Common Core Coach
2010-2015

Common Core Coach

Publisher
School Specialty, Inc.
Subject
Math
Grades
3-8
Report Release
10/24/2018
Review Tool Version
v1.0
Format
Core: Comprehensive

EdReports reviews determine if a program meets, partially meets, or does not meet expectations for alignment to college and career-ready standards. This rating reflects the overall series average.
Alignment (Gateway 1 & 2)
Does Not Meet Expectations

Materials must meet expectations for standards alignment in order to be reviewed for usability. This rating reflects the overall series average.
Usability (Gateway 3)
NE = Not Eligible. Product did not meet the threshold for review.
Not Eligible
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Showing:
8th Grade

About This Report

Report for 8th Grade

Alignment Summary

The instructional materials reviewed for Common Core Coach Suite Grade 8 do not meet the expectations for alignment to the CCSSM. In Gateway 1, the instructional materials partially meet the expectations for focus and coherence. The instructional materials meet the expectations for focus, but they do not meet the expectations for coherence. In Gateway 2, the instructional materials do not meet the expectations for rigor and the mathematical practices. The instructional materials partially meet the expectations for rigor and balance, and they partially meet the expectations for practice-content connections. Since the materials do not meet the expectations for alignment to the CCSSM, they were not reviewed for usability in Gateway 3.

8th Grade
Gateway 1

Focus & Coherence
09/14
0
7
12
14
Gateway 2

Rigor & Mathematical Practices
10/18
0
10
16
18
Alignment (Gateway 1 & 2)
Does Not Meet Expectations
Gateway 3

Usability
Usability (Gateway 3)
Not Rated
Gateway 1
Gateway 2
Gateway 3
Viewing:
Gateway 1
Overview of Gateway 1

Focus & Coherence

The instructional materials reviewed for Common Core Coach Suite Grade 8 partially meet the expectations for focus and coherence in Gateway 1. The instructional materials do not assess topics before the grade level in which the topic should be introduced, and the materials do spend at least 65% of instructional time on the major work of the grade. The instructional materials do not meet the expectations for being coherent and consistent with the Standards as they partially have: supporting content that enhances focus and coherence by engaging students in the major work of the grade; consistency with the progressions in the Standards; and coherence through connections at a single grade.

Gateway 1
v1.0
Gateway 1

Focus & Coherence
09/14
0
7
12
14
Criterion 1.1: Focus
02/02
Criterion 1.2: Coherence
04/04
Criterion 1.3: Coherence
03/08
Partially Meets Expectations

Criterion 1.1: Focus
02/02
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet the expectations for not assessing topics before the grade level in which the topic should be introduced.

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

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet expectations that they assess grade-level content. The Grade 8 suite includes one summative assessment that contains 50 multiple choice questions and five domain assessments, found in the Digital Assessment blade. Each assessment contains 20 to 25 questions. The suite also contains Performance Tasks for each domain, found in the Print-Only Assessment blade. The Common Core Support Coach component includes two end-of-year summative practice tests, and the Common Core Performance Coach component has summative Domain Reviews. Finally, the suite also includes separate summative assessments that are labeled as PARCC summative assessments.

There is one above grade-level assessment item present but could be modified or omitted without a significant impact on the underlying structure of the instructional materials:

  • Print-Only Assessment, Common Core Coach Performance Task “Describing Functions” Question #4: “Determine whether the function is linear or nonlinear, increasing or decreasing, quadratic, piecewise, and so on. Once the questions have been answered, compare the properties of the functions. Determine which function has the greatest rate of change and which function has the greatest y-intercept.” This is beyond grade-level requirements (8.F.5). “Describe qualitatively the functional relationship between two quantities by analyzing a graph (e.g., where the function is increasing or decreasing, linear or nonlinear). Sketch a graph that exhibits the qualitative features of a function that has been described verbally.” Students are introduced to quadratic and piecewise graphs in the high school standards.

Examples of assessments aligned to grade-level standards include:

  • Digital Assessment, Domain Assessment for The Number System, Question 5: Students identify the set of numbers that contains only irrational numbers (8.NS.1).
  • Digital Assessment, Domain Assessment for Expressions and Equations, Question 13: Students solve a linear equation in one variable with rational coefficients using the distributive property and collecting like terms (8.EE.7b). “Solve for x: –3(2x+1)+3x=6x+3–3(2x +1) + 3x = 6x + 3”
  • Digital Assessment, Common Core Coach Summative Assessment, Question 15: Students examine a table and a graph of two linear functions to determine a true statement from the multiple choice statements regarding their rates of change (8.F.2).
Criterion 1.1: Focus
02/02
Indicator 1A
02/02

Criterion 1.2: Coherence

04/04
Students and teachers using the materials as designed devote the large majority of class time in each grade K-8 to the major work of the grade.

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet the expectations for students and teachers using the materials as designed devoting the large majority of class time to the major work of the grade.

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

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet expectations for spending a majority of instructional time on major work of the grade. Overall, approximately 78 percent of instructional time is spent on major work.

Common Core Coach Suite contains three components: Common Core Coach, Common Core Support Coach, and Common Core Performance Coach. “The Coach products are designed to provide a flexible instructional pathway that fits your classroom needs.” As such, the Implementation and Pacing Guide provides suggested activities and minutes for each day but leaves the decision to the teacher as to which students work with Common Core Support Coach and Common Core Performance Coach on any given day.

Calculations were based on the Implementation and Pacing Guide provided for the Common Core Coach Suite. Since all students work with the Common Core Coach but do not necessarily work with Common Core Support Coach and Common Core Performance Coach, the evaluation of major work in Common Core Coach, and supporting work connected to major work, is most representative of the instructional materials.

  • Common Core Coach contains approximately 25 of 32 lessons focused on major work or support the major work of the grade (78 percent).
  • Lessons are allocated to last between three and six days, and are broken into 20-30 minutes of core instruction using Common Core Coach and 10-20 minutes of differentiation through Common Core Support Coach and Common Core Performance Coach. According to the Implementation and Pacing Guide, students could spend the following minutes on major work of the grade or work that supports the major work of the grade:
    • In Common Core Coach, approximately 3165 minutes out of 3995 (roughly 79 percent of the time) is spent on major work or work that supports major work.
    • In Common Core Support Coach, approximately 1545 minutes out of 1955 (roughly 79 percent of the time) is spent on major work or work that supports major work.
    • In Common Core Performance Coach, approximately 1595 minutes out of 2005 (roughly 80 percent of the time) is spent on major work or work that supports major work.

The amount of lessons focused on major work of the grade or work that supports the major work of the grade is the most appropriate calculation for these materials. The flexibility of the Common Core Support Coach and Common Core Performance Coach cannot be used to determine how much time or how many lessons any student would spend in these materials.

Criterion 1.2: Coherence
04/04
Indicator 1B
04/04

Criterion 1.3: Coherence
03/08
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Common Core Coach Suite Grade 8 do not meet the expectations for being coherent and consistent with the Standards. The instructional materials partially have: supporting content that enhances focus and coherence by engaging students in the major work of the grade; consistency with the progressions in the Standards; and coherence through connections at a single grade.

