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Report Overview
Summary of Alignment & Usability: Math Innovations | Math
Math 6-8
The instructional materials reviewed for Grades 6-8 do not meet the expectations for focus nor for coherence. The materials for Grades 6 and 7 assess the grade-level standards, but the materials lack focus as they do not spend a majority of time on the major work of each grade level. In each grade level, the materials meet the expectations for having the supporting content engage students in the major work of the grade, and they also provide some examples for fostering coherence through connections at each grade level. The materials do not meet expectations, though, for having an amount of content that is viable for one school year at each grade level, and the materials for each grade level do not neet expectations for being consistent with the progressions in the Standards.
6th 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)
7th 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)
8th 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 8th Grade
Alignment Summary
The instructional materials reviewed for Grade 8 do not meet the expectations for alignment to the CCSSM. An exceptional aspect of the materials is the integrated nature of the lessons. No topic is taught in isolation. Major work is incorporated in to supporting topics and many connections are made between domains and clusters. The materials go to great lengths to develop a conceptual understanding of math topics. However, the materials frequently cover off grade-level topics. In doing this, only approximately 50 percent of the time is spent on the major work of the grade. Several assessment items are beyond the Grade 8 CCSSM and those impact the structure of the materials. The materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade level concepts explicitly to prior knowledge, and the lesson objectives are not shaped by the CCSSM cluster headings. Since the materials do not meet expectations for focus and coherence in Gateway 1, they were not reviewed for evidence of rigor and the MPs in Gateway 2.
8th Grade
Alignment (Gateway 1 & 2)
Usability (Gateway 3)
Overview of Gateway 1
Focus & Coherence
The instructional materials reviewed for Grade 8 do not meet the expectation for focus and coherence with the CCSSM. Many included assessment items and there accompanying lesson are above grade-level. Moreover, major work topics only account for approximately 50 percent of the instructional time. Major work is incorporated into lessons that focus on the supporting work, however too many topics are off grade-level. The integrated nature of the materials gives ample opportunity for supporting work to enhance the major work, and there are also many connections made between domains and clusters. However, far too much time is spent covering off grade-level topics, because of this, the amount of content for one grade level is not viable for one school year. Furthermore, the materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade-level concepts explicitly to prior knowledge, and the materials are not shaped by the CCSSM cluster headings.
Gateway 1
v1.0
Criterion 1.1: Focus
The instructional materials reviewed for Grade 8 do not meet expectations for assessing materials at the Grade 8 level. There are too many concepts assessed that are beyond the Grade 8 CCSSM, and the alteration or omission of these items would significantly impact the structure of the materials. Overall, at least 8 lessons would have to be omitted to avoid going above level and some of the concepts that are taught in those lessons are integrated in subsequent lessons.
Indicator 1A
The instructional materials reviewed for Grade 8 do not meet the expectations for assessment because there were too many above grade-level assessment items and their accompanying lessons cannot be modified without impacting the underlying structure of the materials. The instructional materials offer assessment materials on their Flourish website. These assessment materials include a quiz for each section of a unit and a unit test. There is an included test generator, therefore, all above grade-level question could be taken off. For this reason when above grade-level questions were found on the unit tests and quizzes, the corresponding sections were examined to see the extent that students would be expected to understand the above grade-level topics and if it would be possible to modify the lesson. Listed below are the above grade-level assessment items that cannot be modified without impacting the structure of the materials.
Assessment Items that are impacted in the materials:
Shape Up, Unit Test Question 17: This question requires the students to have knowledge of the proof of triangle sum theorem and knowledge of the formula for the sum of interior angles. This is high school cluster G.CO.C and is covered in Lessons 1.2 and 1.3. The lessons build on the proof of triangle sum theorem and then use it to establish the formula for the sum of interior angles.
Shape Up, Unit Test Questions 6, 7 and 10: The questions use knowledge of Angle Side Angle, Side Angle Side and Side Side Side theorems. This is high school cluster G.CO.C and is covered in Lessons 2.1 and 2.4.
Solve It, Unit Test Question 8: This asks students to identify the graph of an exponential functions. This is high school cluster F.IF.C.and is covered in Lessons 4.2 and 4.3.
