4th 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 4 meet the expectations for Gateway 1. The materials do not assess above-grade-level content. Within the materials, there is enough time devoted to the major work of the grade. 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 4 materials are focused and follow a coherent plan.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 4 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 4 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 4 content standards:
- Unit 2 assessments include multi-digit multiplication written both vertically and horizontally; however, there is no requirement of the standard algorithm.
- In alignment with the NF domain for Grade 4, within the fractions units (units 3 and 6), all items on the post-assessment use denominators limited to 2, 3, 4, 5, 6, 8, 10, 12 and 100. Addition and subtraction of fractions is only with like-denominators.
- In unit 6, multi-digit multiplication and division, no assessment items require the standard algorithm; most items allow for student choice of solution strategy. For example, on the post-assessment, item 8 says, “There are 4 friends going to a concert. They are paying a group rate of $176. How much does each friend need to pay? Show your work.”
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 4 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 4 meet the expectations for focus. The instructional materials do allocate the majority of class time to 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 sessions or Number Corner activities focused on supporting clusters and 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.
Some calculations, specifically the number of units and the number of modules (chapters), equaled slightly less than 65 percent of the time spent on major and supporting clusters of the grade. However, looking at the sessions (lessons) and instructional time, when considering both sessions and Number Corners together, the calculations equal more than 65 percent of the time spent on major and supporting clusters of the grade.
- Units – 5 out of 8 units spend the majority of the time on major work of the grade, which is approximately 63 percent -- Units 2, 3, 4, 6, and 7 spend all or most of the instructional time on major work of the grade. Units 1, 5 and 8 do not spend most of the instructional time on major work of the grade. Unit 1 spends most of the instructional time reviewing standards required for Grade 3 and setting up classroom expectations for Grade 4. There are multiplication review problems using arrays and number lines with one step word problems, reviews of strategies for multiplication facts, and some measurement review which is a Grade 3 supporting standard. Unit 8 is set up as project-based learning, however the content is above Grade 4 standards. In Modules 3 and 4, the students are working with concepts of scale, which is a middle school standard. Unit 5 focuses on Grade 4 content that is not major work of the grade.
- Modules (chapters) – 20 out of 32 spend the majority of the time on major work of the grade, which is approximately 63 percent. Modules that spend the majority of the time on major work of the grade are: Unit 1, Modules 1 and 3; Unit 2, Modules 1, 2, 3 and 4; Unit 3, Modules 1, 2, 3 and 4; Unit 4, Modules 1 and 2; Unit 6, Modules 1, 2, 3 and 4; and Unit 7, Modules 1, 2, 3 and 4. Modules that spend about half the time on major or supporting clusters of the grade are: Unit 1, Modules 1 and 3; Unit 4, Module 3; and Unit 5, Module 3. There are no modules in Unit 8 that spend the majority of the time on major work of the grade.
- Sessions (lessons) – 97 out of 147 spend the majority of the time on major work of the grade, which is approximately 66 percent. Approximately 30 percent of the 147 Bridges sessions or 44 sessions address multi-digit multiplication and division (4.NBT.5 and 4.NBT.6), a critical area and major work for Grade 4. For example, 17 out of 18 sessions in Unit 2 address concepts related to multi-digit multiplication and division. In addition, 15 out of 18 sessions in Unit 6 address multi-digit multiplication and division with a focus on strategies and application through solving problems related to perimeter and area, measurement and data, and fractions. Approximately 22 percent of the 147 Bridges sessions or 32 sessions address fractional equivalence and operations with fractions (4.NF), a critical area and major work of Grade 4. For example, all 18 sessions which make up Unit 3 address fraction equivalence, adding and subtracting decimals with like denominators, multiplication of fractions by a whole number, and an introduction to decimals and decimal notation of fractions.
- Instructional Time, including Bridges sessions and Number Corner activities – 8,160 instructional minutes out of 12,020 instructional minutes are spent on the major work of the grade, which is approximately 68 percent. The Bridges sessions alone equate to 5,820 out of 8,820 instructional minutes devoted to major work, which is approximately 66 percent of session instructional time being spent on the major and supporting clusters of Grade 4. The Number Corner activities reflect 2,340 out of 3,200 instructional minutes devoted to major work, which is approximately 73 percent of Number Corner instructional time being spent on the major and supporting clusters of Grade 4.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 4 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 sometimes made between domains and clusters within the grade level with some missed opportunities to make connections. Also the materials lack visible learning objectives shaped by CCSSM cluster headings. Overall, the Grade 4 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 4 meet the expectations for supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. The materials engaged students in major clusters of the grade while focusing on supporting clusters. For Grade 4, reviewers focused on the use of factors and multiples and solving problems involving measurement and conversations in supporting operations with multi-digit whole numbers, fractions, and decimals, in both the daily Bridges Sessions and the Number Corner activities.
