Go Math
2014-2015

Go Math

Publisher
Houghton Mifflin Harcourt
Subject
Math
Grades
K-8
Report Release
02/15/2015
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports 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)
Partially Meets Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.

Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
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About This Report

Report for 7th Grade

Alignment Summary

The instructional materials reviewed for Grade 7 partially meet the expectations for alignment with the CCSSM. The materials partially meet the criterion for Gateway 1. There was not enough time given to the major work of the grade. The supporting clusters did support the major work, but the materials need more focus on the major clusters. The work could be sufficiently completed in one school year, but it lacked in multiple practice opportunities for a student to gain mastery. There was also not a deliberate connection between previous, current, and future content. The materials partially meet the criterion for Gateway 2. In the area of Rigor and Balance the materials do meet the criterion. The instructional and practice materials provided a good balance of conceptual understanding, procedural skill, and application. In the area of Practice Content-Connection the materials partially meet the criterion. It was evident that the eight MPs were embedded throughout materials. They did not always add meaning to the content as they were not always identified correctly or were missing from designated pages. Many questions had students explain their thinking or defend their answers. Often, the materials did not assist in providing opportunities for students to critique the work of others. The students are given opportunity to use precise language of mathematics.

7th Grade
Alignment (Gateway 1 & 2)
Partially Meets Expectations
Usability (Gateway 3)
Not Rated
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Grade 7 partially meet the expectations for alignment to the CCSSM. For focus, the Grade 7 materials reviewed meet the expectations for assessing grade-level content but did not meet the criteria for the time devoted to the major work of the grade. For coherence, supporting work is clearly connected to the focus of the grade and is done so in a meaningful way. Coherence is also evident in the instructional materials. This includes problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. On the other hand the instructional materials only partially meets the expectations for viability and consistency with the progressions in the standards. Overall the Grade 7 materials partially meet the quality expectations for focus on major work and coherence.

Criterion 1.1: Focus

02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Grade 7 meet the expectations for assessing grade-level content. In each of the assessments included in each unit, only Grade 7 content is assessed. Prerequisite skills from previous grades are assessed in the "Are you Ready" assessments. However content from future grades is not assessed. Overall, the instructional materials for Grade 7 meet the criterion for assessing grade level content.

Indicator 1A
02/02
The instructional material assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades may be introduced but students should not be held accountable on assessments for future expectations.

The Grade 7 materials reviewed meet the expectations for assessing grade-level content. The materials also have assessment items for previously learned content to determine if students have the needed prerequisite skills.

  • Module quizzes, assessment readiness review, end-of-unit review and a performance task are included in each unit. In all of these assessment materials, only Grade 7 material was assessed.
  • Each module has an "Are You Ready" assessment. This looks at skills from previous grades that will be needed in order to complete the module successfully.

Criterion 1.2: Coherence

00/04
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 7 do not meet the expectations for having the large majority of class time being devoted to the major work of the grade. For example, only 53% of the lessons and only 51% of the teaching days address the major work of the grade. Overall, the instructional materials for Grade 7 do not meet the criterion for designating the large majority of class time to the major work of the grade.

Indicator 1B
00/04
Instructional material spends the majority of class time on the major cluster of each grade.

The instructional materials reviewed for Grade 7 do not meet the expectations for students and teachers using the materials as designed to devote the large majority of class time to the major work of the grade. Based on the pacing guides in the teacher edition, about 75 of the 148 teaching days, or about 51%, are devoted to major work.  Of the 49 lessons in Grade 7, 26 are focused on the major clusters (53%).

Criterion 1.3: Coherence

06/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 7 partially meet the expectations for coherence and consistency with the CCSSM. The supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade. Coherence is evident both in addressing connections at the Grade 7 level and in the instructional materials. This includes problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. The weak aspects of the materials were that it only partially meets the expectations for viability and consistency with the progressions in the standards. Overall the instructional materials at the Grade 7 partially meet the expectations for the coherence.

Indicator 1C
02/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 7 meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade.

The following examples demonstrate how supporting and additional clusters in geometry and statistics support the major work of proportional relationships.

  • Unit 4 is the geometry unit and supports 7.G.A; unit 5 is the statistics unit and supports 7.SP.B. Both require the students to use proportions to solve problems.
  • Unit 4 also teaches 7.G.B and this supports the major cluster 7.NS.A.
  • Unit 6 (probability) addresses the supporting cluster 7.SP.C. It supports the major cluster 7.NS by working with rational numbers, specifically by writing probability as fractions, decimals and percents.
  • Unit 6 also supports the major cluster 7.RP by using proportions to find information about populations.
Indicator 1D
01/02
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 for Grade 7 do not meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. With only 149 days of lessons accounted for, there need to be additional review days and summative assessment days as well as additional material other than unit tests to ensure sufficient instruction. Overall, the amount of content that is designated for this grade level is short of the amount of material needed to make it truly viable for one school year. According to the pacing guide, there is a suggested 149 days of lessons for 45-minute classes. There is guided practice and independent practice for each lesson. There is also a quiz and a formative assessment check for each module. All of this is included in the pacing guide.