Solve It, Unit Test, Questions 9 and 14: These have students graph and identify features of quadratic equations. This is high school cluster F.IF.C and is covered in Lessons 4.2 and 4.3.
Prove It, Unit Test Questions 8 and 10: These have students identify arithmetic/geometric sequences and write recursive/explicit rules, respectively, which align to the high school cluster F.BF.A and is covered in Lessons 1.1 and 1.2.
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 8 are not developed so that students and teachers using the materials as designed devote the large majority of class time to the major work of the grade. Only about 50 percent of the time is spent on the major work of the grade, while the supporting work does incorporate some major work, too much time is spent on off grade-level topics. Overall the instructional materials do not meet the criteria for the time devoted to the major work of the grade.
Indicator 1B
The instructional materials reviewed for Grade 8 do not meet the expectations for focus by spending a majority of class time on the major clusters of the grade. There are five books/units included in the Grade 8 materials, those five books/units are each divided into at least three sections, which are then divided into lessons. A pacing guide is provided, which breaks down the number of days (45-minute class periods) per lesson. To determine the amount of time spent on major work, three perspectives were evaluated: 1) the number of sections devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. The number of days devoted to major work is the most accurate reflection for this indicator because it specifically addresses the amount of class time spent on concepts. Overall, approximately 52 out of the 103 days (approximately 50 percent) of the class time is devoted to major work, approximately 13 out of 103 days (approximately 13 percent) of class time is devoted to supporting work, and 38 out of 103 days (approximately 37 percent) is spent covering off grade-level topics. At times, some lessons included major or supporting clusters and included above/below level work, in those cases, the time was divided based on the number of examples and problems.
- Shape Up: (8 out of 21 days of major work. 5 days of supporting work. 8 days off grade-level.)
- Section 1: (Four out of five days of major work. Four days off grade-level.)
- Lesson 1:Primarily covers 8.G.A and below grade-level work 7.G.B (one day of major work. One day off grade level).
- Lesson 2: Primarily covers above grade-level work G.CO.C.10 (one days off grade level).
- Lesson 3: Primarily covers above grade-level work G.CO.C.10 (one day off grade level).
- Section 2: (Seven out of 11 days of major work. Four days off grade level).
- Lesson 1: Primarily covers above grade-level work G.CO.C.9 (two days off grade level).
- Lesson 2: Primarily covers 8.G.A (two days of major work).
- Lesson 3: Primarily covers 8.G.A (three days of major work).
- Lesson 4: Primarily covers above grade-level work G.CO.B.8 and G.SRT.A.2 (two days off grade level).
- Lesson 5: Primarily covers 8.G.A (two days of major work).
- Section 3: (Zero out of five days of major work. Five days of supporting work).
- Lesson 1: Primarily covers 8.G.C (two days of supporting work).
- Lesson 2: Primarily covers 8.G.C (one day of supporting work).
- Lesson 3: Primarily covers 8.G.C (two days of supporting work).
- Delving into Data: (1.75 out of 16 days of major work, 3.75 days of supporting work, 3 days of MPs, 8 days off grade-level.)
- Section 1: (0 out of 5 days of major work. 5 days off grade level).
- Lesson 1: Primarily covers below grade-level work 6.SP. B and 7 SP.A (two days off grade-level).
- Lesson 2: Primarily covers below grade-level work 6.SP. B (two days off grade-level).
- Lesson 3: Primarily covers below grade-level work 6.SP. B (one day off grade-level).
- Section 2: (Zero out of six days of major work, three days of MPs, three days off grade-level.)
- Lesson 1: Primarily covers MP5 (zero days of major work).
- Lesson 2: Primarily covers below grade-level work 6.SP. A and 7 SP.B (three days off grade-level).
- Section 3: (1.25 out of 5 days of major work, 3.25 days of supporting work, 0.5 days off grade-level).
- Lesson 1: Primarily covers 8.SP.A (two days of supporting work).
- Lesson 2: Primarily covers 8.SP.A and 8.F.A (one day of major work, one day supporting work).
- Lesson 3: Primarily covers 8.SP.A and 8.EE.B (0.5 days of major work, 0.5 days of supporting work).
- Line It Up: (Nineteen out of 23 days of major work. two days of MPs, two days off grade-level.)