- In Unit 1, Module 1, Session 5, students are working with area models and the relationship between multiplication and division (4.NBT.6) while applying their understanding of the area formula as a multiplication equation with an unknown factor (4.MD.3).
- In Unit 1, Module 3, Session 4, students are working with multiplicative comparison and writing comparison statements to match multiplication equations (4.OA.1) while applying knowledge of factor pairs and multiples (4.OA.4).
- In Unit 6, Module 3, Session 1, fractions (of elapsed time), there are solid connections made between 4.MD and 4.NF while collecting and representing data through a diagram, line plot, and number line.
- In Unit 6, Module 3, Session 2 (Data Analysis), solid connections are made between 4.MD.4 and 4.NF.3 as students use line plots to display measurements (4.MD.4) in fractions and add mixed numbers (4.NF.3).
- In Unit 7, Module 4, Session 3, students work with story problems involving intervals of time, liquid volume, and weight (4.MD.2) while multiplying 2-digit numbers using strategies based on place value and the properties of operations and using equations and rectangular arrays to explain their strategies (4.NBT.5).
- In September Number Corner "Calendar Collector," students are making conversions of inches, feet, and yards involving whole numbers and fractions.
- In October Number Corner "Computational Fluency," students are exploring the relationship between factors and multiples through the use of number lines, while focusing on rounding, estimating, place value, and multi-digit addition and subtraction.
- In April Number Corner "Solving Problems," students are engaging in solving problems in which they add or subtract mixed fractions while working with line plots in whole and fractional amounts.
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 4 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 Bridges Session are 60 minutes in length for Grade 4, with an additional 20 minutes required for the daily Number Corner activities for a total of 80 minutes (60 minutes for Bridges Sessions and 20 minutes for Number Corner Activities).
- There are some sessions that are explicitly designed to take two days and are indicated as such in the Teacher's Manual as seen in Unit 1, Module 2, Sessions 5-6.
- The Number Corner Activities are an essential component of the curriculum emphasizing "opportunities to apply Common Core skills in new settings and real-world contexts."
- 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, including assessments.
- 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 minutes 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 to 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 4 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:
- The Grade 3 Operations and Algebraic Thinking Standards including 3.0A.1, 3.OA.3, 3.OA.4, 3.OA.5 and 3.OA.7 are identified for the purposes of review and extension in Unit 1, Module 1, Sessions 1-6 (Models for Multiplication and Division) alongside standards in major clusters 4.OA.A and 4.NBT.B.
- The Grade 3 Operations and Algebraic Thinking standards including 3.OA.5, 3.OA.7, and 3.OA.9 and Grade 3 Measurement and Data standards 3.MD.7b-3 are identified for the purpose of review and extension in Unit 1, Module 2, Sessions 1 and 3-6 (Primes & Composites), alongside standards in major cluster 4.OA.B.
- In May Number Corner “Calendar Collector,” 5.G.2 is identified alongside supporting cluster 4.MD.A, and 5.NF.4a is identified alongside standards in major cluster 4.NF.B.
- There are references to range, which is well above grade-level and not marked or discussed as such, in Unit 8, Module 1, Session 1; Unit 8, Module 1, Session 3; and Unit 8, Module 2, Session 4 (6.SP.B.5.C).
- 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, Module 2, sessions 3, 4, and 5 has students analyzing data for mode (session 2), range (session 1 and session 3), mean and range (session 4), and range and mode (session 5). All of these are above grade-level standards and are not indicated as such. (6.SP.B.5.C).
- References to scale and scale factor are in Unit 8, Module 3, Sessions 2, 3 and 6, which is a Grade 7 standard. (7.G.A.1). The above grade-level standard is not marked or addressed as above grade level in any way.
- Content from future grades is not always clearly identified. For example Unit 1, Module 2, session 6 (TE page 34) asks students to "enter numbers on the ratio table" in order for students to show the Double-Double-Double strategy in another format. The above grade level standard (6.RP.A) is not clearly identified as such.
