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 Course 3 partially meet the expectations for focus and coherence with the CCSSM. For focus, the instructional materials meet the criteria for summative assessment items on grade-level and delivered in a challenging and effective manner with most units having little or no above grade-level standards. Focus is also met in the time devoted to the major work of the grade with 78.0 percent of the days allocated in the timeline aligning to the major work. For coherence, supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year and will have difficulty fostering coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. The material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade-level learning is not explicit.
Criterion 1.1: Focus
The post, chapter, and standardized assessments that are included in the Teacher's Resources and Assessments were reviewed for Course 3 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 3 addressed the grade-level content in a challenging and effective manner with most units having little or no above grade level standards addressed.
Indicator 1a
The post, chapter, and standardized assessments that are included in the Teacher's Resources and Assessments were reviewed for Course 3 and found to meet the expectations for instructional material that assesses the grade-level content and, if applicable, content from earlier grades. Content from future grades is sometimes introduced, but students should not be held accountable on assessments for those future expectations. If the future grade content was removed, it would not change the underlying structure of the assessments. Overall, the instructional material in the summative assessment items reviewed in Course 3 addressed the grade-level content with most Units having little or no above grade level standards addressed.
Quality, on grade-level examples are:
- Chapter 4, End of Chapter Test. Question 5a-e uses a real-world scenario to assess 8.F by having students create a graph from information given about a quiz and then explain the relationships between the slopes in terms of the context given.
- Chapter 11, End of Chapter Test. Question 6a-d asks students to write and solve a system of equations based off a real-world scenario and interpret the solution in the context of the problem. Using context problems to assess 8.EE allows students to work with the MPs to persevere and allows for multiple entry points to a problem.
The following items are above grade and should not be assessed, but they can be removed without drastically changing the material:
- Chapter 9 Post Test, Question #2 and End of Chapter Test #4, #5, and #6. Students are asked which Similarity Theorem applies. This is not a Grade 8 standard; it is first defined in high school.
- Chapter 9 Post Test, Question #11. Students are asked to construct a perpendicular line through a given point not on the line.
Criterion 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.
Students and teachers using the materials as designed will devote a majority of class time in Grade 8 to the major work of this grade. The instructional materials reviewed for Course 3 meet the expectations for majority of class time on the major clusters of the grade. For example, based on the pacing (one period = 50 minutes), 64 days out of 82 days total have 78.0 percent of the time spent directly on the major work of the grade.
Indicator 1b
Instructional material spends the majority of class time on the major cluster of each grade.
The instructional materials reviewed for Course 3 meet the expectations for spending the majority of class time on the major clusters of each grade. A chapter overview was found at the beginning of each chapter. This included the standards being taught in the lesson and a suggested pacing guide. Overall the instructional materials meet the criteria outlined in the CCSS publisher guidelines for the majority of class time on the major clusters of each grade.
To determine the three perspectives we evaluated: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. It was decided that the number of days devoted to major work is the most reflective for this indicator because it specifically addresses the amount of class time spent on concepts and our conclusion was drawn through this data.
Evidence was determined from the Table of Contents pages FM-6 through FM-56 and the number of days suggested in each chapter overview found in the the Teacher Implementation Guide and written by the publisher.
- Chapters – 12 out of 17 chapters, or approximately 70.58 percent of time spent on major work.
- Lessons – 60 out of 78 lessons, or approximately 76.9 percent of time spent on major work.
- Days – 64 out of 82 days, or approximately 78.0 percent of time spent on major work.
The major clusters of the grade are:
- 8.EE.A - Work with radicals and integer exponents.
- 8.EE.B - Understand the connections between proportional relationships, lines, and linear equations.
- 8.EE.C - Analyze and solve linear equations and pairs of simultaneous linear equations.
- 8.F.A - Define, evaluate, and compare functions.
- 8.F.B - Use functions to model relationships between quantities.
- 8.G.A - Understand congruence and similarity using physical models, transparencies, or geometry software.
- 8.G.B - Understand and apply the Pythagorean Theorem.
Modules and Chapters that contain these Standards are:
- Module 1 (Focus on Linear Equations and Functions): Chapter 1- 1.1, 1.2, 1.3, 1.4 (4 days); Chapter 2- 2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7 (8 days).
- Module 2 (Focus on Rate of Change and Multiple Representations of Linear Functions): Chapter 3- 3.1, 3.2, 3.3, 3.4, 3.5, 3.6 (6 days); Chapter 4- 4.1, 4.2, 4.3, 4.4, 4.5 (6 days).
- Module 3 (Focus on Pythagorean Theorem): Chapter 6- 6.1, 6.2, 6.3, 6.4, 6.5, 6.6 (7 days).
- Module 4 (Focus on Transformational Geometry): Chapter 7- 7.1, 7.2, 7.3, 7.4 (4 days); Chapter 8- 8.1, 8.2, 8.3, 8.4 (4 days); Chapter 9- 9.1, 9.2, 9.3, 9.4 (4 days).
