Illustrative
MathematicsProgram Overview
Algebra 1, Geometry, Algebra 2
All Greens on EdReports
MathematicsProgram Overview
Algebra 1, Geometry, Algebra 2
All Greens on EdReports
Authors, Research, and Certified
Partnership
Dr. Bill McCallum and a team of math leaders authored
Illustrative Mathematics (IM) to improve student outcomes
in mathematics. The problem-based curriculum is built on
best practices and research principles from NCTM, National
Research Council, Smith & Stein, and others. The new IM K–5
Math completes the K–12 series.
Certified Partnership
Imagine Learning is one of Illustrative
Mathematics’ Certified Partners.
The IM Certified designation assures
that materials adhere to IM’s philosophy
and were developed, reviewed, and
approved by Illustrative Mathematics.
The Imagine Learning IM instructional experience aligns with
the Every Student Succeeds Act (ESSA) Theory of Change for
effective, evidence-based programs. The goal is to deliver an
engaging and easy-to-implement instructional solution that
leverages the power of high-quality curricula.
The result? Comprehensive support for teachers and positive
learning outcomes for students.
“The IM 9–12 Math
curriculum is our
teacher-tested,
standards-aligned
curriculum, designed
with high school
learners in mind.
The curriculum
nurtures a
comprehensive
proficiency with
functions, algebra,
geometry, modeling,
and statistics, and it
encourages problem-
solving skills students
need to make use of
mathematics in their
future education
and careers.”
Dr. William McCallum
Partnership
Dr. Bill McCallum and a team of math leaders authored
Illustrative Mathematics (IM) to improve student outcomes
in mathematics. The problem-based curriculum is built on
best practices and research principles from NCTM, National
Research Council, Smith & Stein, and others. The new IM K–5
Math completes the K–12 series.
Certified Partnership
Imagine Learning is one of Illustrative
Mathematics’ Certified Partners.
The IM Certified designation assures
that materials adhere to IM’s philosophy
and were developed, reviewed, and
approved by Illustrative Mathematics.
The Imagine Learning IM instructional experience aligns with
the Every Student Succeeds Act (ESSA) Theory of Change for
effective, evidence-based programs. The goal is to deliver an
engaging and easy-to-implement instructional solution that
leverages the power of high-quality curricula.
The result? Comprehensive support for teachers and positive
learning outcomes for students.
“The IM 9–12 Math
curriculum is our
teacher-tested,
standards-aligned
curriculum, designed
with high school
learners in mind.
The curriculum
nurtures a
comprehensive
proficiency with
functions, algebra,
geometry, modeling,
and statistics, and it
encourages problem-
solving skills students
need to make use of
mathematics in their
future education
and careers.”
Dr. William McCallum
Imagine Learning
Illustrative MathematicsFor Algebra 1, Geometry, Algebra 2
A dynamic, engaging instructional experience that leverages the power
of high-quality curricula:
Students enjoy mathematics, make mathematical connections, and develop
conceptual understanding.
Teachers orchestrate discussions, synthesize understanding, and facilitate
interactive lessons with confidence.
Imagine Learning partners with schools and districts for seamless integration
and implementation.
Table of Contents
Instructional Design .......................................................................................................................................................... 2–3
Design Principles across Algebra 1, Geometry, Algebra 2 ...................................................................................... 4–5
Teacher Experience ........................................................................................................................................................... 6–7
Student Experience ........................................................................................................................................................... 8–9
Equity and Access ............................................................................................................................................................. 10–11
Assessmentt ........................................................................................................................................................................ 12–13
Program Components ...................................................................................................................................................... 14–15
v.TM
Algebra 2
Teacher
Course
Guide
v.TM
Teacher Course Guide
TCG
A2
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Geometry
Teacher
Course
Guide
v.TM
Teacher Course Guide
TCG
G
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Teacher
Course
Guide
Algebra 1
v.TM
Teacher Course Guide
TCG
A1
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Page 1
Illustrative MathematicsFor Algebra 1, Geometry, Algebra 2
A dynamic, engaging instructional experience that leverages the power
of high-quality curricula:
Students enjoy mathematics, make mathematical connections, and develop
conceptual understanding.
