About This Report
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Report Overview
Summary of Alignment & Usability: 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 ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
1st Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
2nd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
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.
3rd Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
4th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
5th Grade
View Full ReportEdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
Report for 1st Grade
Alignment Summary
The instructional materials reviewed for Grade 1 do not meet the expectations for alignment to the CCSSM.
The materials do not devote the large majority of class time to major standards of the grade, but the materials can be utilized to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness mean the instructional materials do not meet 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.
1st Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 1 do not meet expectations for alignment to focusing on major work of the grade and coherence. The instructional materials do not allocate a large percentage of class time to major standards of the grade, but the materials can be utilized to appropriately assess grade-level content. One partial strength was noted in the coherence criterion, but too many areas of weakness lead to the instructional materials not meeting quality expectations for coherence.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Grade 1 meet the expectations for assessing material at the grade level. Although there are multiple units and lessons noted that align to and/or assess standards that are beyond Grade 1, the inclusion of these lessons and units 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 1 meet expectations for assessment because above grade-level assessment items, and their accompanying lessons or units, could be modified or omitted without significantly impacting the underlying structure of the instructional materials. For this indicator, all of the identified assessments and end-of-unit assessments for the 17 units were reviewed. Units and lessons accompanying above grade-level assessment items are noted in the following list.
- In unit 3, lesson 7 has assessment items that align to 2.MD.C.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”. The Key Assessment Opportunities Chart shows the expectation that students be able to solve addition word problems involving two or three whole numbers whose sum is less than or equal to 20 using counters and ten frames. The expectation for students does align to standards in 1.OA.A, “Represent and solve problems involving addition and subtraction,”, but given that the problems in lesson 7 have students use the ¢ symbol appropriately, the problems more closely align to 2.MD.C.8. This lesson accounts for two class sessions of unit 3, which encompasses 13 to 14 class sessions total, so the omission or modification of this lesson would not significantly impact the structure of this unit.
- In unit 5, lessons 2, 3, and 4 have assessment items that align to MD.C.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”, and 2.NBT.A.2., “Count within 1000; skip-count by 5s, 10s, and 100s.” The Key Assessment Opportunities Chart shows the expectation that students be able to skip count by 5s and count on to find the value of a set of coins. These lessons account for six to seven class sessions of unit 5, which encompasses 10 to 12 class sessions total, so the omission or modification of these lessons would have an impact on the structure of this unit.
- In unit 7, lessons 1 and 3 have assessment items that align to MD.C.8, “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?”, 2.NBT.A.2, “Count within 1000; skip-count by 5s, 10s, and 100s,”, and 2.MD.D.10, “…Solve simple put-together, take-apart, and compare problems using information presented in a bar graph. The Key Assessment Opportunities Chart shows the expectation that students be able to represent and identify quantities using connecting links, coins, and symbols; connect representations of quantities; skip count by 5s and 10s and count on to find the value of a set of coins; and read a table or bar graph to find information about a data set. These lessons account for five to seven class sessions of unit 7, which encompasses 12 to 16 class sessions total, so the omission or modification of these lessons would have a minor impact on the structure of this unit.
- In unit 8, lessons 1 – 4 have assessment items that align to standards from 3.MD.C., “Geometric measurement: understand concepts of area and relate area to multiplication and addition.” The Key Assessment Opportunities Chart shows the expectation that students be able to recognize that different shapes can have the same area and find the area of a shape by counting square units and nonstandard units using efficient counting strategies. These lessons account for four to six class sessions of unit 8, which encompasses five to seven class sessions total, so the omission or modification of these lessons would have a significant impact on the structure of this unit. Given the size of this unit, though, its omission or modification would not have a significant impact on the entirety of the materials for the grade.
- In unit 11, lessons 4, 6, and 7 have assessment items that align to MD.C.8. , “Solve word problems involving dollar bills, quarters, dimes, nickels, and pennies, using $ and ¢ symbols appropriately. Example: If you have 2 dimes and 3 pennies, how many cents do you have?” The Key Assessment Opportunities Chart shows the expectation that students be able to use skip counting to find the value of a collection of pennies, nickels, dimes, and quarters and recognize the relationship between larger and smaller units (i.e., one dime is two nickels). These lessons account for five class sessions of unit 11, which encompasses 11 to 13 class sessions total, so the omission or modification of these lessons would have a minor impact on the structure of this unit.
- In Unit 13, Lessons 1 through 4 have assessment items that align to standards from 5.MD.C, “Geometric measurement: understand concepts of volume”. The Key Assessment Opportunities Chart shows the expectation that students be able to solve problems involving volume using repeated addition and skip counting; represent the volume of an object using symbols, connecting cubes, and number sentences; measure and estimate volume by building models and counting cubic units; and recognize that different shapes can have the same volume. These lessons account for seven to 10 class sessions of unit 13, which encompasses 9 to 12 class sessions total, so the omission or modification of these lessons would have a significant impact on the structure of this unit.
