Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 8 partially meet the expectation for alignment to the CCSSM. The materials meet expectations in the areas of focus and coherence, but do not meet the expectations for alignment to the CCSSM in the areas of rigor and the MPs. In the area of focus within the grade, there are above grade-level topics included in the assessment, but they do not impact the structure of the materials. The materials spend 76 percent of the class time on major work. In the area of coherence, the materials include content that is shaped by the CCSSM clusters with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems with supporting and additional content that engages students in the major work of the grade. Natural connections are made between clusters and domains. However, the materials fail to note grade-to-grade progression. In the area of rigor and balance, all three aspects of rigor are sometimes present in the materials. Even though there are glimpses of balance in some units, most of the lessons focus on procedural skill and fluency. There isn't enough opportunities for students to make their own connections or write explanations/reflections to the connections that they are making. A majority of the lessons require memorized tasks and procedures without students having to develop meaningful connections on their own. The extension problems usually ask for reflections on procedural skill. There are several missed opportunities to challenge students to explore their own strategies and reflect on the connections that they are making. The three aspects of rigor are not well balanced. In the area of practice content connections, the Materials attempt to incorporate the MPs in each lesson. However, the materials are so frequently labeled as MPs that a teacher cannot reliably use the materials to know when MPs are being carefully attended to. There are many instances when questions are labeled as an MP, when in fact they are just a computation question. The materials incorporate questions in which students have to justify and explain their answers, but lack lesson structures in which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented but not always incorporated meaningfully into the lesson.

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
13
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
8
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

|

Not Rated

Not Rated

Gateway 3:

Usability

0
22
31
38
0
31-38
Meets Expectations
23-30
Partially Meets Expectations
0-22
Does Not Meet Expectations

Gateway One

Focus & Coherence

Meets Expectations

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Gateway One Details

The instructional materials reviewed for Grade 8 meet the expectation for focus and coherence with the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Even though above grade-level topics are included in the assessment, they do not impact the structure of the materials. For coherence, the materials are explicitly shaped by the CCSSM cluster headings and there are aspects of coherence in the materials that are exceptional, but there is a lack of clear grade-to-grade progressions . Overall, the materials meet the requirements for focus and coherence.

Criterion 1a

Materials do not assess topics before the grade level in which the topic should be introduced.
2/2
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-
Criterion Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for focus within assessment. Above grade-level topics are included on the assessments, but there is minimal impact to the underlying structure of the materials. Most notably, the assessments include high school level work on functions. Overall, the materials reviewed for Grade 8 include a few above grade-level questions that can be modified or skipped without impacting the structure of the materials.

Indicator 1a

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.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for assessment because above grade-level assessment items, and their accompanying lessons could be modified or skipped without impacting the underlying structure of the instructional materials. For this indicator, the four quarterly benchmark tests were reviewed first, then for a more in-depth look at each CCSSM indicator, the chapter tests, extended response tests, and performance tasks were examined.

