3rd 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 3 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 clusters 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 3 materials are focused and follow a coherent plan.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 3 meet the expectations for assessing grade-level content. Overall, the instructional materials can be modified without substantially affecting the integrity of the materials so that they do not assess content from future grades 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 3 meet the expectations for focus within assessment. Overall, the majority of summative assessment items reviewed did assess material in alignment with the Grade 3 content standards:
- In Unit 3, Multi-digit Addition and Subtraction, the standard algorithm is not explicitly assessed, although students could choose to use it. For example, in the post-assessment for the unit, equations are all written horizontally and students are prompted to “Use a strategy that is more efficient than counting on by 1s.”
- In alignment with the NF domain for Grade 3, within the fractions units (units 4 and 6), all items on the post-assessment use denominators limited to 2, 3, 4, 6 and 8.
Assessment items that assessed above, grade-level content:
- In the post-assessment for unit 2, question 1 assesses multiplicative comparison which is a Grade 4 expectation, 4.OA.A.1.
- In the post-assessment for unit 4, question 13b assesses a comparison of fractions that don’t have the same numerator or denominator, which is a Grade 4 expectation, 4.NF.A.2.
- Although these two items assess content standards from above Grade 3, the omission of these items and any lesson material that accompany the concepts would not substantially affect the underlying structure of the materials for Grade 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 reviewed for Grade 3 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 3 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 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 sessions (lessons), equaled less than 65 percent of the time spent on major and supporting clusters of the grade. However, looking at the modules (chapters) 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 – Five out of eight spend the majority of the time on major work of the grade, which is approximately 63 percent. Units 2, 4 and 7 spend all or most of the instructional time on major work of the grade. Units 1 and 3 do not spend any instructional time on major work of the grade. Units 6 and 8 spend instructional time on major work of the grade about half of the time. Unit 1 is largely a review of the Grade 2 critical areas of addition and subtraction within 100 and application of addition and subtraction through measurement and data standards. Unit 8 provides some application for solving problems involving the four operations through the major cluster standards in measuring mass, area, and perimeter when students are designing and building bridges.
- Modules (chapters) – 21.5 out of 32 spend the majority of the time on major work of the grade, which is approximately 67 percent. Modules that spend the majority of the time on major work of the grade are: Unit 2, Modules 1, 2, 3, and 4; Unit 4, Modules 1, 2, 3, and 4; Unit 5, Modules 1, 2, 3, and 4; Unit 6, Modules 3 and 4; Unit 7, Modules 1, 2, 3, and 4; Unit 8, Modules 1, 2, and 3 are spent on major work half of the time. There are no modules in Units 1 and 3 that spend the majority of the time on major work of the grade.
- Bridges Sessions (lessons) – 88 out of 146 spend the majority of the time on major work of the grade, which is approximately 60 percent. Approximately 26 percent of Bridges sessions or 38 out of 146 sessions are spent on multiplication or division, and approximately 15 percent of Bridges sessions or 22 out of 146 sessions are spent on fractions. Some examples of supporting work connected to major clusters are: Unit 2, Module 3, Session 5 has students working with representing and interpreting data, but also has them multiplying during this session which connects to the major work of 3.OA.1 and 3.OA.7 fluently multiplying within 100. Unit 4, Module 4, Session 3 supports the major work of fractions in third grade by using a measurement line plot including fraction units within it. In Unit 6, Module 3, Session 2, the students are working with perimeter, but they are also creating rectangles with different areas which connects to major standard 3.MD.6. Another example is in Unit 6, Module 3, Session 5 where the students are required to rearrange square units to find different areas of tables. While the supporting work here involves mathematics with perimeter and real world problems (3.MD.8), the majority of the work connects to the understanding of area and square units. Unit 6, Module 4, session 1 has the students working with geoboards to explore fractions, supporting the major work of fraction understanding in 3.NF.1 and 3.NF.2.
- Instructional Time, including Bridges sessions and Number Corner activities – 7,860 instructional minutes out of 11,940 instructional minutes are spent on the major work of the grade, which is approximately 66 percent. It is important to note the significance of The Number Corner activities as imperative to the time spent on the major work of Grade 3. The Bridges sessions alone equaled 5,280/8,760 minutes devoted to major work, which equals 60 percent of instructional time being spent on the major work of Grade 3. However, when the Number Corner activities are included, with 2,580/3,180 (approximately 81 percent) minutes devoted to major or supporting clusters, the combined percentage of time devoted to the major work of the grade is approximately 66 percent, making the Number Corner activities a vital component of the overall percentage of time spent on 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 Grade 3 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 3 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 3 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 3, reviewers focused on the use of data and scaled graphs and area measurement to support major work of multiplication and division, as well as the use of geometry and data to support the major work of fractions.
- Unit 2, Module 4 "Story Problems with Graphs & Multiple Operations," session 2 connects multiplication (multiples) with scaled graphing. Directions 5-7 (page 9) discuss labeling the scale with multiples of 4, asking the students what they notice, and then how to show quantities that are not multiples of 4.
- February Number Corner "Solving Problems" involves working with scaled picture and bar graphs that have multiples of 10 represented.
- March Number Corner "Calendar Grid" involves picture and bar graphs with scales of 3 and 4, working with multiples.
