The Number Game and the Silent Version

January 9, 2017

Yoni Nazarathy

My kids and I love playing verbal games. These include "Guess the person", "I spy with my little eye" and other general types of trivia games. Such games are great to play while driving, sitting in public transport or waiting in a queue at a doctor's office. This genre of games also features the "Number Game", a rather simple home brewed, verbal arithmetic game, that quickly becomes exciting and challenging.

Through our number game, my 8 and 11 year old daughters have learned about logarithms, square roots, modulo, absolute value and primes. My 6 year old son, recently joined the club as well. At the moment he plays the simple version. Here is how it goes (simple version):

Dad: Please give me a number.

Child: 8.

Dad: Double.

Child: 16.

Dad: Add 4.

Child: 20.

Dad: Half.

Child: 10.

Dad: Take away 8

Child: 3.

At this point the child made a little mistake...

Dad: Check again, you were at 10 and took away 8. Look at your fingers if you wish.

Child: (Smiling), ohhh... 2.

Dad: Good job! Let's pause and play more later on.

As you can see, this version of the number game is simple. Perhaps almost trivial. Still, as a parent playing it, you give full attention to your child and children love that! In return, the child does his or her best to focus. It builds up confidence for the child and it brings on discussion about new things to explore.

With my daughters, we used the simple version of the number game to introduce negatives, for practicing the multiplication table (also with division). We used it to introduce squares (e.g. 6 squared is 36) and similarly square roots. Log base 2 is fascinating for kids. Really neat actually. Try it, and you'll see that it isn't hard to teach 8 or 10 year olds, the log base 2 of 8, 16, 32, 64 etc... (it is the number of 2's needed to be multiplied by each other to get the number). For e.g. Log base 2 of 32 is 5, since

$32 = 2\times2\times2\times2\times2 = 2^5.$

My 11 year old daughter recently enumerated the operations that we use in the number game (children like to make lists - I do too) and found quite a few:

1. Addition, e.g. "add 17".

2. Subtraction, e.g. "take way 12". Don't hesitate to go negative, kids love that!

3. Double (times 2).

4. Half (divide by 2).

5. General multiplication, e.g. "times 5".

6. General division, e.g. "divide by 4".

... And the nifty stuff....

1. Square root (so far for non-negative numbers only).

2. Square (multiply the number by itself).

3. Log base 2 (do this on 2, 4, 8, 16, 32, 64, 128).

4. Log base 10 (do this on 10 or 100, resulting in 1 or 2 respectively).

5. Absolute value (the absolute value of -7 is 7, the absolute value of 7 is just 7).

6. Modulo 4 (or Modulo anything else). For e.g. 9 modulo 4 is 1 because the remainder of the division of 9 by 4 is 1. Or 15 modulo 5 is 0 and 19 modulo 5 is 4.

7. Nearest prime above. E.g. the nearest prime above 6 is 7.

8. Nearest prime below (similar to the above).

9. Nearest prime (without specifying above or below) - but be careful, don't ask this when the child is at the number 30 because the answer is not well defined between two twin primes.

... You can surely think of more operations, or maybe the child can try and invent her own.

Well that was the simple version: You say the operation and child responds. My daughters don't play this one anymore. It isn't exciting enough. They now like the silent number game. I love it too. It is an amazing game that really gives your child confidence in basic mathematics and arithmetic.

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In the silent number game, the child doesn't tell you where they are on the number line. They simply accept your operations and by saying "OK" or "ahhahha". Then when you reached a number between -2 and 2 (inclusive of -2 and 2) they say the answer. So the game stops at -2, -1, 0, 1 or 2 (or fractions if you are into that). For e.g.

Dad: Give me a number.

Child: 9

Dad: Square root.

Child: Ahhahhha (child then knows the current value is 3 - but doesn't say - you know it too).

Dad: Add 5.

Child: Ahhahah (child is now at 8 - you hope).

Dad: Log base 2 (assuming you spoke about it previously - but start with basic arithmetic).

Child: Ahhahah (she is now at 3 because she knows that log base 2 of 8 is 3 - you hope).

Dad: Take away 5.

Child: -2!!!!

Dad: Well done!

The silent number game is actually incredible. You can start with 2 or 3 steps and little by little increase the complexity. My daughters get extreme satisfaction from going through a sequence of 10 operations and ending up at the right place. I do too.

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I hope that you try the number game as well. Let me know how it went for your kids and you.