EdReports math K-8

Core Content Evidence Guide v2.0
Mathematics
Grades K-8
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Gateway 1: Focus & Coherence
Criterion 1.1
Focus
Materials assess grade-level content and give all students extensive work with grade-level problems to meet
the full intent of grade-level standards.
What is the purpose of this Criterion?
Criterion 1 considers how well the materials focus on college and career ready standards by assessing
students on grade-level content and giving all students extensive work with grade-level problems to meet the
full intent of grade-level standards.
Research Connection
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Focus in Mathematics
● Coherence Map
Scoring:
Meets Expectations
● 17-20 points
Partially Meets Expectations
● 11-16 points
Does Not Meet Expectations
● <11
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Gateway 1: Focus & Coherence
Criterion 1.1 Materials assess grade-level content and give all students extensive work with
grade-level problems to meet the full intent of grade-level standards.
Indicator 1a Materials assess the grade-level content and, if applicable, content from
earlier grades.
Scoring:
2 points
● Materials assess grade-level standards or include
above-grade assessment items that could be
removed or modified without impacting the
structure of the materials.
● Above-grade items are mathematically reasonab

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assess grade-level standards or include
above-grade assessment items that could be
removed or modified without impacting the
structure of the materials.
● Above-grade items are mathematically reasonable.
● For Grades K-5, no topics are explicitly assessed
from (i), (ii), or (iii) below.
0 points
● Materials include above-grade assessment items
that, if removed or modified, would impact the
structure of the materials.
OR
● Above-grade items are not mathematically
reasonable.
OR
● For Grades K-5, topics are explicitly assessed from
(i), (ii), or (iii) below.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1c, and 1d, determines the shift of Focus. In order to maintain Focus, materials
assess grade-level standards. Assessments are determined by the publisher and are series-specific. Content
from future grades may be introduced, but students should not be held accountable on assessments for future
expectations.
Indicator 1a is focused on the assessments embedded in materials for K-8 grade-level standards which define
what students should understand and be able to do in their study of mathematics .

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ectations.
Indicator 1a is focused on the assessments embedded in materials for K-8 grade-level standards which define
what students should understand and be able to do in their study of mathematics . ALL standards in the CCSSM	1
should be considered throughout evidence collection for Gateway 1 indicators 1a, 1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
1 "Common Core State Standards for Mathematics" http://www.corestandards.org/Math/
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Indicator 1a Guiding Question:
Do assessments address grade-level standards?
Evidence Collection
Look at all interim, unit, and/or summative assessments. Look at scoring rubrics, if available, to determine
acceptable responses for the items.

? Please explain.
Mathematically Reasonable:
For this indicator, mathematically reasonable consists of two criteria: number of grade-levels above the current
one and time of year when the item occurs. For example, assessing standards that are one grade level above
the current one could be mathematically reasonable, or assessing above-grade-level standards at the end of
the academic year could be mathematically reasonable. To determine if an above-grade-level item is
mathematically reasonable, consider the following questions:
● Is the above grade-level assessment item connected to current grade-level content?
● How many grade levels above is the assessment item?
● What time of year do students encounter the assessment item?
Cluster Meeting
Discuss evidence of grade-level assessment items that are representative of the materials.
Discuss all above-grade-level assessment items and any additional information:
● Which assessment items are mathematically reasonable? Please explain.
● Which assessment items, if removed or modified, would impact the structure of the materials? Please
explain.
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Gateway 1: Focus & Coherence
Criterion 1.1 Materials assess grade-level content and give all students extensive work with
grade-level problems to meet the full intent of grade-level standards.
Indicator 1b Assessment information is included in the materials to indicate which
standards are assessed.
Scoring:
2 points
● Materials consistently identify
the standards and practices
assessed for formal
assessments.
1 po

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information is included in the materials to indicate which
standards are assessed.
Scoring:
2 points
● Materials consistently identify
the standards and practices
assessed for formal
assessments.
1 point
● Materials consistently identify
the standards and/or practices
assessed for formal
assessments, but do not include
all standards and/or practices
for the grade or course level.
0 points
● Materials do not identify the
standards and practices
assessed for the formal
assessments.
About this indicator:
What is the purpose of this Indicator?
This indicator examines the assessment materials to determine whether they identify the standards being
assessed for all formal assessment types. It is important to note that some assessments may be building toward
the standards and not intended to measure full depth of the standards; these assessments should identify which
aspects of the standards are being assessed and/or being built toward.
Formal assessments are determined by the publisher and could include all types: formative, summative, etc.
Reviewers look for a list of standards assessed for the entire assessment and/or associated with each item/task.
Reviewers look for evidence of identification only. ALL standards in the CCSSM should be considered throughout
evidence collection for Gateway 1 indicators 1a, 1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Indicator 1b Guiding Question:
Does assessment information included in the materials indicate which standards are assessed?
Evidence Collection
Review assessments and corresponding assessment guidance across the series.

sessments are building towards the standards, do the materials identify which aspects of the
standards are being assessed and how these contribute to building toward grade-level/grade-band
standards?
Gateway 1: Focus & Coherence
Criterion 1.1 Materials assess grade-level content and give all students extensive work with
grade-level problems to meet the full intent of grade-level standards.
Indicator 1c Assessments include opportunities for students to demonstrate the full intent
of grade-level/course-level standards and practices across the series.
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Scoring:
4 points
● Assessments include
opportunities for students to
demonstrate the full intent of
grade-level/course-level
standards and practices across
the series.
2 points
● Assessments do not include
opportunities for students to
demonstrate the full intent of
grade-level/course-level
standards across the series.
OR
● Assessments do not include
opportunities for students to
demonstrate the full intent of
grade-level/course-level
practices across the series.
0 points
● Assessments do not include
opportunities for students to
demonstrate the full intent of
grade-level/course-level
standards and practices across
the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1a, and 1d, determines the shift of Focus. In order to maintain Focus, materials
assess grade-level standards.

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s indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1a, and 1d, determines the shift of Focus. In order to maintain Focus, materials
assess grade-level standards. This indicator examines the assessments within and across the materials to
determine whether they include a variety of assessment types that are constructed in a manner that allows for
the depth of the grade-level standards and practices to be assessed.
ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1 indicators 1a,
1b, 1c, 1d, 1e, 1f, 1g, and 1h. The Mathematical Practices are considered for this indicator as well.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSSO Criteria for High Quality Assessment: Section C - Align to Standards - Mathematics
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Focus in Mathematics
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
Indicator 1c Guiding Question:
Do the assessments include opportunities for students to demonstrate the full intent of
grade-level/course-level standards and practices across the series?
Evidence Collection
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Review assessments and corresponding assessment guidance across the series.
Look f

of grade-level standards and mathematical practices across different assessments,
grades/courses, and series?
● Do the assessments include a variety of item types (e.g., performance tasks, discussion questions,
constructed response questions, project- or problem-based tasks, portfolios, justified multiple choice), and
how are these item types designed to fully develop and measure the intent of grade-level standards and
mathematical practices across different assessments, grades/courses, and series?
● Is there an appropriate balance of complexity in assessment tasks to ensure that students are provided
opportunities to fully engage with and demonstrate the intent of grade-level standards and mathematical
practices?
Gateway 1: Focus & Coherence
Criterion 1.1 Materials assess grade-level content and give all students extensive work with
grade-level problems to meet the full intent of grade-level standards.
Indicator 1d Materials give all students extensive work with grade-level problems to meet
the full intent of grade-level standards.
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Scoring:
4 points
● Materials present all students
with extensive work with
grade-level problems.
AND
● Materials present opportunities
for all students to meet the full
intent of grade-level standards.
2 points
● Materials do not present all
students with extensive work
with grade-level problems.
OR
● Materials do not present
opportunities for all students to
meet the full intent of
grade-level standards.
0 points
● Materials do not present all
students with extensi

