Alignment to College and Career Ready Standards: Overall Summary

The instructional materials reviewed for Grade 8 partially meet the expectations for alignment to the CCSSM. The instructional materials partially meet the expectations for Gateway 1 because they meet the expectations for focus on major work and do not meet the expectations for coherence. Since the materials partially meet the expectations for Gateway 1, evidence was collected in Gateway 2. The instructional materials meet the expectations for rigor and balance and do not meet the expectations for practice-content connections. 

See Rating Scale
Understanding Gateways

Alignment

|

Partially Meets Expectations

Gateway 1:

Focus & Coherence

0
7
12
14
9
12-14
Meets Expectations
8-11
Partially Meets Expectations
0-7
Does Not Meet Expectations

Gateway 2:

Rigor & Mathematical Practices

0
10
16
18
12
16-18
Meets Expectations
11-15
Partially Meets Expectations
0-10
Does Not Meet Expectations

Usability

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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

Partially Meets Expectations

+
-
Gateway One Details

The instructional materials reviewed for Course 3 partially meet the expectations for focus and coherence with the CCSSM. For focus, the instructional materials meet the criteria for summative assessment items on grade-level and delivered in a challenging and effective manner with most units having little or no above grade-level standards. Focus is also met in the time devoted to the major work of the grade with 78.0 percent of the days allocated in the timeline aligning to the major work. For coherence, supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year and will have difficulty fostering coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. The material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade-level learning is not explicit.

Criterion 1a

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

The post, chapter, and standardized assessments that are included in the Teacher's Resources and Assessments were reviewed for Course 3 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 3 addressed the grade-level content in a challenging and effective manner with most units having little or no above grade level standards addressed.

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 post, chapter, and standardized assessments that are included in the Teacher's Resources and Assessments were reviewed for Course 3 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 3 addressed the grade-level content with most Units having little or no above grade level standards addressed.

Quality, on grade-level examples are:

  • Chapter 4, End of Chapter Test. Question 5a-e uses a real-world scenario to assess 8.F by having students create a graph from information given about a quiz and then explain the relationships between the slopes in terms of the context given.
  • Chapter 11, End of Chapter Test. Question 6a-d asks students to write and solve a system of equations based off a real-world scenario and interpret the solution in the context of the problem. Using context problems to assess 8.EE allows students to work with the MPs to persevere and allows for multiple entry points to a problem.

The following items are above grade and should not be assessed, but they can be removed without drastically changing the material:

  • Chapter 9 Post Test, Question #2 and End of Chapter Test #4, #5, and #6. Students are asked which Similarity Theorem applies. This is not a Grade 8 standard; it is first defined in high school.
  • Chapter 9 Post Test, Question #11. Students are asked to construct a perpendicular line through a given point not on the line.

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

Students and teachers using the materials as designed will devote a majority of class time in Grade 8 to the major work of this grade. The instructional materials reviewed for Course 3 meet the expectations for majority of class time on the major clusters of the grade. For example, based on the pacing (one period = 50 minutes), 64 days out of 82 days total have 78.0 percent of the time spent directly on the major work of the grade.

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 Course 3 meet the expectations for spending the majority of class time on the major clusters of each grade. A chapter overview was found at the beginning of each chapter. This included the standards being taught in the lesson and a suggested pacing guide. Overall the instructional materials meet the criteria outlined in the CCSS publisher guidelines for the majority of class time on the major clusters of each grade.

To determine the three perspectives we 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. It was decided that 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 and our conclusion was drawn through this data.

Evidence was determined from the Table of Contents pages FM-6 through FM-56 and the number of days suggested in each chapter overview found in the the Teacher Implementation Guide and written by the publisher.

  • Chapters – 12 out of 17 chapters, or approximately 70.58 percent of time spent on major work.
  • Lessons – 60 out of 78 lessons, or approximately 76.9 percent of time spent on major work.
  • Days – 64 out of 82 days, or approximately 78.0 percent of time spent on major work.

