Report for 4th Grade
Overall Summary
The instructional materials reviewed for Grade 4 do not meet the expectations for alignment to the CCSSM.
The materials failed to meet the criteria of gateway 1, where they were reviewed for focus on the major work of the grade and for coherence. The materials assess above Grade 4 standards in a way that negatively impacts the structure of the materials and do not allocate a large percentage of instructional materials to major standards of the grade. Some positive evidence was noted in the coherence criterion, but too many areas of weakness lead to the instructional materials not meeting quality expectations for coherence. Due to the materials not meeting expectations for focusing on major work and coherence, they were not reviewed for rigor and Mathematical practices.
4th Grade
Alignment
Usability
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 4 do not meet the expectations for alignment to focusing on major work of the grade and coherence. The instructional materials do not meet expectations for the two focus criterions because the materials assess standards above Grade 4 in a way that negatively impacts the structure of the materials. The materials do not allocate a large percentage of instructional materials to major standards of the grade. Some positive evidence was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet the quality expectations for coherence.
Gateway 1
Criterion 1.1: Focus
The instructional materials reviewed for Grade 4 do not meet the expectations for assessing grade-level content. Examples of above grade-level standards being assessed can be found in the materials for units 1, 5, 6, 9, and 10. Overall, the omission or modification of lessons that align to the above, grade-level assessment items would create a significant impact on the underlying structure and intent of the materials.
Indicator {{'1a' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet expectations for assessment. The materials assess statistical distributions with questions that align to standards from 6.SP.A , “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions”, and they assess similarity, congruence and geometric transformations with questions that align to 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. There are also many other lessons in the materials that would need to be modified or omitted because of their alignment to above grade-level standards. Units and lessons accompanying above grade-level assessment items are noted in the following list.
- In unit 1, lessons 3, 4, and 5 have assessment items that align to standards from 6.SP.A, “Develop understanding of statistical variability”, and 6.SP.B, “Summarize and describe distributions”. The Key Assessment Opportunities Chart shows the expectation that students be able to find the median of a data set represented in a table, graph, or line plot and make predictions and generalizations about a set of data using the median. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6. These lessons account for seven to eight class sessions of the first unit, which encompasses 12 to 14 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
- In unit 5, lessons 2, 3, 4, and 5 have assessment items that align to standards from 6.SP.A , “Develop understanding of statistical variability,” and 6.SP.B, “Summarize and describe distributions.” . The Key Assessment Opportunities Chart shows the expectation that students be able to draw a best-fit line; find the median and mean of a data set; and make predictions and generalizations using medians and means. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of statistical distributions should not occur before Grade 6. These lessons account for 10 to 12 class sessions of unit 5, which encompasses 16 to 19 class sessions total, so the omission of these lessons would significantly impact the structure of this unit.
- In unit 6, the midterm assessment is lesson 8, which has assessment items that align to standards from 6.SP.A and 6.SP.B, but these items could be omitted without affecting the structure of the assessment or unit.
- In unit 9, lessons 10 and 11 have assessment items that align to standards from 5.G.B, “Classify two-dimensional figures into categories based on their properties,”, and 8.G.A, “Understand congruence and similarity using physical models, transparencies, or geometry software.”. The Key Assessment Opportunities Chart shows the expectation that students be able to classify two-dimensional shapes using their properties; identify congruent shapes; and identify slides, flips, and turns of shapes. According to table 2 on page 9 of the K–8 Publishers’ Criteria for the Common Core State Standards for Mathematics, assessment of similarity, congruence, or geometric transformations should not occur before Grade 8. These lessons account for three to five class sessions of unit 9, which encompasses 16 to 21 class sessions total, so the omission of these lessons would have a minor impact on the structure of this unit.