Indicator 1C
01/02
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that supporting work enhances focus and coherence simultaneously by engaging students in the major work of the grade. Throughout the Common Core Coach Suite of books, standards are taught in isolation from other standards. Connections between supporting work and major work of the grade are rare and unintentional in the materials.

Lessons are organized sequentially by domain and follow the organization of the standards. For example, all lessons aligned to the Ratios and Proportional Relationships domain are grouped and taught in the sequence reflected in the Common Core Standards. The Teacher’s Manual does not provide explicit connections to major work; however, some natural connections are made.

There were some natural connections made between the supporting and the major work standards of the grade:

  • Common Core Coach Lesson 28 Problem Solving: Volume Question 3: “A cone-shaped paper water cup has a radius of 4 centimeters and a volume of 48π48\pi cubic centimeters. What is the height of the cup?” In this problem, students have the opportunity to work with and solve problems using the formulas for the volumes of cones, cylinders, and spheres (8.G.9). Since the formulas for the volumes of cones, cylinders, and spheres involve squared and cubed terms, these problems also present opportunities to use and evaluate square and cube roots (8.EE.2).
  • Common Core Coach Lesson 31 Using Linear Models to Interpret Data Question 4: The instructions state, “Identify slope and y-intercept for each model, then tell what each represents in the problem.” A scatter plot shows the number of years since a new science initiative for girls was started and the number of girls enrolled in science classes at several high schools. “The data is modeled by the function. y=25x+150y = 25x +150.” Students use a model of a bivariate relationship with a linear model and use the linear model to answer questions in the context of the bivariate data set (8.SP.2, 8.SP.3). Modeling a bivariate relationship with a linear model and using the model to answer questions in terms of a context enhances students' opportunities to construct a function to model a linear relationship between two variables and interpret the rate of change and initial value of the function in relationship to the situation being modeled (8.F.4).

Examples of missed opportunities for connections within the materials:

  • Common Core Support Coach Lesson 17 Solving Problems with Volume and Lesson 26 Understanding Volume of Cylinders address 8.G.9 but do not provide opportunities to engage students where they involve problems using square root and cube root (8.EE.2). All problems in Lesson 17 are limited to substituting values into the volume formula and calculating the volume for cylinders, cones, and spheres and composite solids. Problems in Lesson 26 are limited to substituting values into the volume formula and calculating the volume for composite solids, parts of solids, and comparing two different solids.
  • Common Core Performance Coach Lesson 4 misses a connection between the lesson learning objective, “Estimate square roots and cube roots of irrational numbers,” and the estimation of irrational numbers on the number line in Lesson 2.
  • Common Core Support Coach Lesson 1 Irrational Numbers includes the estimation of non-perfect squares. Lesson 2 Square Roots and Cube Roots uses perfect square or cube roots in every problem. There is no connection made between 8.NS.2 and 8.EE.2.
  • In Common Core Coach Lesson 25 Explaining the Pythagorean Theorem (8.G.6) and Lesson 26 Applying the Pythagorean Theorem in Two and Three Dimensions, students use the Pythagorean Theorem to solve problems (8.G.7). In Lesson 26 Example A students estimate the irrational number (18), but the materials miss the opportunity to make explicit the connection to 8.NS.2. Support Coach Lesson 16 also does not make any connections between these standards, even though students estimate the value of an irrational number with a solution that is not the completion of a perfect square when solving for a missing side of a right triangle.
Indicator 1D
00/02
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.

Instructional materials for Common Core Coach Grade 8 do not meet expectations that the amount of content designated for one grade level is viable for one year.

The Pacing and Implementation Guide for the Common Core Coach Suite states that the instructional materials can be completed in 163 days.

  • There are 40 minutes of instruction each day broken down as follows:
    • 20-30 minutes using Common Core Coach
    • 10-20 minutes using Common Core Support or Common Core Performance (differentiated for students as needed)
  • There are 32 Lessons listed in the Pacing and Implementation Guide, the Teacher’s Manual, and the Student Book. Lessons range from 3-6 instructional days including time to complete the fluency pages in the Appendix.
  • There are two review days and two assessment days for each of the five domains and an additional two review days and two assessment days at the end of the year, for an additional 24 instructional days.

Common Core Coach Suite provides an insufficient number of problems to complete in the time allotted for lessons. Teachers would need to make significant supplementation and modifications for the program materials to be viable for one school year. For example:

  • Standard 8.EE.8c is addressed in Domain 2: Expressions and Equations Lesson 12 Problem Solving Using Systems of Equations over four instructional days.
    • Common Core Coach Lesson 12 consists of two guided problems and five practice problems over four days.
    • Common Core Support Coach Lesson 7 includes 10 independent problems and two scaffolded problems over four days.
    • Common Core Performance Coach Lesson 11 has eight problems over four days.
Indicator 1E
01/02
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations for the materials being consistent with the progressions in the standards. In general, the materials develop according to the grade-by-grade progression of the standards, and the majority of the content from prior or future grades is identified in all three components of the material and is used to support the progressions of the grade-level standards. However, the materials do not provide students with extensive work with grade-level problems, and the materials do not meet the full intent of the standards.

Common Core Coach Suite materials typically identify content from prior and future grades although specific standards are not always indicated. Examples of ways that the materials identify these materials include:

  • Common Core Coach Mathematics 8 Teacher’s Manual contains a “Lesson Progression Map” at the start of each of the domains which “offers a visual progression of lesson content across grades,” showing the connections between prior and future lessons to the current grade-level standard being developed in each lesson.
  • Every lesson in the Common Core Coach Mathematics 8 Teacher Edition has a section called, “Before the Lesson.” This section often directs the teacher in a review of prerequisite skills needed for the lesson, thus providing the teacher with information about prerequisite knowledge. However, it does not state from which standards the skills are taken.
  • The Common Core Coach Progressions Booklet found in the “Tools and Glossaries” section of the online Student Edition states, “Domain Progressions are displayed for each domain, providing a clear visual roadmap of how new content builds upon content from previous grade levels and domains, and connects to future domains.”
  • Support Coach Teacher Edition includes a “Foundational Understanding” section for each lesson which aligns both previous and current grade-level standards.