  • The instructional materials offer multiple tiers of assessment on their ConnectEd website. These include pretests, diagnostic tests, chapter quizzes, chapter tests, performance tasks, extended response tests, quarterly benchmark tests, standardized test practice as well as SBAC and PARCC practice test question. Furthermore, a test generator is included so that educators can create their own assessments to suit their needs.
  • The first quarterly benchmark test assesses the following Grade 8 standards 8.NS.1, 8.NS.2, 8.EE.1, 8.EE.2, 8.EE.3, 8.EE.4 and 8.EE.7. These standards are primarily covered in chapters 1-2. The listed CCSSM are covered on the assessments with no above grade-level items.
  • The second quarterly benchmark test assesses the following Grade 8 standards. 8.EE.5, 8.EE.6, 8.EE.8, 8.F.1, 8.F.2, 8.F.3, 8.F.4 and 8.F.5. These standards are primarily covered in chapters 3-4. The listed CCSSM are covered on the assessments. The second quarterly benchmark test and chapter 4 assessments have some above grade-level topics. Question 10 asks about domain. This is high school standard F.IF.A.1, which states, "Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x)." This vocabulary is included in lesson 2 which primarily has students represent relations using tables and graphs. This topic is only briefly covered in lesson 3. Question 7 requires students to match a graph to a quadratic function. The standard 8.F. 5 states “Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.” It is expected that students be able to identify a nonlinear graphs; however, on both the benchmark and chapter test students are expected to graph quadratic functions which is not expected of students until high school. Lesson 7 covers 8.F.5 nicely, but lesson 8, which covers graphing quadratic functions is above grade level. Lesson 8 could be skipped without impacting the materials.
  • The third quarterly benchmark test assesses the following Grade 8 standards 8.G.1, 8.G.2, 8.G.3, 8.G.3, 8.G.5, 8.G.6, 8.G.7 and 8.G.8. These standards are primarily covered in chapters 5-6. The listed CCSSM are covered on the assessments with no above grade-level items.
  • The end of year benchmark test assesses some of the previously covered standards and 8.G.4, 8.G.9, 8.SP.1, 8.SP.2, 8.SP.3 and 8.SP.4. These standards are primarily covered in chapters 7-9. The listed CCSSM are covered on the assessments.The chapter 9 chapter tests include questions on standard deviation. The concept of standard deviation is covered in the high school standard HSS.ID.A4, "Use the mean and standard deviation of a data set to fit it to a normal distribution and to estimate population percentages. Recognize that there are data sets for which such a procedure is not appropriate. Use calculators, spreadsheets, and tables to estimate areas under the normal curve." In the textbook, standard deviation is covered in lesson 5, "Measures of Variation." An educator could skip this lesson without skipping any of the intended Grade 8 standards and create an assessment using the test generator.

Criterion 1b

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.
4/4
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Criterion Rating Details

The instructional materials reviewed for Grade 8 meet the expectation that the majority of class time is spent on the major work of the grade. The materials spend about 76 percent of class time on major work. Even when the lessons primarily focus on supporting clusters they incorporate major work standards. Overall, the instructional materials meet the expectation that materials spend a majority of class time on major work.

Indicator 1b

Instructional material spends the majority of class time on the major cluster of each grade.
4/4
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for focus by spending a majority of class time on the major clusters of the grade. To determine this, three perspectives were evaluated: 1) the number of chapters 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 reflective for this indicator because it specifically addresses the amount of class time spent on concepts. Overall, the materials spend 76 percent of instructional time on the major clusters of the grade. The Grade 8 materials have 9 chapters that contain 62 lessons. (The inquiry labs were considered as part of the lesson that they proceeded.) A total 152 days (optional projects not included) of class time was scheduled for the lessons.

  • 5 out of 9 chapters (56 percent) focus exclusively on the major clusters of Grade 8, while the other 4 chapters have a mix of major and supporting clusters.
  • Each chapter is made up of lessons, when examining the individual lesson 73 percent of class time is spent on the major clusters of the grade. The lesson breakdown is as follows:
    • Chapter 1 has 10 lesson; Lessons 2 – 8 focus on the major clusters (8.EE.1, 8.EE.2, 8.EE.3, and 8.EE.4), while lessons 1, 9 and 10 are focused on supporting clusters (8.NS.1, and 8.NS.2). Seven out of 10 lessons in chapter 1 are on major work.
    • Chapter 2: Five out of five of the lessons are on the major cluster (8.EE.7).
    • Chapter 3: Eight out of eight of the lessons are on the major clusters (8.EE.5, 8.EE.6, 8.EE.8, 8.F.2, 8.F.3, and 8.F.4).
    • Chapter 4 has 9 lessons: Lessons 1, 2, 4, 5, 6, 7 and 9 focus on the major clusters (8.F.1, 8.F.2, 8.F.3, 8.F.4, and 8.F.5), while lessons 3 and 8 are above grade level. Lesson 2 has an above grade-level component, but it was still deemed to focus on a majority of the major clusters. Seven out of nine lessons are on the major clusters.
    • Chapter 5: Seven out of seven lessons are on the major clusters (8.G.5, 8.G.6, 8.G.7 and 8.G.8).
    • Chapter 6: Four out of four lessons are on the major clusters (8.G.1 and 8.G.3).
    • Chapter 7: Seven out of seven lessons are on the major clusters (8.G.1, 8.G.2, 8.G.4, 8.G.5 and 8.EE.6).
    • Chapter 8: Six out of six lessons are on the supporting clusters (8.G.9).
    • Chapter 9: Lessons 1, 2 and 3 are on the supporting clusters (8.SP.1, 8.SP.2, 8.SP.3 and 8.SP.4). Lessons 4-6 are on off grade-level topics.
  • A pacing guide is provided with the materials and gives the number of days each chapter should take. When calculating the number of days, 76 percent of the class time is spent on the major clusters, 16 percent of the class time is spent on supporting clusters. The remainder of the class time is spent on off grade-level work. The breakdown of the number of days spent on the major cluster of the grade are as follows:
    • Chapter 1: Ten lessons should take 18 days, seven of the lessons are major clusters, which should take approximately 15 days.
    • Chapter 2: Five lessons should take 13 days.
    • Chapter 3: Eight lessons should take 20 days.
    • Chapter 4: Nine lessons should take 19 days, seven of the lesson are major clusters, which should take approximately 16 days.
    • Chapter 5: Seven lessons should take 19 days.
    • Chapter 6: Four lessons should take 13 days.
    • Chapter 7: Seven lessons should take 17 days.
    • Chapter 8: Six lessons should take 15 days. However, lesson 6 incorporates similarity (8.G.4) into the concept of volume (8.G.9), so one day of this lesson would be spent on a major cluster.
    • Chapter 9: Six lessons should take 18 days. However, in addition to interpreting graphs, lesson 2 requires students to write an equations of a line of best fit (8.EE.3), so one and a half days are spent on a major cluster.

