Report for 8th Grade
Overall Summary
The instructional materials reviewed for Grade 8 partially meet the expectations for alignment to the CCSSM. While the instructional materials met the expectations for focus and coherence, they did not meet the expectations for rigor and the mathematical practices.
The instructional materials reviewed for Grade 8 had approximately 70% of the work on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B. The content could be covered in 145 days. There are two chapters that connect two or more domains within Grade 8. In the teacher edition, the CCSSM are listed for each lesson. In the student edition, the lesson objective is listed each time and these objectives are based on the CCSSM.
The materials reviewed for Grade 8 do not meet expectations for rigor, balance and practice-content connections. Each lesson is launched with a real-world situation but they are often application problems and do not also build conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters; however, most if not all of the problems are skills-based without attending to conceptual understanding. Non-contrived and/or non-routine real-world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application. The MPs for each chapter are listed in the chapter at a glance pages. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the MP. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice and assessment.
8th Grade
Alignment
Usability
Overview of Gateway 1
Focus & Coherence
The materials reviewed for Grade 8 meet the expectations for focusing on major work and coherence. The instructional materials reviewed for Grade 8 had approximately 70% of the work on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B. The content could be covered in 145 days. There are two chapters that connect two or more domains within Grade 8. In the teacher edition the CCSSM are listed for each lesson. In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.
Gateway 1
Criterion 1.1: Focus
The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level. The items tested are aligned to the CCSSM for Grade 8.
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The instructional materials reviewed for Grade 8 meet the expectations for assessing material at the Grade 8 level.
- All items tested are CCSSM for the Grade 8.
Criterion 1.2: Coherence
The instructional materials reviewed for Grade 8 meet the expectations for spending the majority of class time on the major clusters for Grade 8. The instructional materials reviewed for Grade 8 spend approximately 70% of the time on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B.
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The instructional materials reviewed for Grade 8 meet the expectations for spending the majority of class time on the major clusters for Grade 8.
- The instructional materials reviewed for Grade 8 spend approximately 70% of the time on the major clusters for 8.EE.A, 8.EE.B, 8.EE.C, 8.F.A, 8.F.B, 8.G.A and 8.G.B.
Criterion 1.3: Coherence
The materials reviewed for Grade 8 partially meet the expectations for coherence. The content could be covered in 145 days. “Concepts and Skills Across the Curriculum” link the current material to the skills progression to both the previous and the next grade. In the teacher edition, the CCSSM are listed for each lesson. In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.
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The instructional materials reviewed for Grade 8 partially meet the expectations for the supporting content enhancing the major work.
- The first nine chapters are on major work.
- In chapters 10 and 11, students create scatter plots and are asked to put in a line of best fit and write an equation for this line. Supporting content 8.SP.A makes connections to the major work of 8.F.B where students are using scatter plots to interpret relationships within a function. It also connects to 8.EE.B when it has students write equations for a line of best fit on the scatter plots.
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The materials reviewed for Grade 8 meet the expectations for the amount of content designated being viable for one school year.
- The content could be covered in 145 days.
- This meets the threshold for more than 65% of the year being focused on the major work of 8th grade to foster coherence between Grade 8 and Grade 9.
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The materials reviewed for Grade 8 meet the expectations for the progressions in the standards.
- "Concepts and Skills Across the Curriculum" links the current material to the skills progression to both the previous and the next grade.
- Chapter 11 on probability is identified as meeting Grade 7 standards.
- Every chapter starts with a section of recalling prior knowledge for the students with a review and a quick check practice.
- Math background pages give teachers a review of the background knowledge needed for the unit.
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The materials reviewed for Grade 8 partially meet the expectations for fostering coherence through connections at a single grade.
- In the teacher edition the CCSSM are listed for each lesson.
- In the student edition the lesson objective is listed each time and these objectives are based on the CCSSM.
- There are two chapters that connect two or more domains within Grade 8. Chapter 1 connects exponents and the number system and chapter 7 connecting the Pythagorean Theorem with equation work.
- There are nine chapters that focus on one domain each.
Overview of Gateway 2
Rigor & Mathematical Practices
The materials reviewed for Grade 8 do not meet expectations for rigor, balance and practice-content connections. Each lesson is launched with a real-world situations but they are often application problems and do not also build conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters; however, most if not all of the problems are skill based without attending to conceptual understanding. Non-contrived and/or non-routine real world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application. The MPs for each chapter are listed in the chapter at a glance pages. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the mathematical practice. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice, and assessment.