Common Core Coach Suite does not attend to the full intent of the grade-level standards and does not provide students extensive work with grade-level problems. Examples that show how the materials do not attend to the full intent of the grade-level standards:

  • 8.G.6 Explain a proof of the Pythagorean Theorem and its converse.
    • Common Core Coach Lesson 25 Explaining the Pythagorean Theorem: Questions 1-17 ask students to solve problems using the Pythagorean Theorem. Question 18 requires the use of the converse of the Pythagorean Theorem to show that a triangle is a right triangle. This is the only question in the Practice set that includes any proofs.
    • In Common Core Performance Coach Lesson 24 Understanding the Pythagorean Theorem: In question 2, students are asked to explain how a diagram illustrates the Pythagorean Theorem. All other questions ask students to solve problems related to the Pythagorean Theorem.
    • Common Core Support Coach does not include problems related to proving the Pythagorean Theorem.
  • 8.EE.6 Use similar triangles to explain why the slope m is the same between any two distinct points on a non-vertical line in the coordinate plane; derive the equation y = mx + b for a vertical axis at b.
    • Common Core Coach Lesson 8 Relating Slope and y-intercept to Linear Equations includes problems that address part of the standard to “derive the equation y = mx + b;” however, there are no Example or Practice problems using similar triangles to explain why the slope is the same between any two distinct points on a non-vertical line in the coordinate plane.
    • Common Core Performance Coach Lesson 8 Relating Slope and y-intercept to Linear Equations: Example 1 uses similar triangles to show why slopes are the same. None of the Practice problems address the use of similar triangles.
    • Common Core Support Coach Lesson 5 Slope contains no problems or examples that use similar triangles to explain slope.
  • 8.EE.4 Perform operations with numbers expressed in scientific notation, including problems where both decimal and scientific notation are used. Use scientific notation and choose units of appropriate size for measurements of very large or very small quantities. Interpret scientific notation that has been generated by technology.
    • In Common Core Coach Lesson 6 Scientific Notation, students only perform operations that involve multiplication and division in scientific notation. There are no addition or subtraction problems in the Example or the Practice problems. Example: Practice problem 10: “Express each quotient in scientific notation. (8x102)/(5x105)(8 x 10^2)/(5 x 10^5).“
    • Common Core Performance Coach Lesson 6 Using Scientific Notation includes four problems where students use all operations. For example: Question 1. "Does each expression have a value of 5×10−35\times10^{-3}? A) 3.1×10−6+1.9×10−33.1\times10^{-6}+1.9\times10^{-3}, B) 6×10−3+1×10−36\times10^{-3}+1\times10^{-3}, C) 4×10−3+1×10−34\times10^{-3}+1\times10^{-3}, D) 3.1×10−3+1.9×10−33.1\times10^{-3}+1.9\times10^{-3}?"
    • In Common Core Support Coach Lesson 3 Scientific Notation, students only perform multiplication or division in scientific notation. There are no addition or subtraction problems in the Example or the Practice problems.
  • 8.F.5 Describe qualitatively the functional relationship between two quantities by analyzing a graph. Sketch a graph that exhibits the qualitative features of a function that has been described verbally.
    • Common Core Coach Lesson 17 Describing Functional Relationships from Graphs includes only one question where students sketch a graph. The graph is given with quantitative features (scale and measures), and students use the features of this verbal expression to graph. Students do not describe, analyze, or sketch with qualitative features. Question 5. “Sketch a graph based on this situation. Label the axes and justify your choices. A scuba diver jumps into the water and descends at a constant rate for 4 minutes to a depth of 18 meters. She spends 24 minutes at that depth. She then ascends at a constant rate for 4 minutes to a depth of 6 meters, where she takes a 4-minute safety stop. She then ascends at a constant rate for an additional 4 minutes to reach the surface of the water.” Students are given labels for the axes. Students complete the sentence, “I labeled the x-axis _______ because _________. I labeled the y-axis _______ because _________.”
    • Common Core Performance Coach Lesson 16 Describing Functional Relationships from Graphs includes three Practice problems that have students sketch a graph that exhibits the qualitative features of a function that has been described verbally.
Indicator 1F
01/02
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that materials foster coherence through connections at a single grade, where appropriate and required by the standards. Materials are clearly shaped by domain headings, but some important connections between two or more domains or clusters are missed.

Common Core Coach Suite contains three components: Common Core Coach, Common Core Support Coach, and Common Core Performance Coach. Lessons in Common Core Coach and Common Core Performance Coach are grouped by domain. CCSSM standards alignment can be found in the Table of Contents of the Teacher Edition for each component of the suite and also in a CCSS Correlation Chart that identifies which lessons address specific standards. Most lessons in the suite address one standard.

Examples of lessons in Common Core Coach shaped by domain headings include:

  • Domain 1: The Number System: Lesson 1 Understanding Rational and Irrational Numbers (8.NS.1).
  • Domain 2: Expressions and Equations: Lesson 6 Using Scientific Notation (8.EE.4).
  • Domain 3: Functions: Lesson 15 Linear and Nonlinear Functions (8.F.3).

In the teacher manual the Lesson Progression Maps describe how the domains from previous and future grades connect to domains within the current grade. The majority of the lessons address standards in isolation. Some lessons contain natural mathematical connections between standards. Review sections for each domain contain problems related to the respective domain and are not cumulative across domains.

Examples of how the materials make natural connections include:

  • In Common Core Coach Lesson 31 Using Linear Models to Interpret Data: 8.SP, 8.EE, and 8.F are connected as students work with scatter plots and linear models of association in bivariate measurement data (8.SP.1, 8.SP.2, 8.SP.3) by discussing proportional relationships, lines, linear equations, and linear functions (8.EE.5, 8.EE.6, 8.F.3, 8.F.4).
  • In Common Core Coach Lesson 16 Using Functions to Model Relationships: 8.F and 8.EE are connected as students connect various representations of a function by writing equations, making graphs and tables, and interpreting values within these representations (8.F.3 and 8.EE.6).

However, the materials miss important natural connections. For example:

  • In Common Core Coach Lesson 21 Dilations on the coordinate plane, students determine the effect of dilations on a two-dimensional shape using coordinates (8.G.4). Similar triangles and slope (8.EE.6) are not addressed in the lesson to connect the concept of similarity to work in defining slope. Equations and defining slope are addressed in a previous lesson (lesson 8).
  • In Performance Coach Lesson 26 Understanding Volume of Cylinders, Cones, and Spheres, students use the formulas to find the volumes of cones, cylinders, and spheres when solving real-world and mathematical problems (8.G.9). Students are not asked to solve for the radius of the figures, which would require them to use square root and cube root symbols to represent solutions to equations of the form r2=pr^2 = p and r3=pr^3 = p and to evaluate square and cube roots (8.EE.2).
Criterion 1.3: Coherence
03/08
Indicator 1C
01/02
Indicator 1D
00/02
Indicator 1E
01/02
Indicator 1F
01/02
Overview of Gateway 2

Rigor & Mathematical Practices

The instructional materials reviewed for Common Core Coach Suite Grade 8 do not meet the expectations for rigor and mathematical practices. The instructional materials partially reflect the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application, and they also partially meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice.

Gateway 2
v1.0
Gateway 2

Rigor & Mathematical Practices
10/18
0
10
16
18
Criterion 2.1: Rigor
04/08
Criterion 2.2: Math Practices
06/10
Does Not Meet Expectations

Criterion 2.1: Rigor
04/08
Rigor and Balance: Each grade's instructional materials reflect the balances in the Standards and help students meet the Standards' rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application.

