EdReports math HS

Indicator 1a.i Materials focus on the high school standards.
1a.i. Materials attend to the full intent of the mathematical content contained in
the high school standards for all students.
Scoring:
Notes: The parts of the materials that teachers complete can be used as evidence of attending to the full
intent of the standards for this indicator. If students do not have the opportunity to attend to standards, or
aspects of them, independently but teachers do, then the materials would be attending to the full intent of the
standards for this indicator but not giving students the opportunity to fully learn the standard, which is 1bii.
4 points
● All aspects of all non-plus
standards are addressed by
the instructional materials of
the series with only a few
instances of exception.
2 points
● More than a few aspects of the
non-plus standards have not
been completely addressed by
the instructional materials of
the series.
AND/OR
● Some non-plus standards have
been entirely omitted from the
instructional materials of the
series.
0 points
● Many aspects of the non-plus
standards have not been
completely addressed by the
instructional materials of the
series.
AND/OR
● Many non-plus standards have
been entirely omitted from the
instructional materials of the
series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with the other indicators of Gateway 1, determines the shifts of focus and coherence. This
indicator attends to the shift of focus by specifically examining those standards which do not have a plus (+)
symbol (non-plus standards), and in the case of non-plus standards labeled as opportunities for modeling, this
indicator examines only the content of those non-plus standards. This indicator attends to the shift of coherence
by analyzing non-plus standards across a high school series to determine if the materials limit the aspects (see
below) of non-plus standards that are addressed.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units

● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
Indicator 1a.i Guiding Questions:
Do the materials attend to the full intent (all aspects) of the non-plus high school standards? In other words,
are all aspects of all non-plus standards present?
Evidence Collection
Review the HS CCSSM to become familiar with the non-plus standards and clusters.
For each course in the series, note what aspects of non-plus standards are addressed through any
instructional materials provided, including assessments.
Aspects could include, but are not limited to:
● types of mathematical objects (equation, expression, inequality, systems);
● types of numbers;
● families of functions/equations/inequalities (polynomial, exponential, logarithmic, rational, etc.);
● tools used (paper and pencil, graphing calculators, software, etc.);
● actions required by the teacher (see Notes in Scoring section); and
● actions required of students (see Notes in Scoring section).
For the series, determine if each aspect of the non-plus standards is completely addressed through any
instructional materials provided, including assessments.
For the series, note entire non-plus standards that are not addressed or aspects of non-plus standards that
are not addressed, examples include:
● If a series only offered opportunities with the cluster A-CED that involved mathematical objects from
linear or quadratic families, then the series would not be attending to the full intent of the mathematical
content contained in the cluster A-CED.
● If a series included opportunities addressing A-REI.11 for students to work with linear functions and not
the other function types listed, then the series would not be attending to the full intent of the standard.
● A-SSE.3 states “Choose and produce an equivalent form of an expression…” The series would not meet
the full intent of the standard if students are required to produce equivalent forms without ever having a
choice as to which equivalent form. That is, if students are always directed to produce a specific
equivalent form (e.g. “Rewrite in factored form”) and they are never allowed choice (e.g. “Rewrite in an
equivalent form that reveals the zeros of the function.”), then the series does not meet the full intent of
the standard.
Cluster Meeting
Have all aspects of the non-plus standards been addressed through any instructional materials provided,
including assessments, by the series?
● If yes, be sure to have evidence of where various aspects of different standards are addressed.

● If no, be sure to have evidence of which non-plus standards are omitted or which aspects of non-plus
standards are not fully addressed.
Are there any courses in the series that excel in addressing this indicator?
Are there any courses in the series that do not address this indicator as well as the others?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p. 57 of CCSSM).

Indicator 1a.ii Materials focus on the high school standards.
1a.ii. Materials attend to the full intent of the modeling process when applied
to the modeling standards.
Scoring:
2 points
● The full intent of the modeling
process is used to address all,
or nearly all, of the modeling
standards by the instructional
materials of the series.
OR
● Materials intentionally develop
the full intent of the modeling
process throughout the series
leading to culminating
experiences that address all, or
nearly all, of the modeling
standards.
1 point
● Various aspects of the
modeling process are present
in isolation or combinations,
yet opportunities for the
complete modeling process
are absent for the modeling
standards throughout the
instructional materials of the
series.
AND/OR
● The full intent of the modeling
process has not been used to
address more than a few
modeling standards by the
instructional materials of the
series.
AND/OR
● The full intent of the modeling
process has been omitted for
more than a few modeling
standards by the instructional
materials of the series.
0 points
● Some aspects of the modeling
process are altogether missing
from the instructional materials
of the series.
AND/OR
● The full intent of the modeling
process has not been used to
address many of the modeling
standards by the instructional
materials of the series.
AND/OR
● The full intent of the modeling
process has been omitted for
most of the modeling
standards by the instructional
materials of the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with the other indicators of Gateway 1, determines the shifts of focus and coherence. This
indicator attends to the shift of focus by specifically examining the use of the modeling process with those
standards that have a star symbol but do not have a plus (+) symbol (modeling standards). This indicator attends
to the shift of coherence by analyzing the use of the modeling process with the modeling standards across a

high school series to determine if the materials limit any of the aspects (see below) of the standards in which the
modeling process is used.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Review the progressions document “Modeling, High School”.
● Review “How to Identify Tasks that Engage Students in Mathematical Modeling NCTM-SIAM Committee on
Modeling Across the Curriculum”
● “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”.)
Indicator 1a.ii Guiding Question:
Do the instructional materials attend to the full intent of the modeling process when applied to the modeling
standards?
Evidence Collection
Review the tables of content for both the student and teacher materials, any standards-alignment
information in the materials, and any scope and sequence information provided by the publisher to establish
a foundation of where and how often the modeling standards are addressed.
Review all instructional materials provided, including assessments. For each course in the series, note where
modeling standards are being addressed with the full intent of the modeling process.
Note where modeling standards are being addressed with certain aspects of the modeling process, but not
the full modeling process.
Aspects could include, but are not limited to:
● variable identification;
● approximation of quantities, shapes, behaviors, etc.;
● formulation of models (e.g. geometric, graphical, tabular, algebraic, statistical representations);

● analysis of relationships;
● interpretation of results in the context of the situation;
● validation of conclusions in light of the context;
● revision of models as needed;
● communication of results
● summarization of conclusions, assumptions, and methods; and
● tools used (paper and pencil, graphing calculators, software, etc.).
For the series, note modeling standards that are not addressed with the modeling process and/or aspects of
the modeling process.
The following examples are for illustrative purpose only:
● If the materials regularly direct students to the choice of variables to be used, then the materials do not
attend to the full intent of the modeling process.
● If the materials provide the model or dictate the type of model students should use, then the materials
do not attend to the full intent of the modeling process.
● If the materials dictate what conclusions should be made, then the materials do not attend to the full
intent of the modeling process.
● If the materials do not allow for students to reflect on the appropriateness of results in light of the
context and/or make adaptations to the model, then the materials do not attend to the full intent of the
modeling process.
● If modeling problems are included such that the mathematics students will use is clearly evident, then
the materials do not attend to the full intent of the modeling process. For example, a modeling problem
that requires using quadratic equations or functions is placed at the end of a chapter or lesson on
quadratic equations.
Cluster Meeting
Are individual aspects of the modeling process found in the materials? Do the materials focus on isolated
aspects in order to build up to the fullness of the modeling process? If so, do the materials allow for multiple,
culminating opportunities for students to employ the fullness of the modeling process?
● If yes, document which aspects, or combination of aspects, of the modeling process are found. Provide
evidence of how the materials allow students to grow in the modeling process.
● If no, provide evidence for when different aspects of the modeling process are found in isolation or are
completely omitted.
Has the full intent of the modeling process through any instructional materials provided, including
assessments, been addressed?
● If yes, provide evidence of where the materials provide opportunities for students to employ the full
modeling process.
● If no, provide evidence of where the materials interrupt the modeling cycle. Specify which aspects of
the modeling process are addressed and which aspects are neglected.
Are there any modeling standards, clusters, domains, or conceptual categories that are addressed without
the full intent of the modeling process?
Do the materials allow for growth and sophistication with modeling as specified in the progression
documents?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p. 57 of CCSSM).

Indicator 1b.i Materials provide students with opportunities to work with all high school
standards and do not distract students with prerequisite or additional topics
that do not support the high school standards.
1b.i. Materials, when used as designed, allow students to spend the majority
of their time on the content from CCSSM widely applicable as prerequisites
for a range of college majors, postsecondary programs, and careers.
Scoring:
2 points
● Evidence clearly describes how the materials for
the SERIES, when used as designed, allows
students to spend the majority of their time (>50%)
on the content widely applicable as prerequisites
(WAPs) for a range of college majors,
postsecondary programs, and careers.
0 points
● The SERIES does not spend a majority of time on
the WAPs, and the majority of the remaining
materials address prerequisites or additional
topics that are distracting.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with the other indicators of Gateway 1, determines the shifts of focus and coherence. This
indicator attends to the shift of focus by specifically examining if a majority of the instructional materials are
designed to engage students in content from the CCSSM widely applicable as prerequisites for a range of
college majors, postsecondary programs, and careers. This indicator attends to the shift of coherence because
much of the content from the CCSSM widely applicable as prerequisites for opportunities after high school not
only spans multiple courses at the high school level but also incorporates the application of key takeaways from
grades 6 through 8.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map

