6th Grade - Gateway 1
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Focus & Coherence
| Score | |
|---|---|
Gateway 1 - Partially Meets Expectations | 57% |
Criterion 1.1: Focus | 2 / 2 |
Criterion 1.2: Coherence | 0 / 4 |
Criterion 1.3: Coherence | 6 / 8 |
The instructional materials reviewed for Grade 6 partially 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. However, they do not spend the majority of time on major work, and non-major work rarely, directly reinforces the major clusters of the grade.
Overall, Grade 6 meets expectations for assessment, amount of content provided for a year, and making connections across concepts. However, Grade 6 materials only partially meet expectations in time devoted to major work (including non-major content enhancing major work) and identifying connections to prior knowledge from earlier grades. Therefore, the overall rating for Gateway 1 is partially meets expectations.
Criterion 1.1: Focus
The instructional material reviewed for Grade 6 meets the expectations for focus within assessment. The focus for Grade 6 assessments was appropriate for the major work of the grade, but the materials also assess students on above grade-level content, such as scale factor, steepness of graphs for equations, and formal proportions. Overall, the instructional material does not assess any content from future grades that would impact the integrity of grade-level standards if those questions were modified or omitted.
Indicator 1a
The instructional material reviewed for Grade 6 meets the expectations for focus within assessment. Overall, the instructional material assesses grade-level content. However, there are a few questions that include content from future grades within the suggested summative assessment of each chapter.
The materials reviewed for indicator 1A 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.
- The summative assessments focus on grade level topics.
- All assessments and topics relate to Grade 6 standards or below except for the specific questions noted below.
- In those instances, the problems are mathematically reasonable connections and within the scope of Grade 6 ability. They could also be easily adapted or skipped without impacting the integrity of the grade level work, so they do not impact the over score of meeting expectations.
- The above grade level content that was assessed on the chapter summative tests includes the following:
- Chapter 4, problem 4 is about scale factor and similarity that aligns to 7.G.1 and 8.G.4.
- Chapter 4, problem 6 asks students to “write a proportion” which aligns to 7.RP.2.
- Chapter 7, problem 5 and Chapter 8, problem 2 involve graphs of equations and comparing steepness which is informally introduced in Grade 7 related to unit rates (7.RP.2).
- In Chapter 8, problem 7 assesses stem and leaf plots which, while mathematically reasonable for Grade 6, are not in CCSSM.
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 Grade 6 do not meet the expectations for focus within major clusters. The amount of time spent on major work is 53 percent and there is a significant amount of time spent on work from future grades. Overall, the instructional material does not spend the majority of class time in 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 6 do not 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 not 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, approximately 53 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 materials.
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 counted). Days for assessments, chapter closure, mid-course and full course closure reflections are not included in the data.
- Chapters – Approximately 59 percent of time is spent on major work.
- Lessons – Approximately 53 percent of time is spent on major work.
- Days – Approximately 53 percent of time is spent on major work.
- It is a concern that a large portion of the instructional days are more closely aligned with Grade 7 work. Examples include:
- Three lessons in Chapter 3 that involve computation of integers.
- Two lessons in Chapter 4 that include similarity and scale factor.
- Four lessons in Chapter 9 that are application work with percent.
- In the pacing guide, it would be very beneficial to plan for more days on the lessons that address major work of the grade rather than so many days on future work or stand-alone lessons.
- 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. Although there were some connections found between non-major clusters and major clusters, such as in lessons 2.3.3, 6.1.2 and 7.2.3, these connections were not strong enough to be included as addressing major work of the grade.
Criterion 1.3: Coherence
Coherence: Each grade's instructional materials are coherent and consistent with the Standards.
The instructional materials reviewed for Grade 6 only partially meet the expectations for coherence and consistency with the CCSSM. The Grade 6 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. However, there is limited evidence of supporting content enhancing coherence by reinforcing the major work of the grade. In addition, 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 6 partially 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 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 determining when lessons that are not major clusters directly support major work.
- The strongest support comes from geometry lessons, specifically area, supporting the major work of expressions and equations, which require the students to use formulas/equations to solve problems.
- There was also significant support linking the number system standards to both expressions and equations and ratios and proportional relationships. Examples include dividing decimals to find equivalent rates, using decimal operations in percent problems, calculating equivalent measurements and writing repeated factors as exponents.
- There were several instances where the supporting work missed opportunities to connect to major work. One example of this is Chapter 8 on statistics
could easily have made strong connections to both number system and expressions and equations, but did not. - However, much of the supporting work is “stand-alone” lessons that do not make connections to major work. Examples include multiple lessons on central tendency, work with data displays and scatterplots, and basic computation such as multiplying decimals.
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 6 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.
- The lessons plus a chapter closure and assessment days equal 142 days.
- The work is viable for one school year.
- The number of days fall within the 140-190 range suggested.
- According to the Teacher Guide alignment, all Grade 6 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 6 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 6 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.
Throughout the entire series in the Teacher's Guide, content connections made are within the current course, but 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 helps make connections such as:
- “Your work with similar figures and scale drawings will lay the foundations for much of the rest of the chapter.”
- “In 5.2, you will continue your earlier study of probability.”
- “Since the concepts in this chapter lay the foundation for simplifying and solving equations, they will be revisited throughout the entire course.”
- “In section 3.1, you learned about the multiple representations of portions, now you will return to the idea of portions as you develop strategies for finding parts of parts.”
- 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 it does tie to grade-level work with reasonable connections, but there are no explicit connections made to prior or future standards.
- The materials do address the depth of the standards for the grade level.
- Concept development supports the expected progression of the grade.
1.e.ii
The instructional materials reviewed for Grade 6 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 default strategy for helping all students engage in the problems.
- There is a good balance of time devoted to each standard, though a slightly disproportionate amount is allocated to statistics and probability considering it is supporting work and detracts from time that could be spent on the major work of the grade.
1.e.iii
The instructional materials reviewed for Grade 6 only 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 support grade level work by developing conceptual understanding.
- Some 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.
- 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 learning from prior grades.
- 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 6 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/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 a domain. They include problems and activities that connect two or more domains in a grade, in cases where these connections are natural and important. Overall the materials foster coherence through connections at the Grade 6.
- One of the design principles of the entire course is that 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 6 includes 25 lessons that have significant connections either within a cluster or across domains. Some examples include:
- In lesson 2.3.3: 6.NS.B and 6.EE.A are connected as students use factors to write expressions of products using the area model.
- In lessons 6.1.2, 7.2.3: 6.NS.1 and 6.NS.2 are connected as students use the standard algorithm for division to understand division of fractions.
- In lessons 9.1.1, 9.1.2: 6.G and 6.NS.B are connected as students use decimal computation to find volume and surface area.