## Problem Solving for Fast Finishers

Problem solving is one of those areas that we, as math teachers, are always working on. Instead of teaching a skill, we are really teaching a thinking process. And. . . to complicate the matter even more, there’s not just one way think through most problems. That’s why I really love giving my students a variety of problem solving activities that they can practice with.

This week I used our Problem of the Week in my 6th grade math class today, for the fast finishers. Because we aren’t too “into” a particular topic at the moment, this problem solving activity uses a mix of operations, so students get some practice with basic operations along with the word problem practice.

I intended for students to use mostly division and multiplication, but I saw students using addition as well.

This problem solving activity gives students a ‘bake sale scenario’ and then asks four questions related to that scenario.

## Math Conversations About Solving Word Problems

I really enjoy talking with my students about what they’re thinking when they try to solve problems, for a few reasons:

- They think about problems in a different way than I do
- It makes me rethink the wording of the questions I ask (which makes me improve)
- I learn there will be several ideas to share with class.

I noticed a few different things when the students were solving the different parts of this week’s problem.

For part A, I multiplied 85 times 3 to get the total number of cookies and then divided by 24 (when I wrote the problem, I wanted the students to have to interpret the quotient, so I approached it with a desire to use division). Most students did the same thing (except for the few that multiplied 24 x 3…that gave me some good info.

BUT one student was just sitting and thinking, so I asked him *what* he was thinking. He started to say he divided 24 by 3 and then paused – I almost interrupted his thinking to redirect him to my way, but I successfully restrained myself, and asked why. He said he was thinking about how many baggies could be filled with one batch, and since the numbers worked nicely, he could definitely say that one batch would fill 8 baggies.

### Embrace Differences

I really liked his thinking process, because it hadn’t occurred to me to do it that way. Now, if the numbers hadn’t worked out evenly, it might not have been the best approach, but we could expand our class discussion to explore that.

After deciding he could fill 8 baggies per batch, he added on sets of 8 until he reached the correct number of batches.

As some students worked on part C (below), I started to think I should adjust the wording of the problem.

When I wrote the problem, I thought it would be clear that the number of cookies for part C was the same as part A, but some students thought of the part C as using 85 baggies of 2 cookies (same number of **baggies**), instead of using the same number of **cookies**.

As more students worked on it though, other students seemed to understand that the number of cookies should be the same as the original number they were working with, so I haven’t changed it yet. If you use the problem, please let me know what you think.

Again, a few students approached this part in a different way than I did – they said that in both cases, the cookies cost 25 cents each. Using this reasoning, some students said the cost was the same, while others did not – again, a great opportunity for discussion, both in small groups and as a whole class.

To see and/or use the entire problem and answer key, select the button below.

To access all of the Problem of the Week problems I’ve created over the past several years, check out the **Free Math Resource Center**!

Do you have some favorite problem solving activities?

**Additional Resources to Teach and Practice Problem Solving**

If you are looking for additional resources and activities for teaching problem solving to your math students, then make sure to check out these blog posts and products.