A summative end of the unit test is not included in the pacing guide. Adding one day per unit would bring the total to 154 days.

There are many references in the teacher's guide to online resources that provide more practice opportunities, however it is not accessible in the basic program.

Indicator 1E
01/02
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 7 partially meet the expectations for the material to be consistent with the progressions in the standards. The strongest point is that at the beginning of each module there is a section called "Unpacking the Standards." Although there is a page with progressions, there are no references to other grades' standards anywhere within the lessons. Overall, the materials in Go Math-Grade 7 to some extent identify the progressions from prior grades in the standards.

  • In the beginning of each module there is a section called "Unpacking the Standards." This puts the standards into student-friendly language and provides examples of what students will be learning.
  • This section aligns with the standards and then demonstrates that students will be working only within grade-level expectations.
  • There were no references to other grades within the lessons.
  • There is a page with progressions that shows Grade 6, 7 and 8 progressions.

The instructional materials reviewed for Grade 7 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials give students of varying abilities some, but not extensive work with grade-level problems.

  • The lessons are broken down into five sections: Engage, Explore, Explain, Elaborate and Evaluate. There are also tips and ideas for differentiating and extending the material.
  • The teacher edition includes references to online additional resources, including Math on the Spot, a video available by scanning the QR code in the student edition. Although the teacher edition does not contain all of these resources, access to some of them are available without any separate purchase.

The instructional materials reviewed for Grade 7 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials only generally relate grade level concepts to prior knowledge from earlier grades.

  • There is a chart at the beginning of each unit and module that relates new content to previously taught content, either earlier in the grade or from previous grades.
  • The charts have column headings labeled "Before this Unit," "In this Unit" and "After this Unit" and "Before this Module," "In this Module" and "After this Module" but do not specify standards.
  • Students are assessed on prior knowledge at the beginning of each module.
  • Unit 3, pages 167E-167F, gives the background resources for mathematics. On page 168, it restates what students should know before in this unit and after this unit.
Indicator 1F
02/02
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 7 meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • The standards are referenced all throughout the book.
  • Each lesson has an essential question aligned with the cluster headings.
  • Mathematical practices are clearly explained along with the domains and strands of the focus work.
  • There are also specific "cluster connection" identifiers in the teacher edition.

The instructional materials include problems and activities that serve to connect two or more clusters in a domain. They include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Overall the materials foster coherence through connections at the Grade 7.

  • Unit 3 connects 7.EE.1 to 7.NS.  Operations with rational numbers are used to solve real world application problems.

  • The major work of proportional relationships is used throughout Units 4, 5, and 6 and connected to the work of those units especially within the EE domain.  

Indicator evidence updated 11/02/16

Overview of Gateway 2

Rigor & Mathematical Practices

The Go Math 7 materials reviewed meet expectations for Rigor and Balance. The instructional materials provide students opportunity to practice in all three areas. The materials partially meet the criterion of Practice-Content Connections. There are several places in the materials that clearly identify the standards and the meanings of each. Standards were sometimes not located on identified pages or were misidentified. Students had opportunity throughout the book to explain their mathematical reasoning. There were not as many opportunities for students to discuss the work of classmates or activities that helped teachers in how to engage students in these conversations within the confines of the materials we reviewed. The materials do attend to precise language of mathematics and provide learning opportunities of vocabulary and opportunities to use the vocabulary in the context of the problems. 

Overall the reviewed materials of Go Math 7 Partially Meet the Criteria for Gateway 2. 

 

*Evidence updated 10/27/15

Criterion 2.1: Rigor

08/08
Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The materials reviewed meet the criterion of rigor and balance. In the Grade 7 lessons, there is a focus on conceptual understanding, procedural skill and fluency, and real world application. The layout of the lessons provides teachers with a framework to address each component of rigor.

Indicator 2A
02/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The materials reviewed for Go Math Grade 7 meet the expectations for developing conceptual understanding of key mathematical concepts. 

  • The design of each lesson is set up for conceptual understanding. Each lesson has an Engage, Explore, and Explain process for teachers to follow. This provides essential question, vocabulary, questioning strategies, engagement with whiteboards or manipulatives, how to avoid common errors, focus on critical thinking, and a teaching tip.
  • The standards 7.NS.1 and 7.NS.2 are addressed in Unit 1. The lessons use a variety of models and ask many questions that require students to justify their thinking. The standard 7.EE.1.B is developed in Unit 2 and Unit 5.
  • Each unit has a performance task for students to solve. Most tasks require students to demonstrate conceptual understanding.

Each lesson has a page that breaks down the depth of knowledge of each question being asked. An example of this is on page 65. 

Indicator 2B
02/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The materials reviewed meet the expectations for giving attention to procedural skill and fluency. 

  • Procedural skill and fluency with standards found in 7.NS is expected by the end of Grade 7. Modules one through three give explicit attention to these standards.
  • Each lesson has a guided practice page (e.g. page 156), and most of these pages provide fluency practice.