- In unit 14, lesson 2 has assessment items that align to 3.MD.B.3., “Draw a scaled picture graph and a scaled bar graph to represent a data set with several categories. Solve one- and two-step “how many more” and “how many less” problems using information presented in scaled bar graphs.” The Key Assessment Opportunities Chart shows the expectation that students be able to read a table or bar graph to make predictions and solve problems about a data set. This lesson accounts for two to three class sessions of unit 14, which encompasses 11 to 14 class sessions total, so the omission or modification of this lesson would not have a significant impact on the structure of this unit.
*Evidence updated 10/27/15
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 1 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. Too much time is focused on non-major work of the grade. Major work of Grade 1 includes addition and subtraction within 20 with only two units out of 17 units covering this work. For Grade 1, close to 85% of instructional time should be focused on major work of the grade, and with the amount of above-grade level instruction and assessment, these instructional materials do not approach 85%. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 1 or on standards that are above Grade 1.
Indicator 1B
The instructional materials reviewed for Grade 1 do not meet the expectations for spending the large majority of class time on the major clusters of the grade. Overall, the instructional materials allocate too much instructional time to clusters of standards that are not major work of Grade 1 or on standards that are above Grade 1.
- Major work of Grade 1 includes addition and subtraction within 20. Only two units out of 17 (12%) units cover this work.
- Too much time is focused on non-major work of the grade.
- For Grade 1, close to 85% of instructional time should be focused on major work of the grade, and with the amount of above-grade level instruction and assessment, these instructional materials do not approach 85%.
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 1 do not meet the expectations for being coherent and consistent with the CCSSM. The instructional materials have some instances of supporting work fostering coherence by engaging students in major work of the grade as addressed in indicator 1C, but the amount of content designated for Grade 1 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 1 exhibit some characteristics of coherence as noted in indicator 1C, but for the entire criterion, there are too many weaknesses for the materials to even partially meet the expectations.
Indicator 1C
The instructional materials reviewed for Grade 1 partially 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 1.
- Time and shapes are presented separately and do not engage students in the major work of the grade.
- Representing and interpreting data is not presented in a way so that students are engaged in the major work as evidenced in lesson 6, unit 1, and lesson 5, unit 5.
- The supporting work of representing and interpreting data is present in unit 14.
- Unit 2, lesson 2 describes and compares shapes.
- Unit 15, lesson 1 folds shapes and partitions them into halves and fourths.
Indicator 1D
The instructional materials reviewed for Grade 1 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 far exceeds the amount of content which could be taught/learned in a school year.
- The instructional materials contain 17 units with five to six lessons in a unit.
- The instructional materials contain 109 lessons with up to five activities per lesson.
Indicator 1E
The instructional materials reviewed for Grade 1 do not meet the expectations for having materials that are consistent with the progressions in the CCSSM. Overall, the 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 content is somewhat connected to the major work of the grade, but because the mastery of the off-grade content must occur before the problems can make sense, this becomes a problem as evidenced by lesson 7, unit 3; lesson 2, unit 5; lesson 1, unit 7; lesson 5, unit 5; and lesson 3, unit 7.
- Work from prior grades is identified at the beginning of each unit in the "unit overview."
- Content does not progress appropriately within the major work of each grade as addressed in 1a, 1b and 1c.
- No mention of work in preparation for future grades is identified.
- All units except unit 1 and unit 2 have future grade content.
- The amount of time spent off grade level does not allow for students to spend enough time with grade-level work.
- Daily practice problems and problems of the week are present, but there is no evidence of differentiation for below- or above-level students.
- There are no explanations provided for the teacher or student linking prior knowledge from prior grades.
Indicator 1F
The instructional materials reviewed for Grade 1 do not meet the expectations for having materials foster coherence through connections at a single grade. Overall, the 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.
- Unit 4, lesson 3, aligns to 1.OA.A.1 and 1.OA.A.2 (add and subtract within 20), but there is no evidence in the unit of going beyond 10. Other examples include unit 4, lesson 4; unit 12 lesson 2; and unit 6, lesson 6.
- Units are departmentalized. For example, unit 2 explores shapes, but then it is not until unit 16 that 3-dimensional shapes are introduced.
- Lesson 1, unit 3, is the only lesson in the series that connects two clusters appropriately. There are some other instances where clusters are connected, but those involve future grade level content.
- In unit 2, lesson 2, there is no connection between describing and comparing shapes with place value and 10s, for 1.NBT.
- In unit 7, lesson 5, there is no connection between measuring in inches and adding and subtracting when solving word problems.