Materials give all students extensive work with grade-level problems:
- 136 out of 147 Bridges Sessions provide an opportunity for students to engage with grade-level problems through a Problem & Investigation or a Problem String.
- 104 out of 160 Number Corner Sessions provide an opportunity for students to engage in problem solving through Calendar Grid, Solving Problems and Problem String activities.
- Suggestions for SUPPORT or CHALLENGE are embedded in some sessions (not consistent) and noted in the Teacher’s Guide. Students are working with grade-level content, with modifications. Examples include Unit 3, Module 2, Session 2, teacher direction 11 makes suggestions for playing "The Last Equation Wins" with modifications to support struggling learners as well as modifications to challenge others (page 14).
- 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." (found on last page of Unit Introduction for all units)
- Within the sessions, many of the practice pages related to the lessons are listed as "optional Daily Practice" and "optional Home Connections."
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.
- In Unit 1, Module 1, Sessions 1-6 (Models for Multiplication and Division), Grade 3 Operations and Algebraic Thinking Standards, including 3.OA.1, 3.OA.3, 3.OA.4, 3.OA.5 and 3.OA.7, are identified for the purposes of review and extension alongside standards in major clusters 4.OA.A and 4.NBT.B.
- In Unit 1, Module 2, Sessions 1 and 3-6 (Primes & Composites), Grade 3 Operations and Algebraic Thinking standards, including 3.OA.5, 3.OA.7, and 3.OA.9, and Grade 3 Measurement and Data standards, 3.MD.7.B and 3.MD.7.C are identified for purpose of review and extension alongside standards in major cluster 4.OA.B.
- In Unit 2, Module 1 (Building Multiplication Arrays), Session 3, 3.MD.7 is identified for the purpose of review and extension alongside standards in supporting cluster 4.MD.A.
- In Unit 2, Module 1 (Multiplication Arrays), Session 4, 3.OA.4 and 3.OA.7 are identified for the purpose of review and extension alongside standards in major cluster 4.NBT.A and 4.NBT.B.
- The Module Overview in Unit 3, Module 1, (TM, page 1) states, "Students review fraction skills and concepts from the previous grade and extend their understandings to mixed numbers, improper fractions, and more sophisticated strategies for generating equivalent fractions." The Unit 3 Module Overview is the only unit overview (of eight) to explicitly state connections to previous grade levels.
- In Unit 3, Module 1 (Equivalent Fractions), Session 1, 3.NF.2 is identified for the purpose of review and extension alongside standards in major cluster 4.NF.B.
- In Unit 4, Module 4 (Measurement & Data Displays), Session 1, 3.MD.4 is identified for the purpose of review and extension alongside standards in supporting cluster 4.MD.B.
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 4 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, the materials do not include 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.
- Fair Shares and Fractions & Mixed Numbers, in Unit 3, Module 1, Sessions 2 and 3, could have attended more closely to the cluster heading "Extend understanding of fraction equivalence and ordering."
- Ordering Fractions and Decimals on a Number Line, in Unit 3, Module 4, Session 3, could have attended more closely to to the cluster heading "Extend understanding of fraction equivalence and ordering."
- Looking at Data Displays, in Unit 4, Module 4, Session 2, and Analyzing Grass Data, in Unit 8, Module 3, Session 4, could have attended more closely to the cluster heading "Represent and interpret data."
- Introducing Angles, Benchmark Angles, and Sir Cumference and the Great Knight of Angle, in Unit 5, Module 1, Sessions 2, 3 and 5, could have attended more closely to the cluster heading "Draw and identify lines and angles, and classify shapes by properties of their lines and angles."
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 2, Module 2, Sessions 1, 3 and 4 connect 4.OA.3 (solving multistep word problems with whole number using 4 operations) with 4.NBT.5 (multi-digit multiplication strategies).
- Unit 3, Module 1, Sessions 3, 4 and 5 connect 4.NF.1 (equivalent fraction understanding) with 4.NF.3 (adding, subtracting, and decomposing fractions).
- Unit 4, Module 2, Sessions 3, 4, and 5 connect 4.NBT.1 (Place value understanding with multi-digit numbers) with 4.NBT.4 (Fluently adding and subtracting multi-digit numbers).
- Unit 6, Module 2, Sessions 1-5 connect 4.MD.3 (Solving area and perimeter of rectangle problems with formulas) with 4.NBT.6 (Multi-digit division).