Gateway 2
Criterion 2.1: Rigor
The materials reviewed for Grade 8 do not meet expectations for rigor and balance. Each lesson is launched with a real-world situation but they are often application versus building conceptual understanding. The materials have very few conceptual problems. There are inconsistencies among chapters and concepts on how much conceptual understanding is presented. Procedural skills are evident throughout the chapters however, most if not all of the problems are skill based only with no conceptual understanding. Non-contrived and/or non-routine real world application problems were not present in all chapters. There is no evidence of students making their own assumptions or simplifying to model mathematically in the chapters. The program is not balanced between conceptual understanding, procedural skill and fluency and application.
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The materials reviewed for Grade 8 partially meet the expectations for developing conceptual understanding of key mathematical concepts.
- Each lesson is launched with a real-world situation, and these often support application practice and do not build conceptual understanding.
- Problems are solved for students, and they are shown each step in prescribed process. The materials have few conceptual problems.
- There are strategies provided for teachers to help students understand concepts better, but few problems for students to explore on their own.
- Lessons include practice with procedural work and homework assignments include application.
- There are inconsistencies among chapters and concepts on how much conceptual understanding is presented.
- Lesson 5.1 introduces solving systems of equations through tables to build conceptual understanding, but the rest of the chapter focuses on procedures.
- Lesson 4.4 on understanding slope-intercept form begins with a problem situation about two boys walking at a constant rate but this problem only describes vocabulary of y intercept, x intercept and slope intercept form. The students are not asked to solve a problem using this vocabulary except in rote problems.
- There are a variety of representations used.
- Practice problems are intermingled with contextual problems, tables and number work with scaffolding. Many questions ask for the answer without having students explain or justify.
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The materials reviewed for Grade 8 partially meet the expectations for giving attention to individual standards for developing procedural skills and fluency.
- Procedural skills are evident throughout the chapters; however, most problems are skills-based without attending to conceptual understanding.
- There are instances where students are engaged in problems that require procedural skills and fluency.
- Most of the problems in the lessons and over half of the homework is typically devoted to procedural skills and fluency.
- Fluency is built from practicing the procedures shown to the students in the examples of the lessons.
- Lesson 8.3 builds a conceptual understanding of rotation and then works on procedural fluency of rotating shapes.
- In chapter 9 students are asked to justify their ideas about transformations as they are working on doing the transformations.
- Each chapter has a lot of repeated practice for building procedural fluency.
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The materials reviewed for Grade 8 do not meet the expectations for students spending sufficient time working with engaging applications of the mathematics.
- Non-contrived and/or non-routine real-world application problems were not evident in all chapters.
- There is no evidence of students making their own assumptions or simplification to model mathematically in the chapters.
- Some chapters had more application problems than others.
- There are "Brain Work" problems in each chapter. They are problems that could be multi-step and non-routine but they are scaffolded with step-by-step questions that do not support students in solving the problems themselves.
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The materials reviewed for Grade 8 do not meet the expectations for a balance of the three aspects of rigor.
- The program is not balanced between conceptual understanding, procedural skill and fluency and application.
- There are many more instances of procedural problems.
- There is not a balance of rigor in this Grade 8 series.
- Students are doing the procedural work while teachers need to find their own ways to develop conceptual understand that is not stated in the text.
- There is a lot of fluency, which is mostly non-contextual and some application problems. However, they were not equally balanced.
Criterion 2.2: Math Practices
The materials reviewed for Grade 8 do not meet the expectations for practice-content connections. The MPs for each chapter are listed in the chapter at a glance page. The MPs are there as a structure to design procedural problem work. The lessons do not allow students to construct meaning from the MP. During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices. Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding. There are few instances where students have to justify an explanation and even fewer where they critique others. Mathematical vocabulary is used appropriately at the Grade 8 level. This text excels in mathematical language - it is used consistently throughout instruction, examples, practice, and assessment.
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The materials reviewed for Grade 8 partially meet the expectations for having the Standards for Mathematical Practice (MPs) identified and used to enrich mathematics content.
- The MPs for each chapter are listed on the chapter at a glance page.
- The MPs are there as a structure to design procedural problem work.
- The lessons do not allow students to construct meaning from the MP.
- During lessons, there is no specific mention of the MPs and it is not clearly evident how students might use the practices.
- The lessons do not always match the practices that are listed. For example, chapter 2 says MP1 is spotlighted. The problems are small, scaffolded and the application of a procedure. The students are not applying problem solving strategies or having to persevere through long problems.
- Instances that support MPs include lesson 9.2: Construct arguments, where students have to identify similar triangles and justify how they can prove it; Lesson 5.2: Model mathematics, which sets up systems using bar models; and Lesson 6.2: Model mathematics, which addresses multiple representations of a function, such as words, equations, tables and graphs.