- Section 1: (Six out of 10 days of major work, two days of MPs, two days off grade-level.)
- Lesson 1: Primarily covers MP7 (Zero days of major work).
- Lesson 2: Primarily covers below grade-level work 6.NS.C (two days below grade-level).
- Lesson 3: Primarily covers 8.F.B (two days of major work).
- Lesson 4: Primarily covers 8.F.A (two days of major work).
- Lesson 5: Primarily covers 8.F.A and 8.F.B (two days of major work).
- Section 2: (Eight out of eight days of major work.)
- Lesson 1: Primarily covers 8.F.B (two days of major work).
- Lesson 2: Primarily covers 8.F.B and 8.EE.B (two days of major work).
- Lesson 3: Primarily covers 8.F.B and 8.EE.B (two days of major work).
- Lesson 4: Primarily covers 8.F.B (two days of major work).
- Section 3: (Five out of five days of major work.)
- Lesson 1: Primarily covers 8.EE.A and 8.EE.B (two days of major work).
- Lesson 2: Primarily covers 8.EE.C (one day of major work).
- Lesson 3: Primarily covers 8.EE.C (two days of major work).
- Solve It: (Eighteen out of 26 days of major work, eight days off grade-level.)
- Section 1: (Nine out of nine days of major work.)
- Lesson 1: Primarily covers 8.EE.C (three days of major work).
- Lesson 2: Primarily covers 8.EE.C (two days of major work).
- Lesson 3: Primarily covers 8.EE.C (two days of major work).
- Lesson 4: Primarily covers 8.EE.C (two days of major work).
- Section 2: (Zero out of four days of major work, four days off grade-level.)
- Lesson 1: Primarily covers off grade-level work 7.EE.B (Two days off grade-level).
- Lesson 2: Primarily covers below grade level work 7.EE.B with some above grade-level work A.REI.B (two days off grade-level).
- Section 3: (Eight out of eight days of major work.)
- Lesson 1: Primarily covers 8.EE.A (two days of major work).
- Lesson 2: Primarily covers 8.EE.A (two days of major work).
- Lesson 3: Primarily covers 8.EE.A (one day of major work).
- Lesson 4: Primarily covers 8.EE.A (three days of major work).
- Section 4: (One out of five days of major work, four days off grade-level.)
- Lesson 1: Primarily covers 8.EE.A (one day of major work).
- Lesson 2: Primarily covers above grade-level work F.IF.A and F.IF.C (one days off grade-level).
- Lesson 3: Primarily covers above grade-level work F.IF.A and F.IF.C (one days off grade-level).
- Prove It: (5.5 out of 17 days of major work, 4.5 days of supporting work, three days of MPs, four days off grade-level.)
- Section 1: (One out of eight days of major work, four days off grade-level, three days of MPs.)
- Lesson 1: Primarily covers above grade-level work F.LE.A.2 and F.BF.A.1.A (two days off grade-level).
- Lesson 2: Primarily covers above grade-level work F-BF.A.2 (two days off grade-level).
- Lesson 3: Primarily covers MP1 and MP5 (zero days of major work).
- Lesson 4: Primarily covers MP1 and MP5 (zero days of major work).
- Lesson 5: Primarily covers 8.G.A (one day of major work).
- Section 2: (Three out of three days of major work.)
- Lesson 1: Primarily covers 8.G.B (one day of major work).
- Lesson 2: Primarily covers 8.G.B (one day of major work).
- Lesson 3: Primarily covers 8.G.B (one day of major work).
- Section 3: (1.5 out of 6 days of major work, 4.5 days of supporting work.)
- Lesson 1: Primarily covers 8.EE.2, 8.NS.A and 8.G.B (0.5 days of major work. 1.5 days of supporting work).
- Lesson 2: Primarily covers 8.NS.A and 8.EE.A (One day of major work. One day of supporting work).
- Lesson 3: Primarily covers 8.NS.A and 8.G.B (Two days of supporting work).
