Good math tricks to show kids?

In My Humble Opinion
41

Probably not something you want to teach kids, but I learned this when I was in 5th grade. Using a calculator, you can tell this joke:

There are five thousand prisoners in a cell. One whore walks in (key in 5000 + 1, hit equal to finish the operation). Each prisoner does her seven times (key in *7). What is she now (hit equal)?

35007

42

I think there was a game some of my kids played that was called 24. No, it had nothing to do with fighting terrorists or torturing your friends, but it went like this: Here are four numbers, e.g., - 8, 8, 5, 5 . Can you do arithmetic with them to come up with the number 24? In this case (5*5)- (8/8) = 24. I think you might even be able to buy a game with this theme.

43

That sounds like Krypto. Here’s the Wikipedia article; and here’s a site that Google came up with where you can play Krypto online (requires Java).

Then there’s the Game of Four Fours, where you see how many different numbers you can make using any operations/symbols you want and exactly four of the digit 4 (and no other numbers).

For example, you can get 1 from 44/44
or 4/4 + 4 – 4
or (4^4)/(4^4)

44

Here’s another one with a calculator:

Tell them you can read minds.
Have them notice that the digits 1-9 form a 3x3 square.
Point out that the zero is excluded.
Have them choose any row, column, or diagonal.
Enter the three digits, each only once, but in any order.
Hit ‘times’.
Choose another row, column, or diagonal.
Enter all three digits, once, in any order.
Hit ‘equals’.
They should have a five- or six-digit number.
Tell them to choose any digit (except zero, because you can’t read their mind if they have ‘nothing’ in it*).
Read the rest of the digits to you in any order (to clear them out of their head).
(Mentally add the digits and cast out nines).
Tell them the digit they chose.

For instance:
They multiply 465x978=454770
They choose 7.
They read to you 07445.
You add the digits as they read them. 20
Subtract from the next higher multiple of nine. 27-20=7 (if it already is a multiple of nine, then they chose 9)
Tah-dah!!

  • this is important because, otherwise, you couldn’t tell if they had chosen nine or zero–the rest of the digits would add up to nine (or a multiple) either way.
45

Here’s a neat “manual multiplication” trick I’ve used to keep myself straight many times. Despite being over thirty, and able to do a lot of arithmatic without a calculator, for the life of me I can’t seem to retain the upper end of the multiplication table. With the following, I’ve got from 6x6 to 10x10 “on hand” at any moment.

  1. Hold out your hands. You can use either palms toward you or away, but it’s a little easier for me palms-towards, so that’s the assumption for the rest of the steps. If you want to go the other way, the fingers named will be top-bottom reversed.
  2. Mentally number each finger starting at six at the bottom (pinky) and 10 at the top (thumb).
  3. To multiply two numbers, touch the corresponding fingers together. So for 7 x 8, touch your ring finger on one side to your middle finger on the other.
  4. Count up the touching fingers and all the ones below. This is the ten’s place. (for 7x8 you have 3 below + 2 touching = 5, times 10 is 50)
  5. Multiply the leftover fingers on the left by the leftover fingers on the right. (for 7x8 this is 2 x 3 = 6). If either side has no fingers above the touching ones, then the result is zero.
  6. Add steps 4 and 5 together for the result: (7 x 8 = 50 + 6 = 56).

Feel free to point and laugh, but with this tip I can still appear to be a functioning adult (albeit one who fiddles with his fingers) when having to figure out what 7 x 6 is (umm…30 + 12 = 42).

46

I have this math trick on my website, but to avoid shameless self-promotion, I figured I’d find it on someone else’s website.
http://www.hellam.net/maths2000/agecard.html
This trick is sometimes referred to as “age cards”. It’s a good one and I think it would impress 4th graders.
For those of you who can’t figure this out:

Any positive whole number can be formed by summing the powers of 2:
1; 2; 4; 8; 16; 32
Let’s keep the explanation simple and just make cards for one through seven:
There would be 3 cards, each of which would have 1, 2 and 4 as the upper left digit.
For the number three, we would need to put that on the “1” and the “2” card.
Five would go on the “1” and “4” card.
Six goes on the “2” and “4” card.
Seven goes on all three.

Here’s a good one concerning the Fibonacci number sequence. (Don’t let your students be intimidated by that term.)
Have 2 students call out one small number each. Let’s say “2” and “9”.
Now let’s add those 2 numbers to produce a third, add the second and third to get the fourth; add the third and fourth to get the fifth. Basically, do this until you have a ten number column:
    2
    9
  11
  20
  31
  51
  82
133
215
348
Then anounce to your class that you will sum all ten numbers in your head and give the answer 902.

[spoiler] Whenever numbers are created in this type of 10 number sequence, the sum of all ten numbers will be the 7th number times 11. Eleven is an easy number to multiply in your head by simply “shifting” one of the numbers and then summing.
For example, 82 x 11 = 902 OR

82
82

902
[/spoiler]