● Institute for Mathematics Education Progressions Documents
● Review Table 1 on page 8 of High School Publishers' Criteria for the Common Core State Standards for
Mathematics (Spring 2013) to become familiar with the content from the CCSSM widely applicable as
prerequisites for a range of college majors, postsecondary programs, and careers (WAPs).
Indicator 1b.i Guiding Question:
Do the materials, when used as designed, focus on the Widely Applicable as Prerequisites (WAPs) for a range
of college majors, postsecondary programs, and careers?
Evidence Collection
Review all instructional materials provided, including assessments. For each course in the series, document
how often the WAPs are addressed through any instructional materials provided, including assessments.
For each course in the series, document how often prerequisite or additional topics are included in a way that
distracts students from the WAPs or non-plus standards. When noting a distraction, reviewers should clearly
describe how the prerequisite or additional topics are drawing students’ learning away from the WAPs or
non-plus standards.
The following examples are non-conclusive guides for illustrative purpose only:
● In a first-year high school course, numerous activities, lessons, or chapters that merely review content
standards from grades 6 through 8 could be distracting, prerequisite topics.
● A unit or chapter addressing the concept of limits and the skills associated with calculating limits could
be a distracting additional topic.
● A unit on fractals or tessellations where the CCSSM are not intertwined would be considered an
additional, distracting topic if the unit does not strengthen, support, or introduce CCSSM.
For the series, analyze how often the WAPs are addressed by the instructional materials, including
assessments.
Analysis of how often the materials focus on WAPs could include, but is not limited to:
● amount of instructional materials, including assessment items, aligned to the WAPs;
● amount of instructional materials, not including assessment items, aligned to the WAPs; and
● amount of instructional materials that include distracting prerequisite or additional topics.
Cluster Meeting
Do a majority of the materials in the series, when used as designed, engage students in the WAPs?
● If yes, be able to clearly explain what evidence has been collected and how the evidence justifies your
conclusion.
● If no, be able to clearly justify with evidence how the materials fall short of having a majority. Evidence
could include how the materials might be supplemented to achieve a majority.
Do the materials in the series, when used as designed, distract students with prerequisite or additional topics?
In what ways might topics that align to standards from grades 6 through 8 or the plus standards not be
considered distracting, prerequisite, or additional?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p. 57 of CCSSM).

Indicator 1b.ii Materials provide students with opportunities to work with all high school
standards and do not distract students with prerequisite or additional topics.
1b.ii. Materials, when used as designed, allow students to fully learn each
standard.
Scoring:
4 points
● Evidence clearly describes how
the materials for the series,
when used as designed,
enable students to fully learn
all or most of the non-plus
standards.
2 points
● Materials for the series, when
used as designed, do not
enable students to fully learn
some of the non-plus
standards.
0 points
● Materials for the series, when
used as designed, do not
enable students to fully learn
most of the non-plus standards.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with the other indicators of Gateway 1, determines the shifts of focus and coherence. This
indicator attends to the shift of focus by examining the non-plus standards. This indicator attends to the shift of
coherence by determining if the materials of a series, when used as designed, enable all students to fully learn
every aspect of each non-plus standard.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
Indicator 1b.ii Guiding Question:
Do the materials, when used as designed, allow students to fully learn each non-plus standard?

Evidence Collection
Review the HS CCSSM to become familiar with the non-plus standards and clusters.
Review the tables of contents for both the student and teacher editions, any standards-alignment information
in the materials, and any scope and sequence information provided by the publisher to establish a foundation
of where and how often the non-plus standards are addressed.
Review chapters, lessons, activities, and assessments throughout the series to verify any standards-alignment
information in the materials or given by the publishers.
For each course in the series, reviewers should note what aspects, how often those aspects, and in what
ways those aspects of non-plus standards are addressed through any instructional materials provided,
including assessments.
Aspects could include, but are not limited to:
● types of mathematical objects (equation, expression, inequality);
● types of numbers;
● families of mathematical objects (polynomial, exponential, logarithmic, rational, etc.); and
● tools used (paper and pencil, graphing calculators, software, etc.).
For the series, reviewers should examine all provided materials to document when STUDENTS are provided
with sufficient opportunities to fully learn a non-plus standard, paying careful attention to each aspect of the
standard.
● For example, if students are given numerous opportunities to decide if two figures are similar by using
the definition of similarity in terms of transformations, articulate the transformations required to show the
similarity, and explain the meaning of similarity- all verified with formative assessments and given further
opportunities if needed- then the materials allow students to fully learn standard G-SRT.2.
For the series, reviewers should document when aspects of non-plus standards are addressed on limited
occasions through any instructional materials provided, including assessments.
The following examples are non-conclusive guides for illustrative purpose only:
● If the materials provide only one lesson where students use function notation, then the materials do not
allow students to fully learn F-IF.2.
● If students are required to explain each step in solving a simple equation a limited number of times within
the series, then the materials do not allow students to fully learn A-REI.1.
● If students only calculate average rate of change of linear functions and all other aspects of F-IF.6 are
addressed, then the materials do not allow students to fully learn F-IF.6.
● If materials provide limited exercises for students to practice a standard, then the materials do not allow
students to fully learn the standard.
For the series, reviewers should consider the numbers, equation types, contexts, etc. that students should
encounter as indicated by the non-plus standards. The following examples are non-conclusive guides for
illustrative purpose only:
● If students solve systems of linear equations only with equations in slope-intercept form, then the
materials do not allow students to fully learn A-REI.6.

● If students only factor quadratics with a leading coefficient of 1, then the materials do not allow students
to fully learn A-SSE.3 or A-APR.3.
For the series, reviewers should note where the materials employ formative assessments to help teachers
and students know if students are ready to move on or if students require more work on non-plus standards.
When this occurs, document how teachers and students will know what to do in order to fully learn non-plus
standards.
Cluster Meeting
Do the materials, when used as designed, enable students to fully learn each non-plus standard?
● If yes, be able to clearly describe the various ways in which the materials enable all students to learn all
of the aspects of the non-plus standards.
● If no, be able to clearly describe what characteristics the series is missing and how those characteristics
would inhibit students from fully learning each non-plus standard.
If the series has not enabled all students to fully learn each non-plus standard, then what are the specific
characteristics (for example, limited opportunities for practice, extensive scaffolding, etc.) that the series is
missing?
Do the available materials provide ample opportunity for students to demonstrate that they have mastered
the standard by the end of the series?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p.57 of CCSSM).

Indicator 1c Materials require students to engage in high school mathematics by focusing
on problem contexts and attending to various types of real numbers.
Scoring:
2 points
● Materials regularly use
contexts appropriate for high
school students, use various
types of real numbers, and
provide opportunities for
students to apply key
takeaways from grades 6-8.
1 point
● Materials regularly use
contexts appropriate for high
school students and apply key
takeaways from grades 6-8, yet
do not vary the types of real
numbers being used.
AND/OR
● Materials regularly use various
types of real numbers and
apply key takeaways from
grades 6-8, yet do not use
contexts appropriate for high
school students.
AND/OR
● Materials regularly use
contexts appropriate for high
school students and vary the
types of real numbers being
used, yet some of the key
takeaways from grades 6-8 are
not applied.
0 points
● Materials regularly do not use
contexts appropriate for high
school students or vary the
types of real numbers being
used.
AND/OR
● Materials do not apply most of
the key takeaways from grades
6-8.
About this indicator:
What is the purpose of this Indicator?
This indicator supports the shifts of Focus and Coherence. This indicator examines the materials to determine if
students are given extensive opportunities to work with course-level problems and exercises appropriate to high
school and relates new concepts to students’ prior skills and knowledge.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics

● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Review the far right column in Table 1 on page 8 of High School Publishers' Criteria for the Common Core
State Standards for Mathematics (Spring 2013) to become familiar with the application of key takeaways
from Grades 6-8.
Indicator 1c Guiding Question:
Do materials engage students in mathematics at a level of sophistication appropriate for high school?
Evidence Collection
Review the units, chapters, lessons, and assessments in both student and teacher materials.
Throughout the series, look for mathematical contexts that consist of real-life and relevant situations
appropriate for high school students. Document instances of contexts that are or are not appropriate for high
school students.
Throughout the series, consider the types of numbers being used. Look for opportunities where students
learn new mathematics with simpler numbers and later perform operations and apply concepts using the full
number system including rational, irrational, and complex numbers.
Throughout the series, determine if key takeaways from middle school are applied at a level of sophistication
appropriate for high school students. Materials should not be “re-teaching” standards from Grades 6-8. Note:
standards from Grades 6-8 do not need to be identified in either the teacher or student materials for this
indicator. Key takeaways from middle school include, but are not limited to:
Ratios and Proportional Relationships (6.RP.A; 7.RP.A; 8.EE.B)
● Applying ratios and proportional relationships
● Applying percentages and unit conversions, e.g., in the context of complicated measurement problems
involving quantities with derived or compound units (such as mg/mL, kg/m3, acre-feet, etc.)
Functions (8.F)
● Applying basic function concepts, e.g., by interpreting the features of a graph in the context of an applied
problem
● Use functions to model relationships
The Number System (6-7.NS)
● Performing rational number arithmetic fluently
Geometry (6-8.G)
● Applying concepts and skills of geometric measurement e.g., when analyzing a diagram or schematic
Statistics and Probability (6-8.SP)
● Applying concepts and skills of basic statistics and probability.

Note: “A problem in which students use reference data to determine the energy cost of different fuels might
draw on proportional relationships, unit conversion, and other skills that were first introduced in the middle
grades, yet still be a high-school level problem because of the strategic competence required” (p. 10 HS
Publishers’ Criteria).
If the materials provide resources for differentiated learning, consider whether lower-performing students
and/or special populations still have opportunities to engage in non-plus standards experiences appropriate
for high school. Every student should engage with course-level work. Note: The quality and types of the
differentiation provided by the materials are examined in Gateway 3.
Cluster Meeting
Are the contexts relevant for high school students? Document instances of contexts that are or are not
appropriate for high school students.
Do students regularly practice operations on rational and irrational numbers? Do the tasks and exercises help
students grow in their procedural skills with operations on real numbers?
Which of the key takeaway applications (from Table 1 of the Publishers’ Criteria) are present in the series? Are
the key takeaways being applied, or are standards from Grades 6-8 simply being re-taught? Do the
applications of key takeaways occur throughout the series or only within one course?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p. 57 of CCSSM).