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
7/8
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-
Criterion Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for being coherent and consistent with the standards. The materials include content that is shaped by the CCSSM clusters with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems with supporting content that engages students in the major work of the grade. Natural connections are made between clusters and domains. However, the materials fail to note the grade to grade progressions. Overall the materials meet the expectation for being coherent and consistent with the standards.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation that supporting content enhance focus and coherence simultaneously by engaging students in the major work of the grade. Overall, the lessons that focus on supporting content also engage students in major work where natural and appropriate.

  • Chapter 1, lesson 9, focuses on estimating roots. In doing this students are both using rational number approximations 8.NS.2 and using square root and cube roots 8.EE.2.
  • Chapter 9, lesson 2, focuses on 8.SP.A - Investigate patterns of bivariate data. In completing this lesson, students will analyze scatter plot and write the lines of best fit, this supports major work 8.F.3.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The instructional material are designed to take 152 – 162 days. Many additional resources can be found on the accompanying website. Overall, the amount of content that is designated for this grade level is viable for one school year.

  • Included in the materials is a yearlong pacing guide. According to that pacing guide, completing the work in the student edition would take 152 days. That includes time for a chapter opener, a mid-chapter quiz, a chapter review, and a chapter test. Ten extra days could be spent on the five unit projects.
  • · All of the CCSSM were developed to give students the practice they need to be prepared for Grade 9.
  • There is guided practice, independent practice and common core spiral review for each lesson. Also included in the lessons are Real-World Link, H.O.T. Higher Order Thinking, and Power-up Common Core Test Practice which are more rigorous than the independent practices.

Indicator 1e

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.
1/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 partially meet the expectation for the materials to be consistent with the progressions in the standards. The materials give all students extensive work on grade-level problems. Content from prior and future grades is identified but not explicitly stated and what is below grade level and at grade level is sometimes confusing. The materials attempt to relate grade-level problems to prior knowledge but they fail to mention grade-to-grade progressions. Overall the instructional materials partially meets the expectation to be consistent with the progressions in the standards.

