2015
Eureka Math

6th Grade - Gateway 1

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Gateway Ratings Summary

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 6 meet the expectation for alignment to the CCSSM. For focus, the instructional materials meet the criteria for the time devoted to the major work of the grade. Also, the majority of the chapters and the respective days allocated in the timeline align to the major work of this grade. For coherence, supporting work is clearly connected to the focus of the grade and is done so in a meaningful way. Coherence is also 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. The Grade 6 materials are 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 materials reviewed for Grade 6 assess topics only at this grade level. For example, the mid-module and end-of-module assessments cover grade-level content. There are no examples of above-level assessments in the student edition. Overall, the instructional material meets the expectations for focus within assessment.

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 6 meet the expectations for assessing the grade-level content. There is no content of future grades assessed. Overall, the instructional materials assess grade-level topics.

  • All assessment Items are at grade level and aligned to one or more of the grade-level standards.
  • Mid-module and end-of-module assessments are aligned to grade-level content and do not assess content above the specified grade level.
  • The rubrics for each assessment indicate which standards are assessed in each question. Every question aligns to at least one grade-level standard.

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 materials reviewed for Grade 6 are developed so that students and teachers using the materials as designed devote the large majority of class time to the grade's major work. Sixty-seven percent of the days are suggested for major work of the grade. Three of the six modules are designated as major work and two others contain lessons related to major work. Overall the instructional materials meet the criteria for the time devoted to the major work 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 6 meets the expectations for spending the majority of class time on the major cluster of each grade. Overall the instructional materials meet the criteria outlined in the CCSSM publisher guidelines for the time for the major work of the grade.

  • 6.RP.1-3, 6.NS.1, 6.NS.5-8 and 6.EE.1-9 standards are major work of the grade.
  • Modules 1, 3 and 4 focus on the major work, and Modules 2 and 5 contain lessons related to the major work.
  • The modules in bold are modules aligned to the major clusters of the grade.
    • Module 1: 29 lessons + 6 days = 35 days (ratio and unit rates)
    • Module 2: 19 lessons + 6 days = 25 days (operations and fractions)
    • Module 3: 19 lessons + 6 days = 25 days (rational numbers)
    • Module 4; 34 lessons + 11 days = 45 (expressions and equations)
    • Module 5: 19 lessons + 7 days = 26 days (area, surface area, volume)
    • Module 6: 22 lessons + 3 days = 25 days (statistics)
  • Of the 180 days, 120 days (67%) are spent on the major clusters of the grade.

Criterion 1.3: Coherence

7 / 8

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

The instructional materials reviewed for Grade 6 meet the expectations for coherence and consistency with the CCSSM. The majority of the chapters and the respective days allocated in the timeline align to the major work of this grade. Supporting work is connected to the focus of the grade in a meaningful way. Each module begins with an overview of the foundational standards that have been taught and learned previously and focus, both of which were being addressed in the module. Ample narrative exists throughout the modules explaining how the materials develop from previous material and, sometimes, how the material will be addressed in the future. Coherence is also evident in the instructional materials by the inclusion of problems and activities that serve to connect two or more clusters in a domain and that connect two or more domains in a grade.

Indicator 1c

2 / 2

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

The instructional materials reviewed for Grade 6, by engaging students in the major work of the grade, simultaneously meet the expectations for the supporting content-enhancing focus and coherence. Overall, the majority of the chapters and the respective days allocated in the timeline align to the major work of this grade level. The chapters and the individual lessons support focus and coherence to the major work of the grade level.

  • Supporting work is clearly connected to the focus of the grade and is done so in a meaningful way.
  • Module 2 is a strong example of how supporting work, 6.NS.2-4, is presented in a way that connects to the focus of the grade, providing ample opportunity to work with fractions and ratios.
  • In lesson 1 of module 5, students are asked to solve a problem using equations and fractions (dividing fractions). These two concepts link the topic of area back to previous learning from this grade level.
  • Within lesson 12 of module 6 (statistics), students must perform operations with decimals which support previous learning from the grade level.

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 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. Overall, the amount of content that is designated for this grade level is viable for one school year.

  • There are 181 designated days for all of the modules with one day labeled optional.
  • Each module has built in days for assessment, review and extra practice. This allows for adjustments needed throughout a school year resulting from school activities, weather days and a teacher's professional judgment as to pacing.
  • The following are the designated days for each module:
    • Module 1: 29 lessons + 6 days = 35 days (ratio and unit rates)
    • Module 2: 19 lessons + 6 days = 25 days (operations and fractions)
    • Module 3: 19 lessons + 6 days = 25 days (rational numbers)
    • Module 4; 34 lessons + 11 days = 45 (expressions and equations)
    • Module 5: 19 lessons + 7 days = 26 days (area, surface area, volume)
    • Module 6: 22 lessons + 3 days = 25 days (statistics)

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 6 partially meet the expectations for the material to be consistent with the progressions in the standards. Content from prior grades is identified, although materials do not always relate grade-level concepts explicitly to prior knowledge from earlier grades within each lesson. Connections are not often made to content in future grades. Overall, the materials in Eureka-Grade 6 identify the progressions from prior grades in the standards.

  • Each module begins with an overview of standards being addressed in the module: here, foundational standards that have been taught and learned previously and focus.
  • When appropriate, the connections to lessons and/or topics from previous grade levels are called out at the beginning of a given topic. For instance, in module 5, lesson 16, the beginning information specifies that the upcoming lessons are a continuation of topics A and B from module 5 in the Grade 5 materials.
  • Ample narrative exists throughout the modules explaining how the materials develop from previous material and sometimes how the material will develop in the future.
  • Teachers are provided with sufficient information to help see the connections in the standards, tasks, modules and lessons.

The instructional materials reviewed for Grade 6 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.

  • The materials provide students with extensive work with grade level problems.
  • Modules contain a large mix of tasks that are grade level appropriate. Each module also contains at least one extensive problem set designed to help develop students' procedural skill/fluency.
  • There are occasional comments within the teacher material to help teachers best reach English language learners (ELLs) or below-grade-level students, and little guidance is provided on how to support students that are above grade-level.

The instructional materials reviewed for Grade 6 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.
  • Educators may find it more beneficial to see these connections called out in the lessons as they occur.
  • The student material makes no explicit connections to prior knowledge from earlier grades. However, some of the narrative reminds students of previously learned material within the grade when it is expected to be recalled.

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 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.

  • When both teacher and student materials sometimes end with a lesson summary that reviews student outcomes, they are written in language that can be easily aligned to learning objectives (CCSSM standards) and cluster headings.
  • The first sentence in topic A directly connects the 6.RP standards in the module to the cluster heading.
  • Module 3's overview also connects the RP standards to the cluster heading. In this module there is also a student outcome that says, "Students extend their understanding of the number line, which includes zero and numbers to the right, which are above zero, and numbers to the left, which are below zero."

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.

  • In module 2 of Grade 6, the clusters within the number system are intertwined. The clusters are: "apply and extend previous understandings of multiplication and division to divide fractions by fractions" and "compute fluently with multidigit numbers and find common factors and multiples." The integration of these standards allows students to see and build connections within the number system and the operations.
  • In module 4, lessons 3, 4, 10 and 11, students use their skill in recognizing common factors (6.NS.4) to rewrite expressions (6.EE.3).
  • Module 4, lesson 7, stresses writing, reading, evaluating and transforming the volume formulas V = lwh and V = Bh (6.G.2, 6.EE.2).
  • In module 4, lesson 25, equations of the form px = q (6.EE.7) are unknown-factor problems; the solution will sometimes be the quotient of a fraction by a fraction (6.NS.1).