Indicator 1d Materials are mathematically coherent by making meaningful connections in
a single course and throughout the series, where appropriate and where
required by the Standards.
Scoring:
2 points
● Materials foster coherence
through meaningful
mathematical connections in a
single course and throughout
the series, where appropriate
and where required by the
Standards.
1 point
● Materials partially foster
coherence through meaningful
mathematical connections in a
single course and throughout
the series, where appropriate
and where required by the
Standards.
0 points
● Materials do not foster
coherence through meaningful
mathematical connections in a
single course and throughout
the series, where appropriate
and where required by the
Standards.
About this indicator:
What is the purpose of this Indicator?
This indicator supports the shifts of Focus and Coherence within and across courses throughout the series. This
indicator examines the materials to determine if the materials are making meaningful connections to prior
learning. Connections between and across multiple standards are made in meaningful ways to support
understanding of multiple standards at the same time.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
Indicator 1d Guiding Question:
Do the materials make meaningful connections to prior learning within a course and across the series?

Do the materials connect multiple standards and/or clusters in meaningful ways?
Evidence Collection
Note: Meaningful connections are ones where students build mathematical knowledge by linking and
applying multiple concepts within and across courses. For this indicator, identifications do not have to be
explicit.
Review the units, chapters and lessons in both student and teacher materials.
Review the course and series scope and sequence.
Look for evidence throughout the series where students build mathematical knowledge by linking and
applying multiple concepts within and across courses.
Look for lesson objectives that develop in a systematic way to meet the full depth of the high school
standards.
Identify connections to prior learning from the course or the series for teachers and students. Materials allow
teachers to design lessons and units that carefully connect new content and skills to those learned earlier in
the course or across the series. For example, lessons and activities that serve to connect two or more
clusters in a domain, two or more domains in a conceptual category, or two or more conceptual categories.
Examples of connections between conceptual categories:
● Applying geometric concepts in modeling situations (G-MG) allows students to create equations in one
variable (A-CED.1) and use units as a way to understand problems and guide the solution (N-Q.3).
● The correspondence between numerical coordinates and geometric points allows methods from
algebra to be applied to geometry and vice versa. The solution set of an equation becomes a geometric
curve, making visualization a tool for doing and understanding algebra.
● Functions may be used to describe data; if the data suggest a linear relationship, the relationship can
be modeled with a regression line, and its strength and direction can be expressed through a
correlation coefficient.
Examples of connections among standards, clusters, and domains:
● The progression from congruence to area to similarity can be used to put each of these topics on a
logical footing: The basic assumptions that congruent figures have the same area and that area is
invariant under finite dissection bring coherence to the formulas for calculating areas of polygonal
regions. These formulas, along with results such as the fact that triangles with equal bases and heights
have the same area, can be used to prove properties of dilations and similarity. The triangle similarity
criteria are necessary to develop the trigonometry of right triangles.
● Study of linear associations in statistics and probability (S-ID.6c, 7) builds on students’ understanding of
linear relationships (cf. F-LE.1). Exploration of quadratic relationships in data on two measurement
variables (S-ID.6) depends on understanding key features of a quadratic function and being able to
interpret them in terms of a context (F-IF..4).
Further examples can be found at PARCC HS Model Content Framework starting on page 73.
Cluster Meeting

How is coherence present both within and across courses in the series?
How are the materials using previous course concepts to develop the full depth of the high school
standards?

Gateway 1: Focus & Coherence
Criterion 1.1 Materials are coherent and consistent with “the high school standards that
specify the mathematics which all students should study in order to be
college and career ready” (p.57 CCSSM).

Indicator 1e Materials explicitly identify and build on knowledge from Grades 6-8 to the
high school standards.
Scoring:
2 points
● Connections between Grades
6-8 and high school concepts
are present and allow students
to extend their previous
knowledge.
1 point
● Connections between Grades
6-8 and high school concepts
are partially present but may
not allow students to extend
their previous knowledge.
0 points
● Connections between Grades
6-8 and high school concepts
are not present and do not
allow students to extend their
previous knowledge.
About this indicator:
What is the purpose of this Indicator?
This indicator supports the shifts of Focus and Coherence, looking specifically at how the non-plus standards
coherently connect to and build upon standards from Grades 6-8. This indicator examines the materials to
determine if references to standards from Grades 6-8 are for the purpose of building on students’ previous
knowledge and allowing students to make connections to new learning.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Review criterion 3c on page 11 of the High School Publishers' Criteria for the Common Core State Standards
for Mathematics (Spring 2013).’’
Indicator 1e Guiding Question:
How do materials explicitly identify and build knowledge from Grades 6-8 to the high school standards?
Evidence Collection

Review the units, chapters and lessons in both student and teacher materials.
Review additional documents provided by the publisher, such as scope and sequence materials.
Cluster headings in the Standards sometimes signal key moments where reorganizing and extending
previous knowledge is important in order to accommodate new knowledge. At other times, the cluster
headings signal key connections to Grades 6-8. Look for and be mindful of such clusters.
Examples include but are not limited to:
● N-RN.A “Extend the properties of exponents to rational exponents.”
● A-REI.C “Solve systems of equations” extends 8.EE.8 “Analyze and solve pairs of simultaneous linear
equations.”
● F-IF.A “Understand the concept of a function and use function notation” connects naturally with 8.F.A
“Define, evaluate, and compare functions.”
● G-.SRT.A “Understand similarity in terms of similarity transformations” builds on the work of 8.G.A
“Understand congruence and similarity…”
● G-GMD.A “Explain volume formulas and use them to solve problems” coheres with 8.G.9 “Know the
formulas for the volumes of cones, cylinders, and spheres and use them to solve real-world and
mathematical problems,” 7.G.6 “Solve real-world and mathematical problems involving area, volume…,”
and 6.G.A “Solve real-world and mathematical problems involving area, surface area, and volume.”
● G-CO.A “Prove geometric theorems” extends the work of 7.G.5 “Use facts about supplementary,
complementary, vertical, and adjacent angles in a multi-step problem to write and solve simple equations
for an unknown angle in a figure.”
● S-ID.A “Summarize, represent, and interpret data on a single count or measurement variable” relates well
to 6.SP.B “Summarize and describe distributions.”
Throughout the series, look for:
● Grades 6-8 standards that are clearly identified as such in both the teacher and student materials;
● connections between 6-8 and high school concepts that are clearly articulated for teachers but may not
be explicitly named for students; and
● the design of the materials to focus on the connections to mathematics of the previous grades as
referenced in the Progression documents.
Determine if standards from Grades 6-8 are addressed in an appropriate way for high school; making
meaningful connections rather than materials “re-teaching” Grades 6-8 standards.
Examples of Grades 6-8 to high school coherence could include, but are not limited to:
● Students work extensively with ratios and proportions in Grades 6-8. In high school students work with
trigonometric ratios.
● Students work with transformations in order to understand similarity and congruence. In high school,
students extend their work with transformations to develop similarity and congruence proofs.
● Students in middle grades worked with measurement units, including units obtained by multiplying and
dividing quantities. In high school, students apply these skills in a more sophisticated fashion to solve
problems in which reasoning about units adds insight into the structure of the problem and the solutions
in context (N-Q).
● Students in Grade 8 extended their prior understanding of proportional relationships to begin working
with functions with an emphasis on linear functions. In high school, students will master linear and
quadratic functions. Students encounter other kinds of functions to ensure that general principles are

perceived in generality, as well as to enrich the range of quantitative relationships considered in
problems.
● As students acquire mathematical tools from their study of algebra and functions, they apply these tools
in statistical contexts (e.g., S-ID.6). In a modeling context, they might informally fit a quadratic function to
a set of data, graphing the data and the model function on the same coordinate axes. They also draw on
skills they first learned in middle school to apply basic statistics and simple probability in a modeling
context. For example, they might estimate a measure of center or variation and use it as an input for a
rough calculation.
● In Grades 6-8, students worked with a variety of geometric measures (length, area, volume, angle,
surface area, and circumference). In high school, students apply these component skills in tandem with
others in the course of modeling tasks and other substantial applications (MP4).
● In Grade 8, students learned the Pythagorean theorem and used it to determine distances in a
coordinate system (8.G.6–8). Early in high school, students prove theorems using coordinates
(G-GPE.4–7). Later in high school, students build on their understanding of distance in coordinate
systems and draw on their growing command of algebra to connect equations and graphs of conic
sections (e.g., G-GPE.1).
● Further examples can be found at PARCC HS Model Content Framework starting on page 44.
Cluster Meeting
Are the Grades 6-8 standards explicitly identified?
How are the materials using standards from Grades 6-8 to develop understanding of high school content?
Are the Grades 6-8 connections a purposeful extension or reinforcement of course-level standards, or do the
connections interfere with the work of the course/series?

Gateway 1: Focus & Coherence
Criterion 1.1 The program includes a system of assessments identifying how materials
provide tools, guidance, and support for teachers to collect, interpret, and act
on data about student progress towards the standards.