  • The materials do an excellent job of giving all ability levels an opportunity for learning grade-level standards. The materials provide exercises for all levels of complexity and recommended homework options that are organized for students who are approaching, on level, or beyond level. The materials connect classwork to the homework assignments for all ability levels. For example, the materials use a variety of practice with “Power Up” activities for performance task problems and common core test practice for a challenging review structure. The materials suggests that students from all three levels are encouraged to try these higher order thinking problems, so students who need interventions still get to engage with the full depth of the grade-level standards.
  • Below grade-level work is seemingly listed as preparation for a standard. However, this statement is confusing in some of the lessons that are listed as preparation. For example, chapter 3, lesson 1 is titled "Constant Rate of Change" and it is listed in the materials as preparation for 8.EE.5. 8.EE.5 calls for a connection to be made between unit rate and slope and this lesson makes that connections so it is unclear why it is listed as preparation. Moreover, constant rate of change is better spelled out in 8.F.4, "Construct a function to model a linear relationship between two quantities. Determine the rate of change and initial value of the function from a description of a relationship or from two (x, y) values, including reading these from a table or from a graph. Interpret the rate of change and initial value of a linear function in terms of the situation it models, and in terms of its graph or a table of values." The content in this lesson is well done, however, it is unclear why it is listed as preparation for 8.EE.5 and not just listed as 8.EE.5 or 8.F.4.
  • Lessons that are above grade-level are identified as extensions to Grade 8 standards or preparation for high-school standards. Some examples include, chapter 5, lesson 4 is labeled as an extension of 8.G.5. The topic of this lesson is angles and polygons, it is an extension of the standard and therefore it is correctly identified. Chapter 7, lesson 7 is labeled as an extension of 8.G.4. the topic explores finding the area and perimeter of similar figures, it is an extension of the standard and correctly identified. The final two lessons in chapter 9 identify the lessons as prep for high school standards S.ID.1, S.ID.2 and S.ID.3. Because these are extension of the Grade 8 statistics standards they are correctly labeled and relate to grade-level work.
  • In the teachers edition a graphic is presented under coherence. It show previous, now and next. "Previous" lists what topics students learned that lead up to the current topic. "Now" lists what topics the students are learning now. "Next" lists what related topics the students will be learning. Although, there is an attempt to be Coherent across the grade levels there are no references to other grades' standards within the materials.

Indicator 1f

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.
2/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 meet the expectation for fostering coherence through connections at a single grade. The materials include learning objectives that are clearly shaped by the CCSSM clusters, and the materials incorporate natural connections between clusters and domains, where those connections are natural and important.

  • At the beginning of the teachers edition, there is an index of the CCSSM and the corresponding chapters and lesson where those standards can be found.
  • Each unit in the materials correlates to a Grade 8 CCSSM domain. The units are broken into chapters that focus on standards in that domain. The chapters are broken into lessons that incorporate aspects of each standard. As a result, each lesson's title, objective, and essential question is clearly shaped by the CCSSM cluster headings.
  • The student edition gives a table of the Grade 8 CCSSM and students are given the chance to track their knowledge of the CCSSM throughout the year.
  • One example of connecting two or more clusters in a domain is chapter 4, lesson 4. This lesson connects 8.F.A and 8.F.B, where students construct functions to model linear relationships while they are comparing properties of functions that are represented in different ways.
  • In addition to the connections noted in criteria 1c, there are several examples of connecting two or more domains in Grade 8. These examples include:
    • Chapter 3, lesson 4 connects 8.EE and 8.F where students connect functions and their graph to equations in the form y = mx + b.
    • Chapter 5, lesson 5 connects 8.G and 8.EE when students connect the use of square roots to the understanding of the Pythagorean Theorem.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

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Gateway Two Details

The materials for reviewed Grade 8 do not meet the expectations for Gateway 2: Rigor and Mathematical Practices. All three aspects of rigor are present, however, they are not always balanced, with the majority of the emphasis placed on procedural skill and fluency. Conceptual understanding generally involves a quick activity in which students are guided step-by-step through an activity and are led to a set of rules to follow to solve a problem. The unit projects and Power Up Performance Tasks offer some good application problems where students can pick their own solution paths and engage in some experimentation and discourse, however the application problems incorporated into each lesson are often one-step, routine word problems in which students are directed on the procedure to follow in order to solve the problem. There are a considerable amount of problems labeled as MPs that do not accurately support the full intent of the MPs. Some of the activities and lessons give a way for a student to construct viable arguments and analyze the arguments of others, but this is done through contrived questions and activities. The materials are set up in a way that leads to teacher-directed mathematical learning where there is a lack of investigation, analysis and interpretation on the students' part to truly meet the depth required by the MPs.

Criterion 2a - 2d

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.
4/8
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-
Criterion Rating Details

The materials reviewed for Grade 8 do not meet the expectation for rigor and balance. All three aspects of rigor are occasionally present in the materials. Even though there are glimpses of balance in some units, most of the lessons focus on procedural skill and fluency. There isn't enough opportunities for students to make their own connections or write explanations/reflections to the connections that they are making. A majority of the lessons require memorized tasks and procedures without students having to develop meaningful connections on their own. The extension problems usually ask for reflections on procedural skill. There are several missed opportunities to challenge students to explore their own strategies and reflect on the connections that they are making.