- Module 5 (Focus on Lines and Angle Relationships, Systems of Linear Equations and Functions, and Solving Linear Systems Algebraically): Chapter 10- 10.1, 10.2,10.3, 10.4, 10.5 (6 days); Chapter 11- 11.1, 11.2,11.3, 11.4 (4 days); Chapter 12- 12.1, 12.2,12.3, 12.4, 12.5 (5 days).
- Module 6 (Focus on Properties of Exponents): Chapter 13- 13.1, 13.2, 13.3, 13.4, 13.5, 13.6 (6 days).
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Course 3 partially meet the expectations for being coherent and consistent with the standards. Supporting work is sometimes connected to the focus of the grade with some missed opportunities for natural connections to be made. The amount of content for one grade level is not viable for one school year, and the materials do not foster coherence between the grades. Content from prior or future grades is clearly identified, but materials that relate grade level concepts to prior knowledge from earlier grades is not explicit. Overall, the materials are shaped by the CCSSM and incorporate some natural connections that will prepare a student for upcoming grades. However, the material does lack some consistency for grade-to-grade progressions, and content that is not on grade level or supports on grade-level learning is not explicit.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
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The instructional materials reviewed for Course 3 partially meet the expectations for the non-major content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. In some cases, the non-major work enhances and supports the major work of the grade level, while other areas could be stronger.
Non-major clusters of the Grade 8 are:
- 8.NS.A - Know that there are numbers that are not rational, and approximate them by rational numbers.
- 8.SP.A - Investigate patterns of association in bivariate data.
- 8.G.C - Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.
Evidence of non-major content enhancing focus and coherence and supporting a partially meet's score are:
- 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 5, lesson 2 by having students work with Irrational Numbers so that they are able to fully understand the major work of the Pythagorean Theorem by working with square and cube roots.
- 8.NS.A supports 8.G and 8.EE in Module 3 - Chapter 6, Lesson 1 by having students work with square and cube root symbols so they are able to fully comprehend and solve problems involving right triangles.
- 8.SP.A supports 8.EE and 8.F in Module 7 - Chapter 15, Lessons 1-3 by having students work with grade level vocabulary supporting the major work and interpreting and analyzing scatter plots to determine the relationship between the two variables.
Examples of missed opportunities:
- 8.G.C has no support of major work noted.
- Supports of the major work are not often specifically called out as a support. Often times the connections are there, but a teacher would need to know the cohesiveness on their own to be able to make the connections for the students.
Though the supporting standards have made some connections to major work, they are not specifically written as such, and the non-major clusters of this grade are taught in isolation and miss some opportunities to engage students in the major work of Grade 8, which is why this team supports a partially meets score.
In chapter 15, slopes and intercepts are interpreted as constant rates of change and initial values in the data, which supports major work of Grade 8. - Opportunities to connect student-derived formulas for volume with nonlinear functions (8.F.5) were missed.
- In chapter 13, 8.EE.A, which is major work, is supported by 8.G.C.9.
Indicator 1d
The amount of content designated for one grade level is viable for one school year in order to foster coherence between grades.
The instructional materials reviewed for Course 3 do not meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. Without including any assessment days, there are approximately 82 days of lessons in the materials. There needs to be additional material, other than assessment days, to ensure a students' grasp of all major work at this grade level. Overall, the amount of content that is designated for this grade level is short of the amount of material needed to make it truly viable for one school year.
- According to the pacing guide, each period is 50 minutes in length and there is a suggested 82 days of lessons.
- When pre-tests, mid-chapter tests and post-test assessments are also included in the pacing, this would add an additional 51 days. If all assessments are given during the course of the year, one extra day per assessment, the total would be 133 days.
The guiding focus taken for this indicator for our team was, "Will the non-major and major work of this material be enough to prepare a student for the next grade level?" With the amount of days, many of those days not focusing on major work, the non-major work days not often supporting the major work of the grade, it will require the teacher to make significant modifications to prepare the student for the next grade level and supports this indicator receiving a does not meet rating.
Indicator 1e
Materials are consistent with the progressions in the Standards i. Materials develop according to the grade-by-grade progressions in the Standards. If there is content from prior or future grades, that content is clearly identified and related to grade-level work ii. Materials give all students extensive work with grade-level problems iii. Materials relate grade level concepts explicitly to prior knowledge from earlier grades.
The instructional materials reviewed for Course 3 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grade standards is clearly identified; however above grade-level standards are not clearly marked as such. There is ample practice for students to engage deeply with with the problems related to the Grade 8 standards, but no connections are explicitly made to prior or future content in the Teacher Implementation Guide or the student text.
Some examples of areas where identification of standards from lower grades is beneficial and supports a partially meets rating along with a an example of not meeting the full depth of the standard:
- Lower grade-level material is clearly identified in the grade level outline found in the Teacher Implementation Guide on page FM-30. They are also identified and explained in the same resource at the beginning of each lesson.