Indicator 1f 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 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.
Indicator 1f 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. *Note: this is not an item
analysis.
Look for and record evidence to:

● Describe how and where assessments clearly identify which standards are being assessed. Include the
level at which the assessment is given (unit, lesson, etc.) and the level at which standards are identified
(assessment, task, item, etc.).
● Describe any instances where standards are listed incorrectly or are not from the appropriate grade
level/band.
● In the event that the assessments build toward grade-level or grade-band standards, describe whether the
assessment information identifies which aspects of the standards are assessed. Also, describe how and
where the materials include information that details how the assessments build toward the standards for
the grade level or band.
Cluster Meeting
Discuss and answer the following questions to support consensus scoring conversations:
● Where and how do the materials clearly identify which standards are assessed?
● Do the standards correlations or assessment guidance documents indicate if all standards for the grade
level/band are assessed by the end of the grade level/band?
● If assessments 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 1g Assessments include opportunities for students to demonstrate the full intent
of grade-level/course-level standards and practices across the series.
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 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 and Mathematical Practices should be considered throughout evidence collection
for indicator 1g.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents

Indicator 1g 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
Review assessments and corresponding assessment guidance across the series.
Look for and record evidence to:
● Describe the different types of modalities used in student assessments (e.g., writing, illustrating,
demonstrating, modeling, oral presentations, and performance tasks) and explain how they ensure
students can fully demonstrate the intent of grade-level standards and mathematical practices.
● Describe the different types of items used for student assessments (e.g., performance tasks, discussion
questions, constructed response questions, project- or problem-based tasks, portfolios, justified multiple
choice) and explain how they are designed to measure student performance while fully addressing the
intent of grade-level standards and mathematical practices.
● Demonstrate that assessments address sufficient complexity to ensure students engage meaningfully with
the full intent of grade-level standards and mathematical practices.
Cluster Meeting
Discuss and answer the following questions to support consensus scoring conversations:
● Do the assessments include a variety of modalities (e.g., writing, illustrating, demonstrating, modeling,
oral presentations, and performance tasks), and how do these modalities ensure students can fully
demonstrate the intent 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 2: Rigor & Mathematical Practices
Criterion 2.1
Rigor and Balance
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.
What is the 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
Scoring:
Meets Expectations
● 7-8 points
Partially Meets Expectations
● 5-6 points
Does Not Meet Expectations
● <5 points

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 series.
AND
● Materials provide
opportunities for students to
independently demonstrate
conceptual understanding
throughout the series.
1 point
● Materials do not develop
conceptual understanding
throughout the series.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
conceptual understanding
throughout the series.
0 points
● Materials do not develop
conceptual understanding
throughout the series.
AND
● Materials do not provide
opportunities for students to
independently demonstrate
conceptual understanding
series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2b, 2c, and 2d, determines the shift of Rigor. Conceptual understanding of key concepts
will allow students to be able to access concepts from a number of perspectives in order to see mathematics as
more than a set of algorithmic procedures.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Video: “Building Conceptual Understanding in Mathematics” (NCTM)
● Video: “Conceptual Understanding Excerpt” (The Hunt Institute)

● Review criterion 2a on page 9 of the High School Publishers' Criteria for the Common Core State Standards
for Mathematics (Spring 2013).
● Concrete Representational Abstract: Instructional Sequence for Mathematics
● Reading: “Principles To Actions”, (NCTM) p. 42-48
Indicator 2a Guiding Questions:
Do the instructional materials develop students’ conceptual understanding throughout the series?
Do the instructional materials provide opportunities for students to independently demonstrate conceptual
understanding throughout the series?
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.
Select cluster(s) or standard(s) that specifically relate to conceptual understanding. Be aware that some
cluster(s) and standard(s) lend themselves to more than one aspect of rigor. In such cases, look for evidence
of conceptual understanding.
Look for the evidence in lessons, review lessons, chapter and/or unit assessments, homework assignments,
concept checks (if included), hands-on activities (if included), investigations (if included), simple tasks and
problems, and other areas that appear to be conceptual in nature.
Evaluate whether conceptual understanding present in lessons/chapters/units aligns to the aspect of rigor
indicated by the standard(s).
Determine if the materials feature high-quality conceptual problems and conceptual discussion questions,
including brief conceptual problems with low computational difficulty.
Determine if the materials offer opportunities for students to engage with concrete and representational
(semi-concrete) representations, in writing and/or discussion, when developing conceptual understanding. For
example:

Determine if the materials feature opportunities to identify correspondences across mathematical
representations in order to further develop conceptual understanding.
● Example: Through the series, the materials do not just offer opportunities for students to engage with
different families of functions through equations, tables, graphs, and contexts, but the materials offer
opportunities for students to make connections between the different representations for the various
families of functions.
Evidence must include specific examples from the instructional materials. If evidence is addressing clusters or
standards that relate specifically to conceptual understanding, list the specific clusters/standards and explain
how the evidence demonstrates conceptual understanding. If opportunities to develop conceptual
understanding are missed, specifically list the clusters/standards/opportunities that are missed.
The use of concrete representations (manipulatives) does not necessarily indicate conceptual understanding.
If evidence includes concrete and/or visual representations, explain how the representations are being used
to develop/enhance conceptual understanding. For example, students using algebra tiles to factor quadratic
expressions should be able to explain the connections between the algebra tiles, the process of factoring,
and the corresponding algebraic representations.
Note whether the instructional materials include a specific section in units/chapters/lessons, etc that are
specifically designed for conceptual understanding. Include Unit, Lesson, Lesson Part and page numbers for
reference for all examples.
Examples include, but are not limited to:
Clusters/Standards that relate to Conceptual Understanding
N-RN.1 – Explain how the definition of the meaning of rational exponents follows from extending the
properties of integer exponents to those values, allowing for a notation for radicals in terms of rational
exponents.
A-APR.B – Understand the relationship between zeros and factors of polynomials.
A-REI.A – Understand solving equations as a process of reasoning and explain the reasoning.

A-REI.10 – Understand that the graph of an equation in two variables is the set of all its solutions plotted in
the coordinate plane, often forming a curve (which could be a line).
A-REI.11 – Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y = g(x)
intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using technology
to graph the functions, make tables of values, or find successive approximations. Include cases where f(x)
and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic functions.★
F-IF.A – Understand the concept of a function and use function notation.
F-LE.1 – Distinguish between situations that can be modeled with linear functions and with exponential
functions.
G-SRT.2 – Given two figures, use the definition of similarity in terms of similarity transformations to decide if
they are similar; explain using similarity transformations the meaning of similarity for triangles as the equality
of all corresponding pairs of angles and the proportionality of all corresponding pairs of sides.
G-SRT.6 – Understand that by similarity, side ratios in right triangles are properties of the angles in the
triangle, leading to definitions of trigonometric ratios for acute angles.
S-ID.7 – Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context
of the data.
Cluster Meeting
What does intentional development of conceptual understanding look like in materials?
What specific evidence illustrates intentional development of conceptual understanding?
How do the materials in the series enable students to reason in settings involving the careful application of
concept definitions, relations, or representations?
Do the materials attend to conceptual understanding throughout the series?
Do the instructional materials provide opportunities for students to independently demonstrate conceptual
understanding throughout the series?

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 series.
AND
● Materials provide opportunities
for students to independently
demonstrate procedural skills
and fluencies throughout the
series.
1 point
● Materials do not develop
procedural skills and fluencies
throughout the series.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
procedural skills and fluencies
throughout the series.
0 points
● Materials do not develop
procedural skills and fluencies
throughout the series.
AND
● Materials do not provide
opportunities for students to
independently demonstrate
procedural skills and fluencies
throughout the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2c, and 2d, determines the shift of Rigor. In order to meet the expectations of the
standards materials must attend to three aspects of rigor, attending to a balance among conceptual
understanding, procedural skills and fluency, and application as called for by the standards. Procedural skills and
fluencies are the call for efficiency and accuracy in calculations. Students need to practice core skills in order to
have access to more complex concepts and procedures.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents

● Review criterion 2b on page 9 of the High School Publishers' Criteria for the Common Core State Standards
for Mathematics (Spring 2013).
Indicator 2b Guiding Question:
Do the instructional materials develop students’ procedural skills and fluencies throughout the series as
called for in the standards?
Do the instructional materials provide opportunities for students to independently demonstrate procedural
skills and fluencies throughout the series?
Evidence Collection
Procedural skill includes knowing how and why an algorithm works.
Fluency includes: efficiency, accuracy, flexibility, and appropriate strategy selection.
Select cluster(s) or standard(s) that specifically relate to procedural skills. Be aware that some cluster(s) and
standard(s) lend themselves to more than one aspect of rigor. In such cases, look for evidence of
procedural skills.
Evaluate whether aspects of rigor present in lessons/chapters/units align to the aspect of rigor in the
targeted standard(s).
Look for procedural problems and exercises that include cases in which students use algorithms
efficiently/fluently. For example, solve the system 2x + 3y = -(1/2)x + 6 – y and 2x + 5 = y + 2.
Evidence must include specific examples from the instructional materials. If opportunities to develop
procedural skills are missed, specifically list the clusters/standards/opportunities that are missed. Note
whether the instructional materials include a specific section in units/chapters/lessons, etc that are
specifically designed for procedural skills. Include Unit, Lesson, Lesson Part and page numbers for
reference for all examples.
Examples include, but are not limited to:
Clusters/Standards that relate to Procedural Skills
N-RN.2 – Rewrite expressions involving radicals and rational exponents using the properties of
exponents.
A-SSE.2 – Use the structure of an expression to identify ways to rewrite it.
A-APR.1 – Understand that polynomials form a system analogous to the integers, namely, they are closed
under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
A-APR.6 – Rewrite simple rational expressions in different forms; write a(x)/b(x) in the form q(x) + r(x)/b(x),
where a(x), b(x), q(x), and r(x) are polynomials with the degree of r(x) less than the degree of b(x), using
inspection, long division, or, for the more complicated examples, a computer algebra system.

F-BF.4a – Solve an equation of the form f(x) = c for a simple function f that has an inverse and write an
expression for the inverse. For example, f(x) =2 x3 or f(x) = (x+1)/(x-1) for x ≠ 1.
G-CO.12 - Make formal geometric constructions with a variety of tools and methods (compass and
straightedge, string, reflective devices, paper folding, dynamic geometric software, etc.).
G-GPE.4 – Use coordinates to prove simple geometric theorems algebraically.
G-GPE.5 – Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric
problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a
given point).
G-GPE.6 – Find the point on a directed line segment between two given points that partitions the
segment in a given ratio.
Cluster Meeting
Throughout the series, review evidence of opportunities for students to develop procedural skill and fluency
in the materials completed by teachers.
Throughout the series, review evidence of opportunities for students to independently demonstrate
procedural skill and fluency in the units as completed by teachers.
The Publishers’ Criteria for high school states, “In higher grades, algebra is the language of much of
mathematics. Like learning any language, we learn by using it.”. In what ways do students have sufficient
practice (algebraic or otherwise) in order to be adept/skilled with the operations of mathematics?
How do the materials develop procedural skills over a course? Over a series?