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with grade-level problems.
OR
● Materials do not present
opportunities for all students to
meet the full intent of
grade-level standards.
0 points
● Materials do not present all
students with extensive work
with grade-level problems.
AND
● Materials do not present
opportunities for all students to
meet the full intent of
grade-level standards.
About this indicator:
What is the purpose of this Indicator?
Indicators 1a and 1c determine the shift of Focus. This indicator examines if the materials provide all students with
extensive work with grade-level problems, so that all students engage with the full intent of the grade-level
standards.
ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1 indicators 1a,
1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Focus in Mathematics
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
Indicator 1d Guiding Question:
Do the materials give all students extensive work with grade-level problems to meet the full intent of
grade-level standards?
Evidence Collection
Are all grade-level standards present? If not, which ones are not present?
Do the materials engage all students in extensive work with grade-level problems? Iden

standards are affected.
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Gateway 1: Focus & Coherence
Criterion 1.2
Coherence
Each grade’s materials are coherent and consistent with the Standards.
What is the purpose of this Criterion?
In Criterion 2, reviewers consider the coherence of the materials by examining:
● how much of the materials address the major clusters of the grade,
● the connections between major and supporting standards within each grade,
● the connections between two or more clusters in a domain, or two or more domains in a grade, and
● the connections between grade-level standards to prior and future-grade-level standards.
Research Connection
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Scoring:
Meets Expectations
● 7-8 points
Partially Meets Expectations
● 5-6 points
Does Not Meet Expectations
● <5 points
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Gateway 1: Focus & Coherence
Criterion 1.2 Each grade’s materials are coherent and consistent with the Standards.
Indicator 1e When implemented as designed, the majority of the materials focus on the
major clusters of each grade.
Scoring:
2 points
● The materials, when implemented as designed, focus on
the major clusters of the grade.
○ K-2 at least 75%
○ 3-8 at least 65%
0 points
● Less than the majority of the materials,
when im

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ing:
2 points
● The materials, when implemented as designed, focus on
the major clusters of the grade.
○ K-2 at least 75%
○ 3-8 at least 65%
0 points
● Less than the majority of the materials,
when implemented as designed, focus on
the major clusters of the grade.
○ K-2 < 75%
○ 3-8 <65%
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1f, 1g, and 1h, determines the shift of Coherence. This indicator addresses
coherence within the grade level by examining if the majority of the materials focus on the major clusters of the
grade, including connections between major and supporting clusters.
This indicator is informed by the other indicators in Coherence and should be reviewed at the end of Gateway 1.
ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1 indicators 1a,
1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Focus Component 2: Major Clusters of the Grade
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Indicator 1e Guiding Question:
Do at least 75% (Grades K-2) and 65% (Grades 3-8) of the materials, when implemented as d

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Indicator 1e Guiding Question:
Do at least 75% (Grades K-2) and 65% (Grades 3-8) of the materials, when implemented as designed, focus on
the major clusters of the grade?
Evidence Collection
This indicator is informed by the other indicators in Coherence and should be reviewed at the end of Gateway
1. Connections between supporting work and major work should be included in the calculations for different
perspectives.
Collect evidence in the Table provided in the 1c Reviewer Evidence Collection document.
For this indicator, you should consider multiple perspectives when collecting evidence, including:
● Units/chapters (including assessments):
○ List the units/chapters that address the major work of the grade and connections between supporting
and major work.
○ Explain the specific standards/clusters being addressed.
○ What percent of units/chapters address the major work of the grade and connections between
supporting and major work?
○ State the units/chapters included in the numerator and denominator of your calculation.
● Lessons/Activities (including assessments):
○ List the lessons/activities that address the major work of the grade and connections between
supporting and major work.
○ Explain the specific standards/clusters being addressed.
○ What percent of lessons/activities address the major work of the grade and connections between
supporting and major work?
○ State the units/chapters included in the numerator and denominator of your calculation.
● Instructional Time (including assessment

ne (e.g., 60%-64% for grades 3-8) with EdReports staff.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● Review the evidence collected from at least three perspectives. (Chapters/units, lessons, days, minutes,
etc.)
● Which perspective is most representative of the materials? Why?
● Do the materials spend a minimum of 75% for grades K-2 or 65% for grades 3-8 of instructional time on
major work of the grade, including supporting work connected to major work of the grade? Please explain.
● How similar are each reviewer's calculations? If there are differences in calculations between reviewers,
those differences should be clearly evident in reviewers evidence collection documents.
● If the materials spiral concepts and skills within each grade level, please explain how you integrated the
spiraling within your calculations?
● Evidence that reflects difficulty in calculating percentages for the materials should be discussed with
EdReports staff to determine appropriate placement within the grade-level report.
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Gateway 1: Focus & Coherence
Criterion 1.2 Each grade’s materials are coherent and consistent with the Standards.
Indicator 1f Supporting content enhances focus and coherence within the grade
simultaneously by engaging students in the major work of the grade.
Scoring:
2 points
● All connections between
supporting and major work
enhance focus on major work
through explicit use of the
coherence map.
1 point
● Any connections in the
coherence map between
supporting

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g:
2 points
● All connections between
supporting and major work
enhance focus on major work
through explicit use of the
coherence map.
1 point
● Any connections in the
coherence map between
supporting and major work are
entirely absent from the
grade-level materials.
0 points
● Supporting work is treated
separately and does not include
connections to major work.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1e, 1g, and 1h, determines the shift of Coherence. In order to maintain
Coherence, materials should connect mathematics within and across grade levels. Materials should indicate how
learning progresses from previous learning and toward future learning. This indicator addresses one aspect of
coherence - connections within the grade level.
ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1 indicators 1a,
1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Focus Component 2: Major Clusters of the Grade
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Indicator 1f Guiding Questions:
Is supporting work connected to the major

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cus Component 2: Major Clusters of the Grade
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Indicator 1f Guiding Questions:
Is supporting work connected to the major work of the grade?
Is supporting work addressed independently?
Evidence Collection
For connections between supporting standards/clusters and major standards/clusters, please answer the
following questions:
● What connections are made?
● Where are the connections made?
● How are those connections made?
When supporting standards/clusters are not connected to the major standards/clusters of the grade, is the
separation mathematically reasonable?
Mathematically Reasonable:
For this indicator, mathematically reasonable refers to the content of the standards. Not all supporting
standards are intended to connect with the major work of the grade; for example, in Kindergarten, K.G.5 may
not connect to the major work of the grade, and this would be considered mathematically reasonable.
Determining these connections or their absence should be guided by the coherence map, with intentionality
required in linking supporting and major work to ensure alignment and coherence within the grade.
Are there connections between supporting and major standards/clusters of the grade that are entirely absent
from the materials?
Note: A missed connection between supporting and major work standards/clusters is defined as a connection
that is entirely absent from the materials.