- In unit 10, lesson 5 has assessment items that align to standards from 5.G.A “Graph points on the coordinate plane to solve real-world and mathematical problems,” and 6.EE.C, “Represent and analyze quantitative relationships between dependent and independent variables.”. The Key Assessment Opportunities Chart shows the expectation that students be able to name variables in an investigation and make a point graph using ordered pairs with decimal values. This lesson accounts for three to four class sessions of unit 10, which encompasses 13 to 17 class sessions total, so the omission of these lessons would have a minor impact on the structure of this unit.
*Evidence updated 10/27/15
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 4 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. A large amount of time is devoted to off grade-level expectations both above and below Grade 4, and very little time is spent solving problems involving the four operations. Only three units out of the 12 (or 25%) are focused on the major work of the grade, units 6, 8 and 10. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 or on standards that are not in Grade 4.
Indicator {{'1b' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. The instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 4 or on standards that are not in Grade 4.
- A large amount of time is devoted to off grade-level expectations both above and below Grade 4, and very little time is spent solving problems involving the four operations.
- The majority of the curriculum is not focused on the major work of the grade. The four operations are absent, and only three units out of the twelve (or 25%) are focused on the major work of the grade, units 6, 8 and 10.
- Majority of the materials is not on the major work of Grade 4 as a large amount of time includes above grade-level work.
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 4 do not meet the expectations for being coherent and consistent with the CCSSM. The instructional materials have a very few instances of supporting work fostering coherence, but the amount of content designated for Grade 4 is not viable for one school year. Also, the instructional materials are not consistent with the progressions in the CCSSM, and they do not foster coherence through connections at a single grade. Overall, the instructional materials for Grade 4 exhibit some characteristics of coherence, but for the entire criterion, there are too many weaknesses for the materials to meet the expectations.
Indicator {{'1c' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet the expectations for having the supporting content enhancing focus and coherence simultaneously. Overall, the instructional materials miss opportunities to connect non-major clusters of standards to major clusters, and as a result, the supporting content does not engage students in the major work of Grade 4.
- Supporting content is treated separately and is not used to support the major work of the grade. An example of this is factors and multiples, which is handled separately and does not support the major work of the grade.
- The expectations do not align or support major clusters for 4.NBT.A or 4.NBT.B. In the answer key, there is not one problem that asks students to do multi-digit arithmetic to solve problems.
- The expectations of unit 9 do not connect to 4.NF.A-4.NF.C, the major work of the grade.
- Some of the expectations for unit 1 involve finding the median of a data set and using coordinate pairs, which are above Grade 4 standards.
Indicator {{'1d' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet the expectations for having an amount of content designated for one grade level as viable for one school year. Overall, the amount of time needed to complete the lessons is not appropriate for a school year of approximately 170-190 days.
- The content is designed for 220 days, which exceeds the amount of content that can be taught or learned in a school year.
- There are 98 lessons in 13 units, designed for 220 instructional days.
Indicator {{'1e' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet the expectations for having materials that are consistent with the progressions in the CCSSM. Materials do not give students extensive work with grade-level problems, and grade-level concepts are not always explicitly related to prior knowledge from earlier grades. Also, the materials do not develop according to the grade-by-grade progressions, with non grade-level content not being clearly identified.
- The off grade content is not clearly identified or related to the grade-level work as evidenced by lessons 3 and 5, unit 1; lesson 3, unit 5; and lesson 8, unit 9.
- Because of the amount of time spent on off-grade level work, students are not given extensive work with grade-level problems as seen in units 1, 3, 5, 6, 9, 10 and 13.
- There is no evidence of differentiation for below or above level students. All students and all learning levels are not accounted for.
- There are no explanations provided for the teacher or student linking prior knowledge from prior grades. For example, unit 12 focuses on division-which is introduced in Grade 3-but the materials do not make an explicit connection to material covered in prior grades.
- Other examples are units 4 and 11 where connections to prior grade-level concepts exist, but the connections are not explicitly made.
