are evenly spread across eight units of instruction, including assessments.
- Most of the sessions are 60 minutes of instruction or assessment, however some sessions, especially in Unit 8, are up to 160 minutes of instruction.
- In addition to daily sessions, daily Number Corner activities are an essential component of the curriculum.
- For Number Corners, there are 20 days in September, October, January, February, March, April, May/June; and 15 days in November and December, which equals 170 days of Number Corner activities.
- Number Corner activities are daily 20-minute workouts that introduce, reinforce, and extend skills and concepts related to the critical areas of study at each grade level.
- While a district, school or teacher would not need to make significant changes to the curriculum scope and sequence, reviewers indicated concerns for the amount of time necessary to complete all required components of each daily requirement, including sessions and Number Corners.
- The materials are structured so that a teacher could make modifications of days or time if necessary.
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 Grade 5 partially meet the expectations for the materials being consistent with the progressions in the standards. Content from prior grades is clearly identified and related to grade-level work, however content from future grades is not clearly identified and is not always clearly related to grade-level work. Materials give all students extensive work with grade-level problems. Materials relate grade-level concepts explicitly to prior knowledge from earlier grades.
Content from prior grades is clearly identified and relates to grade level work, however content from future grades is not identified and does not always relate to grade-level work:
- Students engage with previous, grade-level content in Unit 1: “In Unit 1, an exploration of volume serves as a bridge between fourth and fifth grade. Working with volume provides a context in which students review and extend skills and concepts from fourth grade, while introducing skills and concepts that are central to this year’s studies.” (From the unit overview, page ii.)
- Previous standards are noted in the sessions in which students engage in them. For example, in Unit 1, Module 1, Session 4, students are working with cubes to find different rectangular prism arrangements for 24 cubes, working with factors related to a base that makes 24 cubic units, and recording their arrangements with expressions that use parentheses, which connects 4.OA.B.4 with Grade 5 concepts of understanding volume and writing numerical expressions.
- In Unit 4, Module 2, Sessions 3 and 4, students engage with Grade 6 content (6.G.A) on surface area (“How Much Cardboard?” and “Cardboard Forum”). The above grade-level standard is not marked or addressed as above grade level in any way.
- There is a large amount of work integral to Unit 8 that is well above grade level and not marked or discussed as such. For example, in Module 1, Session 5, students are “Varying the Surface Area” (6.G.A). In Module 3, Session 3, "Students use what they have learned about solar energy to design a solar house and draw it to scale.” Vocabulary listed is “Scale Factor” (page 11) and teacher direction 3 (page 12) says, “Review the terms scale and scale factor” (7.G.A.1). The above grade-level standard is not marked or addressed as above grade level in any way.
Materials give all students extensive work with grade-level problems:
- In daily sessions, 138 out 146 provide an opportunity for students to engage with grade-level problems through a Problem & Investigation or a Problem String.
- In Number Corners, 91 out of 160 provide opportunities for students to engage in grade-level problems through Calendar Grid, Solving Problems, and Problem String activities.
- Suggestions for support or challenge are noted in the Teachers Guide in the Differentiation Table at the end of the introduction pages for each unit. Students are still working with the grade-level standards, but with modifications. For example, in Unit 3, Module 2, Session 6 during Work Places, teacher direction 12 suggests for support to "Suggest specific Work Places for struggling students to work on critical skills."
- In addition to the explicit suggestions for support or challenge contained in the sessions as identified in the Differentiation Table, the Problem & Investigations and Problem Strings are "open-ended and lend themselves to differentiated instruction by the nature of the task design" (Units 1-8 last page of Unit Introduction).
- Within the sessions, many of the practice pages related to the lessons are listed as "optional daily practice" and optional "home connections." While there are additional opportunities for extensive practice of grade-level work in these components, they are always listed as optional.
Materials relate grade-level concepts explicitly to prior knowledge from earlier grades:
- All grade-level standards are identified in the Skills and Concepts section at the beginning of each session including prior, grade-level standards.
- Unit 2, Module 1, Session 4 clearly identifies prior, grade-level standards (4.NF.1) in using equivalent fractions to add and subtract fractions with unlike denominators (page 21).
- Unit 4, Module 1, session 2 clearly identifies prior, grade-level standards as being reviewed or extended including 4.OA.4, 4.NBT.5, and 4.NBT.6 (page 9).
- Unit 4, Module 2, sessions 1, 2 and 4 clearly identify 4.NBT.5 connecting fractions to whole numbers and playing multiplication games (pages 3, 11 and 25).
- Unit 4, Module 3, sessions 1, 2, 3, 4, 6 and 7 clearly identify 4.NBT.5 in multiplying multi-digit numbers using the algorithm with arrays and partial product strategies (pages 3, 9, 13, 19, 31 and 37).
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 reviewed for Grade 5 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials lack learning objectives that are visibly shaped by CCSSM cluster headings, however the materials do include problems and activities that serve to connect two or more clusters in a domain and two or more domains in a grade.
There are missed opportunities to attend to cluster-level headings in Bridges sessions, including:
- The "Introducing Common Denominators" session does not attend to the concept of fraction equivalence when adding and subtracting fractions.
- The "Whole Number and Decimal Place Value" session does not attend to "understanding the place value system."
- The "Multiplication and Volume" session does "relate volume to multiplication and addition" but does not attend to "understand concepts of volume."
- The "Multiply Fractions by Fractions" session does not attend to "apply and extend previous understandings of multiplication and division to multiply and divide fractions."
There are many instances of problems and activities within the materials that serve to connect two or more clusters in a domain and two or more domains in a grade:
- Unit 1, Module 2, Session 2: 5.OA.2, 5.NF.5.A, 5.MD.3.A, 5.MD.B and 5MD.5.A (making connections between volume and multiplication).
- Unit 2, Module 2, Session 4: 5.NF.3 and 5.NBT.7 (word problems involving division, fractions, and decimals).
- Unit 4, Module 3, Session 7: 5.NBT.6, 5.NBT.7 and 5.MD.5.B (problem solving including division, decimals, and volume).