Indicator 2a

Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.
1/2
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-
Indicator Rating Details

The instructional materials for Grade 8 partially meet the expectations to develop conceptual understanding of key mathematical concepts, especially when called for in specific content standards or cluster headings. Overall, the instructional materials present inquiry labs and some visual examples as a way to develop conceptual understanding. However, the materials lack a fully developed conceptual understanding in some areas that are called for in the common core standards.

  • Conceptual understanding is called for in 8.EE.B. This standard is covered in chapter 3.
    • Lesson 1 covers linear proportional relationships and rate of change. The examples offer many visuals in graph and tables and the guided practice encourages students to explain if a relationship is linear of not.
    • Lesson 2 covers slope. The examples offer only one problem for students to get a visual example of what slope means. (Example 1 shows a treadmill and explains rise over run.) There is one example where students count rise over run on a graph, and one example where students find the change in yand change in x in a table. After those three examples, students are expected to use the slope formula. There is a lack of problems intended for students to form their own meaning of slope.
    • There is an inquiry lab that calls for students to use similar triangles to explain why the slope is the same between any two points, but there are only two problems for students to practice this. Also, the inquiry lab comes after students have already practiced slope using the formula.
  • Conceptual understanding is called for in 8.F.A and this topic is covered in chapter 4.
    • Lesson 4, 5 and 6 offer some concrete examples where students will develop an understanding of functions by looking at graphs, tables, and equations.
    • The inquiry lab and lesson 3 gives a formal definition of functions, but the lessons fail to give students concrete examples, where one can find the value of one thing when another is changing. Rather than giving concrete examples, the materials quickly jump to abstract explanations of domain and range in lesson 2 and function notation in lesson 3.
  • Conceptual understanding is called for in 8.G.1 and this topic is covered in chapters 6 and 7.
    • The inquiry labs in these two chapters help to give students a conceptual understanding of transformations and similarity by using hands on activities.
      • The first inquiry lab in chapter 6 begins by having students physically move objects to understand transformations.
      • The second inquiry lab in chapter 6 has students use tracing paper to understand rotational symmetry.
      • Another inquiry lab in chapter 6 uses a ruler to connect scale factor and dilatation.
      • The first inquiry lab in chapter 7 has students use patty paper to see congruence of triangles.
      • Another inquiry lab in chapter 7 shows students how to use geometer's sketchpad in a way that helps them understand congruence and similarity.

Indicator 2b

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

The instructional Materials for Grade 8 meet the expectations to give attention throughout the year to individual standards that set an expectation of procedural skill and fluency. Overall, there are multiple opportunities for students to develop procedural skills and fluency which include many rapid-fire questions, various questioning strategies for students to explain procedural skills, and chances for students to apply procedural skills to new situations.

  • Procedural skill and fluency is called for in 8.EE.7. Chapter 2 covers this topic, the entire chapter is comprised of lessons with questions that give students many chances to develop fluency.
    • On the sidebar in the teachers edition, there are questioning strategies that give students the chance to articulate procedures. For example, it suggests that teachers ask the students, "In order to isolate the variable, what should we do first?" (page 123), and suggests the teacher ask, "Could we have started our first step by doing something differently?" (page 146.)
  • Procedural skill and fluency are called for in 8.G.9. The first three lessons in chapter 8 cover this topic. The questions in these lessons include problems that have pictures and verbal descriptions and focus on students fluently using formulas to solve problems.
    • The problems gives students the chance to use fluency in new situations. For example, question 3 on page 592 asks students to find the volume of platform designed to hold a sculpture. It is comprised of two rectangular prisms and a cylinder.

Indicator 2c

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
1/2
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Indicator Rating Details

The instructional materials for Grade 8 partially meet the expectations that teachers and students spend sufficient time working with engaging applications of the mathematics without losing focus on the major work of each grade. Overall, the materials have multiple opportunities for application but in many of those application problems students are directed on the procedure to follow to solve the problem.

