8th Grade - Gateway 1
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Focus & Coherence
Gateway 1 - Meets Expectations | 92% |
|---|---|
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 4 / 4 |
Criterion 1.3: Coherence | 7 / 8 |
The instructional materials reviewed for Grade 8 meet expectations for Focus and Coherence. The materials do primarily assess grade-level work. A true strength is providing rich, grade-level problems for all students that connect multiple clusters and domains. In addition, they spend the majority of time on major work, and non-major work often directly reinforces the major clusters of the grade.
Overall, Grade 8 meets expectations for assessment, amount of content provided for a year, making connections across concepts, and time devoted to major work (including non-major content enhancing major work). The Grade 8 materials partially meet expectations in identifying connections to prior knowledge from earlier grades. The overall rating for Gateway 1 is meets expectations.
Criterion 1.1: Focus
The instructional material reviewed for Grade 8 meets the expectations for focus within assessment. All of the summative assessment questions focus on grade-level topics or below. Overall, the instructional material does not assess any content from future grades.
Indicator 1a
The instructional materials reviewed for Grade 8 meet the expectations for focus within assessment. Overall, the instructional material does not assess any content from future grades within the summative assessment sections of each chapter.
The materials reviewed for this indicator were the Individual Chapter Tests that are pre-made for Chapters 2-9. Chapter 1 does not have an individual test. Also, the online component for Core Connections has an extensive item bank that can be used to create individual assessments.
- All assessments and topics relate to Grade 8 standards or below.
- The summative assessments focus on grade level topics.
- No above grade-level content was assessed on the chapter, summative tests.
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 material reviewed for Grade 8 meets the expectations for focus within major clusters. The amount of time spent on major work is 76 percent with additional support from content in the non-major clusters that directly connects with major work. Overall, the instructional material spends the majority of class time on the major clusters 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 Grade 8 meet the expectations for focus within major clusters. This program integrates a spiral curriculum, including in homework and on assessments. Overall, the instructional material does spend the majority of class time on the major clusters of each grade.
Three perspectives were considered: 1) the number of chapters devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of instructional days devoted to major work. The number of days, at approximately 76 percent, devoted to major work is the most reflective for this indicator because it addresses the amount of class time spent on concepts, especially given the spiraling nature of the curriculum.
For the purpose of consistency when calculating, all lessons (even those labeled optional) are included in the data and the maximum number of days in the range suggested was included (for example, if a lesson was labeled 1-2 days, 2 days was used). Days for assessments, chapter closure, mid-course and full course closure reflections are not included in the data.
- Chapters – Approximately 72 percent of time is spent on major work.
- Lessons – Approximately 76 percent of time is spent on major work.
- Days – Approximately 76 percent of time is spent on major work.
- We also reviewed the non-major clusters to determine if they could be factored in due to how strongly they support major work of the grade and found that there are connections made to major work in the supporting clusters.
- Grade 8 does spend the majority of time on major work because 76 percent meets the threshold of 65 percent.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 8 meet the expectations for coherence and consistency with the CCSSM. The Grade 8 materials do include lessons that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials also provide all students with extensive work at grade-level problems. Lessons are consistent with the depth and progressions in the standards. In addition, there is evidence of supporting content enhancing coherence by reinforcing the major work of the grade. However, connections to prior knowledge or content from prior grades are not explicitly identified.
Indicator 1c
Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.
The instructional materials reviewed for Grade 8 meet the expectations for the supporting content enhancing focus and coherence simultaneously by engaging students in the major work of the grade. To determine this, we looked at the student lessons that were not major work to identify connections and support they provided to the major clusters. We also considered if there were missed opportunities to make strong connections. In the Teacher's Guide, the lessons are correlated to standards, so there was some guidance in determining where connections were being made.
- In general, the standards alignment in the Teacher’s Guide is accurate, therefore it is a reliable source for seeing when lessons that are not major clusters directly support major work.
- The strongest support comes from Chapter 7 on statistics, specifically scatterplots and lines of best fit, which connect strongly to both expressions and equations and functions.
- There was also significant support linking geometry with both number system and expressions and equations as students wrote and solved Pythagorean theorem equations where solutions had to be approximated.
- Also, Chapter 10 on geometry provided many connections to expressions and equations when students used formulas/equations to solve problems.
- There is some supporting work as stand-alone lessons that do not make connections to major work.
- There were no glaring instances where the supporting work missed opportunities to connect to major work.
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 Grade 8 meet the expectations for the amount of content designated for one grade level being viable for one school year in order to foster coherence between grades. The Teacher’s Guide offers three different pacing plans –
- One for traditional schedules
- One for block schedules
- One for Acceleration – combining Course 2 and 3 into one year
The traditional plan was used to determine the number of instructional days since it seemed to best represent the way the course was designed.
The pacing provided by the publisher is reasonable for lessons to be completed in the time suggested.
- Lessons plus a chapter closure and assessment days equal 148 days.
- This is viable for one school year.
- This falls within the 140-190 range suggested.
According to the Teacher's Guide alignment, all Grade 8 standards are included.
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 Grade 8 partially meet the expectation to be consistent with the progressions in the standards. Materials do provide all students with extensive work at grade level problems. However, content from prior grades is rarely identified and materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades. Connections are also not made to content in future grades. Overall, the materials in Grade 8 are consistent with the depth and progressions in the standards, but explicit connections to prior or future grade-level content are never identified for teachers or students.
1.e.i
Throughout the entire series in the Teacher's Guide, content connections made are within the current course – they never explicitly tie to prior or future work.
- On the chapter introduction page, students are given a very clear overview of what the chapter will be, and it helps make connections such as:
- Chapter 5 – “In the last chapter, you….:
- Chapter 8 – “In previous chapters, you have investigated….in 8.1, you will …”
- Chapter overviews include a chart with a column of “Concepts Introduced/Reviewed” as well as identifying “Section Content Revisited”, but they are within the course.
- Each chapter overview includes “Where is this going?” that makes connections to extensions of the concept later in the year since this curriculum spirals.
- Teacher notes at the beginning of each lesson sometimes include a mathematical background section – these provide information, but do not make direct connections to prior or future work.
- When off grade-level material is present, it is sometimes labeled as “preparation for” and does tie to grade-level work with reasonable connections, but it does not make explicit connections to prior or future work.
- The materials do address the depth of the standards for the grade level.
- Concept development aligns to the expected progression of the grade.
1.e.ii
The instructional materials reviewed for Grade 8 meet the expectation of giving all students extensive work with grade-level problems. Overall, the materials do consistently give students extensive work with grade-level problems, however there is extensive dependency on peer interactions for learning concepts that could be a significant challenge for many students. All students are expected to do the same work.
- Students have ample opportunity to engage deeply in grade-level work.
- Every lesson requires student teams to start by solving non-routine problems where clear pathways or expected answers are not obvious.
- Problems presented are frequently relevant, authentic, and require students to make connections.
- Some problems develop through multiple extensions throughout the entire course, spiraling back with new connections.
Working with a collaborative team is the main strategy for helping all students engage in the problems.
There is a fair balance of time devoted to each standard, with the following concern. Based on correlations provided in the Teacher's Guide:
- Several standards in Expressions and Equations are only addressed in one or two lessons throughout the year which indicates weak development of an important concept. Examples include:
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- EE.3 and 4, which involve using scientific notation, are only correlated in one lesson each (8.2.1 and 8.2.4).
- EE.5 which makes connections between unit rate, slope, and proportional relationships is only correlated in two lessons (1.2.1 and 7.2.4).
- EE.8.A and EE.8.B, which relate to simultaneous linear equations, are only correlated in one and two lessons, respectively (5.2.1 and 5.2.3, 5.2.4).
1.e.iii
The instructional materials reviewed for Grade 8 partially meet the expectation of relating grade-level concepts explicitly to prior knowledge from earlier grades. Overall, materials do not relate grade-level concepts explicitly to prior knowledge from earlier grades other than noting that certain lessons are “preparation for” a grade-level standard.
- Lessons identified as “preparation for” lessons (less than one-fourth) support grade level work by developing conceptual understanding.
Approximately 15 lessons are not aligned to a standard at all, these lessons generally review or build concepts necessary for grade-level standard understanding, which could be explicitly linked to previous standards. Examples include: background review on interpreting graphs, vocabulary for writing algebraic expressions, using algebra tiles to simplify and compare expressions, extending patterns.- Connections between concepts are addressed on the chapter introduction page, so students can begin to see how content relates (see 1.e.i for examples), though concepts are never explicitly connected to prior learning.
- Within the teacher materials, each chapter contains narrative stating topics that may be “reintroduced” from previous courses.
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 Grade 8 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.
- Generally, chapter titles and lesson objectives make connections to CCSSM cluster headings, though never verbatim, and it's not always clear or obvious.
- The Teacher's Guide does connect every cluster heading to problems that address it, with each one being engaged in multiple times throughout the course.
- Correlation is available in two forms: 1) CPM Core Connections as aligned to the CCSSM and 2) CCSSM as aligned to CPM Core Connections.
- Teacher lessons have the CCSSM of the lesson listed in the upper right hand corner of the opening pages of instruction information.
- For the teacher, when looking into the actual lessons, the chapter overview makes the alignment to CCSSM clusters easier to see.
The instructional materials do include problems and activities that serve to connect two or more clusters in cases where these connections are natural and important. Overall the materials foster coherence through connections in Grade 8.
- One of the design principles of the entire course is: Mathematics is a coherent, intellectual system, not a collection of disjointed facts, and needs to be taught in a way that makes this coherence clear.
- Grade 8 includes 34 lessons that have significant connections either within a cluster or across domains. Some examples include:
- In lessons 7.3.1, 7.3.2: 8.SP and 8.F.B are connected as students use equations to make predictions and associations involving data.
- In lessons 9.2.2, 9.2.5, 9.2.7: 8.EE.A and 8.G are connected as students write equations to solve Pythagorean theorem problems.
- In lesson 9.2.3: 8.EE.A, 8.G.B and 8.NS are connected as students find side lengths of triangles using equations and approximations of irrational numbers.
- In lesson 9.2.4, 10.1.1: 8.NS and 8.EE.A are connected as students find decimal approximations of roots.