## Sunday, November 1, 2015

### 6's

Elsewhere on this site, I gave some general times tables tips. Here, we'll have a closer look at the six times tables. You can use this page to show your kids the hidden patterns in the nine times tables, and make it easier for them to learn. Keep in mind that these patterns will mean infinitely more to your children if you can somehow coax them to realize the rule for themselves, rather than just pointing it out to them.
Here's the six times table. By the way, you might like to download the printable six times table chart on this site, and stick it to the wall of your classroom, or your kid's bedroom!
 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60 6 x 11 = 66 6 x 12 = 72

If you have a look at every second row, you might notice an interesting pattern. Inspect carefully the ones digit.
 6 x 1 = 6 6 x 2 = 12 6 x 3 = 18 6 x 4 = 24 6 x 5 = 30 6 x 6 = 36 6 x 7 = 42 6 x 8 = 48 6 x 9 = 54 6 x 10 = 60 6 x 11 = 66 6 x 12 = 72

Did you see the pattern?
The ones digit of six times something is the ones digit of the something, at least if the something is even.

What about odd 'somethings'?
 6 x 1 = 6 (and 6-1=5) 6 x 2 = 12 6 x 3 = 18 (and 8-3=5) 6 x 4 = 24 6 x 5 = 30 (and 5-0=5) 6 x 6 = 36 6 x 7 = 42 (and 7-2=5) 6 x 8 = 48 6 x 9 = 54 (and 9-4=5) 6 x 10 = 60 6 x 11 = 66 (and 6-1=5) 6 x 12 = 72
There you have it!
For odd 'somethings', the ones digit of six times something is five more or less than the ones digit of the something.

Some other facts about the answers in the six times table :
• Since the answers are always even, the last digit must always be 0, 2, 4, 6 or 8.
• If you add the digits together, and do that again and again, you'll eventually get 3, 6 or 9. For example :
• 6 x 1 = 6...
• 6 x 2 = 12, and 1 + 2 = 3...
• 6 x 3 = 18, and 1 + 8 = 9...
• 6 x 4 = 24, and 2 + 4 = 6...
• 6 x 5 = 30, and 3 + 0 = 3...
• 6 x 6 = 36, and 3 + 6 = 9...
• 6 x 7 = 42, and 4 + 2 = 6...
• 6 x 8 = 48, and 4 + 8 = 12, and 1 + 2 = 3...
• 6 x 9 = 54, and 5 + 4 = 9...
• 6 x 10 = 60, and 6 + 0 = 6...
• 6 x 11 = 66, and 6 + 6 = 12, and 1 + 2 = 3...
• 6 x 12 = 72, and 7 + 2 = 9...
Amazingly, this pattern, 6,3,9,6,3,9,... continues forever.
• 6 x 5468 = 38208, and 3+8+2+0+8=21, and 2+1=3...
• 6 x 5469 = 38214, and 3+8+2+1+4=18, and 1+8=9...
• 6 x 5470 = 38220, and 3+8+2+2+0=15, and 1+5=6...
• 6 x 5471 = 38226, and 3+8+2+2+6=21, and 2+1=3...
• 6 x 5472 = 38232, and 3+8+2+3+2=18, and 1+8=9...
How's that for an interesting pattern?
Before I close this page, if your child can easily multiply by 5, or by 2 and 3, there are a couple of easy ways to multiply by 6.
• 6 times something is twice 3 times something. So if I want 6 times 9, I can say 3 times 9 is 27, then 27+27 is 54. Not easy for every kid, but maybe it'll work for yours.
• Probably, it's easier to use this trick : 6 times something is 5 times something, plus another something. So to work out 6 x 7, I'd remember 5 x 7 is 35, then add another 7 to get 42. Or to find 6 x 12, I'd remember 5 x 12 is 60, then add another 12 to get 72.