The major clusters of the grade are:

  • 8.EE.A - Work with radicals and integer exponents.
  • 8.EE.B - Understand the connections between proportional relationships, lines, and linear equations.
  • 8.EE.C - Analyze and solve linear equations and pairs of simultaneous linear equations.
  • 8.F.A - Define, evaluate, and compare functions.
  • 8.F.B - Use functions to model relationships between quantities.
  • 8.G.A - Understand congruence and similarity using physical models, transparencies, or geometry software.
  • 8.G.B - Understand and apply the Pythagorean Theorem.

Modules and Chapters that contain these Standards are:

  • Module 1 (Focus on Linear Equations and Functions): Chapter 1- 1.1, 1.2, 1.3, 1.4 (4 days); Chapter 2- 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 (8 days).
  • Module 2 (Focus on Rate of Change and Multiple Representations of Linear Functions): Chapter 3- 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 (6 days); Chapter 4- 4.1, 4.2, 4.3, 4.4, 4.5 (6 days).
  • Module 3 (Focus on Pythagorean Theorem): Chapter 6- 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 (7 days).
  • Module 4 (Focus on Transformational Geometry): Chapter 7- 7.1, 7.2, 7.3, 7.4 (4 days); Chapter 8- 8.1, 8.2, 8.3, 8.4 (4 days); Chapter 9- 9.1, 9.2, 9.3, 9.4 (4 days).
  • Module 5 (Focus on Lines and Angle Relationships, Systems of Linear Equations and Functions, and Solving Linear Systems Algebraically): Chapter 10- 10.1, 10.2,10.3, 10.4, 10.5 (6 days); Chapter 11- 11.1, 11.2,11.3, 11.4 (4 days); Chapter 12- 12.1, 12.2,12.3, 12.4, 12.5 (5 days).
  • Module 6 (Focus on Properties of Exponents): Chapter 13- 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 (6 days).

Criterion 1c - 1f

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
3/8
+
-
Criterion Rating Details

The instructional materials reviewed for Course 3 partially meet the expectations for being coherent and consistent with the standards. Supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, and the materials do not foster coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. However, the material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade-level learning is not explicit.

Indicator 1c

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
1/2
+
-
Indicator Rating Details
  • The instructional materials reviewed for Course 3 partially meet the expectations for the non-major content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. In some cases, the non-major work enhances and supports the major work of the grade level, while other areas could be stronger.

    Non-major clusters of the Grade 8 are:

    • 8.NS.A - Know that there are numbers that are not rational, and approximate them by rational numbers.
    • 8.SP.A - Investigate patterns of association in bivariate data.
    • 8.G.C - Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

    Evidence of non-major content enhancing focus and coherence and supporting a partially meet's score are:

    • 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 5, lesson 2 by having students work with Irrational Numbers so that they are able to fully understand the major work of the Pythagorean Theorem by working with square and cube roots.
    • 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 6, Lesson 1 by having students work with square and cube root symbols so they are able to fully comprehend and solve problems involving right triangles.
    • 8.SP.A supports 8.EE and 8.F in Module 7 - Chapter 15, Lessons 1-3 by having students work with grade level vocabulary supporting the major work and interpreting and analyzing scatter plots to determine the relationship between the two variables.

    Examples of missed opportunities:

    • 8.G.C has no support of major work noted.
    • Supports of the major work are not often specifically called out as a support. Often times the connections are there, but a teacher would need to know the cohesiveness on their own to be able to make the connections for the students.

    Though the supporting standards have made some connections to major work, they are not specifically written as such, and the non-major clusters of this grade are taught in isolation and miss some opportunities to engage students in the major work of Grade 8, which is why this team supports a partially meets score.

    In chapter 15, slopes and intercepts are interpreted as constant rates of change and initial values in the data, which supports major work of Grade 8.
  • Opportunities to connect student-derived formulas for volume with nonlinear functions (8.F.5) were missed.
  • In chapter 13, 8.EE.A, which is major work, is supported by 8.G.C.9.