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orking with radicals and integer exponents (8.EE.A) anywhere in the materials, then this would be a
missed connection.
Note: Evidence should not include connections from supporting work to major work. Those connections are
addressed in Indicator 1f.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● What connections from major clusters/domains to major clusters/domains of the grade were identified,
and where are those connections located?
● How were the connections made in the materials?
● If connections are entirely absent from the materials, explain/provide an example of what and where that
connection might have occurred as specified in the Coherence Map.
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Gateway 1: Focus & Coherence
Criterion 1.2 Each grade’s materials are coherent and consistent with the Standards.
Indicator 1h Content from future grades is identified and related to grade-level work, and
materials relate grade-level concepts explicitly to prior knowledge from earlier
grades.
Scoring:
2 points
● There are connections from
future grades that are clearly
identified and related to the
current grade-level work.
AND
● Materials make explicit
connections between
grade-level concepts and prior
knowledge from earlier grades.
1 point
● Multiple connections from
future grades are entirely
absent and not related to
grade-level work.
OR
● Materials entirely lack explicit
connections between
grade-level concepts and prior
knowledge from earlier grades.
0 points
● No connections are made
between content from

grade that are entirely absent
from the materials?
Note: A missed connection between supporting and major work standards/clusters is defined as a connection
that is entirely absent from the materials. For example:
● In Grade K, if the materials do not connect classifying shapes into categories (K.MD.3) with counting the
number of shapes in the categories (K.CC.5) anywhere in the materials, then this would be a missed
connection.
● In Grade 7, if the materials do not connect scale drawings (7.G.1) with ratios and proportional relationships
(7.RP.A) anywhere in the materials, then this would be a missed connection.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● What connections between supporting and major standards/clusters of the grade were identified?
● Where were connections of supporting and major standards/clusters of the grade found?
● How were the connections made in the materials?
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Gateway 1: Focus & Coherence
Criterion 1.2 Each grade’s materials are coherent and consistent with the Standards.
Indicator 1g Materials include problems and activities that serve to connect two or more
clusters in a domain or two or more domains in a grade.
Scoring:
2 points
● There are connections from
major work to major work
throughout the grade-level
materials, when appropriate.
1 point
● Multiple appropriate
connections from major work to
major work are entirely absent
from the grade-level materials.
0 points
● There are no connections from
major work to major work
throu

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te.
1 point
● Multiple appropriate
connections from major work to
major work are entirely absent
from the grade-level materials.
0 points
● There are no connections from
major work to major work
throughout the grade-level
materials.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1e, 1f, and 1h, determines the shift of Coherence. In order to maintain
Coherence, materials should connect mathematics within the grade level. Materials should indicate how learning
progresses from previous learning and toward future learning. This indicator addresses connections within the
grade level.
Indicator 1g supports coherence by identifying where materials connect across clusters and/or domains within a
grade. ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1
indicators 1a, 1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Focus Component 2: Major Clusters of the Grade
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Indicator 1g Guiding Question:
Are there connections between major domains and/or clusters?
Evidence Collection
Note: Evi

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Indicator 1g Guiding Question:
Are there connections between major domains and/or clusters?
Evidence Collection
Note: Evidence collection should address connections between clusters and/or domains and not individual
standards.
For connections between major clusters/domains, please answer the following questions:
● What connections are made?
● Where are the connections made?
● Are the connections purposeful and supportive of student learning?
When major to major clusters/domains are not connected, is the separation mathematically reasonable?
Mathematically Reasonable:
For this indicator, mathematically reasonable refers to the content of the clusters/domains, do the connections
enhance the mathematics/support student learning. Not all clusters/domains address content that should be
connected to other clusters/domains.
Are there connections between major to major clusters/domains that are entirely absent from the materials as
indicated by the Coherence Map?
Note: A missed connection is defined as a connection that is entirely absent from the materials. For example:
● In Grade 8, if the materials do not connect understanding and applying the Pythagorean Theorem (8.G.B)
with working with radicals and integer exponents (8.EE.A) anywhere in the materials, then this would be a
missed connection.
Note: Evidence should not include connections from supporting work to major work.

orking with radicals and integer exponents (8.EE.A) anywhere in the materials, then this would be a
missed connection.
Note: Evidence should not include connections from supporting work to major work. Those connections are
addressed in Indicator 1f.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● What connections from major clusters/domains to major clusters/domains of the grade were identified,
and where are those connections located?
● How were the connections made in the materials?
● If connections are entirely absent from the materials, explain/provide an example of what and where that
connection might have occurred as specified in the Coherence Map.
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Gateway 1: Focus & Coherence
Criterion 1.2 Each grade’s materials are coherent and consistent with the Standards.
Indicator 1h Content from future grades is identified and related to grade-level work, and
materials relate grade-level concepts explicitly to prior knowledge from earlier
grades.
Scoring:
2 points
● There are connections from
future grades that are clearly
identified and related to the
current grade-level work.
AND
● Materials make explicit
connections between
grade-level concepts and prior
knowledge from earlier grades.
1 point
● Multiple connections from
future grades are entirely
absent and not related to
grade-level work.
OR
● Materials entirely lack explicit
connections between
grade-level concepts and prior
knowledge from earlier grades.
0 points
● No connections are made
between content from

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ted to
grade-level work.
OR
● Materials entirely lack explicit
connections between
grade-level concepts and prior
knowledge from earlier grades.
0 points
● No connections are made
between content from future
grades and grade-level work.
AND
● No connections are made
between grade-level concepts
and prior knowledge from
earlier grades.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with indicators 1e, 1f, and 1g determines the shift of Coherence. This indicator examines
coherence across grades through identifications of future content related to grade-level work and relations of
grade-level concepts explicitly to prior knowledge from earlier grades.
ALL standards in the CCSSM should be considered throughout evidence collection for Gateway 1 indicators 1a,
1b, 1c, 1d, 1e, 1f, 1g, and 1h.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
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Indicator 1h Guiding Question:
Is content from future grades identified and related to grade-level work?
Do the materials relate grade-level concepts explicitly to prior knowledge from earlier grades?
Evidence Collection
Identify evi

e purpose of this Criterion?
Criterion 1 considers the ways in which the materials for each grade reflect the balances in the Standards and
help students to meet the rigorous expectations by providing students with opportunities to make their own
connections to the mathematics to develop conceptual understanding, procedural skill and fluency, and
application.
Research Connection
● Common Core State Standards Mathematics
● K-8 Publishers’ Criteria for the CCSSM (Summer 2012)
Scoring:
Meets Expectations
● 7-8 points
Partially Meets Expectations
● 5-6 points
Does Not Meet Expectations
● <5 points
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.1 Materials reflect the balances in the Standards and help students meet the
Standards’ rigorous expectations by giving appropriate attention to:
developing students’ conceptual understanding; procedural skill and fluency;
and engaging applications.
Indicator 2a Materials support the intentional development of students’ conceptual
understanding of key mathematical concepts, especially where called for in
specific content standards or clusters.
Scoring:
2 points
● Materials develop conceptual
understanding throughout the
grade level.
AND
● Materials provide opportunities
for students to independently
demonstrate conceptual
understanding throughout the
grade level.
1 point
● Materials do not develop
conceptual understanding
throughout the grade level.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
conceptual unders

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rk to Evaluate Cognitive Complexity in Mathematics Assessments
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Reading: “Principles To Actions”, (NCTM) p. 42-48
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)
● Video: “Building Conceptual Understanding in Mathematics” (NCTM)
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● Video: “Conceptual Understanding Excerpt” (The Hunt Institute)
● Concrete Representational Abstract: Instructional Sequence for Mathematics
Indicator 2a Guiding Questions:
Do the materials develop students’ conceptual understanding?
Do the materials provide opportunities for students to independently demonstrate conceptual understanding
throughout the grade level?
Evidence Collection
Conceptual Understanding is a flexible web of connections and relationships within and between ideas,
interpretations, and images of mathematical concepts that supports students in making sense of the main
ideas of mathematics. Students with conceptual understanding can apply and adapt prior knowledge to new
tasks, beyond solving a single math problem.
Example: In Grade 4, students use their understanding of place value and properties of operations to perform
multi-digit arithmetic.
Note: The use of manipulatives does not necessarily indicate conceptual understanding.

conceptual
understanding throughout the grade?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.1 Materials reflect the balances in the Standards and help students meet the
Standards’ rigorous expectations by giving appropriate attention to:
developing students’ conceptual understanding; procedural skill and fluency;
and engaging applications.
Indicator 2b Materials provide intentional opportunities for students to develop procedural
skills and fluencies, especially where called for in specific content standards
or clusters.
Scoring:
2 points
● Materials develop procedural
skills and fluencies throughout
the grade level.
AND
● Materials provide opportunities
for students to independently
demonstrate procedural skills
and fluencies throughout the
grade level.
1 point
● Materials do not develop
procedural skills and fluencies
throughout the grade level.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
procedural skills and fluencies
throughout the grade level.
0 points
● Materials do not develop
procedural skills and fluencies
throughout the grade level.
AND
● Materials do not provide
opportunities for students to
independently demonstrate
procedural skills and fluencies
throughout the grade level.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2c, and 2d, determines the shift of Rigor.

