Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 7 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 Mathematical Practices. In the area of focus within the grade, a minimal number of above grade-level questions are included on the assessments. Furthermore, the materials are designed to devote the majority of class time to the major work of the grade. 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, though all three aspects of rigor are present in the materials, they are often presented separate from each other and not used in a balanced way to develop a concept. The inquiry labs are used to develop conceptual understanding, however, the concepts developed in the inquiry labs are not referenced in the lessons. There is an abundance of procedural skills, but without solid work at conceptual understanding students are left to memorize procedures. The application problems presented in the materials often tell students how to solve the problem with only limited opportunities for students to find their own solution path. In the area of practice content connections, the Materials attempt to incorporate the Mathematical Practices in each lesson. However, the materials are so frequently labeled as a Mathematical Practice that a teacher cannot reliably use the materials to know when a Mathematical Practice is being carefully attended to. There are many instances when questions are labeled as a Mathematical Practice standard, 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
7
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

+
-
Gateway One Details

The instructional materials reviewed for Grade 7 meet the expectation for focus and coherence to the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. There are some above grade-level topics included in the assessment but they do not impact the structure of the materials. For coherence, the materials are explicitly shaped by the CCSSM with enough work to be viable for one school year. All students engage in extensive practice with grade-level problems and supporting content engages students in the major work of the grade. Natural connections are made between clusters and domains, but there is a lack of clear grade-to-grade progressions. Overall, the materials meet the expectations for focus and coherence with the CCSSM.

Criterion 1a

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

The instructional materials reviewed for Grade 7 assess a few topics that are above grade-level. However, the affected assessments and their accompanying lessons can be modified or skipped without impacting the underlying structure of the instructional materials. Moreover, there is a variety of included assessment types that cover all of the CCSSM. Overall the instructional materials meet the expectation for focus within assessment.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 meet the expectations for assessment because above grade-level assessment items and their accompanying lessons, can be modified or omitted without significantly 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 7 standards: 7.RP.1, 7.RP.2, 7.RP.3, with some elements of 7.NS.3, 7.EE.2 and 7.EE.3. The standards are primarily covered in chapters 1-2. The listed CCSSM are covered on the assessments. One above grade-level topic is assessed. Questions 8 and 21 are questions about slope. Slope is first introduced in Grade 8. The Grade 7 standard that leads to slope is 7.EE.2.B and it reads "Identify the constant of proportionality (unit rate) in tables, graphs, equations, diagrams, and verbal descriptions of proportional relationships." These two concepts are closely related, and the lesson offers an explanation of that relationship thus the inclusion of this Grade 8 topic is mathematically reasonable.
  • The second quarterly benchmark test assesses the following Grade 7 standards: 7.NS.1, 7.NS.2, 7.NS.3, 7.EE.1, 7.EE.2 and 7.EE.3. The standards are primarily covered in Chapters 3-5. The listed CCSSM are covered on the assessments. One above grade level topic is assessed. Questions 10 and 24 are questions about arithmetic sequences. Arithmetic sequences are formally addressed in high school. HSF.BF.A2 says, "Write arithmetic and geometric sequences both recursively and with an explicit formula, use them to model situations, and translate between the two forms." The corresponding lesson on sequences is in chapter 5, lesson 2. The questions are more closely related to identifying a pattern, and students are asked to understand the vocabulary "arithmetic sequence" and find the nth term which reasonably extends the Grade 7 standards. This lesson could be skipped without affecting the other lessons in the chapter. The affected questions on the test could be skipped or explained, or a teacher could use the test generator to create a test without sequences.
  • The third quarterly benchmark test assesses the following grade 7 standards 7.G.1, 7.G.2, 7.G.3, 7.G.4, 7.G.5, 7.G.6 7.EE.3 and 7.EE.4. These standards are primarily covered in Chapters 6 - 8. The stated CCSSM are covered on the assessments, with one above grade-level topic assessed. Question 9 requires knowledge of cross sections of a cylinder. The standard 7.G.3 states “Describe the two-dimensional figures that result from slicing three-dimensional figures, as in plane sections of right rectangular prisms and right rectangular pyramids.” The standard does not mention cylinder, and in Grade 7 students are just learning to find area and circumference of circles. The chapter tests do not include questions covering cross sections of cylinders thus there was no significant impact on the structure of the materials.
  • The End of the Year benchmark test covers many of the grade 7 standards covered on the prior benchmark tests, and 7.SP.1, 7.SP.2, 7.SP.3, 7.SP.4, 7.SP.5 7.SP.6, 7,SP,8 and 7.SP.9. These standards are primarily covered in chapters 9 - 10. All of the listed CCSSM are covered on the assessments with no new above grade-level items.

