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Illustrative Mathematics with Imagine Learning is a dynamic, engaging instructional experience that leverages the power of high-quality curricula.

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This is a short video guide through the Imagine Learning Classroom where the effective Illustrative Mathematics curriculum is housed.

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URL: https://ca-review.ilclassroom.com/
Login as a teacher
Username: careviewpt@example.com
Password: Imaginelearning23

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Our IM K-12 comprehensive program is classroom ready and

enhanced with exclusive features to make instruction come alive.

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Imagine IM New Features Highlights Brochure

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We are so excited to help in your journey of reviewing Illustrative Mathematics with Imagine Learning! Please use this padlet to access valuable information of various aspects of the program. As you move left to right, some sections will have vertical scrolling capability, where you can find even more valuable information. Should you have any questions, please reach out to your account executive.

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The 5 practices were designed to help teachers use

students’ responses to advance the mathematical

understanding of the class as a whole.

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Assessments
Illustrative Mathematics offers opportunities for both formative and summative assessment that empower teachers to measure student understanding and progress against learning goals.

Data Reporting
Real-time reporting gives teachers access to actionable data. The data dashboard and display lets them track student progress.

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Brochure - IL IM Assessment Grades 6–12 (2)

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There are 3 major design principles to support all learners: provide access to all, presume competence, provide a strength-based approach.

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A brochure with a high-level overview of the components that make up Imagine Learning Illustrative Math. Each component will be explored further on this padlet.

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The instructional design of the materials supports all learners through a coherent progression of the mathematics based

on the standards and research-based learning trajectories.

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Each unit includes a guide that explains the key ideas and concepts in family-friendly language.

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The instructional routines embedded within the Imagine Learning Illustrative Mathematics lessons create structures

so that all students can engage in and contribute to mathematical conversations.

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Imagine Learning has many supports embedded into the platform to support teachers in addressing student gaps.

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IM 6-12 Math: Grading and Homework Policies and Practices - IM CERTIFIED® BLOG

Practice and homework are important with any mathematics curriculum. Please take a moment to read through Illustrative Math's homework and practice policies.

Note: Imagine Learning Classroom houses TWO sets of practice problems for every lesson in grades 9-12.

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IM 6-12 Math: Grading and Homework Policies and Practices - IM CERTIFIED® BLOG

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Detailed teacher guides are available for each unit of instruction. Print received in fall of 2024 will reflect what is seen here.

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Sampler - IL IM Grade 6 Unit 1 Teacher Guide 

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Select classroom activities include an opportunity for differentiation for students ready for more of a challenge. We think of them as the “mathematical dessert” to follow the “mathematical entrée” of a classroom activity.

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Example of consumable student workbook that students would utilize during a lesson. Print received in fall of 2024 will reflect what is seen here.

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Sample - IL IM Grade 6 Unit 1 Student Workbook

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Eight Math Language Routines (MLRs) are embedded into lessons to support in both learning the English language and learning the language of mathematics.

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Many Spanish resources are available for students and parents.

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Kori McAbee
714-300-8373
kori.mcabee@imaginelearning.com

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Here is an example of a digital applet that is used to explore quadratic functions in vertex form. Digital applets are often used to support student exploration as they learn new topics.

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IM Author Bill McCallum paints a picture of what Illustrative Mathematics will look like in your classroom.

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By William McCallum, IM CEO
Here at IM we are excited by and proud of the reception IM K-12 Math™ is getting. As more and more districts adopt it, we are thinking about how to support them. What are the next steps? Our vision of a classroom community informs this work. We picture students actively engaged with and excited by the materials, confidently persevering in solving problems and sharing their thinking. We envision the teacher leading productive and meaningful discussions that help synthesize the students' learning of rigorous grade-level content. How can we make this vision a reality in more schools?

A coherent curriculum , like IM K-12 Math™, is critical to building classroom community, but more is needed to support teachers, schools, and districts with instructional shifts that promote access and equity for all students. There should be a shared vision of what the classroom will look like, and consideration of the support teachers will need. At IM, we call our vision the IM Classroom.

What is the IM Classroom?

IM's work is anchored in the belief that all students are capable of learning grade-level mathematics. Our curriculum supports a problem-based instructional model, where students are invited to the mathematics through relevant and affirming contexts. This draws on their naturally inquisitive nature, and their experience with the world around them. Problems provide multiple access points and solution paths, making them accessible to students at different points in their learning journey.

Problem-based instruction means believing all students can solve problems on their own and giving them a chance to try. This sets them on a path to developing mathematical identities as learners who can know, use, and enjoy mathematics. When students are engaged in their learning, they develop stronger perseverance and better retention of knowledge.