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rk to Evaluate Cognitive Complexity in Mathematics Assessments
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Reading: “Principles To Actions”, (NCTM) p. 42-48
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
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● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)
● Concrete Representational Abstract: Instructional Sequence for Mathematics
Indicator 2b Guiding Questions:
Do the instructional materials develop students’ procedural skills and fluencies throughout the grade level as
called for in the standards?
Do the instructional materials provide opportunities for students to independently demonstrate procedural
skills and fluencies throughout the grade level?
Evidence Collection
Procedural skill includes knowing how and why an algorithm works.
Fluency includes efficiency, accuracy, flexibility, and appropriate strategy selection.
Procedural skill and fluency may not be addressed in every unit, but should be addressed over the grade,
especially with those standards that explicitly call for fluency.
Collect evidence from each unit that shows how the materials develop procedural skill and fluency and where
students independently demonstrate procedural skill and fluency.
Identify where there are opportunities for students to progress toward fluency and procedural skill interwoven
with students’ developing conceptual understanding.
Note whether the materials include a specific section in units/chapters/less

the balances in the Standards and help students meet the
Standards’ rigorous expectations by giving appropriate attention to:
developing students’ conceptual understanding; procedural skill and fluency;
and engaging applications.
Indicator 2c Materials support the intentional development of students’ ability to utilize
mathematical concepts and skills in engaging applications, especially where
called for in specific content standards or clusters.
Scoring:
2 points
● Materials include multiple
routine and non-routine
applications of the mathematics
throughout the grade level.
AND
● Materials provide opportunities
for students to independently
demonstrate multiple routine
and non-routine applications of
the mathematics throughout the
grade level.
1 point
● Materials do not include multiple
routine and non-routine
applications of the mathematics
throughout the grade level.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
multiple routine and non-routine
applications of the mathematics
throughout the grade level.
0 points
● Materials do not include multiple
routine and non-routine
applications of the mathematics
throughout the grade level.
AND
● Materials do not provide
opportunities for students to
independently demonstrate
multiple routine and non-routine
applications of the mathematics
throughout the grade level.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2b, and 2d, determines the shift of Rigor.

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utine
applications of the mathematics
throughout the grade level.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2b, and 2d, determines the shift of Rigor. Materials should include activities with a
variety of contexts for both routine and non-routine applications. Students should apply mathematical knowledge
in real-world contexts to make meaning of and access the content.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Reading: “Principles To Actions”, (NCTM) p. 42-48
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● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)
● Video: “Building Conceptual Understanding in Mathematics” (NCTM)
● Video: “Conceptual Understanding Excerpt” (The Hunt Institute)
● Concrete Representational Abstract: Instructional Sequence for Mathematics
● Achieve the Core: Situation Types for Operations in Word Problems
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Indicator 2c Guiding Questions:
Do the instructional materials develop students’

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Types for Operations in Word Problems
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Indicator 2c Guiding Questions:
Do the instructional materials develop students’ ability to utilize mathematical concepts and skills in engaging
applications throughout the grade level?
Do the instructional materials provide opportunities for students to independently demonstrate application of
mathematical concepts and skills in real-world contexts throughout the grade level?
Evidence Collection
Application problems often, but not always, present a real-world scenario. Students have opportunities to both
employ a prescribed mathematical strategy and choose their own strategy to find a solution. Example:
students apply knowledge about multiplication (Grade 3) to calculate volume (Grade 5).
Collect evidence of problems/activities that align to the standards/clusters for each grade level that address
application. Note whether the materials include a specific section in units/chapters/lessons, etc. that is
specifically designed for application.
Collect evidence of problems/activities where students independently demonstrate applying mathematics.
Evidence should include students solving problems in a variety of contexts, and students should be able to
make their own assumptions or simplifications in order to model the contexts mathematically.
Routine applications are prescriptive word problems that provide a situation and a question. They have a real
world context, but the problems generally include all necessary (and no extraneous) information.

NS.3
7.EE.3
Grade 8 8.EE.8c
8.F.B
8.G.7
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● How do the materials include multiple routine and non-routine applications throughout each grade?
● How do the materials provide opportunities for students to independently demonstrate multiple routine
and non-routine applications throughout each grade?
● Do the materials have a consistent lesson structure for including multiple routine and non-routine
applications?
● Based on the student-facing materials, how do students independently demonstrate multiple routine and
non-routine applications?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.1 Materials reflect the balances in the Standards and help students meet the
Standards’ rigorous expectations by giving appropriate attention to:
developing students’ conceptual understanding; procedural skill and fluency;
and engaging applications.
Indicator 2d The three aspects of rigor are not always treated together and are not always
treated separately.

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dents’ conceptual understanding; procedural skill and fluency;
and engaging applications.
Indicator 2d The three aspects of rigor are not always treated together and are not always
treated separately. There is a balance of the three aspects of rigor within the
grade as reflected by the standards.
Scoring:
2 points
● All three aspects of rigor are
present independently and
multiple aspects of rigor are
engaged simultaneously to
develop students’ mathematics
understanding of a single
topic/unit of study throughout
each grade level.
0 points
● Multiple aspects of rigor are not
engaged simultaneously to
develop students’ mathematical
understanding of a single
topic/unit of study throughout
each grade level.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2b, and 2c, determines the shift of Rigor. In order to be considered rigorous,
program materials must include a balance of conceptual understanding, procedural skills and fluencies, and
application as reflected in the standards.

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hift of Rigor. In order to be considered rigorous,
program materials must include a balance of conceptual understanding, procedural skills and fluencies, and
application as reflected in the standards. This balance should be evident in all aspects of the grade level to
support students as they develop mathematical understanding.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Reading: “Principles To Actions”, (NCTM) p. 42-48
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)
● Video: “Building Conceptual Understanding in Mathematics” (NCTM)
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● Video: “Conceptual Understanding Excerpt” (The Hunt Institute)
● Concrete Representational Abstract: Instructional Sequence for Mathematics
● Achieve the Core: Situation Types for Operations in Word Problems
Indicator 2d Guiding Question:
Do the instructional materials balance the three aspects of rigor?
Evidence Collection
Review lessons, chapter/unit assessments, and homework assignments.
Look for individual lessons/topics, as well as complete units, that

thematics (CCSSM)
Scoring:
Meets Expectations
● 7-8 points
Partially Meets Expectations
● 4-6 points
Does Not Meet Expectations
● <4 points
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2e Materials support the intentional development of MP1: Make sense of
problems and persevere in solving them, for students, in connection to the
grade-level content standards, as expected by the mathematical practice
standards.
Scoring:
1 point
● There is intentional development of MP1 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP1 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2f, 2g, 2h, 2i, 2j, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present in the form of activities or problems that stimulate
students to develop the habits of mind described in the practice standards. This indicator specifically looks at MP
1 which addresses overarching, mathematical practices.