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The materials reviewed for Grade 8 do not meet the expectations for carefully attending to the full meaning of each practice standard.
- The MPs are listed at the beginning of each chapter on the chapter at a glance page.
- MPs are not referenced throughout lessons, homework, or assessments.
- Many of the lessons and homework are procedural in nature and do not offer many opportunities for students to apply the practices in order to extend learning and understanding.
- In the majority of lessons, the work is teacher and text driven, and the students are provided step-by-step processes and just expected to mirror what is provided to them.
- An example is in lesson 4.3. The teacher edition states that the students are using MP1. The lesson is on writing equations of a line in slope-intercept form. The lesson does not have them persevere through a problem instead they fill in blanks to follow a set way to create the equations.
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The materials reviewed for Grade 8 do not meet the expectations for prompting students to construct viable arguments and analyze the arguments of others.
- There are few instances where students have to justify an explanation and even fewer where they critique others.
- There are math journal problems in some of the homework that do lend themselves to students constructing viable arguments.
- There are few instances of students being able to engage in critiquing reasoning of others. There is some evidence of students explaining answers.
- One example is practice 3.2 on page 108. However there is no evidence of supporting student discussion in class.
- The questions are scaffolded into one- and two-step problems with much support from the teacher.
- Multi-step problems and problems that require open-ended answers are not common.
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The materials reviewed for Grade 8 partially meet the expectations for assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others.
- The materials are scaffolded to the point where true, rich discussion may not be possible.
- For example, in lesson 5.3, the teacher edition states, "Best Practices--You may want to ask volunteers to show how this system of equations could be solved using the substitution method." This statement implies that this strategy may or may not be employed. It in no way encourages teachers to use this authentic discussion daily.
- In most lessons, there are hints to the teacher that would prompt some analysis to begin discussions such as in lesson 6.2; teachers have a prompt telling them to have a student explain in their own words the "Caution" in the example problem.
- Many of the "Best Practices" boxes provide suggestions to teachers that ask the students to think about what is presented.
- In Lesson 4.4, it prompts teachers to have students verify the slope by using two points or in Lesson 5.2, the prompt is to solve it in another way.
- Some of the "Think Math" strategies could help students construct viable arguments but there is no guarantee that these strategies will be utilized by teachers.
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The materials reviewed for Grade 8 meet the expectations for explicitly attending to the specialized language of mathematics.
- Mathematical vocabulary is used appropriately at the Grade 8 level.
- For example, vocabulary for chapter 7 on the Pythagorean Theorem is hypotenuse, leg and Pythagorean Theorem.
- The vocabulary is referred to throughout the chapter, as it is introduced, highlighted and then clarified in an "ELL Box."
- This text excels in mathematical language. It is used consistently throughout instruction, examples, practice, and assessment.
Overview of Gateway 3
Usability
Criterion 3.1: Use & Design
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Criterion 3.2: Teacher Planning
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Criterion 3.3: Assessment
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Criterion 3.4: Differentiation
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Criterion 3.5: Technology
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Report Overview
Summary of Alignment & Usability for Math in Focus | Math
Product Notes
Kindergarten assessments were not reviewed because they are not included in the materials. The assessment book is available for purchase separately from the main materials. Grades 1 and 2 assessments were reviewed.
Math K-2
The grade band texts include several future grade-level assessments. The grade band texts do not meet the publisher criteria for having the large majority of time spent on the major work of the grade. Supporting and additional clusters are treated separately therefore not counted as a part of the major work. The materials are not coherent or consistent with the standards. There is not enough content for one school year.
Kindergarten
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Usability
1st Grade
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Usability
2nd Grade
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Usability
Math 3-5
The grade band texts have several future grade-level assessments. The grade band texts do not meet the expectations for the large majority of time spent on the major work of the grade. Supporting and additional clusters are treated separately and do not enhance the major work. The materials are not coherent or consistent with the standards. There is not enough content for one school year.
3rd Grade
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Usability
4th Grade
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Usability
5th Grade
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Usability
Math 6-8
The materials reviewed for grades 6-8 do not meet the expectations for alignment to the CCSSM. The materials devote the majority of class time to the major work for Grades 6 through 8. The materials are coherent and consistent with the CCSSM for Grade 8, but Grades 6 and 7 have concepts beyond those grades. There are a few times that the supporting work enhances the understanding of the major clusters. The CCSSM are visibly listed on the student pages and in the teacher edition. Since the materials did not meet the expectation for Gateway 1 in Grades 6 and 7, those grades were not reviewed in Gateway 2. The Grade 8 text excels at mathematical language, but does not address the full meaning of the mathematical practices or spend sufficient time on building conceptual understanding.