Four Elements of the IM Classroom

1. Teachers use an IM Certified® curriculum. practice IM's problem-based instructional model with integrity, and believe that all of their students are capable of learning grade-level mathematics.

2. Teachers participate in IM Certified Professional Learning, and have access to implementation support.

3. School leaders and administrators understand and support the systemic changes that are necessary to change the teachers' practice.

4. Families and communities engage with and support their students' learning.

Let's take a closer look at each pillar.

Pillar 1: Implementing problem-based instruction with IM Certified curriculum

IM Classroom teachers are passionate about learning and implementing our problem-based instructional model with integrity. They make sure their students understand each problem, monitor their students' work and advance their thinking with probing questions, provide information as appropriate, and, importantly, synthesize their students' learning at the end to make sure the goals of the activity have been met.

In an IM Classroom, the curriculum is obtained from one of our IM Certified Partners or by accessing the free, open educational resource (OER) on our website. IM Certification guarantees alignment with our coherent progressions of concepts and procedures. IM certified solutions include print and online tools, such as instructional videos and digital centers and manipulatives that support teachers to meet the needs of all learners.

Pillar 2: Teachers participate in IM Certified Professional Learning

When professional learning is certified by Illustrative Mathematics, it means that high- quality curriculum-aligned content is delivered by qualified facilitators who undergo rigorous training and ongoing development. IM Certified Professional Learning provides a coherent suite of offerings, both onsite and virtual, that support teachers and leaders through initial adoption and ongoing learning.

IM Certified Professional Learning Facilitators are experts in IM K-12 Math™ and the problem-based instructional model. In the IM Classroom, teachers continue to grow in both their practice and their understanding of the curriculum. Their participation in ongoing professional learning supports these efforts.

Pillar 3: School leaders and administrators understand and support necessary changes

While teachers have a direct impact on students' learning experiences, school and district leaders play an important role in making sure teachers have the appropriate tools and resources for their students to thrive. For successful implementation of IM K-12 Math™, leaders have a deep understanding of the problem-based instructional model, pedagogical practices, and planning protocols in order to create systems of support.

The IM Classroom exists in a building where school leaders and administrators support teachers and create systemic change through coaching, collaborative planning, implementation, and long-term support. IM Certified Professional Learning offers products and services for building leaders in order to support this effort.

Pillar 4: Families and communities engage with and support student learning

Families are students' first teachers. At IM, we believe that students should be empowered to recognize and explore math in the world around them, whether they are at school, at home, or in their communities. IM curricular materials include family supports that provide an overview of each unit and interactive mathematical questions that families can ask their children as the unit progresses.

IM is also developing relationships with organizations such as Family Engagement Lab, whose (Families and Schools Talk) tool includes families as instructional partners by providing curriculum-aligned learning activities to families via text message in their home language. The IM Classroom honors caregivers as critical stakeholders, which moves everyone towards a collaborative and supportive learning experience.

What happens in an IM Classroom?

When a student enters an IM Classroom, they enter a space that will encourage participation, develop confidence, inspire collaboration, and most importantly, equip them to know, use, and enjoy mathematics. The essence of the IM Classroom is the idea that learning happens when you pay attention to all of the actors-the students, the teachers, and the mathematics (yes, mathematics is alive in the IM Classroom!)-and build an instructional model that supports the complex community that they form.

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Beyond Curriculum Adoption: A Vision of the IM Classroom - IM CERTIFIED® BLOG

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By William McCallum, IM CEO Here at IM we are excited by and proud of the reception IM K-12 Math™ is getting. As more and more districts adopt it, we are thinking about how to support them. What are the next steps? Our vision of a classroom community informs this work.

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Lizzie Skousen explains in detail what a lesson synthesis will entail. A well-executed lesson synthesis is essential to accomplishing the learning goals of a problem-based lesson.

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By Lizzy Skousen, 6-12 Curriculum Writer, IM Certified® Facilitator

During a problem-based lesson, the teacher does a lot of listening while monitoring student learning. When teachers are introduced to a problem-based lesson structure, they may wonder:

"Do we just hope that students will think about what we want?"

"How will students learn the things they need to know?"

"When do I actually teach?"

"Is this doable with the amount of instruction time I have?"

One answer to all of these questions is a well-executed lesson synthesis.

There is an overall structure to an IM lesson. We begin with inviting students to the mathematics of the day, then dive more deeply into concepts and procedures. After the lesson activities and before the cool-down, there is a lesson synthesis when we consolidate and apply the learning. What does it mean to consolidate the learning of the day?

