Solving Problems with Models

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SWBAT draft problems and create models to match.

Big Idea

Models can assist students in "seeing" the problem at hand.


10 minutes

Who can tell me what this picture tells you? Who can tell me a problem that matches this model?  How do expert problem solvers use models to solve problems?

We begin our dialogue about models and how they help us “see” the problem more clearly.

I’ve noticed that even as we progress through the year, students are still struggling to recognize how a model matches a problem, or how to draw a model to illustrate a problem. I think it’s important to spend time modeling how we can use models to make sense of addition or subtraction problems.

Mathematical Practice 4 - Model with mathematics stresses the importance of giving students many opportunities to make sense of the meaning of the math by creating representations.

Guided Practice

20 minutes

Each pair of students uses a whiteboard to work together to draw a model and then write a problem to match.

You and your partner have a white board and dry erase marker, and you’re going to get to create your own model for all of us to see. You need to write a problem and draw a model to match it, and then you will present it to the rest of us! Make sure it’s something that will challenge the rest of us to think hard!

While students are working I am working with students who have shown in previous days that they struggle to show a model to match their problem. It's a good time to provide more guidance for struggling students or groups, but if you don't have anyone who needs that guidance you can check-in with each group. A great guiding questions I like to use is 'Can you tell me what this represents?' or a similar open ended question.

I spend the time allowing students to present their work instead of just holding it up for me to see because they love to present their work, and they often find their own mistakes when they come up to explain it or their classmates ask them questions about it.

Partner Work

20 minutes

Hmmm...seeing all of your creative problems and unique models have given me some great ideas for problem solving! When you go back to your seats I want you to work with your new partner at your table to write and model new, and different problems. Remember that we can really stretch our thinking when we think about other ways to do things. Our classmates all gave us great examples today of what some other ways we can try might look like.


5 minutes

Alright I’m going to pull sticks to allow a few groups to share. Make sure you and your partner agree on which problem you’d like to present if either of your names gets called.

I think partner talk and discussion with the math classroom is a really critical part of developing a community of discussion and debate. Students feel confident to discuss concepts, ask questions and thoughtfully disagree. Students are using clear and precise language in their discussions with others and in their own reasoning (MP6).