Indicator 1d

The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
0/2
+
-
Indicator Rating Details

The instructional materials reviewed for Course 3 do not meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. Without including any assessment days, there are approximately 82 days of lessons in the materials. There needs to be additional material, other than assessment days, to ensure a students' grasp of all major work at this grade level. Overall, the amount of content that is designated for this grade level is short of the amount of material needed to make it truly viable for one school year.

  • According to the pacing guide, each period is 50 minutes in length and there is a suggested 82 days of lessons.
  • When pre-tests, mid-chapter tests and post-test assessments are also included in the pacing, this would add an additional 51 days. If all assessments are given during the course of the year, one extra day per assessment, the total would be 133 days.

The guiding focus taken for this indicator for our team was, "Will the non-major and major work of this material be enough to prepare a student for the next grade level?" With the amount of days, many of those days not focusing on major work, the non-major work days not often supporting the major work of the grade, it will require the teacher to make significant modifications to prepare the student for the next grade level and supports this indicator receiving a does not meet rating.

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 Course 3 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grade standards is clearly identified; however above grade-level standards are not clearly marked as such. There is ample practice for students to engage deeply with with the problems related to the Grade 8 standards, but no connections are explicitly made to prior or future content in the Teacher Implementation Guide or the student text.

Some examples of areas where identification of standards from lower grades is beneficial and supports a partially meets rating along with a an example of not meeting the full depth of the standard:

  • Lower grade-level material is clearly identified in the grade level outline found in the Teacher Implementation Guide on page FM-30. They are also identified and explained in the same resource at the beginning of each lesson.
  • Chapter 5, pages 281-310, titled "The Real Number System" starts with 7.NS.3, a below grade-level standard, as indicated in the pacing guide and in the chapter overview, Teacher Implementation Guide page 281A. This standard is included, as stated by publisher, to review the sets of natural numbers, whole numbers, integers, and rational numbers.
  • Occasionally, the lessons do not seem to go to the full depth of the standards.
    • Chapter 5 which is suppose to cover 8.NS.1 and 8.NS.2 does not cover 8.NS.2 as deeply as suggested in the standards. 8.NS.2 states, "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of the expressions (e.g., pi squared)." The lesson and skills practice only asks the students to compare or place numbers on a number line to the hundredths place. This is not a common occurrence in the curriculum for this grade.

The instructional materials reviewed for Grade 8 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.

Some examples of giving all students extensive work with grade-level problems, but not of varying abilities and supports a partially meets rating:

  • There is ample practice for each standard. Every lesson has guided practice with a script for the teacher to follow. This portion has the students conceptually developing the skill being taught and are given practice problems as well. Along with the guided practice are assignments. The number of assignments and number of problems varies per lesson. In addition there are skill practice pages to accompany each lesson as well. The number of skill pages also varies with each lesson.
  • The Teacher Implementation Guided does not list any lessons or ideas for differentiated instruction except when it talks about the Mathia Software product. No differentiated or extension lessons in the Student Text, Students Skills Practice book, or the Student Assignment book were found by the reviewers.

The instructional materials reviewed for Grade 8 do not meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, no support materials were found that relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • The Teacher Implementation Guide is a wrap around of the Student Text. In the margins of the Teacher Implementation Guide, the authors have reworded the question asked in the student text but these does not seem to add anything to the instruction. The margins also have steps for the teachers to follow, ways to groups students (i.e., "Have students complete questions 2 and 3 with a partner. Then share the responses with a class," page 5), and guiding questions to ask students. However, it does not clearly make connections between previous knowledge and new concepts. There are not any indicators that knowledge is being extended.
  • The warm-up sections for each lesson listed would be an ideal place to include connections to prior standards covered in this curriculum. For instance:
    • Chapter 10, lesson 4, when equations of perpendicular and parallel are introduced.
    • Chapter 12, lesson 2, students are asked to write a linear system to represent each graph, yet there are no discussion questions that could guide discussion to perpendicular and/or parallel linear equations.

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.
1/2
+
-
Indicator Rating Details

The instructional materials reviewed for Course 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.