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es or problems that stimulate
students to develop the habits of mind described in the practice standards. This indicator specifically looks at MP
1 which addresses overarching, mathematical practices. It assesses whether the provided opportunities for
student engagement with the math practices are a) used to enrich the mathematics content of the courses and
and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP1: Make sense of problems and persevere in solving them
● Mathematical Practices Compilation
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Indicator 2e Guiding Questions:
Across the grade level, is MP1 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP1 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP1 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP1 is misleading in the curricular materials (e.g.

, and
● create reflection opportunities.
Check to see if any of the materials address only the Standards for Mathematical Practice (meaning they are
not connected to grade-level mathematical content). Record any instances where the Standards for
Mathematical Practice are not connected to the grade-level mathematics content.
Across the grade level, verify that students use the MP to its full intent (all aspects) within the materials.
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Review all aspects of teacher and student-facing materials. If MP1 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where they are not identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is the MP1 identified and connected to grade-level mathematical content?
● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2f Materials support the intentional development of MP2: Reas

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Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2f Materials support the intentional development of MP2: Reason abstractly and
quantitatively, for students, in connection to the grade-level content standards,
as expected by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP2 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP2 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2g, 2h, 2i, 2j, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards.

---

ar of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP2 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP2: Reason abstractly and quantitatively
● Mathematical Practices Compilation
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Indicator 2f Guiding Questions:
Across the grade level, is MP2 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP2 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP2 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP2 is misleading in the curricular materials (e.g.

ctions between multiple representations.
Check to see if any of the materials address only the Standards for Mathematical Practice (meaning they are
not connected to grade-level mathematical content). Record any instances where the Standards for
Mathematical Practice are not connected to the grade-level mathematics content.
Across the grade level, verify that students use the MP to its full intent (all aspects) within the materials.
Review all aspects of teacher and student-facing materials. If MP2 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where they are not identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
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● When is MP2 identified and connected to grade-level mathematical content?
● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2g Materials support the intentional development of MP3: Construc

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erion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2g Materials support the intentional development of MP3: Construct viable
arguments and critique the reasoning of others, for students, in connection to
the grade-level content standards, as expected by the mathematical practice
standards.
Scoring:
1 point
● There is intentional development of MP3 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP3 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2h, 2i, 2j, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards.

---

ar of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP3 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP3: Construct viable arguments and critique the reasoning of others
● Mathematical Practices Compilation
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Indicator 2g Guiding Questions:
Across the grade level, is MP3 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP3 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP3 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP3 is misleading in the curricular materials (e.g.

ify that students use the MP to its full intent within the materials.
Review all aspects of teacher and student-facing materials. If MP3 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where it is not identified.
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Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP3 identified and connected to grade-level mathematical content?
● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2h Materials support the intentional development of MP4: Model with
mathematics, for students, in connection to the grade-level content standards,
as expected by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP4 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP4 to
meet its full intent in connection to grade-level
content.

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this report cannot be provided, but it can be
downloaded by googling “The GAIMME Report”.)
● Reading: “Math Modeling: Getting Started & Getting Solutions” (A link to this handbook cannot be provided,
but it can be downloaded by googling “SIAM and Moody's modeling handbook”.)
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Indicator 2h Guiding Questions:
Across the grade level, is MP4 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP4 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP4 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP4 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
To check that MP4 is connected to grade-level content and developed to its full intent, look at lessons,
assessments, and any examples/descriptions of anticipated student work that require students to:
MP4
Put the problem or situation in their own words and identify important information in the problem or
situation.
Use the math they know to solve problems and everyday situations.
Model the situation with an appropriate representation and use an appropriate strategy (part-part- whole, bar
model, place value chart, etc.).
Describe what they do with the model(s) and how it relates to the problem situat

ify that students use the MP to its full intent within the materials.
Review all aspects of teacher and student-facing materials. If MP4 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where they are not identified.
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Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP4 identified and connected to grade-level mathematical content?
● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2i Materials support the intentional development of MP5: Use appropriate tools
strategically, for students, in connection to the grade-level content standards,
as expected by the mathematical practice standards.
Scoring:
1 point
● There is intentional
development of MP5 to meet its
full intent in connection to
grade-level content.
0 points
● There is no intentional
development of MP5 to meet its
full intent in connection to
grad

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here is intentional
development of MP5 to meet its
full intent in connection to
grade-level content.
0 points
● There is no intentional
development of MP5 to meet its
full intent in connection to
grade-level content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2j, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP5 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP5: Use appropriate tools strategically
● Mathematical Practices Compilation
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Indicator 2i Guiding Questions:
Across the grade level, is MP5 used to enrich the mathematical content?
Across the grade level, is there inte

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Indicator 2i Guiding Questions:
Across the grade level, is MP5 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP5 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP5 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP5 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
To check that MP5 is connected to grade-level content and developed to its full intent, look at lessons,
assessments, and any examples/descriptions of anticipated student work that require students to:
MP5
Choose appropriate tools and/or strategies that will help develop their mathematical knowledge.
Recognize both the insight to be gained from different tools/strategies and their limitations.
Use technological tools, as appropriate, to explore and deepen their mathematical understanding.
Know how to use a variety of tools, or whether to use tools at all.
Look at teacher directions and how teachers are guided to carry out the lessons so that students are engaged
in the MP.

ify that students use the MP to its full intent within the materials.
Review all aspects of teacher and student-facing materials. If MP5 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where they are not identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is the MP5 identified and connected to grade-level mathematical content?
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● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2j Materials support the intentional development of MP6: Attend to precision, for
students, in connection to the grade-level content standards, as expected by
the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP6 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP6 to
meet its full intent in connection to grade-level
cont

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ntional development of MP6 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP6 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2i, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP6 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP6: Attend to precision
● Mathematical Practices Compilation
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Indicator 2j Guiding Questions:
Across the grade level, is MP6 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP6 t

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Indicator 2j Guiding Questions:
Across the grade level, is MP6 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP6 that reaches the full intent of the MP?
Across the grade level, is the specialized language of mathematics intentionally developed?
Evidence Collection
Look through all teacher and student materials to ensure that MP6 and the specialized language of
mathematics are developed throughout the grade level. This includes, but is not limited to: lessons, unit
overviews, scope and sequence charts, and/or other instructional guides.
Record any instances where MP6 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
Record any instances where the specialized language of mathematics is misleading and/or erroneous in the
curricular materials (e.g. the materials use made up words versus mathematical terminology, the use of
symbols is incorrect or confusing, etc.).
To check that MP6 is connected to grade-level content and is developed to it full intent, look at lessons,
assessments and any examples/descriptions of anticipated student work that require students to:
● communicate using grade-level appropriate vocabulary and conventions,
● formulate clear explanations,
● state the meaning of symbols,
● calculate accurately and efficiently,
● specify units of measure,
● use and label tables, graphs, etc.