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
+
-
Criterion Rating Details

The instructional materials reviewed for Grade 7 meets the expectation that the majority of class time is spent on the major work of the grade. The materials spend about 66 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 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 represents a true reflection for this indicator because it specifically addresses the amount of class time spent on concepts. Overall, the materials spend 66 percent of instructional time on the major clusters of the grade. The Grade 7 materials have 10 chapters that contain 72 lessons. (The inquiry labs were considered as part of the lesson that they supported.) A total 158 days (optional projects not included) of class time was scheduled for the lessons.

  • Six out of 10 chapters (or 60 percent) focus exclusively on the major clusters of Grade 7, while the other four chapters have a mix of major and supporting clusters.
  • Each chapter is made up of lessons, when examining the individual lesson 64 percent of class time is spent on the major clusters of the grade. The lesson breakdown is as follows:
    • Chapter 1: Nine out of nine lessons are on major clusters (7.RP.1, 7.RP.2, 7.RP.3 and 7.EE.3).
    • Chapter 2: Eight out of eight of the lessons are on the major clusters (7.RP.2, 7.RP.3, 7.EE.2 and 7.EE.3).
    • Chapter 3: Five out of five of the lessons are on the major clusters (7.NS.1, 7.NS.2, 7.NS.3 and 7.EE.3).
    • Chapter 4: Eight out of eight of the lessons are on major clusters (7.NS.1, 7.NS.2, 7.NS.3, 7.RP.3 and 7.EE.3)
    • Chapter 5: Eight out of eight lessons are on the major clusters (7.EE.1, 7.EE.2 AND 7.NS.3).
    • Chapter 6: Eight out of eight lessons are on the major clusters (7.EE.3 and 7.EE.4).
    • Chapter 7: Six out of six of the lessons are supporting clusters (7.G.1, 7.G.2, 7.G.3 and 7.G.5).
    • Chapter 8: Eight out of eight of the lessons are on supporting clusters (7.G.4 and 7.G.6).
    • Chapter 9: Seven out of seven of the lessons are on supporting clusters (7.SP.5, 7.SP.7, and 7.SP.8)
    • Chapter 10: Five out of five lessons are on supporting clusters (7.SP.1, 7.SP.2, and 7.SP.4).

A pacing guide is provided with the materials and gives the number of days each chapter and lesson should take. When calculating the number of days, 66 percent of the class time is spent on the major clusters, 32 percent of the class time is spent on supporting clusters. The breakdown of the number of days spent on the major clusters of the grade are as follows:

  • Chapter 1: Nine lessons should take 16 days.
  • Chapter 2: Eight lessons should take 16 days.
  • Chapter 3: Five lessons should take 14 days.
  • Chapter 4: Eight lessons should take 15 days.
  • Chapter 5: Eight lessons should take 17 days.
  • Chapter 6: Eight lessons should take 18 days.
  • Chapter 7: Six lessons should take 15 days. This chapter is considered supporting clusters, but in lesson 1, 2 and 3 about 25 percent of the problems involve using the properties of angles and triangles to find angle measures that have embedded equations. These problems incorporate 7.EE.4. In lesson 4 the problems use proportions to solve scale problems. These problems incorporate 7.RP.2 Therefore, approximately three and a half days are spent on major work.
  • Chapter 8: Eight lessons should take 19 days. This chapter is considered supporting clusters, but the area, surface area, and volume problems supply problems that incorporate rational numbers thus incorporating 7.NS.A. Therefore, approximately nine and a half days are spent on major work.
  • Chapter 9: Seven lessons should take 15 days. This chapter is considered a supporting cluster, but in lesson 1 students write probabilities as a percent, prep for 7.RP.3, so half of this lesson is considered major work. Lesson 4 simulations require students to use ratio and percents to solve real-world problems (7.RP.3), so half of this lesson is considered major work. Lesson 5 students are expected to find the percent of an event occurring incorporating 7.RP.3 so half of this lesson is considered major work. Therefore, approximately two days are spent on major work.
  • Chapter 10: Five lessons should take 13 days. Five of the lessons are supporting clusters. However, in lesson 1 students express probability as a percent (7.RP.3). This same lesson has students use a probability to make predictions of future events. In doing this students have to set up and solve a proportion so they are engaged in (7.RP.A). Therefore, one day is spent on major work.

Criterion 1c - 1f

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

The instructional materials reviewed for Grade 7 meets the expectations 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 and supporting content 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. 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
+
-
Indicator Rating Details

The Instructional materials reviewed for Grade 7 meets the expectation for the supporting content enhancing 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.

  • In chapter 7, lesson 1 uses vertical and adjacent angles to find missing angle measures. In example 3 and the corresponding practice problems, one of the angles is labeled with an algebraic expression. As a result, students will need to set up and solve an equation to find the missing angle measure. Thus, students are simultaneously practicing 7.G.3, a supporting cluster, and 7.EE.4.A, a major cluster.
  • Chapter 7, lesson 4 uses proportional reasoning to solve problems involving scale.Thus, they are simultaneously engaged in 7.G.1, a supporting cluster and 7.RP.1, a major cluster.
  • Chapter 8, lesson 5 involves finding the volume of a pyramid. This is supporting cluster 7.G.6. In example 3 and the corresponding practice problems, students use the formula to find the height of a pyramid. To do this students need to solve an equation. Thus, students are also practicing 7.EE4.B.
  • Chapter 9, lesson 1 involves finding the probability of a simple event. In doing this students are expected to relate this information as a ratio and a percent. This supports major work 7.RP.3.
  • In chapter 9, lesson 2 example 3, students use theoretical and experimental probability to predict future events. In doing this students have to set up and solve a proportion, so they are engaged in 7.RP.A.
  • In Chapter 10, lesson 1 students express probability as a percent. This supports major work 7.RP.3. This same lesson has students use probability to make predictions of future events. In doing this, students have to set up and solve a proportion so they are engaged in 7.RP.A.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 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. The instructional material are designed to take 158 – 168 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 158 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 8.
  • 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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 partially meet the expectations 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. 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 listed as preparation for a standard. For example, chapter 3, lesson 1, is listed as prep for 7.NS.3. Though it is identified, it is not clear from which grade it comes from, and knowing this would help a teacher adjust pacing.
  • Lessons that are above grade-level are identified as extensions. For example, chapter 10, lesson 3 is labeled as an extension of 7.SP.1. The topic of this lesson, misleading graphs, is an extension of the standard and therefore it is correctly identified.
  • In the teacher 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.
  • In Grade 7, the CCSSM have one cluster that states “apply and extend” past knowledge to current learning. 7.NS.A says “Apply and extend previous understandings of operations with fractions to add subtract multiply and divide rational numbers” In chapter 3, students extend their understanding of integers for Grade 6 to using a number line to add, subtract, multiply and divided integers. In chapter 4, students combine their understanding of integers and fractions to add subtract multiply and divide all rational numbers.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 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 domains, where those connections are natural and important.