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 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
series.
AND
● Materials provide
opportunities for students to
independently demonstrate
multiple routine and
non-routine applications of
the mathematics throughout
the series.
1 point
● Materials do not include
multiple routine and
non-routine applications of
the mathematics throughout
the series.
OR
● Materials do not provide
opportunities for students to
independently demonstrate
multiple routine and
non-routine applications of
the mathematics throughout
the series.
0 points
● Materials do not include multiple
routine and non-routine
applications of the mathematics
throughout the series.
AND
● Materials do not provide
opportunities for students to
independently demonstrate
multiple routine and non-routine
applications of the mathematics
throughout the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2a, 2b, and 2c, 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)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
● CCSS Mathematics Curriculum Materials Analysis Project

Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Review criterion 2c on page 10 of the High School Publishers' Criteria for the Common Core State
Standards for Mathematics (Spring 2013).
● Reading: Chapter 1 of The GAIMME Report (A link to 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”.)
● Reading: “How to Identify Tasks that Engage Students in Mathematical Modeling NCTM-SIAM Committee on
Modeling Across the Curriculum”.
Indicator 2c Guiding Question:
Do the instructional materials develop students’ ability to utilize mathematical concepts and skills in engaging
applications throughout the series?
Do the instructional materials provide opportunities for students to independently demonstrate application
of mathematical concepts and skills in engaging applications throughout the series?
Evidence Collection
Application problems often, but not always, present a real-world scenario. Applications take the form of
problems to be worked on individually as well as classroom activities centered on application scenarios.
Students have opportunities to both employ a prescribed mathematical strategy and choose their own
strategy to find a solution.
Select cluster(s) or standard(s) that specifically address application of mathematics. Be aware that some
cluster(s) and standard(s) lend themselves to more than one aspect of rigor. In such cases, look for evidence
of application.
Determine if there is a variety of contextual problems, including non-routine problems, that develop the
mathematics of the non-plus standards.
Look for evidence where application problems particularly stress applying the content of the non-plus
standards.
Consider if applications build greater levels of complexity over the series.
Determine if the materials include an ample number of contextual problems that develop the mathematics of
the course.
Note when the materials:
● afford opportunities for students to engage in and practice problem solving,
● allow or require students to make their own assumptions or simplifications in order to model a situation
mathematically, and
● provide problems to be worked individually as well as classroom activities centered on application
scenarios.

Evidence must include specific examples from the instructional materials. If opportunities for application are
missed, specifically list the clusters/standards/ opportunities that are missed. Note whether the instructional
materials include a specific section in units/chapters/lessons, etc that are specifically designed for
application. Include Unit, Lesson, Lesson Part and page numbers for reference for all examples.
Examples include, but are not limited to:
Clusters/Standards that relate to Applications
N-Q.A – Reason quantitatively and use units to solve problems.
A-SSE.3 – Choose and produce an equivalent form of an expression to reveal and explain properties of
the quantity represented by the expression.★
A-CED.3 - Represent constraints by equations or inequalities, and by systems of equations and/or
inequalities, and interpret solutions as viable or nonviable options in a modeling context.
A-REI.11 – Explain why the x-coordinates of the points where the graphs of the equations y = f(x) and y =
g(x) intersect are the solutions of the equation f(x) = g(x); find the solutions approximately, e.g., using
technology to graph the functions, make tables of values, or find successive approximations. Include cases
where f(x) and/or g(x) are linear, polynomial, rational, absolute value, exponential, and logarithmic
functions.★
F-IF.B – Interpret functions that arise in applications in terms of the context.
F-BF.1 – Write a function that describes a relationship between two quantities.★
G-SRT.8 – Use trigonometric ratios and the Pythagorean Theorem to solve right triangles in applied
problems.★
G-GMD.3 – Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems.★
G-MG.2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per
square mile, BTUs per cubic foot).*
S-ID.2 – Use statistics appropriate to the shape of the data distribution to compare center (median, mean)
and spread (interquartile range, standard deviation) of two or more different data sets.
S-CP.7 – Apply the Addition Rule, P(A or B) = P(A) + P(B) - P(A and B), and interpret the answer in terms of
the model.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● How do the materials include multiple routine and non-routine applications throughout the series?
● How do the materials provide opportunities for students to independently demonstrate multiple routine
and non-routine applications throughout the series?

● 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?

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. 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 the series.
0 points
● Multiple aspects of rigor are not engaged
simultaneously to develop students’ mathematical
understanding of a single topic/unit of study
throughout the series.
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. This balance should be evident in all aspects of the high school series
and in each course to support students as they develop mathematical understanding.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● Achieve Framework to Evaluate Cognitive Complexity in Mathematics Assessments
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● Video: "The Balance Between Skills and Understanding" (The Hunt Institute)
● Video: “Mathematics Fluency: A Balanced Approach” (The Hunt Institute)
● Reading: “Additional Aspects of the Rigor and Balance Criterion” (Publishers' Criteria, p. 10)
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 include more than one aspect of rigor.
Look for a balance of all three aspects of rigor, considering the program materials as a whole and as individual
units of study.
● Consider whether the content/topic is being introduced to students for the first time or is an extension of
previous learning.
● Consider whether materials in the series simultaneously develop conceptual understandings and
procedural skills.
● Be mindful of where students are encouraged to use multiple representations and written explanations to
support their work in application problems.
For this indicator, consider the intent of the series to balance the three aspects of rigor, not the quality of the
materials—indicators 2a-c focus on the quality of rigor within the materials.
Determine if the materials consistently balance the three aspects of rigor while allowing for dedicated focus
on each individual aspect. Look for the evidence in lessons, review lessons, routine daily checks, chapter and
unit assessments, homework assignments, and other sections demonstrating connections between
procedural skills and conceptual understanding.
Determine if the materials neglect to attend to all aspects of rigor specified by the standards or clusters.
Examples may include, but are not limited to:
● With A-APR.1, the materials fully develop students adding, subtracting, and multiplying polynomials, but
the materials do not engage students in understanding that polynomials form a system closed under
addition, subtraction, and multiplication.
● With A-REI.11, the materials have students find solutions to systems of equations through applications, but
the materials do not have students develop conceptual understanding by explaining why the
x-coordinates of the points where two graphs intersect are the solutions to setting the two equations
equal to each other.
Evidence must include explicit examples of where more than one aspect of rigor is present (can be two or
three aspects, but does not have to include all three). Look for lessons that call out specific components of
rigor, and lessons that focus on individual aspects of rigor.
Cluster Meeting
Do the materials intentionally focus on one aspect of rigor over the others in specific units? If so, do the
materials work to maintain balance throughout each course and the series?
In what ways do the materials maintain balance of the aspects of rigor throughout each course and the series?
In what ways do the materials neglect one, or more, aspect(s) of rigor throughout each course and the series?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2
Standards for Mathematical Practice
Materials meaningfully connect the Standards for Mathematical Content and the Standards for Mathematical
Practice (MPs).
What is the purpose of this Criterion?
The purpose of this criterion is to ensure the Standards for Mathematical Practice are identified and connected
to grade-level mathematical content, and the materials present opportunities for students to both learn and
independently demonstrate each of the MPs.
Research Connection
● Common Core State Standards Mathematics
Scoring:
Meets Expectations
● 7-8 points
Partially Meets Expectations
● 4-6 points
Does Not Meet Expectations
● <4 points

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
high school content standards, as required by the mathematical practice
standards.
Scoring:
1 point
● There is intentional development of MP1 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP1 to
meet its full intent in connection to course-level
content across the series.
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. This indicator specifically looks at MP1 which addresses making sense of problems and
persevere in solving them. 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 b) fully developed across the
series to meet the level of expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP1: Make sense of problems and persevere in solving them
● This compilation document
Indicator 2e Guiding Question:
Across the series, is MP1 used to enrich the mathematical content?
Across the series, is there intentional development of MP1 that reaches the full intent of the MP?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP1 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP1 is
occurring throughout the courses of the series.
Record any instances where MP1 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP1 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places that
require students to:
● analyze and make sense of problems
● find solution pathways
● engage in problem solving
● persevere in solving problems
● monitor and evaluate their progress in solving problems
● determine if their answers make sense
● reflect on and revise their problem solving strategies
● check their answers with different methods
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● pose rich problems
● provide time for students to make sense of problems
● provide opportunities for students to engage in problem solving
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where a MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only 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 the MP1 identified and connected to series-level mathematical content?
● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2f Materials support the intentional development of MP2: Reason abstractly and
quantitatively, for students, in connection to the high school content
standards, as required by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP2 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP2 to
meet its full intent in connection to course-level
content across the series.
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. This indicator specifically looks at MP2 which addresses the practices of reasoning. 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 b) fully developed across the series to meet the level of
expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP2: Reason abstractly and quantitatively
● This compilation document
Indicator 2f Guiding Question:
Across the series, is MP2 used to enrich the mathematical content?
Across the series, is there intentional development of MP2 that reaches the full intent of the MP?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP2 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP2 is
occurring throughout the courses of the series.
Record any instances where MP2 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP2 is being used to enrich the mathematics content and is fully developed to meet the level of
expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places
that require students to:
● represent situations symbolically
● consider units involved in a problem and attend to the meaning of quantities
● understand the relationships between problem scenarios and mathematical representations
● explain/discuss what the numbers or symbols in an expression/equation represent
● determine if their answers make sense
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● ensure students make connections between mathematical representations and scenarios
● provide opportunities for students to engage in active mathematical discourse
● ask clarifying and probing questions
● model the use of mathematical symbols and notation
● support students in analyzing quantities and their relationships
● facilitate connections between multiple representations
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is identified in the
materials, but also look at places where it is not identified.
Cluster Meeting

