This podcast video is from my Free Math Worksheets series, which you can access here.
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Download Free Worksheets: 9x Tables
Multiplying by 9 raises some really simple and interesting patterns, which you can use to help children to learn this set of number facts or times tables.
Teaching the 9x Nine Times Tables
9x Tables: Start With 10
As explained in the video, if you start with the equivalent multiple of 10, you can then compensate to quickly find the 9x answer. For example, think about 8×9:
- 8 x 9 = ?
- 8 x 10 = 80
- Subtract 8 ones (one for each set of 10): 80 – 8 = 72
- 8 x 9 = 72
9x Tables: Sum of Digits Equals 9
Look at the multiples of 9 up to 90, and check out the sum of the tens digit and the ones digit in each multiple:
- 09 : 0 + 9 = 9
- 18 : 1 + 8 = 9
- 27 : 2 + 7 = 9
- 36 : 3 + 6 = 9
- 45 : 4 + 5 = 9
- 54 : 5 + 4 = 9
- 63 : 6 + 3 = 9
- 72 : 7 + 2 = 9
- 81 : 8 + 1 = 9
- 90 : 9 + 0 = 9
Students can use a two-step process which takes advantage of the above pattern:
- 6 x 9 = ?
- There must be 5 tens (because we know it is a bit less than 60)
- So, 6 x 9 = 5?
- If the digits in the answer add up to 9, what is the other digit; ie, 5 + ? = 9. The other digit must be ‘4’
- 6 x 9 = 54
9x Tables: Finger Trick
Put both hands up in front of you, palms facing away. Imagine that each finger is numbered, from left to right, from 1 to 10.
To find a multiple of 9:
- 3 x 9 = ?
- Hold up your hands, thumbs together
- Put down the finger that corresponds to the number multiplying the 9: the third finger
- Count the fingers to the left of the finger that is down: 2 – this is the number of tens
- Count the fingers to the right of the finger that is down: 7 – this is the number of ones
- 3 x 9 = 27
x9 is my favorite set in the times table. I really like your 2-step using “sum of digits equals 9,” letting kids find that patterns are everywhere in math. Unfortunately, I had to learn the times table through fear: we had to hold our palms out, teacher would walk around room with large stick, point to one of us and say, “5 times 9,” and if we didn’t spit out the answer right there and then, we’d get a sharp whack with the stick on our palm. I got hit couple times, learned quickly after that!
There are many “magic tricks” that use casting-out nines too. Thanks, Peter!
Thanks, Fawn. I too love the 9s, but as a child I thought they were really hard.
Wow – your description reminded me of times in the old days when teachers used a stick to motivate us to learn. I thought those methods had finished before my readers’ childhood 🙂 obviously not.
I’d forgotten about casting out 9s, and none of my teachers mentioned it at school. It’s a pretty cool trick, discovered by the Romans, according to Wikipedia: http://en.wikipedia.org/wiki/Casting_out_nines .
There’s just so much cool mathematics to teach our students, it’s a wonder that so many think math is boring!