How to Teach the 9’s Multiplication Facts

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.

 

STRATEGY #1

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.

 

STRATEGY #2

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.

 

STRATEGY #3

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.

 

STRATEGY #4

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.

9×1=9

9×2=18

9×3=27

9×4=36

9×5=45

9×6=54

9×7=63

9×8=72

9×9=81

9×10=90

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!

 

NEXT STEPS

  • 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:

multiplying by 9 task cards

 

 

OR FIND THE FULL BUNDLE OF MULTIPLICATION TASK CARDS HERE.

 

Or choose from the following recommended resources for teaching multiplication fact mastery:

The Multiplication Station: A Self-Paced, Student Centered Program for Basic Multiplication Facts

Multiplication Strategy Posters

Multiplication Equation of the Day Booklet

Basic Multiplication Equation of the Day: a booklet for students

8 Comments

Leave a Comment

Your email address will not be published. Required fields are marked *

This site uses Akismet to reduce spam. Learn how your comment data is processed.