# How to Incorporate Creative and Engaging Problem Solving Into Your Math Class

Have you ever tried using Fermi problems in your math class? If you haven’t, I highly encourage you to try it. The kids love it and I have never seen such high levels of engagement and determination to solve a challenging problem!

I had not heard of this until a couple years ago, but now I am hooked!

**Who is Enrico Fermi?**

“Fermi Math” is named after Enrico Fermi. He was a scientist/mathematician who loved playing with numbers! He found that by using estimation and sample size he was able to calculate seemingly impossible questions in his head.

**What is a Fermi Math Problem?**

Fermi math problems require

*estimation

*questioning

*research

*communication

*reasonable assumptions

*creativity

*flexibility

*number sense

*perseverance!

A couple of classic Fermi questions are:

How many water balloons would it take to fill your classroom?

How many jelly beans fill a one liter bottle?

Fermi problems emphasize the process of solving problems over getting the exact answer. Fermi problems require students to ask many questions and organize their thinking as they expand on their calculations step by step.

Fermi problems will not result in an exact answer (usually), and different kids may come to their answers using different strategies. This is a great way to get kids talking about math and justifying how they came to their answers.

**How do I Use This in My Classroom?**

This is a great activity for any time of the year, but I usually use Fermi questions as a fun break between units, as a fun project for kids to work on if they finish early, or at the end of the year when you have finished the “required” curriculum but still want to keep your class engaged in math.

I start by posing a question to the whole class that we can solve together. A good question that has worked well for me is “How many novels would it take to fill our classroom?”

This leads us to brainstorm all the information we would need to solve the question.

- how big are the novels? (gather dimensions of a typical novel in your room)
- how big is our room? (measure length, width and height of room)
- how many novels would we need to stack to get from the floor to the ceiling?
- How many novels would cover the floor of our classroom?

Rounding is your “friend” in Fermi math problems, so I encourage the kids to round their information to friendly numbers to make their computation easier. We then discuss how to use our numbers to calculate a conclusion to our original question.

Once we have worked through how to solve a Fermi problem together the kids are usually dying to get started on their own question!

I have each kid come up with their own Fermi math question. A typical question usually involves “how many ____” would it take to “fill/cover a _____”. The kids are instantly interested because they get to make up their question and get to include things that are interesting to them.

Some of my sports fans ask questions about how many footballs it would take to fill a specific stadium, how many hockey pucks would it take to cover the ice on a NHL rink. An examples of a question involving candy is shown in the pictures below.

**How do Students Share Their Work?**

After completing the project, I have students share their question, steps/process and final answer with their classmates. I typically have my students make a poster using 12″ x 18″ paper, but you could use technology resources like PowerPoint, Google Slides, Glogster, Explain Everything, and many others if you have access to them.

Give it a try with your students! I bet they will love it just as much as my students do! I have many Fermi Math products in my Teachers Pay Teachers store that you can use with your students. I have two Fermi Math freebies in my store that you can try right now!