Indicator {{'1f' | indicatorName}}
The instructional materials reviewed for Grade 4 do not meet the expectations for having materials foster coherence through connections at a single grade. Materials do not include learning objectives that are visibly shaped by the CCSSM cluster headings, and the materials do not always connect two or more clusters in a domain or two or more domains in a grade when appropriate.
- It is not clear the learning objectives have been shaped by the cluster headings due to the amount of off grade level objectives.
- The student guides and "at home practice" are not labeled with objectives.
- The instructional materials do not connect clusters or domains in the grade level. Clusters and domains are treated separately.
- Units are compartmentalized and lack connections amongst them.
Overview of Gateway 2
Rigor & Mathematical Practices
Criterion 2.1: Rigor
Indicator {{'2a' | indicatorName}}
Indicator {{'2b' | indicatorName}}
Indicator {{'2c' | indicatorName}}
Indicator {{'2d' | indicatorName}}
Criterion 2.2: Math Practices
Indicator {{'2e' | indicatorName}}
Indicator {{'2f' | indicatorName}}
Indicator {{'2g' | indicatorName}}
Indicator {{'2g.i' | indicatorName}}
Indicator {{'2g.ii' | indicatorName}}
Indicator {{'2g.iii' | indicatorName}}
Overview of Gateway 3
Usability
Criterion 3.1: Use & Design
Indicator {{'3a' | indicatorName}}
Indicator {{'3b' | indicatorName}}
Indicator {{'3c' | indicatorName}}
Indicator {{'3d' | indicatorName}}
Indicator {{'3e' | indicatorName}}
Criterion 3.2: Teacher Planning
Indicator {{'3f' | indicatorName}}
Indicator {{'3g' | indicatorName}}
Indicator {{'3h' | indicatorName}}
Indicator {{'3i' | indicatorName}}
Indicator {{'3j' | indicatorName}}
Indicator {{'3k' | indicatorName}}
Indicator {{'3l' | indicatorName}}
Criterion 3.3: Assessment
Indicator {{'3m' | indicatorName}}
Indicator {{'3n' | indicatorName}}
Indicator {{'3o' | indicatorName}}
Indicator {{'3p' | indicatorName}}
Indicator {{'3p.i' | indicatorName}}
Indicator {{'3p.ii' | indicatorName}}
Indicator {{'3q' | indicatorName}}
Criterion 3.4: Differentiation
Indicator {{'3r' | indicatorName}}
Indicator {{'3s' | indicatorName}}
Indicator {{'3t' | indicatorName}}
Indicator {{'3u' | indicatorName}}
Indicator {{'3v' | indicatorName}}
Indicator {{'3w' | indicatorName}}
Indicator {{'3x' | indicatorName}}
Indicator {{'3y' | indicatorName}}
Criterion 3.5: Technology
Indicator {{'3aa' | indicatorName}}
Indicator {{'3ab' | indicatorName}}
Indicator {{'3ac' | indicatorName}}
Indicator {{'3ad' | indicatorName}}
Indicator {{'3z' | indicatorName}}
Report Overview
Summary of Alignment & Usability for Math Trailblazers | Math
Product Notes
Along with access to digital materials for students and teachers, the student workbooks for each grade level were also reviewed.
Math K-2
The instructional materials reviewed for Kindergarten through Grade 2 do not meet the expectations for alignment to the CCSSM. The instructional materials do not meet the expectations for Gateway 1 as they do not appropriately focus on the major work of the grades or coherence within and across the grade levels. The instructional materials were not reviewed for Gateway 2.
Kindergarten
View Full ReportAlignment
Usability
1st Grade
View Full ReportAlignment
Usability
2nd Grade
View Full ReportAlignment
Usability
Math 3-5
The instructional materials reviewed for Grades 3 through 5 do not meet the expectations for alignment to the CCSSM. The instructional materials do not meet the expectations for Gateway 1 as they do not appropriately focus on the major work of the grades or coherence within and across the grade levels. The instructional materials were not reviewed for Gateway 2.