  • The Chapter titles are clearly labeled and aligned to the standards without a need for much interpretation.
    • Chapter 2 - Linear Functions (8.F)
    • Chapter 4 - Multiple Representations of Linear Functions (8.EE)
    • Chapter 6 - Pythagorean Theorem (8.G.B)
    • Chapter 9 - Similarity (8.G.A)

The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 3.

  • For the majority of the work, most standards were taught and covered within one Unit out of the entire series and not aligned with any other concept throughout the year.
  • There are no connections identified by publisher. However, there are connections within the Grade 8 standards that are just not noted or stated by the publisher.

Some examples of where connections were made and support a partially meets rating is:

  • Chapter 3, "Slope: Unit Rate of Change," lessons 1 and 5 connect 8.EE.B.5 and 8.F.A by having students determine the rate of change from graphs by using the formal definition of rate of change and using rise/run formula. Students will compare the rates of graphs, compare the steepness of four lines on the same graph and relate the steepness of the lines to the magnitudes of their rates of change.
  • Chapter 4, "Multiple Representations of Linear Functions," lessons 1 through 3 connect 8.EE.C.7.B and 8.F.A by having students, given linear equations written in standard form, complete tables by evaluating each equation and solving for the value of either x or y. The points are graphed and then used to calculate slope. Finally, the students convert the standard form linear equations into slope-intercept form.
  • Chapter 6, "Pythagorean Theorem," lesson 1 connects 8.NS.A and 8.EE.A.2 by having students determine the area of a larger square and the sum of the areas of the two smaller squares to prove they are equal. Students also use the Pythagorean Theorem to solve for the length of unknown sides of right triangles set in a variety of contexts. In lessons 2 through 6, 8.EE.A.2 and 8.G.B are connected by having students use the Pythagorean Theorem to determine that the diagonals in a rectangle and square are congruent along with the diagonals of a trapezoid only when the figure is isosceles.

Gateway Two

Rigor & Mathematical Practices

Partially Meets Expectations

+
-
Gateway Two Details

The materials reviewed for Course 3 partially meet the expectations for Gateway 2: Rigor and Mathematical Practices.

The materials reviewed for Course 3 meet expectations for rigor and balance by providing a balance of all three aspects of rigor throughout the lessons. The Grade 8 instructional materials reflect the balances in the standards and help teachers to help their students meet rigorous expectations. They do this by helping students develop conceptual understanding, procedural skill and fluency, and application. The materials weakest section, but still enough quality representations to receive the "meets" rating, is on conceptual understanding. Students are able to work in groups to develop understanding, but then sometimes the narrative, in the text, scaffolds the work in such a way that the students are just walking through that understanding step by step.

The materials reviewed for Course 3 do not meet the expectations for practice-content connections. The materials attempt to incorporate the MPs in each lesson but all instruction of the MPs happens at the beginning of the Teacher Implementation Guide and never directly links the standards to the lessons using the MP vocabulary. This makes it extremely difficult for a teacher to reliably use the materials to know when MPs are being carefully attended to. The materials incorporate questions in which students have to justify and explain their answers, but no teacher supports are given which creates a lack of lesson structures for which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented and almost always incorporated meaningfully into the lesson.

Overall, the materials partially meet the expectations for Gateway 2 in rigor and mathematical practices.

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.
8/8
+
-
Criterion Rating Details

The materials reviewed for Course 3 meet expectations for rigor and balance. The Grade 8 instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The materials weakest section, but still enough quality representations to receive the "meets" rating, is on conceptual understanding. Students are able to work in groups to develop understanding, but then sometimes the narrative, in the text, scaffolds the work in such a way that the students are just walking through that understanding step by step.

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.
2/2
+
-
Indicator Rating Details

The instructional materials for Course 3 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 real-world situations and multiple visual examples as a way to develop conceptual understanding.