Criterion 1.3: Coherence
The instructional materials reviewed for Grade 8 do not meet the expectations for being coherent and consistent within the standards. The integrated nature of the materials gives ample opportunity for supporting work to enhance the major work, and there are also many connections made between domains and clusters. However, far too much time is spent covering off grade-level topics, because of this, the amount of content for one grade level is not viable for one school year. Furthermore, the materials fail to follow the grade-by-grade progression, content from prior or future grades is not clearly identified, the materials do not relate grade-level concepts explicitly to prior knowledge, and the materials are not shaped by the CCSSM cluster headings.
Indicator 1C
The instructional materials reviewed for Grade 8 meet the expectation for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. It is noted that the theme of the materials is to integrate several topics into one lesson and as a result no one topic is taught in isolation. Overall, the major work of Grade 8 is incorporated into lessons that focus on the supporting clusters some examples of this indicator are listed below.
- Prove It:
- Lesson 3.1. The focus of this lesson is the Pythagorean theorem (8.G.7). In using the Pythagorean theorem to find the missing side of right triangle, students simultaneously use square roots ( 8.EE.2) and use rational approximations in their answers (8.NS.2).
- Lesson 3.2. The focus of this lesson is irrational numbers (8.NS.1). In learning about irrational numbers students also learn about perfect squares and learn that the square root of 2 is irrational (8.EE.2).
- Delving Into Data:
- Lesson 3.2. and 3.3. The focus of these lessons is that students construct and analyze scatter plots (8.SP.1). In doing this they write equations of lines of best fit (8.F.3).
Indicator 1D
The instructional materials for Grade 8 do not meet the expectations for the amount of content designated being viable for one school year. The materials claim to take approximately 165 days to cover. However, there are many off grade-level concepts covered in that time frame and some of the Grade 8 standards are not fully attended to.
- The instructional materials would take 165 days to cover, however much time is spent on off, grade-level work. If a teacher skipped these topics that would remove about 50 days of work, taking the amount of content to 115 days. It is noted that three extra days per unit was built in to allow teachers the flexibility they need to fully prepare students for high school mathematics. However, no additional materials or guidance on how to do that is included.
- Some of the Grade 8 CCSSM are not taught to the depth required by the standard.
- 8.SP.4. There are very few times when students are required to understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table.
- 8.EE.2. There are no examples where a student has to use cube root symbols to represent solutions to equations of the form x 3 = p or where students evaluate cube roots of small perfect cubes.
Indicator 1E
The instructional materials reviewed for Grade 8 do not meet the expectation for having materials that are coherent and consistent with the standards. Materials attempt to following grade-by-grade progression, however too much attention is given to off grade-level standards. Materials do not give all students extensive work with grade-level problems, and grade-level concepts are not explicitly related to prior knowledge.
Materials do not develop according to the grade-by-grade progressions in the standards. Content from prior or future grades is clearly identified and related to grade-level work
- Off grade-level work is present in every book/unit. Though it may be a plausible extension of grade-level work, when there is content from prior or future grades, the content is not clearly identified and not explicitly stated.
- Some of the materials attempt to relate to prior knowledge by addressing below grade-level standards, but the materials claim that almost every lesson teaches a grade-level standard when, in fact, they does not. For example, in "Solve It," section 2 covers inequalities. The materials state, "Students explore inequalities. Using many of the same properties and principles that they applied to equations, students analyze inequalities. Students find solution sets for inequalities, which contrast with the single value they found when solving equations. Students graph those solution sets on a number line." Inequalities are not part of the Grade 8 standards in the CCSSM.
- The notes in the Teachers’ Edition at the start of each section, “Teaching the Lesson,” attempt to explain what concepts need to be developed first before they are able to be successful in the grade-level concepts and even above-level concepts. The progressions with the concepts are somewhat explained here, yet, it does not identify any standards within the unit.
- There is evidence that the materials are following the progression. However, they are not necessarily concentrating on the mathematics of the grade. For example, the progression for statistics and probability indicates:
- in Grade 6, students focus on developing a deeper understanding of variability and more precise descriptions of data distributions, using numerical measures of center and spread. They begin to use histograms and box plots to represent and analyze data distributions;
- in Grade 7, students move from concentrating on analysis of data to production of data; and
- in Grade 8, students apply their experience with the coordinate plane and linear functions in the study of association between two variables related to a question of interest.
