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1. Going Deeper_ Tailoring Digital Resources Directions.pdf

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Resources that support Illustrative Mathematics teaching & learning K-12

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By Kristin Gray, Jenna Laib, Sarah Caban
Open House. Back-to-School Night. Family Welcome. Math Night. No matter what the name of the event that launches the school year, family members will arrive at your school with the same burning questions: What do I need to know to set up my child up for success in math this year? and How can I continue to support them throughout the school year?

Although families and teachers both understand the importance of a home/school partnership, that relationship is often complicated. As the year gets rolling, both parties may feel short on time to make it work and sometimes even the best intentions conflict. In the spirit of being proactive instead of reactive, we have developed a downloadable

We developed each of these grade-level family night lesson plans to mirror problem-based lessons in where the focus is on the math and math learning rather than the typical monologue on procedures and policies. These activities are meant to invite families to think about the following questions: What does it look like to do math? What are the advantages of having students do math in a problem-based curriculum, instead of in a more traditional lecture-and-practice format? What resources are available to help set our students up for success this year?

This structure reflects the overarching design of units and lessons. Each lesson begins with an invitation for students to do the mathematics before launching into the heart of the work. Each unit follows the same structure. Each grade level at large follows this design, too, as does the experience across the 6-8 continuum. It makes sense to think about the home/school partnership with the same flow: an invitation, then the heart of the work, and then application.

How do we want to invite families to engage?

As with every curriculum lesson, it is important to start with the learning goals.
Family Night Learning Goals

Begin a supportive, year-long relationship of math learning

Understand how a problem-based lesson looks and feels

Understand the connection between what students are learning in class and the family support materials

Understand how to access the student and family materials

Each grade level lesson plan is estimated to last about an hour with a focus on Unit 1 in the curriculum. The plans each follow the same outline and include suggested modifications for longer or shorter amounts of time. The general structure and purpose for each section is described below, with more detailed teacher notes available in the downloadable lesson plan.

*For ease of reading, we interchangeably refer to family members as participants in these descriptions.

1. We launch the time together by asking for words or phrases in response to the question, What does it mean to you to 'do math'? Family members, students, and teachers may have very different perspectives on this question. Just as we do with students, we begin without judgment and record participants' words and phrases accurately. Family members arrive with their own mathematical identities and a wealth of different experiences, so it is important to honor and respect these experiences. It is our hope that over the course of the hour together, there will be shared mathematical experiences that unite participants, and perhaps shift some perspectives on what it means to ' '.

2. Next, family members experience a warm-up from the curriculum lesson. Teachers may need to contextualize this, explaining how it fits into the unit's narrative arc, and then facilitate it as written in the curriculum. We purposefully chose an activity with a warm-up that is more open in order to invite everyone into the mathematics. In addition to demonstrating a curriculum lesson that students experience, this time also gives family members time to warm up their own mathematical thinking.

3. The warm-up segues into a lesson activity that follows. This is an anchoring experience meant to set the stage for what it looks and sounds like for the students to learn math this year. We purposefully chose an activity that is hands-on, involves some intuition outside of simply knowing or not knowing the math, and can be supported by the use of mathematical tools. It is important to be mindful that this may be the first time families are engaging with a mathematical task like the ones in the curriculum, so they must feel supported as they work, be encouraged to collaborate, and experience moments of success.

4. To extend the experience of the lesson activity, families are invited to read through a portion of the Unit 1 family support letter. Teachers should encourage families to make connections to the warm-up and lesson activity as they read. Just as we suggest doing throughout the school year, we chose to only include the portion of the letter from the section of the unit they experienced to keep the reading length manageable and content-focused. This is an opportunity for the teacher to also demonstrate how to access the family letters and student materials as well as offer strategies for using them, e.g., to understand content before jumping into homework help, to support students that need or want extra practice, etc.