Teachers orchestrate discussions, synthesize understanding, and facilitate
interactive lessons with confidence.
Imagine Learning partners with schools and districts for seamless integration
and implementation.
Table of Contents
Instructional Design .......................................................................................................................................................... 2–3
Design Principles across Algebra 1, Geometry, Algebra 2 ...................................................................................... 4–5
Teacher Experience ........................................................................................................................................................... 6–7
Student Experience ........................................................................................................................................................... 8–9
Equity and Access ............................................................................................................................................................. 10–11
Assessmentt ........................................................................................................................................................................ 12–13
Program Components ...................................................................................................................................................... 14–15
v.TM
Algebra 2
Teacher
Course
Guide
v.TM
Teacher Course Guide
TCG
A2
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Geometry
Teacher
Course
Guide
v.TM
Teacher Course Guide
TCG
G
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Teacher
Course
Guide
Algebra 1
v.TM
Teacher Course Guide
TCG
A1
We have taken the next step on our journey to
empower more educators, engage more students,
and connect more families to learning, by bringing
together our products under one brand, united by
a shared mission.
LearnZillion is now Imagine Learning
Page 1
Instructional DesignThe instructional design of the materials supports all students through a coherent progression of mathematics
based on the standards and research-based learning trajectories.
Units
Each unit starts with an invitation to
mathematics. The first few lessons
provide an accessible entry point for
all students and allow teachers to
observe students’ prior understandings.
Next, they move toward a deep study
of concepts with time for consolidating
and applying.
Lessons
Each lesson starts with a warm-up to
set up the day’s work or strengthen
number sense and procedural fluency.
The overarching design structure at each level is as follows:
Each activity and
lesson are part of a
mathematical story
across the units. This
coherence allows
students to view
mathematics as a
connected set of ideas
that makes sense.
Invitation to the
mathematics
Introductory
lesson
Warm-up
Launch
Deep study of concepts
and procedures
Instructional lessons
Classroom activities
Work time
Consolidating
and applying
Culminating
lesson
Synthesis and
cool-down
Synthesis
Unit
Level
Lesson
Level
Activity
LevelIM Grades 9-12 Program Overview
Page 2
based on the standards and research-based learning trajectories.
Units
Each unit starts with an invitation to
mathematics. The first few lessons
provide an accessible entry point for
all students and allow teachers to
observe students’ prior understandings.
Next, they move toward a deep study
of concepts with time for consolidating
and applying.
Lessons
Each lesson starts with a warm-up to
set up the day’s work or strengthen
number sense and procedural fluency.
The overarching design structure at each level is as follows:
Each activity and
lesson are part of a
mathematical story
across the units. This
coherence allows
students to view
mathematics as a
connected set of ideas
that makes sense.
Invitation to the
mathematics
Introductory
lesson
Warm-up
Launch
Deep study of concepts
and procedures
Instructional lessons
Classroom activities
Work time
Consolidating
and applying
Culminating
lesson
Synthesis and
cool-down
Synthesis
Unit
Level
Lesson
Level
Activity
LevelIM Grades 9-12 Program Overview
Page 2
Instructional Activities
Next, instructional activities introduce students
to new concepts, procedures,
contexts, and representations
— and help them make
connections between them.
Synthesis
Each lesson ends with a synthesis to consolidate
understanding and make the
learning goals of the lesson
explicit, followed by a cool-down
to apply their learning.
Practice Problems
Practice problems are included with each lesson
for independent work in class or homework.
Teachers have the option to assign
work by paper and pencil or digitally
through the Imagine Learning (IL)
Classroom. There is also another
digital set of problems
that teachers can
assign for additional
practice opportunities.
The practice problem set includes
lesson-specific questions and
distributed practice from earlier
in the unit or previous units to
ensure fluency.
Instructional Design Page 3
Next, instructional activities introduce students
to new concepts, procedures,
contexts, and representations
— and help them make
connections between them.
Synthesis
Each lesson ends with a synthesis to consolidate
understanding and make the
learning goals of the lesson
explicit, followed by a cool-down
to apply their learning.