The materials in the Teachers Implementation Guide, student text, and student assignments were all used to gather evidence. In the Teachers Implementation Guide it states that they provide many opportunities for conceptual understanding, especially those in which the standard calls for it. Each chapter begins with an overview and in this overview is a column titled "highlights." This section summarizes what the students will be able to do after the lesson and was a guide to searching for the evidence below to justify the meets rating.

  • Chapter 3, Lesson 2: Students use visual representations and linear graphs to represent a situation from a given context.
    • Problem 1, page 164, gives students information about a school soccer team trip and then has follow-up questions that ask students to determine rate of speed during the trip. They are then asked create a concrete visual representation of the story based upon facts presented.
  • Chapter 4: Students interpret meanings of equations and analyze intervals. The lessons have students use tables and graphs to see the relationships of the function which correlates with standards in 8.F and 8.EE.
  • Chapter 6: Teaches the use of the Pythagorean Theorem (8.G). Lesson 1 has students use shapes to develop the Pythagorean Theorem. They use grid paper to show the relationship of the area of the triangles.
  • Chapter 7: Students explore transformations (8.G) with shapes in the coordinate plane. Many questions require students to explain their thinking.
  • Chapter 9: Students work with understanding dilation and similarity (8.G) by investigating and exploring shapes in the coordinate plane.

In the lessons listed below and others, the students are asked to explain their reasoning or explain why they believe the answer to be correct. The student assignment book allows individual students to show their understanding through the following questions in the listed lessons.

  • Lesson 1.2 - Why Doesn't This Work?
  • Lesson 2.1 - Patterns, Patterns, Patterns ...
  • Lesson 7.4 - Mirror, Mirror
  • Lesson 12.3 - Making Decisions
  • Lesson 14.2 - Piling On!

An area of concern for this review team was that many of the guided lessons walk students through entire procedures and do not allow them to explore or discover concepts on their own.

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
+
-
Indicator Rating Details

The instructional materials for Course 3 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 various questioning strategies for students to explain procedural skills, and chances for students to apply procedural skills to new situations. Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency meeting the expectations for this indicator.

  • Based on where the lesson is in the timeline of the unit, the level of difficulty varies. As expected, it starts off with a low level of difficulty, and as the students gain more practice, the difficulty increases as the unit progresses.
  • Along with problems during the guided lessons, each lesson begins with a warm up that is procedural practice.
  • Some of the student assignments are procedural in nature as well as each lesson having suggested pages for students to complete in the student skill practice book.

Examples of fluency practice that justify the meets rating are:

  • Chapter 1, Lesson 1.1, when the students start by having to write the steps they follow to solve multi-step equations with one variable then they move onto just solving the problems.
  • Chapter 5, Lesson 5.1, students practice writing fractions as decimals.
  • Chapter 8, Lesson 8.2, students practice determining what transformation is present.

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
2/2
+
-
Indicator Rating Details

The instructional materials for Course 3 meet the expectation 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. Overall, the materials have multiple opportunities for real-world application.

There are a variety of single and multi-step contextual application problems found in the student text, students' assignment book and student skills practice.

  • Chapter 2, Lesson 2.6 has students calculate the cost for orders of T-shirts for various given values from a competitor with a different cost value, determine the amount of shirts that can be purchased, and create a table and graph to represent the situation.
  • Chapter 3, Lesson 3.3 asks the students to determine the rate of change based on a soccer tournament.
  • Chapter 11, Lesson 11.3 asks the students to apply what they know about rate of change and linear equations to solve real-world problems such as how much money a person will make if they work at an hourly rate. It also asks them to apply what they know about functions and graphing to demonstrate a variety of scenarios for a person to earn a certain amount of money.

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.
2/2
+
-
Indicator Rating Details

The instructional materials reviewed for Course 3 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, but do balance that out with conceptual understanding and application problems. The material's weakest section, but still enough quality representations to receive the "meets" rating, is on conceptual understanding. Students are able to work in groups to develop understanding, but then sometimes the narrative, in the text, scaffolds the work in such a way that the students are just walking through that understanding step by step.