  • At the beginning of the teacher 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 7 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 7 CCSSM and students are given the chance to track their knowledge of the CCSSM through-out the year.
  • In addition to the connections noted in criteria 1c there are several examples of connecting two or more domains. In Grade 7 some of these examples include: chapter 1, lesson 2 connects 7.RP.1 and 7.NS.3 where students will connect complex fractions to unit rates while dividing fractions. Chapter 2 connects 7.RP.A and 7.EE.3 where students will solve percent problems with proportions while they solve multi-step real-life and mathematical problems. Chapter 7, lesson 7 connects 7.RP.3 with 7.NS.2 and 7.NS.3 where students convert between measurement systems by setting up a proportion and using the operations of rational numbers to solve them.

Gateway Two

Rigor & Mathematical Practices

Does Not Meet Expectations

+
-
Gateway Two Details

The materials for Grade 7 do not meet the expectations for 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. Lessons, activities, and questions are frequently labeled as MPs when in fact they are not, and guidance is not given to help guide students into the full meaning of the MSs. 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; 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.
3/8
+
-
Criterion Rating Details

The materials reviewed for Grade 7 do not meet the expectations for rigor and balance. Though all three aspects of rigor are present in the materials, they are often presented separate from each other and not used in a balanced way to develop a concept. The inquiry labs are used to develop conceptual understanding, however, the concepts developed in the inquiry labs are not referenced in the subsequent lessons. There are an abundance of problems that focus on procedural skills, but without solid work at conceptual understanding students are left to memorize procedures. The application problems presented in the materials often tell students how to solve the problem with only limited opportunities for students to find their own solution path. Overall, the materials do not meet the expectation for rigor and balance.

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
+
-
Indicator Rating Details

The instructional materials for Grade 7 partially meet the expectations to develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings. Overall, the instructional materials present inquiry labs and higher order thinking questions as a way to develop conceptual understanding, however, the conceptual development is generally a quick activity which hurriedly ends with a set of rules to follow, and there is little time for students to discover their own knowledge.

  • Conceptual understanding is called for in 7.NS.A, this is primarily covered in chapters 3 and 4.
    • Chapter 3 covers operations with integers 7.NS.1. The lessons on adding, subtracting, and multiplying integers have an associated inquiry lab that helps students visualize the operations using counters. The lessons with counters are not incorporated into the lessons themselves and other then a few practice problems in the inquiry lab students don’t use the counters to complete problems.
    • The lessons in chapter 3 use number lines in the examples as a way to explain operations with integers, but do not expect students to use the number lines for practice. In order to be in full alignment with the intent of the standards, students should have multiple opportunities to develop their ability to demonstrate understanding using number lines.
    • Chapter 4 covers operations with all rational numbers (7.NS.2 and 7.NS.3). Two inquiry labs give some conceptual understanding of rational numbers. The inquiry lab prior to lesson 1 uses number lines to explain ordering negative fractions. The inquiry lab prior to lesson 3 uses a number line to show adding and subtracting positive and negative fractions. Both labs offer a nice introduction to conceptual understanding, however, that understanding is not reinforced in the corresponding lessons and practice problems.
    • The lessons on multiplying and dividing rational numbers start by showing the algorithm and do not develop a conceptual understanding.
  • Conceptual understanding is called for in 7.EE.A. This is primarily covered in Chapter 5.
    • In chapter 5 students use the properties of operations to generate equivalent expressions. This chapter gives students some practice with algebra tiles to help students get a conceptual understanding of equivalent expressions. For example, the materials develop a nice conceptual understanding of factoring linear expressions. At the start, an inquiry lab shows students how to use algebra tiles to get a visual of factoring. In the lesson, students are shown two ways to factor. Method 1 encourages the use of a model, and method 2 shows students how to use the greatest common factor.
    • At the end of each lesson there are Higher Order Thinking Problems. These give students the opportunity to develop conceptual understanding. Students are asked to explain their understanding by justifying conclusions, finding errors or looking at a problem's structure.

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.
1/2
+
-
Indicator Rating Details

The materials reviewed for Grade 7 partially meet the expectations of attending to fluency and procedural work within the lessons. Overall, there are multiple opportunities for students to develop procedural skill and fluency, however, one of the standards that calls for fluency 7.EE.B.4 is not thoroughly attended to.

