Games to play in the car

When my kids were younger, they made up a math game to play while we drove on long trips. It started as a quiz game. "Ask me a math problem!" So we would take turns asking each other questions like "What is 3 plus 2?" or What is 8 minus 3?". Kids don't always know what makes a problem hard, but they know I can do "bigger" and "harder" math problems than they can, so sometimes I'd get problems too big to do in my head. "What is 327 times 589?" "Sorry, I would need paper or a calculator to figure that out." They were usually willing to give me smaller problems to keep the game going.

At one point, after I asked my daughter a question with an answer of zero, she got excited about zero and said "Ask with another with the answer zero!" Which I did, but after a few more rounds I began to feel that I was doing all the arithmetic for both of us. (She was just excited by the pattern she was noticing: that any number minus itself got you zero). I asked, "Can I tell you what answer my questions should have?"

"Of course" she agreed. So I would tell her "Ask me a question with the answer 4" and she would create a math problem and I would answer "4". Then she told me what answer she wanted and I would create a problem with that answer.

So now each of us has to do arithmetic when it's our turn to ask, instead of our turn to answer. The new game has more flexibility. Arguably it's harder. There are infinitely many math problems with the answer 4. If we limit ourselves to addition, then to build a problem first think of a number smaller than 4 (0,1,2, or 3 if your kid isn't doing negative numbers yet), then subtract it from 4 to get a second number, to create something like 2+2. Children won't necessarily have a neat algorithm like that. They may guess and check several times to find something with the right answer or modify a known equation ("Hmm, I know 2+3 = 5, but I want only 4, so try 1+3")

To build a subtraction problem with answer 4, pick a number (example: 6), add 4 to it (10) and subtract the first number from the second( "What is 10 - 6 ?").

The other cool thing about this game, is that you can see when your child is comfortable with other operations on your turn, when you get asked "What is 64 divided by 8?" rather than having to try asking a division problem and having them possibly struggle if they weren't ready.