The elegant number nine is so fascinating and fun to play with. Nine is built out of 3’s, like:
- 3 + 3 + 3
- 3 x 3
There are several Fun Facts for playing with the Number 9.
For example, did you know:
1. If you can count up to 10 and back down again, learning to skip-count by 9s (one step away from your times tables) is an easy thing to do.
2. It’s helpful to keep in mind that 9 is one less than 10.
3. The digits of any multiple of 9 add up to 9, or a multiple of 9.
4. Count down from 10s to check your math.
5. If you have two hands with 10 fingers, you already know your 9 times tables.
Let’s start with Fun Fact #1: Counting Up and Down with 9.
On a piece of paper, list the counting numbers, 0 – 9, in a column, like this:
0
1
2
3
4
5
6
7
8
9
Now create a second column to the right of the first one, lining up the numbers, counting down from 9 to 0, like this:
0 9
1 8
2 7
3 6
4 5
5 4
6 3
7 2
8 1
9 0
You now have a sequence for skip-counting by nines!
09 (9 x 1)
18 (9 x 2)
27 (9 x 3)
36 (9 x 4)
45 (9 x 5)
54 (9 x 6)
63 (9 x 7)
72 (9 x 8 )
81 (9 x 9)
90 (9 x 10)
But it actually doesn’t stop there; you can start the sequence again, with a minor twist on the very first one:
9 9 = 99 (9 x 11)
10 8 = 108 (9 x 12)
11 7 = 117 (9 x 13)
12 6 = 126 (9 x 14)
13 5 = 135 (9 x 15)
14 4 = 144 (9 x 16)
…and so on.
If you chant them out loud you can really hear the rhythm and pattern, and anticipate the next one coming. Try it and you’ll see what I mean!
Here’s where we bring in Fun Fact #2: 9 is one less than 10.
Like I mentioned at first, 9 is one less than 10. It’s a fairly simple thing to add 10 to a number—particularly if it’s only 1 or 2 digits.
For a 1-digit number like 2 or 7, simply put a “1” next to it on the left, indicating that your tens column has grown by 10. Thus 2 becomes 12 and 7 becomes 17.
So skipping to the next number in the 9’s sequence is easy when you just add 10 and then take one away.
Like:
- 9 + 10 = 19, and 1 less is 18—so 18 is the next number when skip-counting by nine.
- 18 + 10 is 28, and 1 less is 27—so 27 is the next number in the sequence when skip-counting by nine.
But what if you’re not looking at the whole sequence, or counting up from a lower number?
What if you just think you know the answer to 9 x 7, but you’re not 100% sure?
Time for Fun Fact #3: The digits of any multiple of 9 add up to 9 (or a multiple of 9).
There’s a really easy way to check your work, so you can know if you’ve made a mistake on a particular multiple of 9 without seeing the whole sequence. All you have to do is add the digits together.
When you add them and your answer is “9”, or a multiple of 9 (like 18 or 27) then you know your number is in the family of nines. If not, it’s not. How cool is that?
So, in the case of 9 x 7: if you guessed 63, and then added the digits together:
6 + 3 = 9
You know for sure that 63 is, in fact, a multiple of 9. (Of course if you guessed that 63 is the answer to 2 x 9, you’re still mistaken, LOL.)
Let’s watch that in action, so you can see what I mean…
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
99 9 + 9 = 18 (9 x 2)
108 1 + 0 + 8 = 9 (or 10 + 8 = 18 = 9 x 2)
117 1 + 1 + 7 = 9 (or 11 + 8 = 18 = 9 x 2)
126 1 + 2 + 6 = 9 (etc., as above)
135 1 + 3 + 5 = 9
144 1 + 4 + 4 = 9
Isn’t that amazing? Numbers are so elegant and fun to play with! I love finding patterns like these.
Fun Fact #4: Count Down from 10s to Check Your Work
You know what? There’s another really neat thing about 9’s. It’s a trick that you’ll use for other fact families as well, called “counting down.”
Counting down works in this way: since you already know that ten times something is just to add a zero on the end, you have a really solid fact family to work from. Did you know that 9 times something is just ten times, minus that same number? Here’s some examples:
10 x 3 = 30
9 x 3 = 10 x 3, minus 3, or: 27
10 x 6 = 60. If you take six away, you are left with 54, or 9 x 6 = 54. Do you see how that works?
It’ll work no matter how small or large the number is.
The next pattern is so very cool, it’s right on the tips of your fingers…
Fun Fact #5: Your 10 fingers hold the key to 9 times tables.
This trick works for 1 x 9 through 9 x 9.
Did you know that you have the nine times tables wrapped around your fingers? In the palm of your hands?
Here’s what I mean:
First, hold both your hands out in front of you, with palm open and facing you. Now, starting with your left thumb, number your fingers from left to right, ending on the right thumb. In this way, your left pinkie is 5 and your right pointer if 9, for example. Get it?
Okay. Now, if you want to do 1 x 9, you bend your #1 finger (left thumb) in toward your palm, like this:
See what’s left? Nine little fingers still standing. That means 1(the left thumb) x 9 = 9 (fingers up). Easy, right? But you already knew that one.
Let’s see if we can make it work for another one. Start again with all your fingers extended. Now bend your left middle finger (that’s #3!) toward your palm, like this:
This means 3 x 9. And what are you left with? Two fingers standing on the left, and seven (count’em—the left ring and pinkie fingers and all the fingers on the right hand) standing in a row on the right. So on the left of the bent finger we have a 2, and on the right of the bent finger we have a 7. Put them together and you have your answer: 2-7. 3 x 9 = 27. Isn’t that cool?
Let’s try one more. Start again with all your fingers extended, palms facing you. Now bend your right pinkie down, like this:
That finger represents #6, remember? So this is the trick for 6 x 9 (or 9 x 6, same thing—remember the commutative property of multiplication). On the left of the bent finger are 5 fingers standing, and on the right of the bent fingers are 4 fingers standing. 5 and then 4—our answer is 54. 6 x 9 = 54.
There is so much more fun to be had with numbers, the things they build and the patterns they create. Next time maybe I'll share with you what pretzels, fudge, Mozart and gravel have taught me about Prime Numbers....
Rachel DeMille is developing a new Core and Love of Learning lesson plan resource for charter and homeschools called, "The Inspired Mind." Watch for announcements from TJEd.org on how to take part, or contact Rachel here to be put on the notification list.
