Embedded Files
Welcome to the Illustrative Mathematics curriculum! This problem-based curriculum makes rigorous middle 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?
Lesson Summaries: Each lesson includes a summary of its key mathematical ideas. The summaries provide worked examples when relevant. Students use this resource when they are absent from class, to check their understanding of the day’s topics, and as a reference when working on practice problems or studying for an assessment.
Practice Problem Sets: Each lesson is followed by a practice problem set. The problems help students synthesize their knowledge and build skills. Some practice problems in each set relate to the content of the current lesson, while others revisit concepts from previous lessons and units. Distributed practice, such as this, has been shown to be more effective at helping students retain information over time.
Learning Targets: Each lesson includes learning targets that summarize the goals of the lesson. Each unit’s complete set of learning targets is available on a single page that students use as a self-assessment tool as they progress through the course.
Family Support Materials: Each unit includes two or more (depending on the unit length) overviews of the math content, each with examples and a problem to work on with your student.
What can my student do to be successful in this course?
At first, learning in a problem-based classroom can be challenging for students. Our students are not used to discussing and writing their thoughts. It will take time for them to learn, that is ok. Over time, students gain independence as learners when they share their rough drafts of ideas, compare their existing ideas to new concepts they are learning, and revise their thinking. Many students and families tell us that while 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 make a guess? Can you describe an answer that’s definitely wrong? Can you draw a diagram or a representation?
Be patient and resist the urge to teach your child a "trick" or the standard algorithm. Their method may not be the most efficient, but working through the process and developing a method, and than developing more efficient methods is the point of this program.
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.
At the end of class or when you are studying, take time to write some notes. Ask yourself, “Do I understand the lesson summary? Do the learning targets describe me?” If not, write a sentence such as, “I understand _____, but I don’t understand why _____.” Share it with a classmate, teacher, or other resource who can help you better understand.
I am excited to support your student in their journey toward knowing, using, and enjoying mathematics!
From the IM Math website LINK
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