Practice Problems
Practice problems are included with each lesson
for independent work in class or homework.
Teachers have the option to assign
work by paper and pencil or digitally
through the Imagine Learning (IL)
Classroom. There is also another
digital set of problems
that teachers can
assign for additional
practice opportunities.
The practice problem set includes
lesson-specific questions and
distributed practice from earlier
in the unit or previous units to
ensure fluency.
Instructional Design Page 3
Design Principles across
Algebra 1, Geometry, Algebra 2Learning Mathematics by Doing Mathematics
A problem-based instructional framework supports teachers in structuring lessons so students are the ones
doing the problem solving to learn the mathematics. Activities and routines allow teachers to see what students
already know—and what they can notice and figure out—before explaining concepts and procedures.
Balancing Rigor
Three aspects of rigor are essential to mathematics: conceptual understanding, procedural fluency, and the
ability to apply these concepts and skills to mathematical problems, both with and without real-world contexts.
Illustrative Mathematics develops them together to support student understanding.
Establishing Norms
Structures around doing math together and sharing understandings play an essential role in the success of a
problem-based curriculum. Students must take risks, listen to each other, disagree respectfully, and honor equal
airtime when working together in groups. Establishing norms helps teachers cultivate a community of learners
where making thinking visible is both expected and valued.
Instructional Routines
Instructional routines create structures so all students can engage
and contribute to mathematical conversations. Throughout the
curriculum, routines are introduced in a purposeful way to build a
collective understanding of their structure.
Card Sort encourages students to
categorize mathematical entities based
on shared characteristics or connections. IM Grades 9-12 Program Overview
Page 4
Algebra 1, Geometry, Algebra 2Learning Mathematics by Doing Mathematics
A problem-based instructional framework supports teachers in structuring lessons so students are the ones
doing the problem solving to learn the mathematics. Activities and routines allow teachers to see what students
already know—and what they can notice and figure out—before explaining concepts and procedures.
Balancing Rigor
Three aspects of rigor are essential to mathematics: conceptual understanding, procedural fluency, and the
ability to apply these concepts and skills to mathematical problems, both with and without real-world contexts.
Illustrative Mathematics develops them together to support student understanding.
Establishing Norms
Structures around doing math together and sharing understandings play an essential role in the success of a
problem-based curriculum. Students must take risks, listen to each other, disagree respectfully, and honor equal
airtime when working together in groups. Establishing norms helps teachers cultivate a community of learners
where making thinking visible is both expected and valued.
Instructional Routines
Instructional routines create structures so all students can engage
and contribute to mathematical conversations. Throughout the
curriculum, routines are introduced in a purposeful way to build a
collective understanding of their structure.
Card Sort encourages students to
categorize mathematical entities based
on shared characteristics or connections. IM Grades 9-12 Program Overview
Page 4
Mathematical Modeling
Mathematical modeling is the process of choosing and using appropriate mathematics and statistics to analyze
empirical situations, understand them better, and improve decisions. The program offers modeling prompts and
guidance to support students in making inferences, evaluating choices, and validating outcomes.
Use of Digital Tools
The curriculum empowers students to become fluent in using digital tools to produce representations, solve
problems, and communicate their reasoning. The Imagine Learning (IL) Classroom embeds Desmos, GeoGebra,
and other interactive tools at point-of-use to amplify understanding and engagement.
Guiding Principles across Algebra 1, Geometry, Algebra 2 Page 5
Mathematical modeling is the process of choosing and using appropriate mathematics and statistics to analyze
empirical situations, understand them better, and improve decisions. The program offers modeling prompts and
guidance to support students in making inferences, evaluating choices, and validating outcomes.
Use of Digital Tools
The curriculum empowers students to become fluent in using digital tools to produce representations, solve
problems, and communicate their reasoning. The Imagine Learning (IL) Classroom embeds Desmos, GeoGebra,
and other interactive tools at point-of-use to amplify understanding and engagement.
Guiding Principles across Algebra 1, Geometry, Algebra 2 Page 5