The instructional materials reviewed for Common Core Coach Suite Grade 8 partially meet the expectations for reflecting the balances in the Standards and helping students meet the Standards’ rigorous expectations, by helping students develop conceptual understanding, procedural skill and fluency, and application. The instructional materials partially attend to each aspect of rigor, and they also partially attend to balance among the three aspects of rigor.

Indicator 2A
01/02
Attention to conceptual understanding: Materials develop conceptual understanding of key mathematical concepts, especially where called for in specific content standards or cluster headings.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that the materials develop conceptual understanding of key mathematical concepts, especially where called for in specific standards or cluster headings.

The materials develop conceptual understanding using concrete visual models during class instruction and present students with opportunities to explain their thinking through Discussion Questions and prompts. For example:

  • Common Core Coach Lesson 10 Solving Systems of Two Linear Equations Graphically addresses the understanding that the solutions to a system of two linear equations in two variables correspond to the point of intersection of their graphs, because points of intersection satisfy both equations simultaneously (8.EE.8a). Discussion Questions for Examples A and B prompt students to demonstrate conceptual understanding by explaining how they would test a conjecture and how they know whether or not the given system of equations has infinitely many solutions. Three of the 19 practice problems prompt the student to explain. Problems 17 and 18 state: “Without graphing, determine whether each system of equations will have no solution, one solution, or infinitely many solutions. Explain your answer.”
  • Common Core Coach Lesson 13 Introducing Function addresses the understanding that a function is a rule that assigns to each input exactly one output (8.F.1). Students see examples of functions represented in verbal descriptions, input-output tables, graphs, and mappings. Students are prompted to “Explain how you can tell from a graph whether a relation is a function.” Problem 11 states: “Yoshi draws a vertical line on the graph of a relation. His vertical line intersects only 1 point of the graph. He determines that the relation is also a function. Assess Yoshi’s conclusion and explain why it is or is not necessarily correct.” Students engage in conceptual understanding to explain the solutions to these prompts.

However, students are given few opportunities to independently demonstrate conceptual understanding. During Independent practice, students solve problems similar to the examples from class instruction, with slight differences in the context and/or numbers. Students rarely create visual representations on their own. There are Practice questions with labels such as “Write Math,” “Describe,” or “Compare” where students explain mathematical concepts. The questions elicit students' ability to restate the mathematics ideas addressed during class instruction by the teacher. The materials address conceptual understanding standards in a proceduralized way and do not enhance the student's ability to form a conceptual understanding of major work within the grade. For example:

  • In Common Core Coach Lesson 8 Relating Slope and Y-intercept to Linear Equations, the materials use similar triangles to explain why the slope is the same between points on a non-vertical line in the coordinate plane and the derivation of the equations y=mx and y=mx+b (8.EE.6). Students do not have an opportunity to develop a conceptual understanding of the relationship between similar triangles, slope, and equations in slope intercept form. In the Understand section students are given several examples:
    • In Example 1, students are given two similar triangles on a line in the coordinate plane. Example 2 leads students through a derivation of the equation y = mx. In the final example, students are given a procedure for finding the equation of a line. “1. Find ordered pairs from the graph; 2. Determine the slope, m, of the line; 3. Determine if y = 2x is the equation of the line. Compare the graph of y = 2x with the given graph; 4. The slope-intercept form for a linear equation is y = mx+b, where m is the slope of the line and b is the y-intercept. Adding 4 units to each point of y = 2x results in the equation y = 2x + 4, where the slope is 2 and the y-intercept is 4.” All Practice problems are related to using the procedural steps outlined in the example and working with the equation of a line.
  • In Common Core Coach Lesson 19 Understanding Congruence of Two Dimensional Figures (8.G.A) Understand and Connect sections, students are given the definition of congruence as well as examples of different ways to show that the figures are congruent. Students are prompted to “Identify the type of rigid motion that could be used to show in one step that each pair of triangles is congruent” and have six practice problems to identify congruent figures. However, students do not explain why the figures are congruent, the underlying concept for the lesson.
Indicator 2B
01/02
Attention to Procedural Skill and Fluency: Materials give attention throughout the year to individual standards that set an expectation of procedural skill and fluency.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that they attend to those standards that set an expectation of procedural skill and fluency.

Many lessons in the suite provide students with opportunities to use computation skills. Common Core Coach lessons conclude with two pages of practice problems, Common Core Support Coach lessons conclude with three practice problems, and Common Core Performance Coach lessons conclude with independent practice problems. Additional pages for practicing procedural skills are found in Appendix A of the Common Core Coach Teacher’s Guide. For example:

  • Common Core Coach Lessons 3, 4, 5, and 6 address cluster 8.EE.A (Work with radicals and integer exponents). In Lesson 4 Cube Roots Practice Problems 13 through 24, students develop procedural skills as students solve problems in the form of x2=yx^2 = y. Problem 22 states, “Solve the equation for x. x2=2.25x^2 = 2.25”

Throughout the Common Core Suite, students are given examples with step-by-step procedures at the beginning of each lesson. The majority of practice problems involve working with these procedures; however, students do not have opportunities to independently demonstrate the full intent of some standards that address procedural skills. For example, in Cluster 8.EE.C, students analyze and solve linear equations and pairs of simultaneous linear equations:

  • In Common Core Coach Lessons 10 and 11, students have opportunities to solve systems of equations both graphically and algebraically. However, within these lessons there are limited opportunities to develop procedural skills with solving systems of linear equations resulting in infinitely many or no solutions.
  • Common Core Support Coach Lesson 6 Linear Equations with Rational Coefficients includes 10 problems where students solve linear equations with one variable. Problem 7 states, “Solve for z. If there are infinitely many solutions, write infinitely many solutions. If there is no solution, write no solution. 0.5(10z + 20) - 5 = 0.1(50z + 50)”

In Grade 8, there are few lessons that specifically address procedural skills, so there are few opportunities for students to independently demonstrate procedural skills throughout the year. There are lessons in all three components of the suite that develop procedural skills, but students do not independently demonstrate those skills. Many procedural skills needed to solve problems are scaffolded so that students fill in spaces and do not demonstrate the skills on their own.

Indicator 2C
01/02
Attention to Applications: Materials are designed so that teachers and students spend sufficient time working with engaging applications of the mathematics, without losing focus on the major work of each grade

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that the 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 the grade. Engaging applications include single and multi-step problems, routine and non-routine, presented in a context in which the mathematics is applied.

In the Common Core Coach Teacher’s Edition, the Table of Contents denotes lessons that apply skills to real-world problems. Common Core Support Coach does not label specific lessons as application. In Common Core Performance Coach, there is one Performance Task at the end of each domain that applies concepts and skills to real-world problems. Non-routine problems are addressed in the Performance Tasks, and there are five Performance Tasks throughout the year.

Students have some opportunities to engage in routine application problems; however, they are often given a solution strategy. There are few opportunities for students to engage with non-routine problems, and those opportunities present in either Common Core Support Coach or Common Core Performance Coach are not assigned to all students.