Consider the following question(s) as evidence is synthesized:
● When is MP2 identified and connected to series-level mathematical content?
● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2g Materials support the intentional development of MP3: Construct viable
arguments and critique the reasoning of others, in connection to the high
school content standards, as required by the mathematical practice
standards.
Scoring:
1 point
● There is intentional development of MP3 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP3 to
meet its full intent in connection to course-level
content across the series.
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. This indicator specifically looks at MP3 which addresses the practice of reasoning and
explaining. 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 b) fully developed across the series to meet the
level of expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP3: Construct viable arguments and critique the reasoning of others
● This compilation document
Indicator 2g Guiding Question:
Across the series, is MP3 used to enrich the mathematical content?
Across the series, is there intentional development of MP3 that reaches the full intent of the MPs?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP3 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP3 is
occurring throughout the courses of the series.
Record any instances where MP3 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP3 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places
that require students to:
● explain/justify their reasoning
● construct mathematical arguments.
● create their own conjectures
● listen or read the arguments of others, decide whether they make sense, and ask useful questions to
clarify or improve the arguments
● perform error analysis of provided student work/solutions/arguments.
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● ensure students make connections between mathematical representations and scenarios
● provide opportunities for students to engage in active mathematical discourse
● ask clarifying and probing questions
● help students compare methods and strategies.
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is identified in the
materials, but also look at places where it is not identified. It may help to search for keywords like conjecture,
explain, justify, discuss, analyze, ask, and clarify.
Cluster Meeting

Consider the following question(s) as evidence is synthesized:
● When is MP3 identified and connected to the series-level mathematical content?
● In what ways do the students use MP3 to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with MP3?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2h Materials support the intentional development of MP4: Model with
mathematics, for students, in connection to the high school content
standards, as required by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP4 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP4 to
meet its full intent in connection to course-level
content across the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2i, 2j, 2k, and 2l, determines the meaningful integration of the Standards for
Mathematical Practice. This indicator specifically looks at MP4 which addresses mathematical modeling. 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 b) fully developed across the series to meet the level of
expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP4: Model with mathematics
● This compilation document
Indicator 2h Guiding Question:
Across the series, is MP4 used to enrich the mathematical content?
Across the series, is there intentional development of MP4 that reaches the full intent of the MPs?

Evidence Collection
Note: If all aspects of the modeling cycle are present in the materials, then the materials meet the full intent
of MP4.
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP4 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP4 is
occurring throughout the courses of the series.
Record any instances where MP4 is misidentified in the curricular materials (e.g. a lesson is marked as
aligned to an MP when only a small part addresses that, or vice versa).
To check that MP4 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places
that require students to:
● engage in the modeling cycle
● apply prior knowledge to new problems
● identify important relationships and map relationships with tables, diagrams, graphs, rules, etc.
● draw conclusions from solutions as they pertain to a situation
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for
places where teachers are expected to:
● Pose problems connected to previous concepts
● Provide a variety of real world contexts
● Provide meaningful, real-world, authentic performance tasks
● Promote discourse and investigation that could lead to refining and/or revising models
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is
identified in the materials, but also look at places where it is not identified.

Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP4 identified and connected to series-level mathematical content?
● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2i Materials support the intentional development of MP5: Use appropriate tools
strategically, for students, for students, in connection to the high school
content standards, as required by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP5 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP5 to
meet its full intent in connection to course-level
content across the series.
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. This indicator specifically looks at MP5 which addresses the use of appropriate tools. 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 b) fully developed across the series to meet the level of
expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP5: Use appropriate tools strategically
● This compilation document
Indicator 2i Guiding Question:
Across the series, is MP5 used to enrich the mathematical content?
Across the series, is there intentional development of MP5 that reaches the full intent of the MPs?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP 5 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP5 is
occurring throughout the courses of the series.
Record any instances where MP5 is misidentified in the curricular materials (e.g. a lesson is marked as
aligned to an MP when only a small part addresses that, or vice versa).
To check that MP5 is being used to enrich the mathematics content and are fully developed to meet the
level of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places
that require students to:
● choose appropriate tools
● use multiple tools to represent information in a situation
● create and use models to represent
● reflect on whether the results make sense, possibly improving or revising the model
*also consider whether the materials encourage opportunities for students to use technological tools to
explore and deepen their understanding of concepts
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for
places where teachers are expected to:
● Make a variety of tools available
● Allow student to have choice when selecting tools
● Model tools effectively, including their benefits and limitations
● Encourage the use of multiple tools for communication, calculation, investigation, sense-making, etc.
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is
identified in the materials, but also look at places where it is not identified.
Cluster Meeting

Consider the following question(s) as evidence is synthesized:
● When is the MP5 identified and connected to series-level mathematical content?
● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

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 high school content standards, as required by
the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP6 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP6 to
meet its full intent in connection to course-level
content across the series.
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. This indicator specifically looks at MP6 which addresses attending to precision. 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 b) fully developed across the series to meet the level of
expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP1: Make sense of problems and persevere in solving them
● MP6: Attend to precision
● This compilation document
Indicator 2j Guiding Question:
Across the series, is MP6 used to enrich the mathematical content?
Across the series, is there intentional development of MP6 that reaches the full intent of the MP?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP6 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP6 is
occurring throughout the courses of the series.
Record any instances where MP6 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP6 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places that
require students to:
● use accurate, precise mathematical language (vocabulary and conventions)
● specify units of measure
● state the meaning of symbols
● formulate clear explanations
● calculate accurately and efficiently
● use and label tables, graphs, etc. appropriately
● introduce and use definitions accurately
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● ensure students know and use clear definitions
● model accurate, precise mathematical language (vocabulary and conventions)
● provide feedback to students on the accurate use of mathematical language
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where a MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only 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 the series-level mathematical content?
● In what ways do the students use MP6 to its full intent across the series?
● 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 MP6?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2k Materials support the intentional development of MP7: Look for and make use
of structure, for students, in connection to the high school content standards,
as required by the mathematical practice standards.
Scoring:
1 point
● There is intentional development of MP7 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP7 to
meet its full intent in connection to course-level
content across the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2i, 2j, and 2l, determines the adherence to the Standards for
Mathematical Practice. This indicator specifically looks at MP which supports the intentional development of
seeing structure. 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 b) fully developed across the series
to meet the level of expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP7: Look for and make use of structure
● This compilation document
Indicator 2k Guiding Question:
Across the series, is MP7 used to enrich the mathematical content?
Across the series, is there intentional development of MP7 that reaches the full intent of the MPs?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP7 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP8 is
occurring throughout the courses of the series.
Record any instances where MP8 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP8 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places that
require students to:
● Look for patterns and make generalizations.
● Look and explain the structure of expressions.
● Look at and decompose “complicated” into “simpler” things.
E.g. seeing sin2x + 2sinx + 1 as u2 + 2u + 1.
● Analyze a problem and look for more than one approach.
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● Provide tasks/problems with patterns.
● Prompt students to look for structure and patterns.
● Prompt students to describe what they see in the structure/pattern.
E.g. Ask a student to explain how his/her expression “4n + 1” can be seen in the tile pattern.
● Provide a variety of examples that explicitly focus on patterns and repeated reasoning.
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is identified in the
materials, but also look at places where it is not identified.
Cluster Meeting

Consider the following question(s) as evidence is synthesized:
● When is MP7 identified and connected to series-level mathematical content?
● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

Gateway 2: Rigor & Mathematical Practices
Criterion 2.2 Materials meaningfully connect the Standards for Mathematical Content and
the Standards for Mathematical Practice (MPs).

Indicator 2l Materials support the intentional development of MP8: Look for and express
regularity in repeated reasoning, for students, in connection to the high
school content standards, as required by the mathematical practice
standards.
Scoring:
1 point
● There is intentional development of MP8 to meet
its full intent in connection to course-level content
across the series.
0 points
● There is not intentional development of MP8 to
meet its full intent in connection to course-level
content across the series.
About this indicator:
What is the purpose of this Indicator?
This indicator, along with 2e, 2f, 2g, 2h, 2i, 2j, and 2k, determines the adherence to the Standards for
Mathematical Practice. This indicator specifically looks at MP 8 which supports the intentional development
looking for and expressing regularity in repeated reasoning. 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
b) fully developed across the series to meet the level of expectation of high school mathematical study.
Research or Standards connection:
● Common Core State Standards for Mathematics (CCSSM)
● High School Publishers' Criteria for the CCSSM (Spring 2013)
● Student Achievement Partners (SAP) Instructional Materials Evaluation Tool for High School Mathematics
● Achieve EQuIP Rubric for Lessons & Units
● CCSS Mathematics Curriculum Materials Analysis Project
Resources:
● SAP Coherence Map
● Institute for Mathematics Education Progressions Documents
● MP8: Look for and express regularity in repeated reasoning
● This compilation document
Indicator 2l Guiding Question:
Across the series, is MP8 used to enrich the mathematical content?
Across the series, is there intentional development of MP8 that reaches the full intent of the MPs?

