I am back with another chapter review from What’s Your Math Problem? I felt like this chapter was really key for those states that are shifting to Common Core. As the students are presented with more challenging problems, they need more advanced thinking strategies in their toolbox. Let’s take a look at some of these strategies.

I am in love with this advanced thinking strategy! I use this all the time to help my students conceptually understand a math situation. A lot of times I will even introduce a skill with a simpler problem that relates to the more complex problem. However, I never thought of teaching and prompting the students to use this strategy. In this strategy, the students simplify the problem in order to understand it better before solving. Here are some suggested ways the students can do this:

- User simpler numbers: This will help the students to recognize the setting of the problem and identify the operation to use.
- Begin with a simpler case of the problem and gradually build on until you have solved the problem.

***Click here to see TWO example problems that would be great for modeling!

This is a sophisticated way of looking at problem solving that has the students considering all possibilities of a problem. This problem to me works well with probability questions or questions that require the students to find all answers or situations.

This advanced thinking strategy works well when the final outcome of a situation is given and the question asks about the original situation. This strategy is useful when teaching inverse operations of addition and subtraction and then multiplication and division. Here are some helpful ways to approach working backward:

- Write an open sentence.
- Draw a picture or diagram.
- Check the solution by working the problem “forward.”

- Discard their previous notions
- Think outside the box
- Give consideration to new ideas

To help the students with this strategy the book suggests using creative and critical thinking activities such as brain teasers and mathematical puzzlers.

These are definitely some advanced thinking strategies. Some of these would take quite a bit of modeling and thinking through to the students familiar with and comfortable with each strategy. However, can you imagine how the students would perform if they were familiar with these strategies? It would be pretty amazing!

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B. Hensley says

This chapter overwhelmed me as I thought of my students attempting these new advanced thinking strategies. I am grateful that these strategies are spelled out for me. Most likely, the nervousness comes from me never taking my students this far. I have attempted solve a simpler problem in the past with great success but I now see that I tried to take him to the next level too quickly. I became excited with his success of solving a simpler problem that I didn't give him time to practice and enjoy the success at that level or discuss discovered patterns as the author suggested on page 123 .