Examples where students engage with routine application problems:

  • In Common Core Coach Lesson 12 Problem Solving: Using Systems of Equations, examples are presented for a four-step method for problem solving. Practice problems 3-5 are routine word problems that follow the given four-step method.
  • Digital Assessment, Domain Assessment: Expressions and Equations: Problems 24 and 29 prompt students to identify a system of equations for a word problem (24) and solve a system of equations using elimination (29). Both problems are similar to the examples provided in the lesson.
  • In Common Core Performance Coach Lesson 15: Using Functions to Model Relationships, the Practice problems are routine applications of problems with questions asking for the initial value and rate of change. In Practice Problem 8, students are given a graph that shows the height of a balloon during the first 30 seconds it is released. Practice Problem 8 states, “The graph shows the height of a balloon during the first 30 seconds after it is released. Part A: Find the initial value and the rate of change of the function represented by the graph. The initial value is ___. The rate of change is ___. Part B: Write an equation in slope-intercept form that shows the relationship between the number of seconds, x, and the height in feet, y. Interpret the meaning of the initial value and the rate of change in terms of the situation.” This context is similar to the lesson examples.

Examples where students engage in non-routine application problems:

  • Common Core Performance Coach Lesson 11 Solving Systems of Two Linear Equations Algebraically Practice Problems 1, 5 and 6 provide students with an opportunity to solve non-routine mathematical problems involving systems. For example, Practice Problem 1 gives a point (2, -4) and prompts students to find the values of a and b in the system: ax + 2y = -2, ax + by = 10. However, not all students will be assigned these problems.
  • Common Core Support Coach Lesson 7 Linear Equations in Two Variables provides examples for solving systems of equations through graphing and algebraically. Students solve seven word problems using systems of equations. Three of these problems are non-routine and do not identify the variables or equations for students.
Indicator 2D
01/02
Balance: The three aspects of rigor are not always treated together and are not always treated separately. There is a balance of the 3 aspects of rigor within the grade.

The instructional materials for Common Core Coach Suite Grade 8 partially meet expectations that the three aspects of rigor are not always treated together and are not always treated separately. All three aspects of rigor are present in the program; however, they are mostly treated separately, with an emphasis on procedural skill and fluency over the other aspects of rigor.

Common Core Coach designates lessons that are specifically identified as procedural skill, concept, or problem solving (application) lessons. However, the majority of the materials present the mathematics procedurally.

The Common Core Coach Teacher’s Manual states,“1. Concept Lessons begin with an underlying concept that connects directly to the skill or skills taught in that lesson. 2. Skill Lessons start directly with a skill and work through many variants of its application. All skills are developed through Examples. 3. Problem-Solving Lessons apply skills to real-world problem situations. Students will use a four-step problem-solving process to approach mathematical problems.”

Throughout the Common Core Coach suite, students engage with mathematics through scaffolding and problem-solving strategies that proceduralize lessons addressing conceptual understanding and application. For example, in Common Core Support Coach Lesson 16 Using Functions to Model Relationships, students identify the slope (rate of change) and y-intercept (initial value) in twelve routine practice problems based on the examples in the lesson.

Criterion 2.1: Rigor
04/08
Indicator 2A
01/02
Indicator 2B
01/02
Indicator 2C
01/02
Indicator 2D
01/02

Criterion 2.2: Math Practices
06/10
Practice-Content Connections: Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical Practice

The instructional materials reviewed for Common Core Coach Suite Grade 8 partially meet the expectations for meaningfully connecting the Standards for Mathematical Content and the Standards for Mathematical Practice. The instructional materials attend to prompting students to construct viable arguments and analyze the arguments of others and explicitly attending to the specialized language of mathematics. The instructional materials partially attend to identifying the mathematical practices and using them to enrich mathematics content and assisting teachers in engaging students to construct viable arguments and analyze the arguments of others.

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

The instructional materials reviewed for Common Core Coach Suite Grade 8 partially meet expectations that the Standards for Mathematical Practice are identified and used to enrich mathematics content within and throughout the grade level.

The Standards for Mathematical Practice (MPs) are identified in the Teacher Editions of all three components of the suite. The MPs are identified in the “teacher notes” and are mostly found during the discussion portion of the lessons. Common Core Coach Teacher’s Manual page 10 states, “The Standards for Mathematical Practice are connected to content throughout Common Core Coach. The Standards for Mathematical Practices are aligned to interactive questions, practice questions, and assessment items. Correlations to Standards for Mathematical Practices are indicated by tags.” The following examples illustrate how the MPs are identified across the Common Core Suite:

  • Common Core Coach Lesson 20 Rigid Motion on the Coordinate Plane identifies MP1 and MP5: “TRY MP1 MP5 Contrast the rule with the rule in the example. Have students predict the translation of the triangle from the rule.” This is associated with the following prompt found in the student materials: “Now use the following rule to translate $$\triangleABC$$ to form $$\triangleA"B"C"$$:(x,y)→(x−5,y+6)(x, y) → (x - 5, y + 6).”
  • Common Core Support Coach Teacher Edition includes a “Spotlight on Mathematical Practices” section in each lesson, providing the teacher with more detail on where the MPs are woven into the lesson and “notes that support teachers at point-of-use to develop strong mathematical behaviors.”
  • Common Core Performance Coach Teacher’s Manual, page xx, states, “The following Standards for Mathematical Practice are leveraged throughout Performance Coach.” The MPs are listed, defined, and describe examples of use within a mathematical context.

Although MPs are identified throughout the suite, they do not serve to enrich the mathematical content. Since they are identified primarily in discussion questions, the materials lack guidance for teachers on how the highlighted MPs connect to the mathematics in which students are engaged. Thus, the treatment of the MPs is fragmented across the suite and do not provide opportunities for students to make connections and interact with the MPs in a meaningful way. For example:

  • In Common Core Coach, each lesson identifies the MP’s within the “Understand” section with a heading “Discuss” or “Try,” along with some example problems titled “Check, Discuss, or Model.” However, there is no guidance on how to use the MPs to help enrich the mathematics within the lesson.
  • In the Common Core Support Coach Teacher’s Manual “Introduce Concepts and Vocabulary” and the “English Language Learners” sections, connections are made to MP6. While teachers are given suggestions on how to assist students with developing vocabulary (e.g., Lesson 1 vocabulary decimal states: “Have students identify the root word, terminate, in the term and determine a definition for the word.”), teachers are not provided with further direction within the lesson on how to carry out this lesson to ensure that students are developing MP6.
  • In Common Core Performance Coach Lesson 12 Introducing Functions, the Teacher’s Manual provides aligned discussion questions to MPs:
    • MP5 - "Explain how a vertical line test can be used to decide if a graph shows a function or only a relation. Why won’t a horizontal line test work?”
    • MP2 - "How can you change a relation into a function? a function into a relation?”
    • MP6 - "How are relations and functions alike? How are they different?”