The student text, along with the wrap around Teacher Implementation Guide help guide the educator and student to the level of rigor needed to prepare the student for upcoming mathematics. An example of this is in Chapter 3, Analyzing Linear Equations.

  • The chapter begins with introducing students to finding two points on a line and then determining the rate of change.
  • Delving deeper into this skill, students are then asked, on page 143 problem 1, to determine the unit rate of four different cars using the same graph.
  • They are then asked to describe what the steepness of each line implies regarding their individual unit rate.
  • Then each lesson ends with a complex problem which delves deeper into student understanding of the standard.

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 Course 3 do not meet the expectations for practice-content connections. The materials attempt to incorporate the MPs in each lesson. However, all instruction of the MPs happens at the beginning of the Teacher Implementation Guide and never directly links the standards to the lessons using the MP vocabulary. This makes it extremely difficult for a teacher to reliably use the materials to know when MPs are being carefully attended to. The materials incorporate questions in which students have to justify and explain their answers, but no teacher supports are given which creates a lack of lesson structures for which students would discover their own solution paths, present their arguments, and justify their conclusion. Vocabulary is presented and almost 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 Course 3 partially meet the expectation for identifying and using MPs to enrich mathematics content within and throughout each grade. While each practice is represented in this book, they are not often used in a way that would promote or enrich the mathematics content, are not user-friendly and are under-identified in many of the units because they are not specifically stated.

  • MPs are described on pages FM-34 through FM-42 in the Teacher's Implementation Guide, along with a description of what it looks like in the student text.
  • On pages FM-45 through FM-55, there are more examples of how the practices are implemented throughout the series. This section also defines symbols that clue teachers and students that they should discuss to understand, think for yourself, work with your partner, and share with the class. It also defines that a "thumbs up" means a worked example is correct and a "thumbs down" means a worked example is incorrect.
  • Specifically, FM-45 through FM-49 attempt to define the academic terms analyze, explain your reasoning, represent, estimate, and describe. When these verbs appear in the series, they are suppose to correlate with the MPs listed. There is no further identification of MPs in the Teacher's Implementation Guide.
  • All eight MPs are evident throughout the materials, but it was very difficult to find them since they are not specifically marked and not all practices had identifying academic terms to label them.
  • The MPs could be used to enrich the mathematical content, but one would have to keep referencing the only guide to using them in the first few pages of the Teachers Implementation Guide, in order to have a better understanding of what practices to emphasize and how to use the problems to enrich them. Since all of the chapters have an overview section, this would be a place to identify the practices for each lesson and further encourage the use of these practices to enrich the mathematics content.

Indicator 2f

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

The instructional materials reviewed for Course 3 do not meet the expectations for carefully attending to the full meaning of each practice standard. The publisher rarely attends to the full meaning of the practice standard and when they do, it is cumbersome to use since they are not specifically called out.

  • The lessons are set up for students to work in groups and then the teacher is to guide them through discussion of their findings. The graphs, tables, equations, etc., are usually created for the students, which doesn't allow them to have to model with mathematics.
  • There are sequential questions to lead the students through the process, so they are not having to make sense of the problem, or persevere, because the text book does it for them. With this guidance on how to complete the problem, there is usually only one way to solve the problem, not allowing for multiple entry points.
  • Students are not given the opportunity to choose tools to help them with the mathematics, the tools are provided.
  • Almost all of the lessons are designed for group work. Students are rarely asked to work independently, and given opportunity to compare.
  • There are a variety of questions for teachers to pose during each lesson, however there are no MPs indicated and no sample student responses given to aid a teacher who is unsure what MP is involved and how students may be thinking as related to that 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 Course 3 partially meet the expectation for appropriately prompting students to construct viable arguments and analyze the arguments of others. Each chapter provides opportunities for students to construct viable arguments and places to critique worked examples that are sometimes correct and sometimes wrong, however, each time they let the students know which argument is correct and which is incorrect by putting a thumbs up or a thumbs down with the problem. This directs students thinking and doesn't force them to go through the thought process of finding viable arguments to critique the reasoning of others.

