3-1-4 Pi Day Number Challenge

This 3-1-4 Number Challenge is the perfect way to challenge your brain on Pi Day! How many different numbers can you come up with mathematical expressions for using only the digits 3, 1, and 4?

Instructions

Use the digits 3, 1, and 4 exactly one time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the given numbers.

Usually, I find that it helps to break down the instructions a bit more for my students.

• Each digit must be used exactly one time. You can’t use 4+1 as an expression for 5 since the digit 3 has not been used.

• Add your choice of mathematical symbols between the digits.

• Digits can be combined to make multi-digit numbers. This is known as concatenation. 3 and 1 can be combined to make either 31 or 13.

• Need more ideas? Exponents, square roots, and factorials might help!

Three Different Challenges to Choose From

For my high school students, I am challenging them to find expressions for each of the numbers between 1 and 30.

I created two additional versions that challenge students to find expressions for 1-10 and 1-20.

There are solutions to all of the numbers from 1 to 30. To be honest, there are solutions to all of the numbers from 1 to 38, but I thought that a 38 number challenge would be very strange.

If you are working with younger students, I would suggest giving them one of the shorter challenges.

If your students are not familiar with the concept of a factorial and you don’t want to introduce the idea to them, you will want to do the 1-10 challenge. All of the numbers from 1 to 10 can be found without using the factorial symbol.

Both the 1-20 and 1-30 challenge require the factorial symbol for some of the solutions.

Factorial Resources

I created a factorial poster that prints on 11 x 17 cardstock that can be hung next to the challenge to help students with the concept of a factorial.

I have also previously shared a printable factorial and double factorial chart which can be provided to students as a resource.

Presenting the 3-1-4 Pi Day Challenge to Students

My students will be on Spring Break on Pi Day, so I decided to put up the 3-1-4 Pi Day Challenge a week early.

I created a display on the dry erase board in my classroom.

I printed a poster with the name of the challenge and smaller posters with the rules of the challenge which I taped to the board. I printed these posters on colorful cardstock to help catch my students’ eyes.

Below the posters, I hung three posters for students to write their solutions on. I printed each one of these solution posters on 11 x 17 cardstock.

Then, I put the 11 x 17 cardstock inside 11 x 17 dry erase pockets which I hung on the board with magnetic clips.

In the past when I have done number challenges like this, I have just printed the challenges on cardstock and had my students write directly on the cardstock. Inevitably, students would write their solutions on the wrong line or make a mistake while writing their solutions.

The dry erase pockets make it super easy for students to correct their mistakes. Plus, it means I can save my posters for next year and reuse them for future Pi Day celebrations.

Don’t want to go to the trouble of creating a classroom display? Just print and hand out the 3-1-4 Pi Day Challenge to your students.