DIY Number Function Box

Function boxes, or “in and out machines”, are a great way to introduce basic algebraic thinking to young learners. Students analyze the input and output numbers to determine the rule, or function, of the box. In and out tables can be found on worksheets, but the actual boxes are much more fascinating! They have a special chute that transforms a number card by flipping it over on the way out. My students quickly discover the “secret” flip, but the process is still fun and extremely engaging.

The complexity of the task can easily be adapted to many levels by simply changing the input and output numbers on the cards. I usually start with basic operations and then work my way up to very challenging, multi-step rules.

You can easily make a number function box out of a recycled juice carton. The trick is in the way you tape the chute. Here’s how!

First, gather your materials. You will need an empty juice carton, such as the orange juice container shown. You will also need some duct tape, scissors, a razor blade, and a few sheets of flexible cardboard. I used the back of a few notepads.

Open the top of the juice carton. Then use scissors to cut down, along the edge of each corner of the top part, as shown.

My carton had a pour spout, so I cut that out to make the top fold down flat. Just fold everything in and secure it with a piece of tape.

Use your razor blade to carefully cut slots for your in and out chute. Cut a slot at the top and bottom, approximately the same size and location as shown. My slots are about 2.5 inches wide and a half inch tall. Make sure that the two slots are lined up from top to bottom.

Once you have your slots, cover the whole carton with duct tape. Then use the razor blade again to remove the duct tape that covers each slot.

Now it’s time to make the chute. Cut a piece of cardboard that is the width of your slot (2.5 inches) and about 8 inches long.

Feed the chute down through the juice container. Use a piece of duct tape to secure the TOP of the chute to the TOP of the TOP slot.

Flex the chute so that it comes back out through the bottom slot. I used a ruler to help pull it through. It will be curved inside the box. Use another piece of duct tape to secure the BOTTOM of the chute to the BOTTOM of the BOTTOM slot.

Add some “in” and “out” labels. You could write these with a permanent marker, or type and print them like I did. I used some clear packaging tape to secure my labels. Now your box is ready to go!

Cut up the rest of your cardboard to make some number cards. I make mine in sets of five that use the same rule. Draw an “up” arrow above the “in” number. Then flip the card over from bottom to top and write the “out” number on the back. It should be upside down, when compared to the front number. The arrow indicates which way to insert the card into the box. Try it out to make sure your number card flips over when it goes down the chute.

Here’s an example of a card set that uses the “subtract 9” rule.

Here’s another card set. Can you guess the rule? *The answer is at the bottom of post.* 🙂

I like to use my in and out machine as a warm up at the beginning of a math lesson. They also work well for early finishers and centers. Once your students get the hang of it, you can increase the difficulty. Just use larger numbers, different operations, or multiple operations.

Here’s one last piece of advice. Clip your number sets together or code them in some way so that cards using the same function stay together.

I hope that you will try out a number function box in your classroom! It is totally worth the time investment to make just one box and use it whole group. You can always add more to your collection over the years, like I did. Enjoy!

*Answer= “divide by 3”