MP to its full intent within the materials.
If MP6 is only located in a specific part of the teacher manuals (e.g. the teacher-led portion of the lesson), you
will need to look at other sections (e.g. independent work, homework, assessments) to ensure that the MP is
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intentionally connected to the content. Look where the MP is identified, but also look at places where it is not
identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP6 identified and connected to grade-level mathematical content?
● In what ways do the students use the MP to its full intent across the grade level?
● In what ways is the specialized language of mathematics intentionally developed?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2k Materials support the intentional development of MP7: Look for and make use
of structure, for students, in connection to the grade-level content standards,
as expected by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP7 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP7 to
meet its full intent in connection to grade-level

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intentional development of MP7 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP7 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2i, 2j, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP7 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP7: Look for and make use of structure
● Mathematical Practices Compilation
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Indicator 2k Guiding Questions:
Across the grade level, is MP7 used to enrich the mathematical content?
Across the grade level, is there intentional

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Indicator 2k Guiding Questions:
Across the grade level, is MP7 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP7 that reaches the full intent of the MPs?
Evidence Collection
Look through all teacher and student materials to ensure that MP7 is developed throughout the grade-level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP7 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
To check that MP7 is connected to grade-level content and are developed to their full intent, look at lessons,
assessments, and any examples/descriptions of anticipated student work that require students to:
MP7
Look for patterns or structures to make generalizations and solve problems.
Look for and explain the structure within mathematical representations.
Analyze a problem and look for more than one approach.
Look at and decompose “complicated” into “simpler” things.
Look at teacher directions and how teachers are guided to carry out the lessons so that students are engaged
in the MP.

ify that students use the MP to its full intent within the materials.
Review all aspects of teacher and student-facing materials. If MP7 is only located in a specific part of the
teacher manuals (e.g. the teacher-led portion of the lesson), you will need to look at other sections (e.g.
independent work, homework, assessments) to ensure that the MP is intentionally connected to the content.
Look where the MP is identified, but also look at places where they are not identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP7 identified and connected to grade-level mathematical content?
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● In what ways do the students use the MP to its full intent across the grade level?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?
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Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice.
Indicator 2l Materials support the intentional development of MP8: Look for and express
regularity in repeated reasoning, for students, in connection to the grade-level
content standards, as expected by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP8 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP8 to
meet its full intent in

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oring:
1 point
● There is intentional development of MP8 to meet
its full intent in connection to grade-level content.
0 points
● There is no intentional development of MP8 to
meet its full intent in connection to grade-level
content.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2i, 2j, and 2k, determines the meaningful integration of the Standards for
Mathematical Practice into grade-level learning. Over the course of any given year of instruction, each
mathematical practice standard is meaningfully present through activities or problems that stimulate students to
develop the habits of mind described in the practice standards. This indicator specifically examines MP8 by
determining whether the provided opportunities for student engagement with the practice are: a) connected to
the mathematical content of the grade level, and b) fully developed across the grade level.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● K-8 Publishers' Criteria for the CCSSM (Summer 2012)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for K-8 Mathematics
● Achieve EQuIP Rubric for Lessons & Units
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP8: Look for and express regularity in repeated reasoning
● Mathematical Practices Compilation
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Indicator 2l Guiding Questions:
Across the grade level, is MP8 used to enrich the mathematical content?
A

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Compilation
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Indicator 2l Guiding Questions:
Across the grade level, is MP8 used to enrich the mathematical content?
Across the grade level, is there intentional development of MP8 that reaches the full intent of the MP?
Evidence Collection
Look through all teacher and student materials to ensure that MP8 is developed throughout the grade level.
This includes, but is not limited to: lessons, unit overviews, scope and sequence charts, and/or other
instructional guides.
Record any instances where MP8 is misleading in the curricular materials (e.g. a lesson is marked as aligned to
an MP when only a small part of the lesson addresses the MP).
To check that MP8 is connected to grade-level content and are developed to their full intent, look at lessons,
assessments, and any examples/descriptions of anticipated student work that require students to:
MP8
Notice repeated calculations to understand algorithms and make generalizations or create efficient,
mathematically sound shortcuts.*
Create, describe, explain a general formula, process, method, algorithm, model, etc.
Evaluate the reasonableness of their answers and thinking.
Use repeated reasoning as a tool.
*This is different from mnemonics and “tricks”
Look at teacher directions and how teachers are guided to carry out the lessons so that students are engaged
in the MP.

ular focus on students’ mathematical development, understanding the
instructional approaches of the program and the research-based strategies employed, and improving their own
knowledge of mathematics beyond the grade level. It also aids teachers in understanding the role of standards
in the context of the overall series, and in planning effective instruction by providing appropriate materials and
offering guidance on how caregivers can support student progress and achievement. Lastly, the materials
provide support for interpreting and evaluating student performance throughout the assessment system,
ensuring teachers have the tools they need to assess and respond to student learning needs effectively.
Scoring:
Meets Expectations
● 9-10 points
Partially Meets Expectations
● 5-8 points
Does Not Meet Expectations
● <5 points
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3a Materials provide teacher guidance with useful annotations and suggestions
for how to enact the student materials and ancillary materials, with specific
attention to engaging students to guide their mathematical development.
Scoring:
2 points
● Materials provide
comprehensive guidance that
will assist teachers in
presenting the student and
ancillary materials.
AND
● Materials include sufficient and
useful annotations and
suggestions that are presen

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ights on how to engage with the materials. Such guidance can include tips for differentiating
instruction, addressing diverse learning needs, and integrating ancillary materials to reinforce learning. Ultimately,
it helps teachers optimize the use of the provided resources to improve student mathematical outcomes.
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Indicator 3a Guiding Question:
Do the materials provide teacher guidance with useful annotations and suggestions for how to enact the
student and ancillary materials to support students' mathematical development?
Evidence Collection
In the instructional materials being reviewed:
● Check that the guidance for teachers is clear and detailed, providing explicit instructions on how to use
both the student and ancillary materials effectively.
● Ensure that annotations and suggestions are directly linked to the specific learning objectives. They
should provide context for how instructional strategies support students in achieving these objectives.
● Confirm that the guidance includes ways to integrate ancillary materials seamlessly within lessons to
enhance learning. This might involve cross-referencing with core materials or suggested supplementary
activities.
● Identify practical tips and real-world examples that help teachers implement the materials effectively.

in using the materials effectively.
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3b Materials contain explanations and examples of grade-level/course-level
concepts and/or standards and how the concepts and/or standards align to
other grade/course levels so that teachers can improve their own knowledge
of the subject.
Scoring:
2 points
● Materials contain explanations
and examples of
grade/course-level concepts
and/or standards so that
teachers can improve their own
knowledge of the subject.
AND
● Materials contain explanations
and examples of how the
concepts and/or standards align
to other grade/course levels so
that teachers can improve their
own knowledge of the subject.
1 point
● Materials contain explanations
and examples of
grade/course-level concepts
and/or standards so that
teachers can improve their own
knowledge of the subject.
OR
● Materials contain explanations
and examples of how the
concepts and/or standards align
to other grade/course levels so
that teachers can improve their
own knowledge of the subject.
0 points
● Materials do not contain
explanations and examples of
grade/course-level concepts
and/or standards so that
teachers can improve their own
knowledge of the subject.
AND
● Materials do not contain
explanations and examples of
how the concepts and/or
standards align to other
grade/course

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or standards so that
teachers can improve their own
knowledge of the subject.
AND
● Materials do not contain
explanations and examples of
how the concepts and/or
standards align to other
grade/course levels so that
teachers can improve their own
knowledge of the subject.
About this indicator:
What is the purpose of this Indicator?
This indicator examines whether materials deepen teacher understanding of mathematics standards and
concepts that are specific to each grade level. It also aims to show how these concepts and standards align with
those taught in other grades or courses. By offering this information, the materials support teachers in deepening
their understanding of the subject matter they are teaching, facilitating more effective instruction. This alignment
helps educators see the progression of learning objectives and how current content builds on prior knowledge
while preparing students for future learning. Ultimately, it aids teachers in delivering more cohesive and informed
instruction, benefiting student learning outcomes.
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Indicator 3b Guiding Question:
Do the materials contain adult-level explanations and examples of the more complex grade/course-level
concepts and concepts beyond the current course so that teachers can improve their own knowledge of the
subject?
Evidence Collection
In the instructional materials being reviewed:
● Ensure that explanations of grade-or course-level concepts and standards are thorough, clear, and
accessible.

as charts, diagrams, or flowcharts, to help
illustrate how concepts and standards are connected across grade levels.
● Discuss whether the materials highlight connections between the subject's concepts and standards and
those of other subjects, fostering interdisciplinary learning.
● Discuss whether there are insights or annotations aimed explicitly at teachers that explain the rationale
behind the concepts and standards and how they fit into the broader curriculum.
● Discuss whether there are suggestions or links to professional development resources that can further
enhance teachers' understanding of subject matter progression.
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3c Materials include a year-long scope and sequence with standards correlation
information.
Scoring:
1 point
● Materials include a year-long scope and sequence
with standard correlation information.
0 points
● Materials do not include a year-long scope and
sequence with standard correlation information.
About this indicator:
What is the purpose of this Indicator?
This indicator examines whether materials contain a standards correlation information document, which maps or
aligns the content and activities within the materials to specific Mathematics Common Core State Standards.

