Welcome to the Illustrative Mathematics curriculum! This problem-based curriculum makes rigorous elementary school mathematics accessible to all learners.

What is a problem-based curriculum?

A problem-based curriculum is one in which students spend most of their class time working on carefully crafted and sequenced problems. Teachers help students understand the problems, ask questions to push their thinking, and orchestrate discussions to ensure that the mathematical takeaways are clear. Learners gain a rich and lasting understanding of mathematical concepts and procedures as well as experience applying this knowledge to new situations. Students frequently collaborate with their classmates—they talk about math, listen to each other’s ideas, justify their thinking, and critique the reasoning of others. They communicate their ideas both verbally and in writing, developing skills that will serve them well throughout their lives.

This kind of instruction may look different from what you experienced in your own math education. Current research demonstrates that students need to think flexibly in order to use their mathematical skills in real life (and on the types of tests they will encounter throughout their schooling). Flexible thinking relies on understanding concepts and making connections between them. Over time, students acquire the skills and the confidence to independently solve problems they've never seen before.

What supports are in the materials to help my student succeed?

• Warm-ups: Each lesson begins with a warm-up routine that invites students to the mathematics of the lesson. The same routines are used throughout the entire curriculum, and students become comfortable with their structure. During the warm-up routines, all students are encouraged to share their developing ideas, ask questions, and respond to the reasoning of others.
• Activity and Lesson Syntheses: Each activity and each lesson include a synthesis that provides an opportunity for students to discuss the key mathematical ideas and incorporate their new insights into a big-picture understanding.
• Section Summaries: Each section is followed by a summary of its key mathematical ideas. The summaries include visuals and worked examples of problems when relevant. Students use this resource to review the topics covered in the section.
• Representations: A limited number of representations are thoughtfully introduced in the curriculum, and students are encouraged to use those that make sense to them. The representations are designed to help students develop an understanding of the content as well as solve problems.
• Family Support Materials: Each unit includes an overview of the math content, along with questions to ask and problems to work on with your student.

What can my student do to succeed in this course?

Learning in a problem-based classroom can challenge students at first. Over time, students gain independence as learners when they share their rough drafts of ideas, compare their existing ideas to new things they are learning, and revise their thinking. Many students and families tell us that while this was challenging at first, becoming more active learners in math helped them build skills to take responsibility for their learning in other settings. Here are some ideas for encouraging your student:

• If you’re not sure how to get started on a problem, that’s okay! What can you try? Can you draw a picture or a diagram? Can you make a guess? Can you describe an answer that’s definitely wrong?
• If you’re feeling stuck, write down what you notice and what you wonder, or a question you have, and then share that when it’s time to work with others or discuss.
• Your job when working on problems in class is to come up with rough-draft ideas and share them. You don’t have to be right or confident at first, but sharing your thinking will help everyone learn. If that feels hard or scary, it’s okay to say, “This is just a rough draft . . .” or “I’m not really sure, but I think . . .”
• Whether you feel stuck or confident with the material, listen to your classmates and ask them about their ideas. Learning happens when you compare your ideas to those of other people, just like you learn history by reading about the same events from different perspectives.

We are excited to support your student(s) in their journey toward knowing, using, and enjoying mathematics!