We need to bring together all of the learning that has happened with individuals and groups and make it explicit for the entire class. During each activity, students generate solution methods and then reflect and discuss how they solved the problems. There may be as many different ideas as there are students. Some students or groups will generate strategies or make connections that align with the learning goals of the lesson, but not every student will. Sometimes they may choose a more familiar but less efficient strategy or struggle to make a specific connection.

"Do we just hope that students will think about what we want?"

I like to imagine that teaching is a bit like taking my students for a wilderness exploration hike. I want the hikers to explore, see new things, and get to play, but I also don't want them to get lost or wander onto a trail going the wrong direction. As the leader of the hike, I need to start by knowing the area. What are the major landmarks? Where do we start, where do we end, and what are some major pitfalls we need to avoid?

In a lesson, I need to know the same things. What is the purpose of the lesson? Where do I want students to end up? What do I want students to be able to accomplish?

The learning goals and cool-downs are really clear signposts to help answer these questions. The learning goals help the teacher know what students should understand and be able to do, and the cool-down shows how students will demonstrate it. With this information, I can go into each activity with a clear idea of where the lesson is going. During the lesson synthesis, I check in to make sure all students have heard the important takeaways of the lesson so I know they are ready to demonstrate their learning on the cool-down.

"How will students learn the things they need to know?"

When students are exploring mathematical ideas, they are not all going to do it in the same way. On the wilderness hike, some explorers will carefully follow a pre-marked path, while others will try hopping on rocks or logs, and still others may follow an interesting bug. During the lesson, some students will want to use a familiar representation instead of trying a new one, others will skip using a diagram at all, and some may get focused on a different approach. One group of students may already be showing that they can meet the learning goal, while another group is still unsure. This is why it's important to consolidate the learning of the day.

The lesson synthesis gives teachers the opportunity to bring together students' ideas and focus on the learning goals for the lesson. Targeted questions during the lesson synthesis highlight the learning that has already happened during each activity and help make this learning explicit for all of the students in the class.

"When do I actually teach?"

When I have my wilderness explorers hiking with me, I think of myself as a scout leader. We may be exploring and having fun, but there is also an intended direction to travel. With my students, they explore and play with ideas, but there is a mathematical direction in a lesson as well.

The lesson synthesis is a brief but vital component of the lesson where teachers can make sure that students have all heard and seen important vocabulary words, strategies, and connections. In this discussion with the students, the teacher asks targeted questions, and a few students will share their thinking. The teacher may revoice important ideas, highlight strategies that align with the learning goals, and explicitly state an important concept or vocabulary term. Most of the students will be listening during this part of the lesson.

"Is this doable with the amount of instruction time I have?"

Even on the most relaxed hike, there are time limits. If I know that we have to meet back at camp before sundown, I have to plan ahead to make sure that my hikers all get there on time. Since I've already looked ahead at the map, I know about where we should be throughout the day and can set a pace for the hike.

Pacing a lesson can be a challenge. It can seem like there is not enough time in a day to do the synthesis, but the lesson synthesis is critical to student learning. Each lesson synthesis should take about 5 minutes of class time before the cool-down. One way to pace the lesson effectively is to work backwards. Plan for the last 5 minutes of class to be the cool-down, and the 5 minutes before that to be the lesson synthesis. Then look at how much instructional time is left and adjust the pace for the other activities as needed.

Since the lesson synthesis brings together all of the learning that happens in each activity and makes it explicit for the whole class, it's not necessary for every student to have completed every activity perfectly before moving from one activity to the next.

Conclusion

After students complete the cool-down, take a moment to reflect. If most students showed evidence of accomplishing the learning goals, what happened during the lesson synthesis that helped consolidate the learning for all students? If most students struggled with the cool-down, how could the lesson synthesis have gone differently? Connecting the day's lesson synthesis with the cool-down can help you plan ahead for future lessons.

A well-executed lesson synthesis is essential to accomplishing the learning goals of a problem-based lesson. This is the point where teachers make explicit what students should take away from the lesson and give students the necessary preparation for the cool-down. When preparing for a lesson, make sure to plan time for the lesson synthesis and work backwards from there to pace the other learning activities.

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Exploring the Lesson Synthesis: When do I actually teach? - IM CERTIFIED® BLOG

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By Lizzy Skousen, 6-12 Curriculum Writer, IM Certified® Facilitator During a problem-based lesson, the teacher does a lot of listening while monitoring student learning. When teachers are introduced to a problem-based lesson structure, they may wonder: "Do we just hope that students will think about what we want?"