5. To close, we suggest revisiting the framing question: What does it mean to 'do' math? Families will have experienced three activities as a group: a warm-up, a lesson activity, and family letter. Consider asking: What did it feel like to do math tonight? What felt different from what you remember about doing math when you were in middle school? How might this approach improve learning and understanding in math? How can these resources help you support your child this year?

If there are other items on the agenda for family night-e.g., some brief discussion of policies, expectations, or rules-the suggested time spent on each section may be trimmed down. Communicating expectations is important. Before you devote your entire time with families to rules, however, remember to ask yourself: Is this how I want to invite families to partner with me? What might best achieve your goals?

To download the lesson plan and materials, click here.

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Building a Supportive Home/School Partnership - IM CERTIFIED® BLOG

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By Kristin Gray, Jenna Laib, Sarah Caban Open House. Back-to-School Night. Family Welcome. Math Night. No matter what the name of the event that launches the school year, family members will arrive at your school with the same burning questions: What do I need to know to set up my child up for success in [...]

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

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By Lisa Matthews, IM Certified® Facilitator and PL Specialist Team for Grades 6-12 The IM curriculum is so thoughtfully designed and written that even those of us who have spent years with IM often find content that is new,...

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How do you get ready for a new school year? There is a lot to do, physically and emotionally.

We hope you start the 2022-23 school year feeling rested, rejuvenated, and prepared. To support you, we have curated a collection of back-to-school blog posts. These posts are organized around 5 topics: building classroom community, problem-based learning, lesson planning (K-5 and 6-12), instructional routines, and access for all.

Start with one that sparks your curiosity. The post might anchor your thinking, affirm some of your beliefs and practices, raise new ideas, or have you question prior practices. After you finish reading, you might want to extend the conversation with a colleague from your school or within an online community. And you might want to check out another one! Our full archive of blog posts is available on illustrativemathematics.blog

Building Classroom Community

What do you want your classroom community to look like? Feel like? Establishing norms helps teachers cultivate a community of learners where making thinking visible is both expected and valued. How do you want to start the year?

Problem-Based Learning

Problem-based instruction means believing all students can solve problems on their own, and giving them a chance to try. All IM curricula, K-12, are designed to support this. What might this look like?

Lesson Planning

Let's dig into lesson planning! Where do you start? What are some important things to keep in mind?
K-5 6-12

By Jennifer Wilson and Vanessa Cerrahoglu

Instructional Routines

Instructional Routines have a predictable structure and flow so that students and teachers can focus on the content. They are designed to invite all students to engage in the mathematics of each lesson. Here are a few examples:

By William McCallum and Kate Nowak

Access for All

All students, each with unique knowledge and needs, enter the mathematics learning community as capable learners of meaningful mathematics. How can educators leverage student strengths to support all students in learning grade-level mathematics?

Next Steps

Which post-or posts!-do you want to explore first?

After reading, you might want to think about:

How did it help you build on, change, or shape your thinking about math teaching and learning?

How can you continue this conversation?

What do you want to explore next?

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Getting Ready for 2022-23: Back to School Blog Posts - IM CERTIFIED® BLOG

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How do you get ready for a new school year? There is a lot to do, physically and emotionally. We hope you start the 2022-23 school year feeling rested, rejuvenated, and prepared. To support you, we have curated a collection of back-to-school blog posts. These posts are organized around 5 topics: building classroom community, problem-based [...]

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Providing access & challenge to math students

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Providing access & challenge to math students

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By Max Ray-Riek, Director of 6-12 Professional Learning

In my role at IM, working with teachers and administrators, I am asked to help with the challenges of implementing an IM curriculum. We are often asked, "How can I differentiate instruction while using this curriculum?" or "What resources does IM offer to support differentiation?"

When we created the teaching guide for the curriculum, we chose not to use the word differentiation . This was deliberate, as differentiation is interpreted in many ways. One common interpretation is providing different instructional tasks for different students, either through differentiated student materials or by pulling small groups based on some diagnosis and providing different instruction to those groups.

