The 9’s facts – my favorite set of facts! People often are surprised when I tell them that the 9’s are a really simple set of facts to learn. This is because there is one trick in particular that makes them easy, not to mention really fun.
But before I teach you that trick, I’m going to teach you a couple of 9’s tricks that I DON’T like.
There are several tricks out there for the 9’s facts. The first one that I’ll show you uses your fingers.
So, if you want to multiply 9×4, you put down your fourth finger.
Then you are left with 3 fingers on one side, and 6 fingers on the other. So the product is 36.
If you want to multiply 9×8, you put down your eighth finger.
Then you are left with 7 fingers on one side, and 2 fingers on the other. So the product is 72.
So I’ll admit that this is kind of a neat trick. However, I just don’t like my students to rely on their fingers. I feel like we are always trying to get our students AWAY from finger counting as a strategy, so I’d rather not have them rely on this one.
Here’s another strategy that I don’t like:
For this one, we list the numbers from 0-9, and then list the numbers from 9-0 beside that.
Now you’ll see that this shows all of the products of the 9’s facts from 0-10. For example, the second row down shows the product of 9 and 2:
The sixth row down shows the product of 9 and 6:
So again, this is a neat trick, but in my mind it’s not practical. When my students are faced with a 9’s equation, the last thing that I want them to do is take 3 minutes to list out all of the numbers, and then count the rows down to figure out the product.
This next strategy is a true mental math strategy. This is one that you’ll want to introduce your students.
We know that the 10’s multiplication facts are an easy set to learn – just add a 0. So for the 9’s facts, we can use a 10’s fact, and then just subtract one group.
For example, for 9×3, first do 10×3 to make 30, and then subtract one group of 3 to make 27.
For 9×7, first do 10×7 to make 70, and then subtract one group of 7 to make 63.
Now, FINALLY, I’d love to show you the trick that I always use with my students. I love this one because it is FUN, motivating, and SO fast once you get the hang of it. I always start out by telling my students that it will seem confusing at first. I tell them that they probably won’t get it the first time. But by the second or third time I show it to them, they’ll be starting to catch on, and by about the 5th time I show them, a little light bulb will go off and they will get it! I find that this little “disclaimer” helps take care of any frustration they might have when they don’t understand it the first time around.
I begin by listing all of the 9’s facts from 0-10. I ask students what they notice about the products. In particular, I want them to add the digits in each product.
So what do you notice? In every product, the digits can be added together to make 9. Students have to remember this.
Here’s how to perform the strategy:
Step One: Look at the equation. Point to the number that is NOT the 9. For example, in the equation 9×4=___, point to the 4.
Step Two: Subtract 1 from the number that you are pointing to. In this example, you would think “4-1=3.” The difference (in this case, 3) will be the first number of your product. So now our equation looks like this: 9×4=3__.
Step 3: When you add the numbers in the product together, they will make 9. So now we need to think, “What can I add to 3 to make 9?” In this case the answer is 6. Add this 6 as the second digit in your product: 9×4=36.
Let’s try another one: 9×8.
Step One: Look at the equation. Point to the number that is NOT the 9. For example, in the equation 9×8=___, point to the 8.
Step Two: Subtract 1 from the number that you are pointing to. In this example, you would think “8-1=7.” The difference (in this case, 7) will be the first number of your product. So now our equation looks like this: 9×8=7__.
Step 3: When you add the numbers in the product together, they will make 9. So now we need to think, “What can I add to 7 to make 9?” In this case the answer is 2. Add this 2 as the second digit in your product: 9×8=72.
As you can see, this works with any basic multiplication fact involving a 9. Notice that in every case, the sum of the numbers in the product add up to 9!
As I mentioned before, you’ll need to show this to your students several times in order for it to really make sense, but once they understand, it is SO effective!
- Download a free poster for the 9’s trick from my Teachers Pay Teachers store HERE.
- Ready to tackle multiplication once and for all? Join me for a free mini-course – “Teaching Basic Multiplication and Division for Mastery.” It’ll only take about an hour to complete and you’ll leave with tons of great ideas, a game-plan, free resources, a PD certificate, and more! REGISTER HERE.
- Reinforce the 9’s multiplication facts with this set of task cards. Students will learn conceptually through problem-solving, using arrays, strategic thinking, finding missing numbers, skip-counting, picture representations, and more:
Or choose from the following recommended resources for teaching multiplication fact mastery: