2016
MathLinks

8th Grade - Gateway 1

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Gateway Ratings Summary

Focus & Coherence

Gateway 1 - Meets Expectations
85%
Criterion 1.1: Focus
2 / 2
Criterion 1.2: Coherence
4 / 4
Criterion 1.3: Coherence
6 / 8

The instructional materials reviewed for Grade 8 meet the expectations for focus and coherence in the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Seventy-four percent (74%) of the days allocated in the timeline align to the major work of this grade. For coherence, supporting work is rarely connected to the focus of the grade. Coherence is evident in the instructional materials including problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade. Overall, the Grade 8 materials are partially coherent and consistent with the standards.

Criterion 1.1: Focus

2 / 2
Materials do not assess topics before the grade level in which the topic should be introduced.

The instructional material reviewed for Grade 8 meets the expectations for focus within both assessment and time on major work. The summative test of each packet assesses topics at this grade level without assessing any content from future grades with one exception, that is test 3, problem 3. Seventy-four percent (74%) of the days are suggested for major work of the grade and there is some support from content in the non-major clusters that directly reinforces major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of class time in the major clusters of the grade.

Indicator 1a

2 / 2
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 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 packet with one exception, namely test 3 problem 3.

For this indicator, the summative test for each packet was evaluated.

  • All assessments and topics relate to Grade 8 standards or below except for one question on Test 3.
  • Test 3 problem 3 asks students to state the “recursive rule” which is in the high school functions standard – Building Functions: HSF.BF.A.1.A - Determine an explicit expression, a recursive process, or steps for calculation from a context. The Grade 8 standard simply requires verbal descriptions and does not introduce recursive vocabulary. Recursive versus explicit rules are embedded throughout the instruction for this entire unit. The content could easily have been addressed without introducing the recursive rule; however, because of its extensive use, the work could not be completed without knowing what recursive means. This test question could easily be modified or skipped completely in the assessment with no impact. Therefore, it does not impact the score of 2 for this indicator.

Criterion 1.2: Coherence

4 / 4

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 both assessment and time on major work. The summative test of each packet assesses topics at this grade level without assessing any content from future grades with one exception, that is test 3, problem 3. Seventy-four percent (74%) of the days are suggested for major work of the grade and there is some support from content in the non-major clusters that directly reinforces major work. Overall, the instructional materials meet the criteria for grade level assessment as well as spending the majority of class time in the major clusters of the grade.

Indicator 1b

4 / 4

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. Overall, the instructional material spends the majority of class time on the major clusters of each grade.

To determine this, three perspectives were evaluated: 1) the number of units/packets devoted to major work, 2) the number of lessons devoted to major work, and 3) the number of days devoted to major work. 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. The conclusions are based on that data.

The number of days suggested by the publisher for the “enriched” pacing option is the one most dedicated to grade-level work with the least review.

  • Units/Packets – percentage of time spent on major work is 80 percent.
  • Lessons – percentage of time spent on major work is 70 percent.
  • Days – the percentage of time spent on major work is 74 percent.
  • Days allotted to review lessons are minimal.
  • Also, the non-major clusters were evaluated to determine if they could count due to how strongly they support major work of the grade. Some evidence, such as Packet 10: Bivariate Data, does a significant amount of work with writing and using the equation for a line of best fit which supports 8.F: Functions.
  • At 74 percent within the 65 percent - 85 percent standard, Grade 8 spends the majority of time on major work.

Criterion 1.3: Coherence

6 / 8

Coherence: Each grade's instructional materials are coherent and consistent with the Standards.

The instructional materials reviewed for Grade 8 partially meet the expectations for coherence and consistency with the CCSSM. There is limited evidence of supporting content enhancing coherence by reinforcing the major work of the grade because so much of the content is stand-alone. The Grade 8 materials provide a list of previous skills/knowledge that is foundational for the current work, but they don't explicitly tie the previous skills/ knowledge to the lessons. The materials include lessons that serve to connect two or more clusters in a domain, or two or more domains in a grade. The materials also develop by the grade-by-grade progressions in the standards. However, most of the lessons meet individual standards and do not consistently promote the coherent connections that allow students to apply and transfer the learning. Overall, the Grade 8 materials partially address the key aspects of coherence and consistency with the standards

Indicator 1c

1 / 2

Supporting content enhances focus and coherence simultaneously by engaging students in the major work of the grade.

The instructional materials reviewed for Grade 8 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, the connections that the teacher guide stated were considered, and the student lessons were reviewed to validate the connections from the teacher guide as well as determine if there were missed opportunities to make strong connections.

Some examples include:

  • The strongest support comes from statistics supporting the major work of functions. Units 4 (Patterns and Linear Functions) and 10 (Bivariate Data) support 8.F. Both of these require the students to use functions to model relationships between quantities.
  • Unit 10 also has a strong connection to Equations and Expressions (8.EE.C) solving line of best fit equations.
  • There were instances where the supporting work missed opportunities to connect to major work such as developing work with equations in both Unit 15 (Geometry) and Unit 16 (Real Number System).
  • In Packet 4, Lesson 3, standards 8.F.A, 8.F.B and 8.SP.A are connected as students measure and record heights of stacked cups. Only one day is allotted for this lesson, and this amount of time does not allow for the connection to be fully developed for all students.
  • There were only 5 out of 16 packets that include supporting work; Packet 15 is "stand-alone" and did not support major work.

Indicator 1d

2 / 2

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 guide offers six different pacing plans –

  • Three for traditional schedules.
  • Three for block schedules.
  • Each has the Modified Plan for students who require extensive review.
  • The Basic Plan for students who require some review.
  • The Enriched Plan for students who only need minimal review.
  • All of them plan for 32 weeks of instruction.

For the report the Traditional Enriched Plan was used since it best represented a focus on grade-level work.

The pacing provided by the publisher is reasonable for lessons to be completed in the time suggested.

  • Lessons plus a catch-up day (built into each unit) and the assessment day equal 158 days.
  • This Falls within the 140-190 range suggested.
  • According to the scope and sequence, all Grade 8 standards are included.

However, there is concern about the three pacing suggestions.

  • Students needing more review early in the year spend equal or less time on Units later in the year, which is new material.
  • It is not clear how students who need Modified Plan A could finish all packets in the same amount of time as students on Enriched Plan C, though there are suggestions about items that could be omitted.

Overall, the number of days suggested is viable and provides the content needed to be prepared for the next grade level.

Indicator 1e

1 / 2

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 expectations for the material to be consistent with the progressions in the standards. Content from prior grades is clearly identified, although materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not made to content in future grades. Overall, the materials in Grade 8 identify the progressions from prior grades in the standards.

  • The teacher guide includes a page delineating how the major work standards for Grade 8 intersect with major clusters in grades 6-HS.
  • Each packet lists an overview of standards being addressed including foundational standards that have been taught and learned previously.
  • In general, lessons are taught as a series of 3, where each builds or connects to the one before.

· Teachers are provided with sufficient information to help see the connections in the standards, tasks, packets and lessons.

· There are standards where the materials are only partially representative of the progressions. For example: 8.F is included in seven units (Units 3, 4, 7, 8, 9, 10 and 13). In Units 4 and 7, 8.F is addressed through specific examples (Growing Shapes, Going to the Park, Stacking Cups and Rate Graphs). However, the knowledge may not transfer to other functional relationships. The work with functional relationships is very specific to certain tasks throughout the units. Overall understanding of the concept of a function as a whole and representation of a functional relationship as an equation may be limited.

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.

  • Not all students have the opportunity to engage deeply with problems related to grade-level standards as the material is not as rigorous as needed and doesn't have the depth that is needed to truly master the standards.
  • Each packet primarily contains problem sets designed to help develop students' procedural skill/fluency.
  • Some of the performance tasks and proficiency assessments do allow for more application and rigorous engagement with the standards.
  • It is recommended, in the teacher guide, that struggling students spend the majority of time on basic lessons, skill builders, and review and to avoid extensions and more challenging questions. This is limiting their interaction and mastery of grade level standards.

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 only generally relate grade-level concepts explicitly to prior knowledge from earlier grades.

  • Each module lists the foundational standards at the beginning of the module to explicitly connect prior learning to current learning.
  • It would be more beneficial to see these connections listed in the lessons as they occur.
  • Connections to lessons and/or topics from previous grade levels that will be helpful in upcoming lessons are frequently reviewed in the “warm-up” at the beginning of a given topic, though no explicit connections are made for the students.

Indicator 1f

2 / 2

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.

  • Each packet lists the lessons with the student outcomes clearly stated, which are easily aligned to CCSSM standards and cluster headings.
  • In general, lessons and tasks require students to demonstrate the standards. However, they rarely connect these concepts beyond what naturally occurs with lessons following one another.
  • The teacher guide provides a page of content emphasis by cluster.
  • Each packet identifies the standards addressed and bolds the major cluster.
  • Occasionally a lesson title will not have a clear connection – such as “Going to the Park” – however the learning objective clarifies the connection.

The instructional materials 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 Grade 8.

  • In packets 3, 4 and 9, students connect the ideas of functions and linear equations (8.EE.B, 8.F.B).
  • Students continue this work by using functions to determine best buys in packet 7 (8.EE.B, 8.F.A).
  • However, one missed opportunity that is visible is that 8.EE.B and 8.G.A are not connected with the linear function work. Here, the concept of similarity could have been connected to slope through the use of similar triangles. Those are connected in a later lesson in packet 15.
  • There are other natural connections evident such as using formulas to solve problems (8.EE.C, 8.G.C).