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amines whether materials contain a standards correlation information document, which maps or
aligns the content and activities within the materials to specific Mathematics Common Core State Standards. This
document serves as a resource for teachers to quickly identify how and where the material addresses particular
standards, enabling better planning and instruction. It helps ensure that teaching is aligned with required
educational benchmarks and offers transparency on how the materials support meeting those standards.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
Indicator 3c Guiding Question:
Do the materials include a year-long scope and sequence with standards correlation information?
Evidence Collection
In the instructional materials being reviewed:
● Consider how teacher materials provide documentation that addresses how individual units, lessons, or
activities throughout the series are aligned to mathematical concepts and practices (Common Core
Mathematics Standards), as applicable.
● Ensure that the correlation document covers all relevant mathematics standards for the entire grade level
or series, including content and practice standards.
● Check if there is a clear and direct alignment between the material's content and the specific mathematics
standards.

tunities for
parents and caregivers to provide feedback or ask questions, fostering ongoing communication and
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engagement.
● Discuss whether the materials offer tailored support or resources for parents and caregivers based on
various student needs, recognizing that each child may require different levels of support.
● Discuss whether the materials direct parents and caregivers to additional resources, support, or
community programs that can further assist student learning and development.
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3e Materials explain the program’s instructional approaches, identify
research-based strategies, and explain the role of the standards.
Scoring:
2 points
● Materials explain the
instructional approaches of
the program.
AND
● Materials include and
reference research-based
strategies.
AND
● Materials include and
reference the role of the
standards in the program.
1 point
● Materials explain the instructional
approaches of the program.
OR
● Materials include and reference
research-based strategies.
OR
● Materials include and reference
the role of the standards in the
program.
0 points
● Materials do not explain the
instructional approaches of the
program.
AND
● Materials do not include and
reference researc

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tor highlights the role of the
standards, explaining how the program aligns with and supports these benchmarks to meet educational goals
and ensure consistency across different instructional settings. This transparency helps educators understand the
rationale behind the teaching methods and how they contribute to achieving desired learning outcomes, thereby
enhancing instructional fidelity and effectiveness.
Indicator 3e Guiding Question:
Do the materials provide explanations of the instructional approaches of the program, identification of the
research-based strategies, and reference the role of the standards in the program?
Evidence Collection
In the instructional materials being reviewed:
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● Ensure that the materials clearly outline the instructional approaches used within the program, providing
a comprehensive overview of how these methods guide teaching and learning activities.
● Check for detailed descriptions of how these approaches are implemented in various lessons and
activities, helping educators visualize their practical application.
● Look for explicit references to research-based strategies, including citations of studies or educational
research that support the effectiveness of the strategies employed.
● Assess whether the materials explain the reasoning behind choosing specific strategies, illustrating how
they are designed to enhance learning outcomes and support evidence-based teaching practices.
● Confirm that the materials clearly explain how the program aligns with educatio

aches used within the program,
providing a comprehensive overview of how these methods guide teaching and learning activities.
● Discuss whether there are detailed descriptions of how these instructional approaches are implemented
in various lessons and activities to help educators visualize their practical application.
● Discuss whether the materials include explicit references to research-based strategies, along with
citations of studies or educational research that support the effectiveness of the strategies employed.
● Discuss whether the materials explain the reasoning behind choosing specific strategies, illustrating how
they are designed to enhance learning outcomes and support evidence-based teaching practices.
● Discuss whether the materials clearly explain how the program aligns with educational standards, such
as state, national, or Common Core standards, highlighting their role in shaping the curriculum.
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3f Materials provide a comprehensive list of supplies needed to support
instructional activities.
Scoring:
1 point
● Materials include a comprehensive list of supplies
needed to support the instructional activities.
0 points
● Materials do not include a comprehensive list of
supplies needed to support instructional activities.
About this indicator:
What is

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supplies
needed to support the instructional activities.
0 points
● Materials do not include a comprehensive list of
supplies needed to support instructional activities.
About this indicator:
What is the purpose of this Indicator?
This indicator examines if the materials include a thorough and detailed list of all supplies and resources required
to support the instructional activities in a program. This comprehensive list allows teachers to effectively plan and
prepare for lessons by ensuring they have all necessary materials available for successful implementation. By
clearly identifying what is needed, educators can minimize disruptions, manage their time efficiently, and create a
conducive learning environment. Ultimately, this clarity supports smoother lesson delivery and enhances the
overall effectiveness of the instructional activities.
Indicator 3f Guiding Question:
Do the materials provide a comprehensive list of supplies needed to support instructional activities?
Evidence Collection
In the instructional materials being reviewed:
● Ensure that the list covers all materials and supplies needed for each activity within the program.

eachers can quickly find and gather materials.
● Discuss whether you can identify which materials are consumable (need to be replaced after use) and
which are reusable (can be used across multiple lessons or years), to support teachers in planning for
future lessons.
● Discuss whether both digital resources (software, online tools) and physical supplies are included, with
clear indications of what is required for digital learning environments, if applicable.
● Discuss whether there are suggested alternatives or substitutions for the materials listed to accommodate
different teaching environments or available resources, adding flexibility for teachers.
● Discuss whether each item in the supply list directly aligns with and support specific instructional
objectives and activities, ensuring relevance and purpose.
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Gateway 3: Teacher and Student Supports
Criterion 3.1 Materials include opportunities for teachers to effectively plan and utilize
materials with integrity and to further develop their own understanding of the
content.
Indicator 3g The assessment system provides consistent opportunities to determine
student learning throughout the school year.

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integrity and to further develop their own understanding of the
content.
Indicator 3g The assessment system provides consistent opportunities to determine
student learning throughout the school year. The assessment system
provides sufficient teacher guidance for evaluating student performance and
determining instructional next steps.
Scoring:
2 points
● The assessment system
provides opportunities to
determine student learning
throughout the school year.
AND
● The assessment system
provides sufficient teacher
guidance for evaluating
student performance.
AND
● The assessment system
provides sufficient teacher
guidance for interpreting
student performance and
determining next instructional
steps.
1 point
● The assessment system
provides opportunities to
determine student learning
throughout the school year, but
not consistently.
OR
● The assessment system
provides sufficient teacher
guidance for evaluating
student performance, but not
consistently.
OR
● The assessment system
provides sufficient teacher
guidance for interpreting
student performance and
determining next instructional
steps, but not consistently.
0 points
● The assessment system does
not provide opportunities to
determine student learning
throughout the school year.
AND
● The assessment system does
not provide sufficient teacher
guidance for evaluating
student performance.
AND
● The assessment system does
not provide sufficient teacher
guidance for interpreting
student performance and
determining next instructional
steps.
About this indicator:
What is the purpose of this Indicator?
This indicator examines wheth

