Bad Calculators

Little kids love playing with calculators.

My toddler Dalia, for example, loves nothing more than grabbing my calculators, along with anything else with buttons, and mashing them to see what happens. Adorably, she refers to her collection of button-based toys as "my growmups," as in "Daddy, these is my growmups"

My older kids like plying with them too, though. My eight-year-old is always trying to figure out what each button does, while my five-year-old tries to type in massive numbers and then say them out loud, proudly and incorrectly.

I was reminded of this by Michael Pershan, who gave me two great recommendations: First, get a big calculator with fun buttons and keep it in the car. You never know what discoveries your kids might make on the way to school!

Secondly, grab a laptop and get them to play Bad Calculators.

How to Play

Bad Calculators is a web game developed by Tyler Auer, a former teacher and software developer from California. 

The game is very simple: You are given a starting number and a target number. You need to use your calculator to get from 0 to 23, to use the first puzzle as an example.

The problem is, your calculator only has two buttons: A +5 button and a -1 button. Can you get from 0 to 23 using only these buttons?

This game really gets your kids thinking creatively with arithmetic. There are bonuses available for reaching the target in a specific number of moves, and typically there are at least two or three (or even infinite) ways to get to the target. 

The game starts simply, but by the end of it your child might be working with negative numbers, exponents, and even the Collatz conjecture!

Does your child need to know the meaning of the Collatz conjecture to explore? Of course not! In fact, it might be fun for them to explore how the conjecture works with various given numbers. They'll be tapping along like my son does when he's trying to figure out the division button, exploring new math ideas on their own terms

Questions to Ask

This game is ideally suited for solitaire, so you might be happy to let your child advance through the puzzles on their own. With that said, you do have an opportunity to ask some thought-provoking questions that this game introduces.

If your child is struggling with their answer, you can ask "What number do you think comes right before the target number?" For example, in the 0 --> 23 puzzle, you can only add 5 or subtract 1. This means that you can win if you get the number to 18 and then add 5, or get it to 24 and then subtract 1. 

Sometimes these puzzles feel like mazes, and lots of kids learn eventually that mazes are often easier to complete backwards than forwards. This is an extremely common mathematical technique, by the way.

Another interesting question to ask is "Are there any numbers that are impossible to reach with this calculator?"

Imagine starting with a 1 and having a calculator that only has the +2 and *2 buttons. Are there any numbers that are impossible to reach? Why or why not? This question starts pushing your child toward proofs, where they make an argument to justify their answer.

Finally you can ask your child "Could you come up with your own Bad Calculator problem and challenge me?" 

The skill of inventing puzzles is even more challenging and fruitful than solving puzzles! If your child is interested, there's no limit to the amount and complexity of the problems that they can create.

Just be sure to send their best ones my way, or to Tyler. I'm sure he'd love to hear from people who are enjoying his game.