  • The questions following 'thumbs up' are usually comparing how two different people solved it correctly, but differently, which does allow for a student to then describe why they are both right.
  • For 'thumbs down' situations, students are asked to find the errors that were made.
  • In the Teacher's Implementation Guide, page FM-45, there are icons that direct student questioning that provide norms for what students are to do when they see the icons throughout the text.
  • In the Teacher's Implementation Guide, page FM-48 students learn specifically how to explain their reasoning which is identified as SMP3.
  • In the Teacher's Implementation Guide, pages FM-52 to FM-55, there is a "Who's correct" option that, if used, better allows students to form their own opinions and arguments for the work done.

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.
0/2
+
-
Indicator Rating Details

The materials reviewed for Course 3 do not meet the expectation of assisting teachers in engaging students in constructing viable arguments and analyzing the arguments of others. Overall, there is not enough guidance in the teacher materials to direct teachers on questioning strategies, setting up scenarios where students experiment with mathematics and based on those experiments construct and present ideas, examples of higher level questions and suggested activities that lead students to construct viable arguments and analyze the arguments of others.

In the Teacher's Implementation Guide, page FM-37 and pages FM-43 through FM-55 do provide teachers with instruction on how to get students to construct viable arguments and critique the work of others, while each lesson also has a "Share Phase" section in the margins that poses questions teachers are supposed to ask for discussion; however, many of the questions being asked are closed ended questions and do not promote discourse. Also, there are no suggestions for how students should share or report out their thinking, and the lessons are written in the same format all the way through the series which does not promote students to think about mathematics in different ways.

As the wrap around teachers edition was reviewed, the publisher did not specifically address potential teacher moves regarding constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics. The vast majority of the time, the areas that addressed MPs were merely closed ended questions added to the practice section of the lessons. Teachers are not given any specific examples on how to address this practice in their daily lessons.

Indicator 2g.iii

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

The materials reviewed for Course 3 meet the expectation for attending to the specialized language of mathematics. Overall, there are several examples of the mathematical language being introduced and appropriately reinforced throughout the unit.

  • In the Teacher Implementation Guide, page FM-40, there is an explanation of MP6.
    • It states that students should communicate clearly and use clear definitions in discussions and writing.
    • It emphasizes that students should label things to clarify their work.
    • This section also states that the answers provided in the Teacher's Implementation Guide are exemplars of student responses and model precision appropriately.
  • Along with information about a vocabulary section in the skill practice for each lesson. The book also states that each lesson provides opportunities for students to communicate precisely in writing and when sharing their solutions.
  • Each chapter has key terms listed in Lesson 1. The words are then defined somewhere in the lesson and written in bold font.
    • The terms are not in bold or referenced after that first lesson.
    • The terms are listed again in the chapter summary, but it does not define or use them in any way.
    • Lesson 1 in the student skills practice book, has students work with the vocabulary and the answers in the teacher's guide provide the precise answers written in the language of mathematics.

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: Fri Apr 08 00:00:00 UTC 2016

Report Edition: 2011

Title ISBN Edition Publisher Year
9781609721121 0
9781609721466 0

About Publishers Responses

All publishers are invited to provide an orientation to the educator-led team that will be reviewing their materials. The review teams also can ask publishers clarifying questions about their programs throughout the review process.

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.

Educator-Led Review Teams

Each report found on EdReports.org represents hundreds of hours of work by educator reviewers. Working in teams of 4-5, reviewers use educator-developed review tools, evidence guides, and key documents to thoroughly examine their sets of materials.

After receiving over 25 hours of training on the EdReports.org review tool and process, teams meet weekly over the course of several months to share evidence, come to consensus on scoring, and write the evidence that ultimately is shared on the website.

All team members look at every grade and indicator, ensuring that the entire team considers the program in full. The team lead and calibrator also meet in cross-team PLCs to ensure that the tool is being applied consistently among review teams. Final reports are the result of multiple educators analyzing every page, calibrating all findings, and reaching a unified conclusion.

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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