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de sufficient teacher
guidance for interpreting
student performance and
determining next instructional
steps.
About this indicator:
What is the purpose of this Indicator?
This indicator examines whether the assessment system within materials offers regular and consistent
opportunities to evaluate student learning progress throughout the school year. It emphasizes the importance of
a well-structured assessment system that not only tracks student performance consistently over time but also
provides teachers with clear guidance on how to interpret assessment results. This includes offering insights on
evaluating student understanding and making informed decisions about instructional next steps. By doing so,
teachers identify areas where students may need additional support or enrichment, allowing for timely
interventions and personalized learning pathways that enhance student growth and achievement.
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Indicator 3g Guiding Question:
Does the assessment system provide consistent opportunities to determine student learning throughout the
school year, sufficient teacher guidance for evaluating student performance, and sufficient teacher guidance
for determining instructional next steps?
Evidence Collection
Note: this indicator looks at the assessment system as a whole and how all of the types of assessments in a
program work together to show student progress toward mastery and provide guidance to teachers about
how to adjust instruction.

regular and active participation in grade-level/grade-band/series
content.
What is the purpose of this Criterion?
This criterion examines how materials provide student supports throughout the program. It considers
how the materials are designed to provide appropriate support and accommodations for students with
diverse learning needs, ensuring their regular and active participation in learning mathematics. It also
examines whether materials should offer extensions for advanced students, allowing them to engage
with mathematical concepts at a greater depth. Additionally, this criterion looks at whether materials
provide opportunities for teachers to employ a variety of grouping strategies and include varied
opportunities for students to share their thinking. Furthermore, this criterion considers whether materials
ensure a range of representation of people, leveraging the diverse cultural and social backgrounds of
students to enrich the educational experience and foster an inclusive learning environment.
Scoring:
Meets Expectations
● 6 points
Partially Meets Expectations
● 4-5 points
Does Not Meet Expectations
● <4 points
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Gateway 3: Teacher and Student Supports
Criterion 3.2 Materials are designed for each student’s regular and active participation in
grade-level/grade-band/series content.
Indicator 3j Materials provide strategies and support for students in special populations to
work with grade-level content and meet or exceed grade-level standards,
which support their regular and active parti

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ing targeted support and resources, the materials
facilitate regular and active participation in learning for all students, helping them to overcome barriers and
achieve success alongside their peers. This approach fosters an inclusive learning environment that recognizes
and accommodates diverse learning needs and styles.
Resources:
● Supporting Special Populations, Office of Elementary and Secondary Education
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Indicator 3j Guiding Question:
Do materials provide strategies, supports, and resources for students in special populations to support their
active participation in grade-level mathematics work?
Evidence Collection
● Ensure the materials include specific strategies for differentiating instruction to meet the diverse needs of
students in special populations. These strategies should be adaptable to individual learning styles and
needs.
● Check if the materials provide scaffolding strategies, such as breaking down mathematical tasks into
manageable steps, using visual models or manipulatives, or offering guiding questions and prompts to
support students in building their understanding and skills.
● Check if the materials incorporate strategies to support the social-emotional needs of students in special
populations, fostering a positive learning environment and encouraging participation.
● Assess whether there are opportunities for cooperative learning where students can work in diverse
groups to enhance peer support and learning through interaction.
● Confirm that the materials include co

professional development resources if applicable.
● Discuss whether there are tools and resources for monitoring the progress of students in special
populations, allowing teachers to assess effectiveness and adjust strategies as needed.
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Gateway 3: Teacher and Student Supports
Criterion 3.2 Materials are designed for each student’s regular and active participation in
grade-level/grade-band/series content.
Indicator 3k Materials regularly provide extensions and/or opportunities for advanced
students to engage with grade-level/course-level mathematics at greater
depth.
Scoring:
2 points
● Materials regularly provide
multiple extensions and/or
opportunities for advanced
students to engage with
grade-level/course-level
mathematics at greater depth.
AND
● There are no instances of
advanced students doing more
assignments than their
classmates.
1 point
● Materials regularly provide
multiple extensions and/or
opportunities for advanced
students to engage with
grade-level/course-level
mathematics at greater
depth.
OR
● There are some instances of
advanced students doing more
assignments than their
classmates.
0 points
● Materials provide few, if any,
opportunities for advanced
students to engage with
grade-level/course-level
mathematics at greater depth.
AND
● There are instances of
advanced students doing more
assignments than their
classmates.
About this indicator:
What is the purpose of this Indicator?
This indicator considers whether materials include strategies and support designed to help student

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more
assignments than their
classmates.
About this indicator:
What is the purpose of this Indicator?
This indicator considers whether materials include strategies and support designed to help students in special
populations, such as students with exceptional needs and those requiring additional learning support, to access
and engage with grade-level content. This indicator aims to promote equity by ensuring that materials enable all
students to meet or exceed grade-level standards. By providing targeted support and resources, the materials
facilitate regular and active participation in learning for all students, helping them to overcome barriers and
achieve success alongside their peers. This approach fosters an inclusive learning environment that recognizes
and accommodates diverse learning needs and styles.
Resources:
Supporting Special Populations, Office of Elementary and Secondary Education
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Indicator 3k Guiding Question:
Do the materials regularly provide extensions for students who are above grade level to engage with
mathematical content and concepts at greater depth?
Evidence Collection
In the instructional materials being reviewed:
● Ensure there are activities that allow advanced students to explore grade-level content at a deeper
level, encouraging higher-order thinking skills such as analysis, synthesis, and evaluation.
● Look for tasks that are more complex rather than just more of the same work.
● Check for enrichment activities that extend mathematical content in meaningful way

Evidence Collection
Review teacher and student materials across the series.
Look for and record evidence to:
● Identify strategies to engage students in reading and accessing grade-level mathematics. Note: strategies
and supports for engaging students in MP1, Make sense and persevere in solving problems and MP6,
Attending to precision in language can also be noted here.
● Identify multiple entry points that present a variety of representations to help struggling readers to access
and engage in grade-level mathematics.
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Cluster Meeting
Discuss and answer the following questions to support consensus scoring conversations:
● How and where do the materials include specific supports or strategies to support students who read
below grade level to engage with grade-level mathematics?
● How and where do the materials scaffold vocabulary or concepts to support readers below grade level?
● How and where do the materials use a variety of representations to engage students with grade-level
content?
● Do materials include “just-right” pre-reading activities that offer visuals and other types of support and
scaffolds for building essential and pertinent background knowledge on new or unfamiliar themes/ topics?
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Gateway 3: Teacher and Student Supports
Criterion 3.2 Materials are designed for each student’s regular and active participation in
grade-level/grade-band/series content.
Indicator 3q Manipulatives, both virtual and phys

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nd Student Supports
Criterion 3.2 Materials are designed for each student’s regular and active participation in
grade-level/grade-band/series content.
Indicator 3q Manipulatives, both virtual and physical, are accurate representations of the
mathematical objects they represent and, when appropriate, are connected
to written methods.
Scoring:
2 points
● Manipulatives are accurate
representations of mathematical
objects and are connected to
written methods.
1 point
● Manipulatives are accurate
representations of mathematical
objects.
OR
● Manipulatives are connected to
written methods.
0 points
● Manipulatives are not accurate
representations of mathematical
objects and are not connected
to written methods.
About this indicator:
What is the purpose of this Indicator?
This indicator determines how materials include manipulatives to support and represent mathematical objects,
and connect to grade-level written methods.
Indicator 3q Guiding Question:
Are manipulatives, both virtual and physical, accurate representations of the mathematical objects they
represent and, when appropriate, are connected to written methods?
Evidence Collection
Review teacher and student materials across the series.
Look for and record evidence to:
● Identify the use of physical and/or virtual manipulatives.