  • Application problems are called for in 8.F.B and this topic is covered primarily in chapter 4.
    • The lessons on 8.F.B give representations of relationships and functions with graphs, equations, and tables. Lesson 5 has students compare functions when multiple representations are given
    • Even though there are many application problems, the materials rarely provide students with opportunities to pick their own strategy for solving the problem. They are usually guided using one given strategy for each step of the problem.
    • The Power Up performance tasks at the end of each lesson offer students multi-step abstract questions where they solve problems by using a variety of solution paths.
    • There is a 21st Century career lesson that explores how physical therapist use functions to do their jobs.
    • The unit project has students work collaboratively to find the cost of growing a vegetable garden and project the profits. In doing this, students use equations and functions to complete the project.
  • Application problems are called for in 8.EE.C.8.C. This topic is covered in chapter 3, lessons 6, 7 and 8.
    • Lesson 6 explains how to write an equation in point slope form and slope intercept form. Lesson 7 explains how to solve systems of equations by graphing. Lesson 8 explains how to solve systems of equations algebraically. All three lessons have some application problems, but the application problems are often one-step, routine problems where students are told how to proceed in a step-by-step manner.

Indicator 2d

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.
0/2
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Indicator Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectation that the materials balance all three aspects of rigor with the three aspects not always combined together nor are they always separate. Overall, the majority of the lessons focus on procedural skills and fluency with very few opportunities for students to discover and apply procedures for themselves.

  • Conceptual understanding is not developed in all of the standards that call for it. When it comes to slope and functions, students are not given the opportunity to fully explore the meaning before they are expected to use formal definitions, notations and formulas.
  • There isn't enough opportunities for students to make their own connections. Occasionally, they will ask students to make a reflection, but a majority of the lessons require memorized tasks and procedures without meaningful connections. The extension problems usually ask for reflections on procedural skill. There are several opportunities missed to challenge students to explore their own strategies and create opportunities for multiple solution pathways.
  • The materials provide mostly procedural skill, even the application type problems are just a contrived extension of the procedural skill. Additional application problems in the unit projects, 21st Century careers and problem-solving investigation helps with the balance between procedural skill and application but this is limited and no additional attention is paid to the standards that specifically call for application.

Criterion 2e - 2g.iii

Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice
4/10
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Criterion Rating Details

The materials reviewed for Grade 8 do not meet the expectations for practice-content connections. The materials attempt to incorporate the MPs in each lesson. However, the materials are so frequently labeled as MPs that a teacher cannot reliably use the materials to know when an MP is being carefully attended to. There are many instances when questions are labeled as an MP when in fact they are just a computation question. The materials incorporate questions in which students have to justify and explain their answers, but lack lesson structures in which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented but not always incorporated meaningfully into the lesson.

Indicator 2e

The Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout each applicable grade.
1/2
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Indicator Rating Details

The instructional materials reviewed for Grade 8 partially meet the expectation for identifying and using MPs. Overall, the materials clearly identify the MPs and incorporate them into the lessons, however the MPs are sometimes over-identified.

  • The MPs are incorporated into each lesson so they are used to enrich the content and they are not taught as a separate lesson.
  • There is a Mathematical Practice Handbook at the start of the textbook. This handbook explains each practice standard and gives example problems for each standard.
  • There is a table of contents that specifically addresses the MPs and it lists the pages where you could find each of the practices. All of the MPs are represented.
  • Each lesson identifies several MPs. For example, chapter 1, lesson 1 states that it incorporates MP1, 3, 4, 6, 7 and 8. The materials point to these MPs in the student practice section of lesson 1.
  • Items are sometimes over identified. In the sidebar of the teacher edition, teaching strategies are suggested. Often those strategies are identified as attending to multiple strategies. For example, in the "Pairs Discussion" in chapter 5, lesson 1, students work in pairs to complete a graphic organizer. Then they share and revise their responses. This activity claims to incorporate MP1, 2, 3, 4, 5 and 6. However, there is no explanation or description as to how these practices are incorporated.

Indicator 2f

Materials carefully attend to the full meaning of each practice standard
0/2
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-
Indicator Rating Details

The instructional materials reviewed for Grade 8 do not meet the expectations for carefully attending to the full meaning of each practice standard. Overall, the materials so frequently label items as MPs that a teacher cannot reliably use the materials to know when an MP is being carefully attended to. This is evident at the start of each lesson which is designed to take a few days to complete, but claims to incorporate three or more MPs.

