When teaching your kids how to memorize their times tables, there’s a little visual trick that allows them to remember the multiples of nine that uses just their fingers. Have them hold up all their ten fingers with the backs of their hands facing them. Tell them to imagine multiplying two times nine. Have them hold down their second finger in from the left, namely the ring finger on their left hand. They will then have one finger up on the left and eight fingers up on the right. Have them combine them as one-eight to make eighteen. And two times nine is eighteen.
For any single digit number that you want to multiply by nine, just count that many fingers from the left, and hold down the finger. The number of fingers held up to the left of the bent finger will represent the tens digit and the fingers to the right represents the ones digit.
My favorite finger trick is a way to teach binary numbers, combinatorics, and out -of-the-box thinking. Ask your kid: how high can you count with the fingers on one hand? The automatic answer might be five. Inform them that it is, in fact, 32. Give them some time to play around with it, then point out to them that each finger has two states, up or down. Hold up your thumb and say that it can represent one. Put it down and hold up just your index finger. That could represent the number two. Just the middle finger could represent three. Do the same for each of the five fingers. Then show that two fingers can be combined to make new numbers. The thumb and index finger could represent one number, and the thumb and middle finger a different number. Have your kid go through all combination of zero, one, two, three, four, and five fingers.
Your kid will likely brute force her way through the combinations, creating all 32. You can then bring up that each finger has two states, and show her how multiplying two to the fifth power gives the answer of 32. You could also have her see that there is a symmetry between how many fingers are held up and how many are held down. That is to say, having one finger down and four up is isomorphic to having one up and four down. She can see that there is one combination each of five and zero, five each of one and four, and so on. If you want you can bust out Pascal’s triangle, but I picture you doing this while waiting at a bus stop, or stuck in traffic, and not having any math texts handy.
Another option with this game is to introduce the concept of binary. Instead of each finger representing a state, and the combination of states being counted based on how many fingers are up, each finger could represent a place value, and a number could be represented ordinarily.
Holding up no fingers would represent zero. Holding up just the thumb could represent one. Holding up just the index finger could represent two, and the thumb and index fingers combined could be three. Have your kid figure out what the place value for each finger is, then hold up different combinations of fingers and have her tell you what number they represent. Then give her some numbers between zero and thirty-two and have her hold up the correct number. Next you could throw in a zinger and give her a larger number, like 60, and see if she can figure out how to add a second hand into the game. Finally, ask her how high she can count using both hands.
Hopefully by this time your bus has come, or the traffic is cleared. If not, you can always comb your fingers together and say, “here is the church, here is the steeple, open up the doors and see all the people.”