Evidence Collection
Look at all lessons in teacher’s manuals and in the student materials to ensure that MP8 is occurring
throughout the courses.
Look in unit overviews, scope and sequence charts, and/or other instructional guides to ensure that MP8 is
occurring throughout the courses of the series.
Record any instances where MP8 is misidentified in the curricular materials (e.g. a lesson is marked as aligned
to an MP when only a small part addresses that, or vice versa).
To check that MP8 is being used to enrich the mathematics content and are fully developed to meet the level
of expectation for high school:
Look at lessons, assessments and any examples/descriptions of anticipated student work. Look for places that
require students to:
● Look for shortcuts and general methods when calculations/processes are repeated
● Describe a general formula, process, or algorithm
● Evaluate the reasonableness of their answers and thinking.
●
Look at teacher directions and how teachers are guided to carry out the lessons. In particular, look for places
where teachers are expected to:
● Provide time for students to look for patterns, structure, shortcuts, generalizations, etc.
● Ask probing questions like “Does that always work?” or “Why does that work?”
● Provide situations in which students can use a strategy to develop understanding of a concept
● Prompt students to make generalizations
Check to see if any materials focus only on the Standards for Mathematical Practice (therefore, they are not
being used to enrich the mathematical content). Record any instances where the Standards for Mathematical
Practice are not being used to enrich course-level, mathematics content.
Verify that student engagement with the lessons and assessments would require use of the Standards for
Mathematical Practice so that across the series students will develop their use of the MP to the full intent of
the standards.
Record any instances where an MP was identified, however, engagement with the lesson or task would only
require minimal or trivial use of the indicated MP.
If you found that the MP is only located in a specific part of the teacher’s 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 used to enrich the content. Look not only where the MP is identified in the
materials, but also look at places where it is not identified.
Cluster Meeting
Consider the following question(s) as evidence is synthesized:
● When is MP8 identified and connected to series-level mathematical content?

● In what ways do the students use the MP to its full intent across the series?
● In what ways, if any, do the materials provided for teachers enable students to engage with the MP?

Gateway 3: Teacher and Student Supports
Criterion 3.1
Teacher Supports
Materials include opportunities for teachers to effectively plan and utilize materials with integrity and to further
develop their own understanding of the content.
What is the purpose of this Criterion?
This criterion examines how the materials support teachers in several key areas: delivering student and
ancillary materials, with a particular 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

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 in 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 presented
within the context of the specific
learning objectives.
1 point
● Materials provide
comprehensive guidance that
will assist teachers in
presenting the student and
ancillary materials.
OR
● Materials include sufficient and
useful annotations and
suggestions that are presented
within the context of the specific
learning objectives.
0 points
● Materials do not provide
comprehensive guidance that
will assist them in presenting
the student and ancillary
materials.
AND
● Materials do not include
sufficient and useful
annotations and suggestions
that are presented within the
context of the specific learning
objectives.
About this indicator:
What is the purpose of this Indicator?
This indicator examines whether materials offer comprehensive guidance for teachers, including annotations and
practical suggestions, to effectively implement both the core student materials and any supplementary resources.
This support aims to enhance teachers' ability to facilitate student mathematical development by providing
strategies and insights 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.

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. This
could include classroom management suggestions, timing considerations, or engagement techniques.
● Review whether the materials offer ways to adapt lessons to different classroom settings or student
populations.
● Look for references to additional resources or professional development opportunities that could further
support teachers in using the materials effectively.
Cluster Meeting
Preparing for the cluster meeting:
● Is the guidance for teachers clear and detailed, providing explicit instructions on how to use both the
student and ancillary materials effectively?
● Are the annotations and suggestions directly linked to the specific learning objectives, providing context
for how instructional strategies support students in achieving these objectives?
● Does the guidance include ways to integrate ancillary materials seamlessly within lessons to enhance
learning, such as cross-referencing with core materials or suggesting supplementary activities?
● Are there practical tips and real-world examples that help teachers implement the materials effectively,
including classroom management suggestions, timing considerations, or engagement techniques?
● Do the materials offer ways to adapt lessons to different classroom settings or student populations?
● Are there references to additional resources or professional development opportunities that could further
support teachers in using the materials effectively?
During the cluster meeting:
● Discuss whether the guidance for teachers is clear and detailed, providing explicit instructions on how to
use both the student and ancillary materials effectively.
● Discuss whether the annotations and suggestions are directly linked to the specific learning objectives,
providing context for how instructional strategies support students in achieving these objectives.
● Discuss whether the guidance includes ways to integrate ancillary materials seamlessly within lessons to
enhance learning, such as cross-referencing with core materials or suggesting supplementary activities.

● Discuss whether there are practical tips and real-world examples that help teachers implement the
materials effectively, including classroom management suggestions, timing considerations, or
engagement techniques.
● Discuss whether the materials offer ways to adapt lessons to different classroom settings or student
populations.
● Discuss whether there are references to additional resources or professional development opportunities
that could further support teachers in using the materials effectively.

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 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.

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. This helps teachers deepen their understanding of the subject matter and facilitates better
teaching.
● Look for relevant, concrete examples that illustrate the concepts and standards. Examples should be
practical and applicable to classroom instruction, helping teachers visualize how to teach the material
effectively.
● Check for explanations of how concepts and standards align with those taught in previous and
subsequent grade or course levels. This can help teachers understand the progression and continuity of
learning objectives.
● Look for clear descriptions of how skills and knowledge build upon each other from one grade or course
to the next. This can guide teachers in ensuring they are preparing students for future learning
challenges.
● Identify whether the materials include visual aids, such as charts, diagrams, or flowcharts, to help illustrate
how concepts and standards are connected across grade levels.
● Consider whether materials highlight connections between the subject's concepts and standards and
those of other subjects, fostering interdisciplinary learning.
● Look for insights or annotations aimed explicitly at teachers, which explain the rationale behind the
concepts and standards and how they fit into the broader curriculum.
● Check if there are suggestions or links to professional development resources that can further enhance
teachers' understanding of subject matter progression.
Cluster Meeting
Preparing for the cluster meeting:
● Are the explanations of grade-or course-level concepts and standards thorough, clear, and accessible to
help teachers deepen their understanding of the subject matter and facilitate better teaching?
● Are there relevant, concrete examples that illustrate the concepts and standards, which are practical and
applicable to classroom instruction to help teachers visualize how to teach the material effectively?
● Do the materials include explanations of how concepts and standards align with those taught in previous
and subsequent grade or course levels to help teachers understand the progression and continuity of
learning objectives?
● Are there clear descriptions of how skills and knowledge build upon each other from one grade or course
to the next, guiding teachers in preparing students for future learning challenges?
● Do the materials include visual aids, such as charts, diagrams, or flowcharts, to help illustrate how
concepts and standards are connected across grade levels?
● Do the materials highlight connections between the subject's concepts and standards and those of other
subjects, fostering interdisciplinary learning?
● Are there insights or annotations aimed explicitly at teachers that explain the rationale behind the
concepts and standards and how they fit into the broader curriculum?

● Are there suggestions or links to professional development resources that can further enhance teachers'
understanding of subject matter progression?
During the cluster meeting:
● Discuss whether the explanations of grade-or course-level concepts and standards are thorough, clear,
and accessible to help teachers deepen their understanding of the subject matter and facilitate better
teaching.
● Discuss whether there are relevant, concrete examples that illustrate the concepts and standards, which
are practical and applicable to classroom instruction to help teachers visualize how to teach the material
effectively.
● Discuss whether the materials include explanations of how concepts and standards align with those
taught in previous and subsequent grade or course levels to help teachers understand the progression
and continuity of learning objectives.
● Discuss whether there are clear descriptions of how skills and knowledge build upon each other from
one grade or course to the next, guiding teachers in preparing students for future learning challenges.
● Discuss whether the materials include visual aids, such 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.

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. 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. The correlation should specify which parts of the materials address each standard.
● Confirm that the document provides specific references, such as page numbers, lesson numbers, or
activities that correlate to each standard.

● Ensure the document cross-references where multiple standards might be addressed simultaneously in
broader activities or projects, emphasizing an integrated approach.
Note:
● if standards correlation is inconsistent between levels (i.e., from the overview to a module or a lesson).
● if standards correlation is inaccurate.
Cluster Meeting
Preparing for the cluster meeting:
● How do 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?
● Does the correlation document cover all relevant mathematics standards for the entire grade level or
series, including both content and practice standards?
● Is there a clear and direct alignment between the material's content and the specific mathematics
standards, specifying which parts of the materials address each standard?
● Does the document provide specific references, such as page numbers, lesson numbers, or activities that
correlate to each standard?
● Does the document cross-reference where multiple standards might be addressed simultaneously in
broader activities or projects, emphasizing an integrated approach?
During the cluster meeting:
● Discuss 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.
● Discuss whether the correlation document covers all relevant mathematics standards for the entire
grade level or series, including both content and practice standards.
● Discuss whether there is a clear and direct alignment between the material's content and the specific
mathematics standards, specifying which parts of the materials address each standard.
● Discuss whether the document provides specific references, such as page numbers, lesson numbers, or
activities that correlate to each standard.
● Discuss whether the document cross-references where multiple standards might be addressed
simultaneously in broader activities or projects, emphasizing an integrated approach.

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 research-based
strategies.
AND
● Materials do not include and
reference the role of the
standards in the program.
About this indicator:
What is the purpose of this Indicator?
This indicator examines whether materials provide a clear and comprehensive explanation of the instructional
approaches used within the program. It emphasizes the identification and justification of research-based
strategies employed in the curriculum, demonstrating how these methods are grounded in educational research
to enhance teaching effectiveness and student learning. Additionally, the indicator 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:

● 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 educational standards, such as
state, national, or Common Core standards, highlighting their role in shaping the curriculum.
Cluster Meeting
Preparing for the cluster meeting:
● Do the materials clearly outline the instructional approaches used within the program, providing a
comprehensive overview of how these methods guide teaching and learning activities?
● Are there detailed descriptions of how these instructional approaches are implemented in various
lessons and activities to help educators visualize their practical application?
● Do 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?
● Do the materials explain the reasoning behind choosing specific strategies, illustrating how they are
designed to enhance learning outcomes and support evidence-based teaching practices?
● Do 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?
During the cluster meeting:
● Discuss whether the materials clearly outline the instructional approaches 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.

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 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. The list
should leave no essential item unmentioned to prevent any disruptions during the actual implementation
of lessons.
● Look for an organized and easy-to-navigate list, possibly categorized by lesson, unit, or type of activity, so
teachers can quickly find and gather materials.
● Identify which materials are consumable (need to be replaced after use) and which are reusable (can be
used across multiple lessons or years), supporting teachers in planning for future lessons.
● Ensure that both digital resources (software, online tools) and physical supplies are included, with clear
indications of what is required for digital learning environments, if applicable.
● Look for suggested alternatives or substitutions for the materials listed to accommodate different
teaching environments or available resources, adding flexibility for teachers.