Examples of specific places where the full meaning of the identified MP not being attended to include:

  • MP1 is identified in chapter 1, lesson 6, question 14. The directions state "Compute and express each value in scientific notation" This is nothing more then a computation problem with unfriendly numbers. This is not a place where students make sense of a problem and persevere in solving it.
  • MP2 is identified in chapter 1, lesson 8, question 23. The directions state: "Explain why (square root) -4 is not a real number, but (cube root) -8 is." This is just a place for students to explain a definition and algorithm there is no call for Inductive reasoning.
  • MP3 in chapter 3, lesson 4, question 14. This problem requires you to write an equation of a line that does not have a y-intercept. This requires basic recall of equations in this given situation without deep abstract reasoning.
  • MP4 is identified in chapter 1, lesson 10, question 20. The directions state: "Identify two numbers, one rational number and one irrational number, that are between 1.4 and 1.6. Include the decimal approximation of the irrational number to the nearest hundredths." There is no indication as to how students are modeling mathematics here.
  • MP5 is identified in chapter 3, lesson 2, question 18. The students are given a tool (table) provided by the text. The students are not being asked to choose their own tools, which takes away from the full meaning of the MP.

Indicator 2g

Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
0/0

Indicator 2g.i

Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 8 partially meet the expectations for appropriately prompting students to construct viable arguments and analyze the arguments of others. Overall, there are problem structures that lead a student to explain and justify their reasoning. However, there are few opportunities for students to analyze the arguments of others.

  • In the practice problems nearly every lesson includes questions that are specifically labeled with the heading "Justify Conclusions." These questions ask students to explain how they got their answers.
  • In some lessons, the questions are labeled in bold with the heading "Construct a Viable Argument." These questions often ask students to explain if something is true or not.
  • Even though there are several prompts that ask the students to justify their answers or construct their own viable arguments, there are some missed opportunities for higher frequencies of this type of problem. Some of these missed opportunities include:
    • Chapter 4, lesson 5, question 8. The question poses a real-world application problem with exchange rates for pounds and euros. Next, the students are asked to analyze four statements and decide which one is true, but the students are not asked to explain their decisions.
    • Chapter 5, lesson 3, question 27. The text asks students to apply what they know about angles and lines to find the values of two missing angles in a given picture of an obtuse triangle. The students were never prompted to explain their reasoning or construct a viable argument on how they found the missing angles.
  • In some lessons the questions are labeled in bold with the heading "Find the Error." In these classic error analysis problems students are presented with someone's solution and asked to simply identify the error. This does not attend to the full meaning of the standard, where students would need to refute claims made by others by offering counter examples and counterarguments. There were very few instances where students were asked to find a counter-example.

Indicator 2g.ii

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.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 8 partially meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, the materials direct teachers with many scaffolding questioning strategies asking higher level questions and offering some suggested activities that lead students to construct viable arguments and analyze the arguments of others. However, the materials lack suggestions or ideas that guide a teacher with setting up scenarios where students experiment with mathematics and based on those experiments construct and present ideas.

  • In the sidebar of the teachers edition, the teacher is provided with many scaffolding questions. The beyond level questions do a great job of asking higher depth of knowledge level questions and provide supportive structures to analyze student arguments.
  • In the sidebar of the teachers edition, there are suggested activities for teachers to use with students. Very often these suggested activities have students compare, critique, and analyze answers. For example, the "Pairs Check" in chapter 1, lesson 3, students work in pairs to complete a worksheet. Then they trade their solutions with another pair of students and discuss the differences.
  • The Higher Order Thinking Problems in the student practice section of the materials incorporate some of the MPs that help students to construct viable arguments and analyze the arguments of others. Students are given opportunities to be persistent in their problem-solving, to express their reasoning, and apply mathematics to real-world situations. However, further guidance on how to promote this and support students in the development of these skills is not given. This is coupled with the fact that many students are rarely given authentic opportunities to develop the true intent of any of the MPs mentioned above.

Indicator 2g.iii

Materials explicitly attend to the specialized language of mathematics.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 8 partially meet the expectation for attending to the specialized language of mathematics. Overall, the materials identify and define correct vocabulary but there are only sporadic places where vocabulary is integrated into the lessons.