- Chapter 5, pages 281-310, titled "The Real Number System" starts with 7.NS.3, a below grade-level standard, as indicated in the pacing guide and in the chapter overview, Teacher Implementation Guide page 281A. This standard is included, as stated by publisher, to review the sets of natural numbers, whole numbers, integers, and rational numbers.
- Occasionally, the lessons do not seem to go to the full depth of the standards.
- Chapter 5 which is suppose to cover 8.NS.1 and 8.NS.2 does not cover 8.NS.2 as deeply as suggested in the standards. 8.NS.2 states, "Use rational approximations of irrational numbers to compare the size of irrational numbers, locate them approximately on a number line diagram, and estimate the value of the expressions (e.g., pi squared)." The lesson and skills practice only asks the students to compare or place numbers on a number line to the hundredths place. This is not a common occurrence in the curriculum for this grade.
The instructional materials reviewed for Grade 8 partially meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do not consistently give students of varying abilities extensive work with grade-level problems.
Some examples of giving all students extensive work with grade-level problems, but not of varying abilities and supports a partially meets rating:
- There is ample practice for each standard. Every lesson has guided practice with a script for the teacher to follow. This portion has the students conceptually developing the skill being taught and are given practice problems as well. Along with the guided practice are assignments. The number of assignments and number of problems varies per lesson. In addition there are skill practice pages to accompany each lesson as well. The number of skill pages also varies with each lesson.
- The Teacher Implementation Guided does not list any lessons or ideas for differentiated instruction except when it talks about the Mathia Software product. No differentiated or extension lessons in the Student Text, Students Skills Practice book, or the Student Assignment book were found by the reviewers.
The instructional materials reviewed for Grade 8 do not meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, no support materials were found that relate grade-level concepts explicitly to prior knowledge from earlier grades.
- The Teacher Implementation Guide is a wrap around of the Student Text. In the margins of the Teacher Implementation Guide, the authors have reworded the question asked in the student text but these does not seem to add anything to the instruction. The margins also have steps for the teachers to follow, ways to groups students (i.e., "Have students complete questions 2 and 3 with a partner. Then share the responses with a class," page 5), and guiding questions to ask students. However, it does not clearly make connections between previous knowledge and new concepts. There are not any indicators that knowledge is being extended.
- The warm-up sections for each lesson listed would be an ideal place to include connections to prior standards covered in this curriculum. For instance:
- Chapter 10, lesson 4, when equations of perpendicular and parallel are introduced.
- Chapter 12, lesson 2, students are asked to write a linear system to represent each graph, yet there are no discussion questions that could guide discussion to perpendicular and/or parallel linear equations.
Indicator 1f
Materials foster coherence through connections at a single grade, where appropriate and required by the Standards i. Materials include learning objectives that are visibly shaped by CCSSM cluster headings. ii. Materials include problems and activities that serve to connect two or more clusters in a domain, or two or more domains in a grade, in cases where these connections are natural and important.
The instructional materials reviewed for Course 3 partially meet the expectations for fostering coherence through connections at a single grade, where appropriate and required by the standards. Overall, materials include learning objectives that are visibly shaped by CCSSM cluster headings.
- The Chapter titles are clearly labeled and aligned to the standards without a need for much interpretation.
- Chapter 2 - Linear Functions (8.F)
- Chapter 4 - Multiple Representations of Linear Functions (8.EE)
- Chapter 6 - Pythagorean Theorem (8.G.B)
- Chapter 9 - Similarity (8.G.A)
The instructional materials do include some problems and activities that serve to connect two or more clusters in a domain. They include a few problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. However, overall the materials only partially foster coherence through connections in Course 3.
- For the majority of the work, most standards were taught and covered within one Unit out of the entire series and not aligned with any other concept throughout the year.
- There are no connections identified by publisher. However, there are connections within the Grade 8 standards that are just not noted or stated by the publisher.
Some examples of where connections were made and support a partially meets rating is:
- Chapter 3, "Slope: Unit Rate of Change," lessons 1 and 5 connect 8.EE.B.5 and 8.F.A by having students determine the rate of change from graphs by using the formal definition of rate of change and using rise/run formula. Students will compare the rates of graphs, compare the steepness of four lines on the same graph and relate the steepness of the lines to the magnitudes of their rates of change.
- Chapter 4, "Multiple Representations of Linear Functions," lessons 1 through 3 connect 8.EE.C.7.B and 8.F.A by having students, given linear equations written in standard form, complete tables by evaluating each equation and solving for the value of either x or y. The points are graphed and then used to calculate slope. Finally, the students convert the standard form linear equations into slope-intercept form.
- Chapter 6, "Pythagorean Theorem," lesson 1 connects 8.NS.A and 8.EE.A.2 by having students determine the area of a larger square and the sum of the areas of the two smaller squares to prove they are equal. Students also use the Pythagorean Theorem to solve for the length of unknown sides of right triangles set in a variety of contexts. In lessons 2 through 6, 8.EE.A.2 and 8.G.B are connected by having students use the Pythagorean Theorem to determine that the diagonals in a rectangle and square are congruent along with the diagonals of a trapezoid only when the figure is isosceles.