4th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The materials reviewed for Grade 4 meet the expectations for Gateway 1. Although there are some questions that align to and/or assess standards that are beyond Grade 4, the inclusion of these questions is either mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials, and these materials spend the majority of the time on the major clusters of each grade level. Teachers using these materials as designed will use supporting clusters to enhance the major work of the grade. Although materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades, the materials develop according to the grade-by-grade progressions in the Standards. Students are given extensive work on grade-level problems, and connections are made between clusters and domains where appropriate. Overall, the materials meet the expectations for focusing on the major work of the grade, and the materials also meet the expectations for coherence.
Criterion 1.1: Focus
The instructional materials reviewed for Grade 4 JUMP Math meet the expectations for not assessing topics before the grade level in which the topic should be introduced. Although there are some questions that align to and/or assess standards that are beyond Grade 4, the inclusion of these questions is either mathematically appropriate or, where not appropriate, their omission would not significantly alter the structure of the materials.
Indicator 1a
The instructional materials reviewed for Grade 4 meet the expectations for assessing the grade-level content and, if applicable, content from earlier grades. The Sample Unit Quizzes and Tests included in the Teacher Resources Part 1 Section K and Teacher Resources Part 2 Section W, along with the answer keys and "Scoring Guides and Rubrics," were reviewed for this indicator.
The assessments are mostly aligned to the standards of the grade-level, and assessment questions that are above grade-level/non-aligned can easily be modified or omitted without making a significant impact on the integrity of the materials.
Assessments containing off grade-level material include the following:
- On the Teacher Resources Part 2 Unit 4 Quiz for Lessons 6 to 11, problems 2b, 2c, 3a, and 3b have fractions that have denominators exceeding the expectations of grade 4. Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
Some assessments contain bonus questions. The rubric indicates that these questions should be marked correct or incorrect and not be assigned a point value. The bonus questions include items that might assess standards that are above grade-level, and in addition, the standard is not identified on the rubric.
- The Teacher Resources Part 1 Unit 4 Quiz for Lessons 32 to 36 emphasizes standard 4.NBT.5; however, the Bonus problem requires the multiplication of a seven digit number by a one-digit whole number.
- The Teacher Resources Part 2 Unit 2 Quiz for Lessons 40 to 43 includes a bonus question that requires dividing a nine digit number by a one-digit whole number. Standard 4.NBT.6 addresses division with up to four-digit dividends and one-digit divisors.
- The Teacher Resources Part 2 Unit 4 Quiz for Lessons 1 to 5 includes a bonus question that compares fractions with 1,000 and 10,000 as a denominator.
Some assessments contain advanced questions. The advanced questions are assigned points but are not included in the total score for the assessment. These questions might assess standards that are above grade-level, and in addition, the standard is not identified on the rubric.
- On the Teacher Resources Part 2 Unit 4 Quiz for Lessons 6 to 11, problems 6 and 7 ask students to write "more" or "less" when comparing fractions that have denominators exceeding the expectations of grade 4. Grade 4 is limited to fractions with denominators 2, 3, 4, 5, 6, 8, 10, 12, and 100.
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 students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade. Overall, the materials devote approximately 74 percent of class time to the major work of Grade 3.
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 spending the majority of class time on the major clusters of each grade. Overall, approximately 74 percent of class time is devoted to major work of the grade.
The materials for Grade 4 include 16 Units. In the materials, there are 186 lessons, and of those, 36 are Bridging lessons. According to the materials, Bridging lessons should not be “counted as part of the work of the year” (page A-59), so the number of lessons examined for this indicator is 150 lessons. The supporting clusters were also reviewed to determine if they could be factored in due to how strongly they support major work of the grade. There were some connections found between supporting clusters and major clusters, and due to the strength of the connections found, the number of lessons addressing major work was increased from the approximately 112 lessons addressing major work as indicated by the materials themselves to 122 lessons.
Three perspectives were considered: 1) the number of units devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of instructional days devoted to major work including days for unit assessments.
The percentages for each of the three perspectives follow:
- Units– Approximately 67 percent, 10 out of 16;
- Lessons– Approximately 75 percent, 112 out of 150; and
- Days– Approximately 74 percent, 122.5 out of 166.
The number of instructional days, approximately 74 percent, devoted to major work is the most reflective for this indicator because it represents the total amount of class time that addresses major work.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 4 meet the expectations for coherence. The materials use supporting content as a way to continue working with the major work of the grade and include a full program of study that is viable content for a school year including 166 days of lessons and assessment. Students are given extensive work on grade-level problems. Materials develop according to the grade-by-grade progressions in the Standards, but materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. These instructional materials are visibly shaped by the cluster headings in the standards, and connections are made between domains and clusters within the grade level. Overall, the Grade 4 materials support coherence and are consistent 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 that supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. When appropriate, the supporting work enhances and supports the major work of the grade.
Examples where connections are present include the following:
- 4.MD.4 supports work with 4.NF.A,B and 4.OA.
- Lessons 27 and 38-40 in Teacher Resources Part 2 Unit 2 have students using line plots and measuring objects with a ruler. These are done with fractions as well as whole numbers supporting the major work of Numbers and Operations with fractions.
- 4.MD.1 supports work from 4.OA.2.
- Lessons 2, 5, and 6 in Teacher Resources Part 1 Unit 6 have students measure and convert within the metric system, so clusters from 4.MD.A support clusters from 4.OA.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 meet the expectations for having an amount of content designated for one grade-level that is viable for one school year in order to foster coherence between grades. Overall, the amount of time needed to complete the lessons is approximately 166 days which is appropriate for a school year of approximately 140-190 days.