Independent Practice, Module Quizzes, Assessment Readiness, and Study Guide Review sections are also opportunities for demonstration of procedural skill. These components are at the end of each module (e.g., 223–226).

Indicator 2C
02/02
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The materials reviewed meet the expectations for giving attention to application without losing focus on the major work of the grade.

  • All lessons contain problems that require real world application. This is demonstrated mostly in the Independent Practice pages (e.g., page 121– 22). This section also designates H.O.T. questions, which stand for higher order thinking.
  • Many problems require students to solve multi-step problems.

Students are expected to apply and use concepts in real world situations in 7.NS.A.3, 7.EE.B.3 and cluster 7.RP.A. Modules one through seven provide opportunities for real world applications of these standards.

Indicator 2D
02/02
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The materials reviewed partially meet the expectations for showing a balance of conceptual understanding, procedural skill, and application. 

  • The layout of each lesson provides an opportunity for a balance of rigor. The five E’s—engage,  explore, explain, elaborate, and evaluate—are the guidelines for instruction, and this structure allows for the opportunity to target conceptual understanding, procedural skill and fluency, and application.

Criterion 2.2: Math Practices

07/10
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The Go Math 7 materials reviewed partially meet expectations for Practice-Content Connections. There are many places that the MPs are referenced. As indicated, the identification is not always accurate. Questions could lead students to have discussions about mathematics, but there is not much guidance for how the teacher should conduct the conversations. The book does use precise vocabulary and has many places for students to use the language of mathematics. 

Indicator 2E
01/02
The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.

The materials reviewed partially meet the expectations for identifying the MPs and using them to enrich the content. 

  • The eight MPs are defined on pages CC8–CC11 of the teacher’s edition. Along with the explanation, there are also pages referenced where the standards are implemented in the student edition. This is not a complete listing but a sample of where they can be found.
  • Pages CC14–CC16 in the teacher’s edition provide more explanation of the standards and provide examples of each standard directly taken from the textbook.
  • Each lesson highlights one MP. There is a box titled “Professional Development” that describes how the practice is addressed within the lesson. An example of this is on pages 117 and 118.
  • The Explore and Explain sections of the teacher’s edition have the words “Mathematical Practices” in bold, but there is not a specific practice identified with the heading. An example of this is on page 117.

Although the MPs are found throughout the materials, they are often not central to the lessons/activities where they are identified. As a result, often the MPs do not enrich the mathematics content of Grade 7.

Indicator 2F
01/02
Materials carefully attend to the full meaning of each practice standard

Materials reviewed partially meet the expectations for carefully attending to the full meaning of each practice. 

  • Some instructional materials were not accurately aligned to MPs. For example, MP4 is listed as being addressed on page 122; however, there is not any identification of MP4 on page 122. MPs 2, 5, and 7 are cited on this page.  
  • MPs are listed in the index; however, they do not use precise language or numbers.

MPs are identified by the publisher. There are inconsistencies with the practice being on the page or it being accurately interpreted. For example, on page 61, MP8 is identified but MP1 and MP3 are cited on the page. Another example is on page 152, where a Critique Reasoning question is aligned to MP 8.

Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
02/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

Materials reviewed meet the expectations for prompting students to construct viable arguments and analyze the work of others. 

  • There are many questions in the teacher’s edition found in the Engage, Explain, and Elaborate headings that, when asked, can lead to discussion of the concepts. An example of this is on page 217 under the Explain section: “Why is adding three + 1 tiles to both sides a better strategy than adding nine -1 tiles to both sides?”
  • The student independent practice sections have questions with the following headings: Critique Reasoning, Error Analysis, Justify Reasoning, and Communicate Mathematical Ideas. See examples are on page 18, problem number 33 and page 54, problem number 28.

All six of the Unit Performance Tasks include at least one question that requires students to explain or justify their answer.

Indicator 2G.ii
01/02
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

Materials reviewed partially meet the expectations for assisting teachers in engaging the students in constructing viable arguments. 

  • Teachers are provided with variety of questions designed to engage students in constructing viable arguments throughout the lesson.

The book does not assist teachers in engaging the students in analyzing the work of other students.  There are a few questions that ask students for an error analysis of a worked problem but never engage them in conversation about each other’s work.

Indicator 2G.iii
02/02
Materials explicitly attend to the specialized language of mathematics.

Materials reviewed meet the expectations for attending to the language of mathematics.

  • Vocabulary is in every module. Each module has two activities to assist with this practice: “Reading Start Up” and an “Unpacking the Standards.” All vocabulary words are high-lighted in yellow throughout the book. 
  • The “Essential Question of each lesson asks for an explanation of the current skill. Students will need to use mathematics vocabulary in their response.
  • “Math Talk” is another tool for teachers in each lesson. The publisher considers this a formative assessment.
  • The “Study Guide Review” includes a re-cap of the vocabulary that is in each unit.
  • The “H.O.T." questions provide students an opportunity to respond and explain using precise language.

MP6 was listed and was evident in four of the six Performance Tasks, units 1, 4, 5 and 6.

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3H
00/02
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
Indicator 3I
00/02
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
Indicator 3J
Read
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Indicator 3AD
Read
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.