  • Procedural skills and fluency are called for in 7.NS.A which is primarily covered in Chapters 3 and 4. The chapters are comprised of lessons that give many questions that help students develop fluency.
    • In the Teachers Edition, on the side bar, there are questioning strategies that give students the chance to articulate procedures. For example, on pages 204 - 205 the teacher is encouraged to refer to example problems on adding integers and asks students to notice when the signs are the same or different and then state what happens to the sum in those cases
    • The Higher Order Thinking (H.O.T) Questions give students a chance to articulate their understanding of procedural skills. For example, Question 14 on page 208 asks students to name the property illustrated by the following x + (-x) = 0 and x + (-y) = -y + x. The H.O.T questions also give students the ability to apply procedural skills to unfamiliar types of problems. For example, Question 15 on page 238 asks: The product of two integers is -21. The difference between the integers is -10. The sum of the two integers is 4. What are the two integers?
    • Students are given opportunities to continually engage in fluency through-out the year. After students have practiced operations with integers in Chapter 3, they continue to use operations with integers in chapter 5 when they are working with expressions.
  • Procedural skills and fluency is called for in 7.EE.A.1 which is primarily covered in Chapter 5. This chapter also includes ample fluency based practice problems in the guided and independent practice sections. As well as H.O.T questions and teacher directed questioning strategies to help students articulate and apply procedural skills.
  • Procedural skills and fluency is called for in 7.EE.B.4. According to the glossary of Common Core Standards at the beginning of the Teachers Edition this topic is covered in Chapter 6. Chapter 6 focuses on solving equations and inequalities. There are no lessons that specifically have students use variables to represent quantities in a real-world or mathematical problem, and construct simple equations and inequalities to solve problems by reasoning about the quantities. Though there are places in the lesson that touch on this, there is a lack of problems that would allow students to develop fluency in constructing simple equations.

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
+
-
Indicator Rating Details

The instructional materials for Grade 7 partially meet the expectation so that teachers and students spend sufficient time working with engaging applications of mathematics, without losing focus on the major work of the grade. Overall, the materials have multiple opportunities for application, but many of the application problems are one-step, routine word problems in which students are directed on the procedure to follow in order to solve the problem.

  • The materials incorporate the following application type of lessons throughout the chapters.
    • The Power Up Performance Tasks at the end of each chapter offer students multi-step abstract questions where they solve problems by using a variety of solution paths.
    • At the end of each unit there is a unit project. This project gives students the opportunity to research a topic and relate that information to the mathematics of the unit.
    • The materials have problem solving investigation through-out each chapter. It gives students step-by-step ways to use a problem solving strategy
  • Application problems are called for in 7.RP.A. The majority of this standard is covered in Chapters 1 and 2.
    • The lessons begin with a real-world link, where students perform a task that introduces the lesson. For example, Chapter 1, Lesson 1 "Rates", students work with a partner to take each other’s pulse and record the results thus beginning the conversation about rates.
    • There are application problems included in the guided and independent practice sections, however, students are rarely given the opportunity to solve problems without being told how to solve them. The materials rarely give students the chance to pick their own process for solving a problem.
  • Application problems are called for in 7.NS.A.3 the majority of this standard is covered in Chapter 4 Lessons 3 - 8.
    • The application problems covering this standard are incorporated into a series of lessons where each lesson teaches the various operations with rational numbers. For example, Lesson 5 "Add and Subtract Mixed Numbers" The majority of the lesson is on procedural skills and fluency with some word problems included at the end of the problem set. The word problems are generally routine and one-step in nature.
  • Application Problems are called for in 7.EE.B.3 this standard is covered throughout chapters 2, 3 and 4.
    • Even though there are many lesson that lead students to covert between mathematical forms, there are very few opportunities for students to discuss why one form would be a better choice then another.

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
+
-
Indicator Rating Details

The instructional materials reviewed for Grade 7 does 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, all three aspects of rigor are present in the materials, however, the majority of the lessons focus on procedural skills and fluency with fewer opportunities for students to discover and apply procedures for themselves.