- Unit 6, Module 4 "Shapes and Fractions," session 1 (Exploring Halves on a Geoboard), session 2 (Fractions on a Geoboard), and session 3 (Geoboard quilt blocks) (3.G.A.2) connect to explaining equivalence of fractions (3.NF.3).
- Unit 5, Module 4 "Introducing Area," sessions 1-5, integrate area and multiplication (3.MD.C).
- Unit 6, Module 3 "Perimeter & Area" integrates area with multiplication (3.OA).
- March Number Corner "Solving Problems" is area and perimeter problems (3.MD.C.7) and connects area and multiplication (3.OA).
- In Unit 8, Module 2, session 3 "Researching & Building Suspension Bridges," students generate bridge length data to the nearest half and plot it on a line plot. (3.MD.B.4 is connected to 3.NF.A).
- In Unit 8, Module 3, session 5 "Long Bridge Analysis, Part 1," students generate and plot measurement data to the nearest halves and fourths, involving bridge span lengths and deck thickness. (3.MD.B.4 is connected to 3.NF.A).
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 3 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 instruction required daily 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, 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 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 3 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 does not always clearly relate 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 always identified and does not always relate to grade-level work:
- All below, grade-level content is marked with the appropriate Grade 2 standards, including: 2.OA.1, 2.OA.2, 2.OA.9, 2.NBT.2, 2.NBT.5, 2.MD.1, 2.MD.3 and 2.MD.5.
- Some sessions use previous grade-level content in support of upcoming Grade 3 content with addition and subtraction. For example, in Unit 1, Module 3, sessions 3, 4 and 5, students are working on addition and subtraction of length with a ruler as a tool in order to prepare students for open number line as a strategy for multi-digit addition and subtraction.
- Some sessions are solely Grade 2 content, such as: Unit 1, Module 1, sessions 4 and 5 “The Addition Table, Part 1" and "The Addition Table, Part 2," and Module 2, sessions 1 and 2, “The Subtraction Table, Part 1” and "The Subtraction Table Part 2," where students are working with addition and subtraction facts within 20.
- Unit 2, Module 3 is called "Ratio Tables and the Multiplication Table" (6.RP.A). Students are working with above grade-level concepts of unit rate and decimal multiplication. In Session 2, teacher direction 5 (page 14) says, "The rabbit food costs 1.50 per pound. What does that mean?" (6.RP.A.2). There is also an example of a ratio table that shows 1, 2 and 4 in the x column, and 1.50, 3.00, and 6.00 in the y column, with an arrow showing 1.50 x 2 (5.NBT.B.7). The above, grade-level standards are not marked or addressed as above grade level in any way.
- In Unit 8, Module 3, Session 6, the students are working with a line plot, and they are asked to calculate mean (6.SP.B.5.C). 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:
- 136 out 146 of Bridges Sessions provide an opportunity for students to engage with grade-level problems through a Problem & Investigation or a Problem String.
- 84 out of 160 Number Corner Sessions provide opportunities for students to engage in problem solving through Calendar Grid and Solving Problems activities.
- Number Corners is a time for practice with grade level concepts (20 minutes each day). “The five Number Corner workouts are the springboard for whole-group skills practice” (pg. iii).
- Within the sessions, many of the practice pages related to the lessons are listed as "optional daily practice" and optional "home connections." While there is additional opportunity for extensive practice of grade-level work in these components, they are always listed as optional.
- 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."
- 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.
Materials relate grade-level concepts explicitly to prior knowledge from earlier grades:
All grade-level standards are identified at the beginning of each unit in a guide called Skills Across the Grade Levels. It lists the skills that are introduced, developed or mastered within each unit. It also includes whether the concept can be extended to higher levels.
- Each unit has a section in the introduction titled "Skills Across the Grade Levels." These tables show "the major skills and concepts addressed" in each unit. It provides a quick snapshot of the expectations for learning during the unit, the skills that are introduced, developed or mastered, and the extensions from previous grades.
- Unit 1 extends or masters standard 2.OA.1 and 2.OA.2 in solving addition and subtraction problems and fluently adding and subtracting within 20. It also includes sums to 100 involving measurement. 2.MD.5.
- Students were introduced to writing whole numbers as fractions in second grade. In third grade, they now work on recognizing fractions that are equivalent to whole numbers and re-visit it again in Unit 7 as well as in Number Corners (Oct. and May).This particular skill also is reviewed in the Grade 4 lessons.
- Students are introduced to area of equal parts as fractions of a whole during second grade. They master this concept in Grade 3 during Unit 7, but it is also found in Units 4,6 and 8.
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 3 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:
- Fractions as Fair Shares and Fractions on a Line Plot; these are the first two fractions modules in Grade 3 and could have attended more closely to the cluster heading, "Develop an understanding of fractions as numbers."
- The sessions "Rounding and Multi-digit Addition," "Estimating to Add and Subtract," and "Exploring the Algorithms for Addition & Subtraction" could have all attended to the cluster heading "Use place value understanding and the properties of operations to perform multi-digit addition and subtraction."
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 4, Module 4: Fractions on a Line Plot includes connections between 3.NF.1, 3.NF.3 and 3.G.2.
- Unit 6, Module 4: Shapes and Fractions includes connections between 3.NF and 3.G.2.
- Unit 2, Module 4: Story Problems with Graphs & Multiple Operations includes connections between 3.OA.8 and 3.MD.3.