We focus on and . IM K-12 Math is designed to give all students access to grade-level mathematics, by providing tasks that students can make sense of, reason about, collaborate to solve, and learn from without specifying the strategies students must use to solve the problem. The curriculum is also designed to give all students opportunities to go deeper with the content, and to make many connections between concepts. In fact, the curriculum is designed for and works best when students come up with a range of approaches (concrete, abstract, correct, incorrect, algorithmic, visual, etc.) and are given multiple opportunities to compare their thinking to peers and to the examples provided in the curriculum. All students benefit from hearing a range of ideas and connecting their ideas to the ideas of peers with different approaches.

We recognize that students come to us with a wide variety of interests, strengths, experiences with math and language, cognitive resources, etc. Providing access to grade-level mathematics does require that teachers make strategic adjustments in order for students to engage, make sense of the questions being asked, persist, collaborate with peers, share their thinking, listen to and understand each others' thinking, internalize and try on new ideas, and practice and apply what they are learning.

Educator and researcher Rhonda Bondie suggests that teachers plan for and use differentiated instruction before, during, and after a lesson as they

adjust common instruction: adjust the launch, directions, sequence of activities

use specific resources: offer a support such as sentence frames to students who need access for participating in conversation with their classmates

individualize practice: offer various practice assignments for students to choose from (2019)

What does this look like in a problem-based classroom? When we apply Bondie's suggestions, we consider what supports are already included in the curriculum, as well as how teachers can plan to support access and challenge for all students. Let's consider an example drawn from experiences with several teachers and coaches using IM across the country. The example is from IM Algebra 1 Unit 4: Functions, and we'll call the teacher Ms. Goodson.

Adjust common instruction: Use a familiar context

Ms. Goodson is preparing to teach Lesson 1: Describing and Graphing Situations . She knows that the purpose of Lesson 1 in each unit is to invite students to the mathematics of the unit and that students will have opportunities throughout the first several lessons to continue to work on these ideas. The lesson goals will help her decide what is most important for all students to consider. She reads the lesson narrative and the learning goals. The learning goals for the lesson are:

Interpret descriptions and graphs of functions in context.

Understand that a relationship between two quantities is a function if there is only one possible output for each input.

Use words and graphs to represent relationships that are functions, including identifying the independent and dependent variables.

Ms. Goodson next looks at the cool-down and student lesson summary. This gives her a sense of what she should be monitoring for as students work-she should listen to students talking about whether one variable is a function of the other, considering whether there is only one output for a given input, and either drawing graphs from descriptions of situations or describing situations based on graphs.

With that information in mind, she takes a look at the warm-up. It's about buying bagels from a bagel shop. There is not a bagel shop in her town, though many students have seen them for sale in prepackaged bags at the grocery store. Ms. Goodson considers whether this is a good opportunity for students having a window into another culture, but is concerned about the complex context and complex mathematics being too big of a barrier.

This problem features a non-linear pricing scheme, which reminds Ms. Goodson of heated conversations students had during this year's homecoming festivities where couples and groups got discounts for dance tickets. She also remembers that at the homecoming fair tickets for the carnival games were sold individually, by the half-dozen, and the dozen. She decides that changing the context from bagel pricing to ticket pricing will help her students quickly access the warm-up and maintain the mathematical intent: surfacing the idea of the output for a given input being ambiguous (for example 13 bagels could be sold for \$11.25, \$13.00, \$13.25, or \$16.25 unless the store owner always sells other quantities of bagels at the best price).

Use specific resources: Blank copies of the table

Based on previous lessons that involved completing tables of values, Ms. Goodson anticipates that some of her students might have a hard time getting started on the task of filling out the best price table. Some students may want to argue for different pricing schemes, others may feel overwhelmed by having to think about all the different possible prices for each number of tickets and narrow down to the best price. She doesn't want students to get bogged down in calculating; she wants them to see and understand the tables and graphs that represent the ambiguous situation versus the situation where price is a (non-linear) function of number of tickets purchased. Therefore she decides to print blank copies of the table of each person's pricing scheme from the activity synthesis to have on hand as needed for groups that are struggling to get started on the best price table.