  • 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 of procedures without meaningful connections. The Higher Order Thinking problems sometimes 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.
  • Some attempt is made at conceptual understanding, however, the conceptual understanding is rarely tied to the students practice.

Criterion 2e - 2g.iii

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

The materials reviewed for Grade 7 do not meet the expectations for practice-content connections. The materials attempt to incorporate the MPs in each lesson. However, 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. There are many instances when questions are labeled as MPs 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
+
-
Indicator Rating Details

The Instructional materials reviewed for Grade 7 partially meet the expectation for identifying and using the MPs. Overall, the materials clearly identify the MPs and incorporate them into the lessons, however the MPs are often 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 mathematical practices. For example, Chapter 3 Lesson 3, claims to incorporate MP1 through MP7. The materials point to these practice standards in the student practice section of Lesson 3 and in the Ideas for Use in the side bar of the teachers edition.
  • Items are often over identified. In the side bar of the teachers edition, teaching strategies are suggested. Often those strategies are identified as attending to multiple strategies. For example, Chapter 6 Lesson 6, "Alternate Strategy" in this activity, students review the symbols used for inequalities and what they mean. Students than come up with key words or phrases that can be used for each symbol. Then they are asked how they know when the symbols should be used for the problem in the Real-World Link. This activity claims to incorporate MP1, MP2 and MP3. 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 7 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 6 Lesson 6, Question 14. The directions state "Solve x + b > c for x" This is nothing more than a computation problem. This is not a place where students make sense of a problem and preserve in solving it.
  • MP2 is identified in Chapter 3 Lesson 1 Question 14. The directions state "If |x| = 3 what is the value of x? This is just a place for students to explain a definition there is no call for Inductive reasoning.
  • MP4 is identified in Chapter 3 Lesson 4 Question 12. The directions state " Write a multiplication sentence with a product of -18." There is no indication as to how students are modeling mathematics and applying it to everyday life.
  • MP5 is identified in Chapter 7 Lesson 4 Questions 10 - 13. A map with a scale is given, students are told to find the actual distance between cities in New Mexico. They are directed to use a ruler. Students are told which tool to use, and not required to make this decision for themselves.

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
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-
Indicator Rating Details

The materials reviewed for Grade 7 partially meet the expectation for appropriately prompting students to construct viable arguments concerning grade-level mathematics detailed in the content standards. Overall, every lesson's problem set, has one or more questions in which students have to explain their reasoning. However, students are only occasionally prompted within problem sets, and application problems to explain, describe, critique, and justify their work.

  • 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 a few 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.
  • 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.
  • Students had a few instances where they were asked to make conjectures. Often this was not really a conjecture as students were not asked to make a generalization, instead they were asked to solve a specific problem. For example, in chapter 7, lesson 2, question 11d, students are asked to generate a conjecture from one observation based on a small drawing of intersecting lines. An exemplary model of creating conjectures would ask students to gather a variety of evidence to look for patterns and then make conjectures.

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
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Indicator Rating Details

The materials reviewed for Grade 7 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 side bar 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 side bar of the teachers edition there are suggested activities for teachers to use with students. Very often these suggested activities have students compare or analyze critique, and analyze answers. For example, chapter 5, lesson 1, "Find the Fib" Students work on a team where one student creates 3 problems, two are solved correctly and one is incorrect. The other students find the one that is wrong and correct it.
  • The Higher Order Thinking Problems in the students 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
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-
Indicator Rating Details

The materials reviewed for Grade 7 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 3 on page 84 asks; How can you determine if a linear relationship is a direct variation from an equation? table? a graph?
  • In each lesson that introduces new mathematical vocabulary there is a Vocabulary Start-Up, that 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. Assumption is made that mastery of vocab 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 math vocabulary with the daily lessons. The materials lack consistent structures to make math terms meaningful and incorporate high levels of mathematical language. There are 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 978-0-02-130152-2 null null null
null 978-0-02-138984-1 null null null
null 978-0-02-144789-3 null null null
null 978-0-07-678687-9 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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