The unit Delving Into Data presents all of these topics almost equally as part of the Grade 8 curriculum.
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- Section 1 states, "In reviewing mean, median and mode, students connect these measures of center to data analysis and basic descriptive statistic. Students examine the characteristics of data sets to include distribution and measures of center. They Organize data for visual analysis using stem and leaf plot.
- Section 2 states, "Students review circle and bar graphs as methods for displaying categorical data. They display numerical data sets using histograms and box and whisker plots. Students differentiate between categorical and numerical data and choose the most appropriate data display."
- Section 3 states, "Students examine data that involve two variables to determine if there is a relationship between the variables. They classify such relationships using the concept of correlation. If a correlation exists between the variables, they determine a line of best fit using one of several methods."
The materials are attempting to cover all of the middle school statistics and probability standards in one grade. As a result, not enough time is spent on the Grade 8 statistics standards and almost no time is spent on 8.SP.4.
Materials do not give all students extensive work with grade-level problems.
- The problems in the On Your Own section provide students with the opportunities to engage deeply with the mathematics. The problem sets begin with writing about mathematics. The problem structures focus on open ended, thought-provoking questions in which a student frequently has to perform an investigation and justify their reasoning.
- The materials do not designate specific problems and examples that are on grade level as being appropriate for struggling students. It is expected that all students will engage in most of the problems. There are some suggested teaching strategies and tips, and some ready made tools to help with special populations. However, if a student is not able to keep up with the high-level questions provided in the On Your Own section of the student materials, no alternates are provided.
- For advanced students, there are Think Beyond Questions that are more rigorous and involve topics from later grades, and these can be found at the end of the On Your Own sections and can be included at the teacher discretion.
Materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades.
- There are no signals or indications of when something is review or new information. The lessons frequently contain topics that are presented in a way that span multiple grade-levels. However, the materials provide no indication of when this is happening and only indicate which grade-level topic is present. Furthermore, because of the integrated nature of the materials, even when a multi-grade topic is covered, it is almost impossible to easily identify the on-grade portion of the lesson.
- The connections between concepts from previous grade levels are not clearly articulated from lesson to lesson. They make an effort to explain this process in the "Goals of the Unit" summary, but they do not clearly identify previous grade-level standards to the current grade-level standards.
Indicator 1F
The instructional materials reviewed for Grade 8 partially meet the expectation to foster coherence through connections at a single grade, where appropriate and required by the standards. The very integrated nature of the materials leads to frequent domain to domain and cluster-to-cluster connections. However, the materials partially have learning objectives that are shaped by the CCSSM. Overall, the materials included lessons that are not presented in isolation of other important topics, but the materials are not shaped by the CCSSM alone.
Materials partially include learning objectives that are visibly shaped by CCSSM cluster headings.
- There are clearly identified lesson objectives at the beginning of each lesson that describe what students should be able to do by the end of the lesson. The problem is that many of the objectives are not at grade level nor is there any indication that they are visibly shaped by CCSSM cluster headings.
- The material sometimes include learning objectives that are shaped by the CCSSM cluster heading and sometimes there is not a clear connection to a CCSSM cluster heading. For example, in "Prove It," lesson 1.2 states, "Students will strengthen their inductive reasoning skills by analyzing a variety of sequences and formulating recursive and explicit rules to describe those sequences, moving beyond linear relationships." and "Students will explore writing an explicit rule for a given sequence that will enable them to determine the value of any term in the sequence." There is no indication of an associated grade-level cluster heading here, moreover, the topics described are above grade-level.
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 materials are very integrated and as a result there are numerous examples of places where connections are made between domains and clusters. Some of these examples are explained below.
- Line it Up, lesson 1.5: In this lesson students explore functions represented in tables, graphs, and equations (8.F.A). In the same lesson students also use functions to model relationships between quantities (8.F.B).
- Line it Up, lesson 2.4: In this lesson students connect what they have learned about the concept of slope (8.EE.B). At the same time they are practicing using slope, they are also analyzing increasing and decreasing functions (8.F.B).
- Shape Up, lesson 3.1: In this lesson students derive the formula for the volume of a cylinder (8.F.C). In doing this, students are encouraged to set up and solve equations for unknown dimensions in a cylinder (8.EE.C).