8th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Partially Meets Expectations | 64% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 3 / 8 |
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.
Criterion 1.1: Focus
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
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: $$–3(2x +1) + 3x = 6x + 3$$”
- 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 1.2: Coherence
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
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 1.3: Coherence
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
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 $$48\pi$$ 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. $$y = 25x +150$$.” 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
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
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. $$(8 x 10^2)/(5 x 10^5)$$.“
- 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 $$5\times10^{-3}$$? A) $$3.1\times10^{-6}+1.9\times10^{-3}$$, B) $$6\times10^{-3}+1\times10^{-3}$$, C) $$4\times10^{-3}+1\times10^{-3}$$, D) $$3.1\times10^{-3}+1.9\times10^{-3}$$?"
- 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
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 $$r^2 = p$$ and $$r^3 = p$$ and to evaluate square and cube roots (8.EE.2).