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Consider what your students need to encounter math more deeply and in collaboration with others. More heads are better than one!

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Math teachers can talk all day about math! We get super excited when we encounter someone else who enjoys these conversations as well.

But too many of our students don't get to experience that joyful discourse, which limits their understanding of and positive experiences with math.

How would our students' math learning and perception about math improve if they also had regular opportunities to talk about math? How might these opportunities help us create a world where learners know, use, and enjoy mathematics?

Let's explore the Math Language Routines, which are embedded in IM K-12 Math.

What are math language routines?

Stanford Graduate School of Education's Understanding Language and the Stanford Center for Assessment, Learning, and Equity (SCALE) designed eight Math Language Routines (MLRs) to help teachers "amplify, assess, and develop students' language" in math class. These routines are structured, but adaptable to the content and classroom context. The routines "emphasize the use of language that is meaningful and purposeful, not inauthentic or simply answer-based . . . [and] can and should be used to support all students learning mathematics." (from Understanding Language/SCALE's Principles for the Design of Mathematics Curricula: Promoting Language and Content Development ) There are four specific design principles used to entice students to discuss the concepts and ensure that the discussions provide opportunities for students to learn something new. The Math Language Routines also provide opportunities for students to engage in the Common Core's Standards for Mathematical Practice .

As students engage in math language routines, MLRs help students to advance their thinking in the following ways:

OPTIMIZING OUTPUT as students describe their own math thinking to others orally and visually or writing as physical, graphical, pictorial, or symbolic representations.

SUPPORT SENSE-MAKING as students scaffold their thinking and amplify language so students can make their own meaning between concepts and representations.

CULTIVATE CONVERSATION by providing opportunities to simultaneously make meaning, communicate that meaning, and refine the way content understandings are communicated.

MAXIMIZE META-AWARENESS as students organize their own experiences, ideas, and learning for themselves through reflection of the experience of discussing their math ideas, reasoning, and language.

This doesn't just mean that teachers tell students to talk about math and they do. We know that if we simply open the space and tell students to talk, much of the discussion will veer off-topic. Math Language Routines help teachers create a structure in which students can bring those four design principles to life.

Let's see what opportunities each MLR provides for students to practice exploring their math thinking and the MLRs' connections to the Standards for Mathematical Practice .

MLR 1: Stronger and Clearer Each Time - Students write a response to a math problem, then verbally share their response with a partner to get feedback from the listener to improve the response, and revise their original written response based on the feedback they received.

Students learn to both listen to their own thoughts and the thoughts of another with the purpose of strengthening their "first draft" thinking. This MLR strengthens student communication of their thinking. They make their explanations clearer through repeated "reviews" and revisions, which allow them to practice giving, receiving, and applying constructive feedback, and develop listening skills. This MLR helps students communicate their mathematical reasoning with greater clarity and focus.
(This connects to Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them, 3: Construct viable arguments and critique the reasoning of others, and 6: Attend to precision. As students verbalize and review in writing the strategies they used and justification of those strategies, students have the opportunity to get feedback which can be used to critique the precision of their solution strategy and answer.)
MLR 2: Collect and Display - Students access their own and others mathematical ideas as the teacher scribes the language, strategies, and concepts students use during partner, small group, or whole-class discussions using written words, diagrams, and pictures.

By creating stable representations of student thoughts, the teacher extends the involvement of students in the math classroom. Student contributions are displayed for everyone to see. During that discussion as well as future conversations, students refer to these written ideas to improve the clarity and focus of their own communication. They can use the vocabulary, reference previous relationships between concepts, and identify new connections. This MLR helps make student thinking visible and promotes student ownership over mathematical ideas.
(Standards for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others, and 6: Attend to precision. As students view the thinking of their classmates from the representation, they can address any differences they see between their representation and their classmates' representation in type and kind, further pushing students to find the most efficient or precise representation to solve the problem.)
MLR 3: Critique, Correct, and Clarify - Students rewrite a math response from an example that is incorrect, incomplete, or otherwise ambiguous.

In addition to providing students with a space to further engage in math, students employ a "growth mindset" and consider revisions to their work in order to strengthen their communication. This MLR helps students "try on" others' math thinking in order to improve it.
(Standards for Mathematical Practice 3: Construct viable arguments and critique the reasoning of others. Similar to doing error analysis, students have the opportunity to engage with a strategy for solving that might be different from theirs in order to find ways to improve the situation representation, address and clarify misconceptions about the math, and "borrow" parts of the strategy that were relevant to add to their toolbox.)
MLR 4: Information Gap - In a group, each student has different parts of the math context and they work together to piece together that information orally and/or visually to bridge the gap between the parameters of a math situation and a question to solve a math problem.