  • At the start of every chapter, there is a list of related vocabulary words that will be used in the chapter. Students are given a box that outlines key concepts and key words are highlighted in yellow and immediately defined.
  • In the guided practice section, students answer a "Building on the Essential Question" question, in which they have to understand the vocabulary to answer the question. For example, question 4 on page 156 asks "How many possible solutions are there to a linear equation in one variable? Describe each one."
  • In each lesson that introduces new mathematical vocabulary there is a Vocabulary Start-Up, which frequently uses a graphic organizer to help students understand the new vocabulary. The materials offer related vocabulary at the start of the lessons, however, minimal reference is made back to them as the lesson progresses. In this way, students are not explicitly supported in coming back and revising/adding to their understanding of these terms. The assumption is made that mastery of vocabulary is immediate.
  • At the end of the chapters there is a vocabulary check included in the chapter review.
  • Students are given sporadic opportunities to express mathematics vocabulary with the daily lessons. The materials lack consistent structures to make mathematics terms meaningful and incorporate high levels of mathematical language. There are too few places where students are given the opportunity to write or explain in a way that the use of mathematical vocabulary is assessed. The vocabulary usually consists of key words highlighted for the introduction of the lesson with a given definition.

Gateway Three

Usability

Not Rated

Criterion 3a - 3e

Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
0/8

Indicator 3a

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.
0/2

Indicator 3b

Design of assignments is not haphazard: exercises are given in intentional sequences.
0/2

Indicator 3c

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.
0/2

Indicator 3d

Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
0/2

Indicator 3e

The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
0/0

Criterion 3f - 3l

Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
0/8

Indicator 3f

Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
0/2

Indicator 3g

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.
0/2

Indicator 3h

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.
0/2

Indicator 3i

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.
0/2

Indicator 3j

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).
0/0

Indicator 3k

Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
0/0

Indicator 3l

Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
0/0

Criterion 3m - 3q

Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
0/10

Indicator 3m

Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
0/2

Indicator 3n

Materials provide strategies for teachers to identify and address common student errors and misconceptions.
0/2

Indicator 3o

Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
0/2

Indicator 3p

Materials offer ongoing formative and summative assessments:
0/0

Indicator 3p.i

Assessments clearly denote which standards are being emphasized.
0/2

Indicator 3p.ii

Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
0/2

Indicator 3q

Materials encourage students to monitor their own progress.
0/0

Criterion 3r - 3y

Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
0/12

Indicator 3r

Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
0/2

Indicator 3s

Materials provide teachers with strategies for meeting the needs of a range of learners.
0/2

Indicator 3t

Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
0/2

Indicator 3u

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).
0/2

Indicator 3v

Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
0/2

Indicator 3w

Materials provide a balanced portrayal of various demographic and personal characteristics.
0/2

Indicator 3x

Materials provide opportunities for teachers to use a variety of grouping strategies.
0/0

Indicator 3y

Materials encourage teachers to draw upon home language and culture to facilitate learning.
0/0

Criterion 3aa - 3z

Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
0/0

Indicator 3aa

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.
0/0

Indicator 3ab

Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
0/0

Indicator 3ac

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.
0/0

Indicator 3ad

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.).
0/0

Indicator 3z

Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
0/0

Additional Publication Details

Report Published Date: Mon Jan 25 00:00:00 UTC 2016

Report Edition: 2014

Title ISBN Edition Publisher Year
null 978-0-02-145425-9 null null null
null 978-0-02-145689-5 null null null
null 978-0-07-667852-0 null null null
null 978-0-07-670446-0 null null null

About Publishers Responses

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Once a review is complete, publishers have the opportunity to post a 1,500-word response to the educator report and a 1,500-word document that includes any background information or research on the instructional materials.

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Math K-8 Rubric and Evidence Guides

The K-8 review rubric identifies the criteria and indicators for high quality instructional materials. The rubric supports a sequential review process that reflect the importance of alignment to the standards then consider other high-quality attributes of curriculum as recommended by educators.

For math, our rubrics evaluate materials based on:

  • Focus and Coherence

  • Rigor and Mathematical Practices

  • Instructional Supports and Usability

The K-8 Evidence Guides complement the rubric by elaborating details for each indicator including the purpose of the indicator, information on how to collect evidence, guiding questions and discussion prompts, and scoring criteria.

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