While each practice is represented in this suite, there are a few instances where the MPs do not enrich the content. For example:

  • In Common Core Support Coach Lesson 3, the content is not enriched by MP4 when the teacher is prompted to, “Have students discuss other examples of very large numbers.” Students are given one example, “The mass of the sun is 1,988,920,000,000,000,000,000,000,000,000 kilograms.” This is not the intent of MP4, as students do not model with mathematics.
  • In Common Core Support Coach Lesson 18, the content is not enriched by MP5 when the teacher is prompted to, “Have partners discuss briefly before group discussion. As needed, have students use graph paper to model the scale on a coordinate grid. How would changing the scale of the x-axis impact the look of the scatter plot?” This is not the intent of MP5, as students are given a tool and do not have the opportunity to use tools strategically.
Indicator 2F
00/02
Materials carefully attend to the full meaning of each practice standard

The instructional materials reviewed for Common Core Coach Suite Grade 8 do not meet expectations that the instructional materials carefully attend to the full meaning of each practice standard.

While there is some guidance for teachers on the MPs, the Common Core Coach Suite does not attend to the full meaning of many MPs, as students do not have opportunities to demonstrate use of the practices independently. For example:

  • MP1: Common Core Performance Coach Lesson 9 Solving Linear Equations in One Variable: In the Discussion Questions, teachers are prompted to ask students the following question labeled as MP1: “What do you think the graph of a linear equation with infinitely many solutions might look like? Explain your reasoning.” While MP1 is noted in the Teacher’s Manual, students do not need to make sense of problems or persevere in solving any problems.
  • MP2: In Common Core Support Coach Lesson 1 Irrational Numbers, the Teacher’s Manual prompts teachers in Introduce and Model to “Support Discussion MP2, Have partners discuss briefly before group discussion. Ask students to identify what the bar over 0.24‾0.\overline{24} means.” While MP2 is noted in the Teacher’s Manual, students do not reason abstractly and quantitatively to solve a problem.
  • MP4: In Common Core Coach Lesson 9 Solving Linear Equations in One Variable, teacher guidance includes “MODEL MP4 Encourage students to look back at the examples and compare the forms of the equations on each side when the equations are in the form of two-step equations.” Students are prompted to “Write an equation that has infinitely many solutions and an equation that has no solution. What must be true about the variable terms on each side of the equations?” Students are not modeling with math as they are told to use equations.
  • MP5: In Common Core Coach Lesson 18 Properties of Rotation, Reflections, and Translations, the Teacher’s Manual instructs teachers to hand out tracing paper to help students verify congruent figures. While tracing paper is a mathematical tool, the students are not engaged with using appropriate tools strategically at this time as the tools for the activity are given to them.
  • MP6: In Common Core Coach Lesson 11 Solving Systems of Two LInear Equations Algebraically, the Teacher’s Manual prompts teachers in Example C to “Check MP6: Review the importance of checking the solution in both equations in the system.” While MP6 is noted in the Teacher’s Manual, students do not attend to precision to solve a problem as they are told to check the solution.
  • MP8: Common Core Coach Lesson 1 Understanding Rational and Irrational Numbers, Understand and Connect includes the following problem: “How could you show that 4.95271 is a rational number using methods shown above?” In the Teacher’s Manual, the following guidance is given: “DISCUSS MP6 MP8 Discuss with students how to use the given methods to verify that the number is rational.” This problem does not meet the full intent of MP8, as student’s are not looking for and expressing regularity in repeated reasoning.
Indicator 2G
Read
Emphasis on Mathematical Reasoning: Materials support the Standards' emphasis on mathematical reasoning by:
Indicator 2G.i
02/02
Materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet expectations that the instructional materials prompt students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics.

There are lessons throughout all three components of the suite that include opportunities for students to discuss problem solving and mathematics, and the materials provide opportunities for students to construct arguments using mathematics or to analyze the reasoning and mathematics in others’ arguments. For example:

  • In Common Core Support Coach Lesson 6, students are prompted, “Kurt simplifies this equation and says it has no solution. What can you tell Kurt about his work?” Students are presented with an incorrectly-solved equation where Kurt forgets to distribute the 2 to -7. In this problem, students critique the reasoning of others.
  • In Common Core Support Coach Lesson 13, students are prompted to discuss if “figures on a coordinate grid with different numbers of sides can ever be dilations of each other,” and if a given design will work given a specific scale factor. These discussion questions lead students to create and analyze mathematical arguments.
  • In Common Core Coach Teacher’s Manual Lesson 13 Understand and Connect states: “Have students explain in their own words what a function is and how to recognize whether a relation is a function. Encourage them to provide a method for recognizing whether a relation is a function, both graphically and from a list of ordered pairs.” The problem in the student materials has a discussion section that states: “Discuss: Explain how you can tell from a graph whether a function is a relation.” Practice Problems provide students opportunities to use their explanation in relation to specific graphs. Students need to explain, justify, or make a conjecture in eleven of thirteen problems. In addition, two Practice problems require students to critique the work of a fictional student. For example, Question 11 states: “JUDGE: Yoshi draws a vertical line on the graph of a relation. His vertical line intersects only 1 point of the graph. He determines that the relation is also a function. Assess Yoshi’s conclusion and explain why it is or is not necessarily correct.”
  • In Common Core Performance Coach Lesson 6 Question 12, Miriam and Priya are subtracting numbers written in scientific notation: Miriam’s expression, 1.4×103−2.83×1041.4\times10^3- 2.83\times10^4 and Priya’s expression, 0.14×104−2.83×1040.14\times10^4-2.83\times10^4. Part A) Without completing the subtraction, how can you determine that Miriam and Priya’s answers will have the same value? Explain. Part B) Which expression would you rather use to subtract? Why? Part C) Complete the subtraction. Show your work. Students analyze the work of others in order to explain in Part A.

The following are examples of lessons that identify MP3, but they do not present opportunities for students to critique the work of other students or to construct an argument.

  • Common Core Coach Lesson 25 Explaining the Pythagorean Theorem presents students with a real-life problem that is solved using the Pythagorean Theorem. The teachers are prompted, “Point out that Rosa only changes the length of the longest pencil. The other two pencils stay the same length. Discuss why this means the Pythagorean theorem can be used to find the desired length of the longest pencil.” Students do not need to construct an argument as to why the Pythagorean Theorem can be used, nor do they critique the reasoning of others.
  • Common Core Performance Coach Lesson 7 Understanding Proportional Relationships presents students with the equation y = 1/4x and a table of values. Students analyze the equation and table, determine if the equation and table have the same slope, and then explain their reasoning. No prompts are given for the students to construct an argument or to compare or analyze the arguments of others.
  • In Common Core Performance Coach Lesson 11 Solving a System of Two Linear Equations Algebraically, students are informed the set of equations x - y = 8 and y - x = c have infinitely many solutions. Students find the value of c and explain their reasoning.
Indicator 2G.ii
01/02
Materials assist teachers in engaging students in constructing viable arguments and analyzing the arguments of others concerning key grade-level mathematics detailed in the content standards.

The instructional materials reviewed for Common Core Coach Suite Grade 8 partially meet expectations that the instructional materials assist teachers in engaging students to construct viable arguments and analyze the arguments of others concerning key grade-level mathematics. There is little teacher guidance on how to lead discussions beyond the provided discussion questions, and there are missed opportunities to guide students in analyzing the arguments of others.