As students work to make sense of individual pieces of information about a math context, they also identify what information they need in order to answer the math question. This creates an environment where students work together as they consider which strategies are the most efficient and what information they need to know to solve the problem. This MLR helps students explore math contexts with a purpose.
(Standards for Mathematical Practice 2: Reason abstractly and quantitatively, and 4: Model with mathematics. As students imagine the kinds of information they need to know and explain why they need to know that information, they are building an understanding of the problem and possible solutions related to the parameters of the problem and the kinds of data they need to solve for an answer.)
MLR 5: Co-Craft Questions and Problems - Students take a provided math "answer" to create a problem that could result in that answer or use a given context to create a problem that can be answered using that context.

With this MLR, students use their creativity to explore a math context as they iterate their understanding in order to identify questions that can be asked and answered by the context. As students share their understandings with others, they also uncover the importance of slowing down to explore and think before they try to answer a question, which results in students understanding the math more deeply. This MLR helps students define math contexts.
(Standards for Mathematical Practice 4: Model with mathematics. By creating their own questions and problems, students learn to visualize the parameters of the problem as they consider what kind of answers are possible with the information the problem provides.)
MLR 6: Three Reads - Students are guided to read the problem three separate times with three separate purposes with quick discussions between each read.

When students slow down to consider how they can use the information in a problem, they notice things about their understanding of the problem context and their own math understanding that they wouldn't have noticed before. Giving students a purpose to read helps to focus students to identify (1) the context of the mathematical situation, (2) relationships that exist within that context, and (3) strategies that can be used to answer the question using the problem context. This MLR helps students think metacognitively about their math problem solving.
(Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them. As students set a purpose for reading each of the three times, students practice and see the importance of understanding the problem context and using the information they know from the problem in order to identify a strategy for solving that relates directly to the problem context and available information.)
MLR 7: Compare and Connect - Students identify, compare, and contrast their own understandings with other students' mathematical approaches, representations, concepts, examples, and language.

As students encounter other's math thinking, this MLR opens the floor for students to consider how they see and talk about math. This MLR specifically helps students interact with each other's thinking.
(Standards for Mathematical Practice 4: Model with mathematics, 6: Attend to precision, and 7: Look for and make use of structure. As students compare (find differences) and connect (find similarities) between their strategy for solving and another classmate's strategy for solving, students mine their understanding of the math concept in relation to the structure and steps of another student's understanding of the math. This allows both students to attend to precision because to be understood by another, they have to be precise with their explanation.)
MLR 8: Discussion Supports - Students access strategies in multi-modal ways, like visuals, aural, animation/movement, and symbols as modes, to help students better make sense of complex language, ideas, and classroom communication.

Enhancing access to the mathematical context through these multi-modal supports helps students develop understanding while also continuing to work on their mathematical communication. This MLR helps students deepen their mathematical understandings, and find ways to communicate their understandings in different ways.
(Standards for Mathematical Practice 1: Make sense of problems and persevere in solving them, 3: Construct viable arguments and critique the reasoning of others, 5: Use appropriate tools strategically, and 6: Attend to precision. Using discussion supports helps students to see the reasoning of others as well as identify which tools to solve are most appropriate. In using these supports, students can be successful with in-depth or multistep problems with support from teachers and classmates.)
Next Steps

Consider what your students need to encounter math more deeply and in collaboration with others. More heads are better than one!

Looking for more support for distance learning ? Check out IM's collection of resources.

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Math Language Routines: Discourse with a Purpose - IM CERTIFIED® BLOG

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Mathematical modeling is the process of choosing and using appropriate mathematics and statistics to analyze empirical situations, to understand them better, and to improve decisions. Teachers can use Math Modeling Prompts as a way to differentiate in the classroom, while maintaining equity.

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Each Extra Support lesson is associated with a lesson in the Algebra 1 course. The intention is that students experience each Extra Support lesson before its associated Algebra 1 lesson. The Extra Support lesson helps students learn or remember a skill or concept that is needed to access and find success with the associated Algebra 1 lesson.

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The integrated courses are currently in production with Int I to be released in 2024 and Int II & III in 2025. Here, you will find guidance on how to use the Illustrative Math curriculum with integrated courses until I, II, and III are released.

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IM 9–12 Math Integrated Guidance -SHARED- (1)