Her goal is for all students to be ready after 7 minutes of group work time to participate in a conversation about why price is not a function of number of tickets purchased, but best price is.

Use specific resources: Manipulatives

Ms. Goodson also has an idea about Activity 2: Be Right Back! While it's unusual for dogs to be tied up outside of stores in her community, it's pretty common for a dog to be tethered in a yard. However, some of the emerging bilingual students in her class might still have a hard time understanding the descriptions of how the dog moves around the post. How could they engage in a conversation about what the graph should look like if they're having trouble visualizing or asking questions about the situation?

Ms. Goodson reads the suggested supports for English learners and students with disabilities, and plans to launch the task as written in the curriculum, demonstrating the dogs' action on Day 3 using a stuffed dog leashed to a spool of thread and inviting multiple students to use the toy dog to show how they interpret the story, and then share how they might sketch a graph of the dog's distance from the pole over time. She makes sure that she has enough toy animals and spools of thread to offer them to small groups as needed to support their sense-making and conversations. She is confident all groups will be able to get started after that launch, but that they will still have to work hard to both translate the words into actions and the actions into a sensible graph.

Individualize practice

As Ms. Goodson studies Activity 1.3: Talk About a Function, she realizes that there are multiple opportunities to individualize practice and give students different amounts of scaffolding to continue to move towards the learning goals. The task itself gives students the opportunity to make a choice about which pair of variables they choose, and she realizes that some pairs of variables might be harder than others. She also thinks about ways she could provide more access, challenge, and choice for students.

Assign some students an activity from the aligned Algebra 1 Supports lesson which gets to the same learning goals but involves matching rather than creating your own graph.

Assign students a particular pair of variables to focus on first, one that she knows will be accessible and will help them get started with confidence.

Create a worksheet for students to help them remember to answer each of the questions and include sentence stems to help students explain their ideas, not just write their answers.

Encourage students to brainstorm additional pairs of variables, and choose one pair to focus on.

Give students the challenge of making up their own story for a partner to graph.

Use a website such as graphingstories.com to find more examples, based on videos, which might give students more access than a written description. She notes that in the graphingstories.com handout time is already on the -axis. Since she would like students to make a choice about which variable to put where, and how to scale the axes, she would need to provide blank graphs.

Given what she sees in Activity 1.3, and what she knows about the cool-down and lesson summary, Ms. Goodson decides that while students are doing more individualized practice during Activity 1.3, she will monitor and note students who might struggle with the cool-down, which is very similar to the practice. She knows that students will have more opportunities in the next lesson to show what they know, so she decides to invite a few students to come to her desk to work on the cool-down collaboratively. Then they spend time reading and highlighting key ideas in the student lesson summary, so she can better understand what makes sense to them now and what they are still grappling with. She will continue to monitor these students' understanding throughout the next several lessons since the cool-down guidance states that students will have more opportunities to work on these mathematical ideas. There is no need to "press pause" until Lessons 4 or 5 if students are not yet able to evaluate and interpret equations given in function notation.

Whew! That is a lot of decisions to make, but Ms. Goodson has been watching and listening to her students and uses many of the suggestions and supports already built in the curriculum and the lesson plan. Ms. Goodson spends her planning time thinking about how she will make adjustments to support her students, rather than having to create lots of additional materials or come up with different standards-aligned activities for different students.

Next Steps

Consider an upcoming lesson.

1. What supports for access and challenge are already included in the lesson?

2. What can you ask, amplify, or adjust during common instruction to provide additional access or challenge?

3. What specific resources can you offer students who need additional access or challenge?

4. How can you individualize practice using:

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Differentiating Instruction with IM 6-12 Math™ - IM CERTIFIED® BLOG

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Middle School Accelerated course information

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Middle School Accelerated course information

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