In Common Core Coach, items marked as addressing MP3 are often related to the teaching of the content with little or no assistance to teachers to engage students in both constructing viable arguments and analyzing the reasoning of others. Most often the materials prompt a discussion about “the topic” to assist students, but there are limited questions or prompts for teachers to support students’ development of arguments. Often suggestions for teachers regarding MP3 focus on students checking their work. Teachers are not provided with strategies for students to analyze the work of others in any of the lessons. For example:

  • In Lesson 11, in the paragraph labeled “Discuss,” the teacher is prompted, “Have students explain in their own words what elimination means. Discuss how to use the meaning of the word to understand the name of the method.” This is shown as aligned to MP3. Questions that prompt students to understand mathematical terminology and methods do not assist teachers in helping students to construct viable arguments or analyze the arguments of others.
  • In Lesson 13 Introducing Functions "Understand-Connect," the teacher is prompted, “Have students explain in their own words what a function is and how to recognize whether a relation is a function. Encourage them to provide a method for recognizing whether a relation is a function, both graphically and from a list of ordered pairs.” This is shown as aligned to MP3. Questions that prompt students to explain in their own words the definition of a function do not assist teachers in helping students to construct viable arguments or to analyze the arguments of others.

Common Core Support Coach provides limited assistance to teachers in engaging students in both constructing viable arguments and analyzing the arguments of others. Most often when MP3 is identified, teachers are directed to “Have partners discuss briefly before group discussion.” Some lessons contain a section titled “Spotlight on Mathematics” that offers additional support for teachers in developing critical thinking by offering probing questions to use with students. In addition, teachers are frequently provided a prompt and sentence starter to assist students. However, these probing questions and prompts do not allow for students to construct arguments or critique the reasoning of others.

  • Lesson 1 “Spotlight on Mathematical Practices” states, “Help students explain their reasoning by asking probing questions: How can you use a place-value chart to compare these numbers?” The materials do not assist teachers in helping students construct their own argument or analyze the arguments of others as students are not asked a question that requires an argument. Instead it encourages students to explain how to use a place-value chart to help them compare numbers.
  • In Lesson 15 “ Support Discussion," the following discussion question is given and aligned to MP3: “Have partners discuss briefly before group discussion. Suggest that they consider the types of angles from the Plug In as well as the ones here.” This discussion question does not assist the teacher in helping students to construct viable arguments or analyze the arguments of others.

In Common Core Performance Coach, there are no directions to assist teachers in engaging students in constructing arguments or analyzing the arguments of others. Although discussion questions and journal prompts are provided, there are no prompts for teachers, or example student answers to guide the teacher. MP3 is addressed within the discussion questions at the beginning of lessons and within the journal prompt that accompany most lessons. Additional support for the teacher related to MP3 is not present within the lessons.

  • In Lesson 2, a Discussion question is presented: “How could you check two approximations of a square root to see which one is more accurate?” This question potentially assists students with constructing their own arguments related to estimating a square root. However, there is little guidance for the teacher as to how and when to present the question, and no guidance to the teacher on having the students analyze the arguments of others.
  • In Lesson 8, a Journal Prompt labeled as MP3 states, “Why do you think that the ratios of the triangles’ corresponding side lengths and the slope of the line are equal? Explain.” There is no guidance to the teacher on having students construct arguments or analyze the reasoning of others to provide an answer.
Indicator 2G.iii
02/02
Materials explicitly attend to the specialized language of mathematics.

The instructional materials reviewed for Common Core Coach Suite Grade 8 meet expectations that materials use accurate mathematical terminology. Overall, the materials appropriately use the specialized language of mathematics and expect students and teachers to use it appropriately as well. When students are introduced to new mathematical vocabulary, it is explained, and teachers are encouraged to tell students to use the new terms.

Examples of where the instructional materials provide explicit instruction on how to communicate mathematical thinking using words, diagrams, and symbols; where the materials use precise and accurate terminology and definitions when describing mathematics; and how the materials support students to use precise mathematical language include:

  • In Common Core Coach, when a lesson introduces new vocabulary, there is a vocabulary box with a list of words and definitions. The teacher materials then guide the teacher on how to help students understand the vocabulary and how to use it when talking through the examples.
  • Often the teacher notes in the “Before the Lesson” or in the “Understand Connect” sections give suggestions for using vocabulary in a lesson. For example, Common Core Coach Teacher’s Manual Lesson 1 Understand Connect (page 18): “Review the definition of a rational number as a number that can be written as the ratio of two integers. Discuss why this definition is the same as a number with a decimal expansion that ends in 0s or in repeating decimal digits. Connect the definitions by considering 1/3, whose decimal expansion is 00. Point out that all terminating decimals and all repeating decimals are rational. Check that students understand why all terminating decimals are rational and end in zeros. Extend the discussion to include irrational numbers. Point out that the square root of a non-perfect square number is always irrational.” Lesson 7 (page 33): “Review the definition of the slope. Use the rise over the run to demonstrate how to move from one point on the graph to another. Remind students that the rise over the run form of the slope is equivalent to the change in y over the change in x.”
  • Common Core Support Coach Teacher’s Manual page xi describes the Spotlight on Mathematical Language as a “series of prompts using appropriate mathematical language and terms that are designed to elicit similar mathematical language from students.” The Spotlight on Mathematical Language section appears in some of the lessons. When it appears, it provides teachers with explicit instruction on how to assist students with communicating mathematical thinking. For example, in Lesson 3, Spotlight on Mathematical Language states, “MP6 Support students in using mathematical language as they work: What is the coefficient in a number written in scientific notation? What is the base in a number written in scientific notation?”
  • New terms are emboldened and defined in the student pages. For example, in Common Core Support Coach Lesson 15 Words to Know: “Complementary angles have measures that add up to 90°90\degree; supplementary angles have measures that add up to 180°180\degree.”
  • New terms are used in context during the Examples, Problems, and Discussion questions in all three parts of the suite. For example, in Common Core Performance Coach Lesson 10, “point of intersection” and “system of linear equations” are defined in the “Getting the Idea” section. Example 1 then includes the terms in its description of the solution steps: “Graph each equation, and identify the coordinates of the point of intersection.” Problem 5: “The first equation in a system of two linear equations is 4x + 2y = 10. The graph of the second equation passes through (0, -3). If the system of equations has no solution, what is the second equation? Write your answer in slope-intercept form. Explain your reasoning.”
Criterion 2.2: Math Practices
06/10
Indicator 2E
01/02
Indicator 2F
00/02
Indicator 2G
Read
Indicator 2G.i
02/02
Indicator 2G.ii
01/02
Indicator 2G.iii
02/02
Overview of Gateway 3

Usability

This material was not reviewed for Gateway Three because it did not meet expectations for Gateways One and Two
Gateway 3
v1.0
Gateway 3

Usability
NE = Not Eligible. Product did not meet the threshold for review.
NE
0
22
31
38
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Not Rated