- The materials are written with 16 units containing a total of 186 lessons.
- Each lesson is designed to be implemented during the course of one 45 minute class period per day. In the materials, there are 186 lessons, and of those, 36 are Bridging lessons. Thirty-six Bridging lessons have been removed from the count because the Teacher's Edition states that they are not counted as part of the work for the year, so the number of lessons examined for this indicator is 150 lessons.
- There are 16 unit tests which are counted as 16 extra days of instruction.
- There is a short quiz every 3-5 lessons. Materials expect these quizzes to take no more than 10 minutes, so they are not counted as extra days of instruction.
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 Grade 4 partially meet the expectation for 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 explicitly relate grade-level concepts to prior knowledge from earlier grades.
The materials develop according to the grade-by-grade progressions in the Standards. Content from future grades is not always clearly identified but often related to grade-level work. The Teacher Resources contain sections that highlight the development of the grade-by-grade progressions in the materials, occasionally identify content from future grades, and state the relationship to grade-level work.
- At the beginning of each unit, "This Unit in Context" provides a description of connections to concepts that have been taught previously and that will occur in future grade-levels. For example, "This Unit in Context" from Unit 4, Number and Operations in Base Ten: Multiplication, of Teacher Resource Part 1 describes how "In Grade 3, students were introduced to multiplication as repeated addition, and they interpreted the product of two numbers as the total number of objects when given a number of equal groups and then number in each group (3.OA.A.1)." Connection to future content is also stated such as "In later grades, students will multiply multi-digit numbers by two-digit number (5.NBT.B.5) and multi-digit decimals (6.NS.B.3), including positive and negative decimals (7.NS.A.2a, c)."
The materials give all students extensive work with grade-level problems. The lessons also include "Extensions," and the problems in these sections are on grade-level.
- Whole class instruction is used in the lessons, and all students are expected to do the same work throughout the lesson. Individual, small-group, or whole-class instruction occurs in the lessons.
- The problems in the Assessment & Practice books align to the content of the lessons, and they provide on grade-level problems that "were designed to help students develop confidence, fluency, and practice." (page A-56, Teacher Resources Part 1)
- In the Extensions sections of the Lessons, students get the opportunity to engage with more difficult problems, but the problems are still aligned to grade-level standards. For example, the problems in Teacher Resource Part 1 Unit 3 Lesson 14 engage students in listing numbers that round to a given number, but these problems still align to 4.NBT.3.
The instructional materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Examples of these missing explicit connections include:
- Every lesson identifies "Prior Knowledge Required" even though the prior knowledge identified is not aligned to any grade-level standards. For example, Teacher Resource Part 2 Unit 4 Lesson 6 identifies that prior to the lessons students "(c)an use pictures to name equivalent fractions" and "(c)an use the phrase 'times as many as' to compare two numbers."
- There are 36 lessons identified as Bridging Lessons; most of these lessons are not aligned to standards from prior grades but state for which grade-level standards they are preparation. Teacher Resource Part 2 Unit 2 Lesson 40, which has students using pictures to divide when there is a remainder, is preparation for 4.OA.3 and 4.NBT.6.
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 meet the expectations for fostering 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.
Overall, units are organized by domains and are clearly labeled. For example, in Teacher Resources Part 1 Unit 1 Operations and Algebraic Thinking: Patterns, Teacher Resources Part 1 Unit 3 Operations and Algebraic Thinking: Rounding, and Teacher Resources Part 1 Unit 5 Operations and Algebraic Thinking: Division are shaped by the Operations and Algebraic Thinking domain. Throughout the course, all standards are addressed, and within lessons, goals are written that are shaped by the CCSSM cluster headings. For example, in Teacher Resources Part 2 Unit 3, Lesson 35 connects all three of the standards in the 4.OA.A cluster in "Equations with Multiplication and Division."
The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. Instances where two or more clusters within a domain are connected include the following:
- In Teacher Resources Part 1 Unit 2 Lesson 16, students add 2-digit numbers without regrouping. This lesson connects 4.NBT.A and 4.NBT.B.
- Teacher Resources Part 2 Unit 2 Lesson 47 connects 4.NBT.A and 4.NBT.B. Students divide 1-digit multiples of powers of ten by the same multiple of a lesser power of ten and divide using expanded form when all digits are divisible by the divisor.
- Teacher Resources Part 2 Unit 5 Lesson 24 connects 4.NBT.A and 4.NBT.B, as well as 4.NF.B and 4.MD.A. In this lesson, students solve problems involving measurements of mass and capacity, including problems requiring conversions.
The instructional materials also include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Instances where two or more domains are connected include the following:
- Teacher Resources Part 2 Unit 2 Lessons 45 and 46 connect 4.NBT and 4.MD. In these lessons students divide 3-digit and 4-digit numbers by 1-digit numbers, including with a remainder.
- In Teacher Resources Part 2 Unit 5 Lesson 33 4.NBT and 4.MD are connected. In this lesson students change measurements in pounds to ounces and solve problems involving mass in pounds and ounces.
- Teacher Resources Part 2 Unit 6 Lesson 41 connects 4.OA and 4.NBT. In this lesson students find factors of numbers up to 100 and determine whether a given 1-digit number is a factor of a given whole number in the range 1-100.
- Problem Solving Lesson 9 connects 4.NBT, 4.NF, and 4.MD. In this lesson students find the perimeter by converting fractional feet lengths to inches and adding the sides.