● Verify that each item in the supply list directly aligns with and supports specific instructional objectives
and activities, ensuring relevance and purpose.
Cluster Meeting
Preparing for the cluster meeting:
● Does the list cover all materials and supplies needed for each activity within the program, leaving no
essential item unmentioned to prevent any disruptions during the actual implementation of lessons?
● Is the list organized and easy to navigate, possibly categorized by lesson, unit, or type of activity, so that
teachers can quickly find and gather materials?
● Can you 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?
● Are both digital resources (software, online tools) and physical supplies included, with clear indications of
what is required for digital learning environments, if applicable?
● Are there suggested alternatives or substitutions for the materials listed to accommodate different
teaching environments or available resources, adding flexibility for teachers?
● Does each item in the supply list directly align with and support specific instructional objectives and
activities, ensuring relevance and purpose?
During the cluster meeting:
● Discuss whether the list covers all materials and supplies needed for each activity within the program,
leaving no essential item unmentioned to prevent any disruptions during the actual implementation of
lessons.
● Discuss whether the list is organized and easy to navigate, possibly categorized by lesson, unit, or type of
activity, so that teachers 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.

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. 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 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.

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. Information specific to formative and summative assessments is looked at in
Gateway 1).
In the instructional materials being reviewed:
● Ensure the assessment system provides regular and structured opportunities throughout the school year
to measure student learning. This should include formative assessments that offer ongoing insights and
summative assessments that evaluate cumulative learning.
● Look for a variety of assessment types (e.g., quizzes, performance tasks, summative assessments,
standardized tests) to capture different aspects of student learning and demonstrate a comprehensive
view of progress.
● Ensure that there is comprehensive guidance for teachers on how to administer the system of
assessments, including instructions, rubrics, and criteria for consistent and fair evaluation of student
performance.
● Confirm that the materials include clear guidance on how to interpret the results of student assessments
throughout all assessments.
● Across the assessment system as a whole, look for specific recommendations or strategies for teachers
on how to use assessment data to inform instructional decisions, adjust teaching plans, and provide
targeted interventions or enrichment activities based on student needs.
● Assess whether the system includes mechanisms for providing timely and constructive feedback to
students, helping them understand their progress and areas for improvement.
● Determine if the assessment system allows for flexibility to accommodate diverse learning environments,
student populations, and instructional methods.
Cluster Meeting
Preparing for the cluster meeting:
● Does the assessment system provide regular and structured opportunities throughout the school year to
measure student learning, including both formative assessments that offer ongoing insights and
summative assessments that evaluate cumulative learning?
● Is there a variety of assessment types (e.g., quizzes, performance tasks, summative assessments,
standardized tests) to capture different aspects of student learning and demonstrate a comprehensive
view of progress?
● Is there comprehensive guidance for teachers on how to administer the assessment system, including
instructions, rubrics, and criteria for consistent and fair evaluation of student performance?
● Do the materials include clear guidance on how to interpret the results of student assessments across all
assessments?
● Are there specific recommendations or strategies for teachers on how to use assessment data to inform
instructional decisions, adjust teaching plans, and provide targeted interventions or enrichment activities
based on student needs?

● Does the system include mechanisms for providing timely and constructive feedback to students, helping
them understand their progress and areas for improvement?
● Does the assessment system allow for flexibility to accommodate diverse learning environments, student
populations, and instructional methods?
During the cluster meeting:
● Discuss whether the assessment system provides regular and structured opportunities throughout the
school year to measure student learning, including both formative assessments that offer ongoing
insights and summative assessments that evaluate cumulative learning.
● Discuss whether there are a variety of assessment types (e.g., quizzes, performance tasks, summative
assessments, standardized tests) to capture different aspects of student learning and demonstrate a
comprehensive view of progress?
● Discuss whether there is comprehensive guidance for teachers on how to administer the assessment
system, including instructions, rubrics, and criteria for consistent and fair evaluation of student
performance.
● Discuss whether the materials include clear guidance on how to interpret the results of student
assessments across all assessments.
● Discuss whether there are specific recommendations or strategies for teachers on how to use
assessment data to inform instructional decisions, adjust teaching plans, and provide targeted
interventions or enrichment activities based on student needs.
● Discuss whether the system includes mechanisms for providing timely and constructive feedback to
students, helping them understand their progress and areas for improvement.
● Discuss whether the assessment system allows for flexibility to accommodate diverse learning
environments, student populations, and instructional methods.

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 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 participation in learning.
Scoring:
2 points
● Materials provide
strategies, supports, and
resources for students in
special populations to
ensure their regular and
active participation in
grade-level mathematical
tasks and problem-solving
activities.
1 point
● Materials provide
strategies, supports, and
resources for students in
special populations to
support their regular and
active participation in
grade-level mathematical
tasks and problem-solving
activities. but not
consistently.
0 points
● Materials do not provide
strategies, supports, and
resources for students in
special populations to
support their regular and
active participation in
grade-level mathematical
tasks and problem-solving
activities.
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
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 comprehensive guidance for teachers on how to implement these
strategies effectively, including professional development resources if applicable.
● Ensure there are tools and resources for monitoring the progress of students in special populations,
allowing teachers to assess effectiveness and adjust strategies as needed.
Cluster Meeting
Preparing for the cluster meeting:
● Do the materials include specific strategies for differentiating instruction to meet the diverse needs of
students in special populations, adaptable to individual learning styles and needs?
● Do 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?
● Do the materials incorporate strategies to support the social-emotional needs of students in special
populations, fostering a positive learning environment and encouraging participation?
● Are there opportunities for cooperative learning where students can work in diverse groups to enhance
peer support and learning through interaction?
● Do the materials include comprehensive guidance for teachers on how to implement these strategies
effectively, including professional development resources if applicable?
● Are there tools and resources for monitoring the progress of students in special populations, allowing
teachers to assess effectiveness and adjust strategies as needed?
During the cluster meeting:
● Discuss whether the materials include specific strategies for differentiating instruction to meet the diverse
needs of students in special populations, adaptable to individual learning styles and needs.
● Discuss whether 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.
● Discuss whether the materials incorporate strategies to support the social-emotional needs of students in
special populations, fostering a positive learning environment and encouraging participation.
● Discuss whether there are opportunities for cooperative learning where students can work in diverse
groups to enhance peer support and learning through interaction.
● Discuss whether the materials include comprehensive guidance for teachers on how to implement these
strategies effectively, including 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.

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 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
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 ways without simply
adding to the workload. These could include complex problem-solving tasks, thematic projects, or
interdisciplinary connections that integrate math with other subjects.
● Ensure materials offer differentiated pathways that cater to the needs of advanced learners, providing
challenges that match their capability without increasing the volume of assignments.
● Look for opportunities within the materials that focus on skill enrichment, such as critical thinking,
problem-solving, or creative expression that align with students' strengths and interests.
● Verify that advanced learners are given choices in how they explore topics or demonstrate
understanding, allowing for greater autonomy and personalized learning experiences.
● Ensure that the advanced materials remain connected to the core curriculum, maintaining relevance
and ensuring coherence with overall learning objectives.
● Check for ways the materials provide opportunities for advanced learners to reflect on their learning
processes and outcomes, enabling them to set personal learning goals and seek further opportunities
for growth.
● Ensure that there are no instances of advanced students doing more assignments than their
classmates.
Cluster Meeting
Preparing for the cluster meeting:
● Are there 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?
● Do the tasks offer complexity rather than just more of the same work?
● Are there enrichment activities that extend the mathematical content in meaningful ways without simply
adding to the workload, such as complex problem-solving tasks, thematic projects, or interdisciplinary
connections that integrate math with other subjects?
● Do the materials offer differentiated pathways that cater to the needs of advanced learners, providing
challenges that match their capability without increasing the volume of assignments?
● Are there opportunities within the materials that focus on skill enrichment, such as critical thinking,
problem-solving, or creative expression that align with students' strengths and interests?
● Are advanced learners given choices in how they explore topics or demonstrate understanding, allowing
for greater autonomy and personalized learning experiences?
● Do the advanced materials remain connected to the core curriculum, maintaining relevance and ensuring
coherence with overall learning objectives?
● Do the materials provide opportunities for advanced learners to reflect on their learning processes and
outcomes, enabling them to set personal learning goals and seek further opportunities for growth?
● Are there any instances of advanced students doing more assignments than their classmates?
During the cluster meeting:

● Discuss whether 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.
● Discuss whether the mathematical tasks offer complexity rather than just more of the same practice,
potentially involving open-ended projects, independent research, or inquiry-based learning opportunities
that challenge students to think critically, explore concepts deeply, and apply their knowledge creatively.
● Discuss whether there are enrichment activities that extend the content in meaningful ways without
simply adding to the workload, such as complex problem-solving tasks, thematic projects, or
interdisciplinary connections that integrate math with other subjects.
● Discuss whether the materials offer differentiated pathways that cater to the needs of advanced learners,
providing challenges that match their capability without increasing the volume of assignments.
● Discuss whether there are opportunities within the materials that focus on skill enrichment, such as
critical thinking, problem-solving, or creative expression that align with students' strengths and interests.
● Discuss whether advanced learners are given choices in how they explore topics or demonstrate
understanding, allowing for greater autonomy and personalized learning experiences.
● Discuss whether the advanced materials remain connected to the core curriculum, maintaining relevance
and ensuring coherence with overall learning objectives.
● Discuss whether the materials provide opportunities for advanced learners to reflect on their learning
processes and outcomes, enabling them to set personal learning goals and seek further opportunities for
growth.
● Discuss whether there are any instances of advanced students doing more assignments than their
classmates.

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.