Criterion 3.1: Use & Design

NE = Not Eligible. Product did not meet the threshold for review.
NE
Use and design facilitate student learning: Materials are well designed and take into account effective lesson structure and pacing.
Indicator 3A
00/02
The underlying design of the materials distinguishes between problems and exercises. In essence, the difference is that in solving problems, students learn new mathematics, whereas in working exercises, students apply what they have already learned to build mastery. Each problem or exercise has a purpose.
Indicator 3B
00/02
Design of assignments is not haphazard: exercises are given in intentional sequences.
Indicator 3C
00/02
There is variety in what students are asked to produce. For example, students are asked to produce answers and solutions, but also, in a grade-appropriate way, arguments and explanations, diagrams, mathematical models, etc.
Indicator 3D
00/02
Manipulatives are faithful representations of the mathematical objects they represent and when appropriate are connected to written methods.
Indicator 3E
Read
The visual design (whether in print or online) is not distracting or chaotic, but supports students in engaging thoughtfully with the subject.
Criterion 3.1: Use & Design
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3A
00/02
Indicator 3B
00/02
Indicator 3C
00/02
Indicator 3D
00/02
Indicator 3E
Read

Criterion 3.2: Teacher Planning

NE = Not Eligible. Product did not meet the threshold for review.
NE
Teacher Planning and Learning for Success with CCSS: Materials support teacher learning and understanding of the Standards.
Indicator 3F
00/02
Materials support teachers in planning and providing effective learning experiences by providing quality questions to help guide students' mathematical development.
Indicator 3G
00/02
Materials contain a teacher's edition with ample and useful annotations and suggestions on how to present the content in the student edition and in the ancillary materials. Where applicable, materials include teacher guidance for the use of embedded technology to support and enhance student learning.
Indicator 3H
00/02
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that contains full, adult-level explanations and examples of the more advanced mathematics concepts in the lessons so that teachers can improve their own knowledge of the subject, as necessary.
Indicator 3I
00/02
Materials contain a teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials) that explains the role of the specific grade-level mathematics in the context of the overall mathematics curriculum for kindergarten through grade twelve.
Indicator 3J
Read
Materials provide a list of lessons in the teacher's edition (in print or clearly distinguished/accessible as a teacher's edition in digital materials), cross-referencing the standards covered and providing an estimated instructional time for each lesson, chapter and unit (i.e., pacing guide).
Indicator 3K
Read
Materials contain strategies for informing parents or caregivers about the mathematics program and suggestions for how they can help support student progress and achievement.
Indicator 3L
Read
Materials contain explanations of the instructional approaches of the program and identification of the research-based strategies.
Criterion 3.2: Teacher Planning
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3F
00/02
Indicator 3G
00/02
Indicator 3H
00/02
Indicator 3I
00/02
Indicator 3J
Read
Indicator 3K
Read
Indicator 3L
Read

Criterion 3.3: Assessment

NE = Not Eligible. Product did not meet the threshold for review.
NE
Assessment: Materials offer teachers resources and tools to collect ongoing data about student progress on the Standards.
Indicator 3M
00/02
Materials provide strategies for gathering information about students' prior knowledge within and across grade levels.
Indicator 3N
00/02
Materials provide strategies for teachers to identify and address common student errors and misconceptions.
Indicator 3O
00/02
Materials provide opportunities for ongoing review and practice, with feedback, for students in learning both concepts and skills.
Indicator 3P
Read
Materials offer ongoing formative and summative assessments:
Indicator 3P.i
00/02
Assessments clearly denote which standards are being emphasized.
Indicator 3P.ii
00/02
Assessments include aligned rubrics and scoring guidelines that provide sufficient guidance to teachers for interpreting student performance and suggestions for follow-up.
Indicator 3Q
Read
Materials encourage students to monitor their own progress.
Criterion 3.3: Assessment
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3M
00/02
Indicator 3N
00/02
Indicator 3O
00/02
Indicator 3P
Read
Indicator 3P.i
00/02
Indicator 3P.ii
00/02
Indicator 3Q
Read

Criterion 3.4: Differentiation

NE = Not Eligible. Product did not meet the threshold for review.
NE
Differentiated instruction: Materials support teachers in differentiating instruction for diverse learners within and across grades.
Indicator 3R
00/02
Materials provide strategies to help teachers sequence or scaffold lessons so that the content is accessible to all learners.
Indicator 3S
00/02
Materials provide teachers with strategies for meeting the needs of a range of learners.
Indicator 3T
00/02
Materials embed tasks with multiple entry-points that can be solved using a variety of solution strategies or representations.
Indicator 3U
00/02
Materials suggest support, accommodations, and modifications for English Language Learners and other special populations that will support their regular and active participation in learning mathematics (e.g., modifying vocabulary words within word problems).
Indicator 3V
00/02
Materials provide opportunities for advanced students to investigate mathematics content at greater depth.
Indicator 3W
00/02
Materials provide a balanced portrayal of various demographic and personal characteristics.
Indicator 3X
Read
Materials provide opportunities for teachers to use a variety of grouping strategies.
Indicator 3Y
Read
Materials encourage teachers to draw upon home language and culture to facilitate learning.
Criterion 3.4: Differentiation
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3R
00/02
Indicator 3S
00/02
Indicator 3T
00/02
Indicator 3U
00/02
Indicator 3V
00/02
Indicator 3W
00/02
Indicator 3X
Read
Indicator 3Y
Read

Criterion 3.5: Technology

NE = Not Eligible. Product did not meet the threshold for review.
NE
Effective technology use: Materials support effective use of technology to enhance student learning. Digital materials are accessible and available in multiple platforms.
Indicator 3AA
Read
Digital materials (either included as supplementary to a textbook or as part of a digital curriculum) are web-based and compatible with multiple internet browsers (e.g., Internet Explorer, Firefox, Google Chrome, etc.). In addition, materials are "platform neutral" (i.e., are compatible with multiple operating systems such as Windows and Apple and are not proprietary to any single platform) and allow the use of tablets and mobile devices.
Indicator 3AB
Read
Materials include opportunities to assess student mathematical understandings and knowledge of procedural skills using technology.
Indicator 3AC
Read
Materials can be easily customized for individual learners. i. Digital materials include opportunities for teachers to personalize learning for all students, using adaptive or other technological innovations. ii. Materials can be easily customized for local use. For example, materials may provide a range of lessons to draw from on a topic.
Indicator 3AD
Read
Materials include or reference technology that provides opportunities for teachers and/or students to collaborate with each other (e.g. websites, discussion groups, webinars, etc.).
Indicator 3Z
Read
Materials integrate technology such as interactive tools, virtual manipulatives/objects, and/or dynamic mathematics software in ways that engage students in the Mathematical Practices.
Criterion 3.5: Technology
NE = Not Eligible. Product did not meet the threshold for review.
NE
Indicator 3AA
Read
Indicator 3AB
Read
Indicator 3AC
Read
Indicator 3AD
Read
Indicator 3Z
Read
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