I love teaching multiplication strategies! They help my students become more fluent and strengthen their knowledge of numbers. Multiplication is more than remembering which product goes with which factors. Knowing strategies improve number sense and help students retain their multiplication facts.
When students unlock multiplication strategies, it’s like handing them a mental toolkit. They not only remember their facts but understand the ‘why’ behind them. This deep understanding helps kids hold onto those facts for the long haul.
Here are some of my favorite methods for teaching multiplication facts, and if you don’t teach multiplication, keep reading so you can see what your students need to know in order to master it in the future.
If you’re looking for fact fluency for addition and subtraction, be sure to read this blog post, where I’ll show you how to break it down for your students, and also check out the Addition and Subtraction Mini Bundle from my TPT shop.
Factors of One
Let’s start with some of the easiest factors – zero and one. These factors have their properties, making them super special. The Zero Property of Multiplication means that any factor multiplied by zero will be zero. The Identity Property of Multiplication means that any factor multiplied by one will remain the same. So, 5 x 0 = 0, and 5 x 1 = 5.
Most students grasp these two multiplication properties reasonably quick; however, you will want to look out for students who are adding instead of multiplying. Tell your students that is a zero or one factor, they’re either not grouping the other number at all (with zero) or grouping it just once (with one).
You can use this multiplication and division game to practice these factors.
Multiplication Strategies for Factors of Two
Learning about factor two is fun! I teach students that the product is the same as the sum of a doubles fact for this strategy. For instance, 7 x 2 is the same as 7 + 7. Both the product and the sum are 14. Another simple strategy is to use skip counting by 2’s.
If students are having trouble with their 2’s facts, then they are likely struggling with their doubles facts in addition. I recommend going back to model two-column or two-row arrays to show how doubles facts are similar to 2’s facts. You can use an abacus or counters for this.
Make sure you read this blog post on how to introduce addition and subtraction to your students.
Factors of 3
The three’s facts are when we begin diving into the Distributive Property of Multiplication. This is basically a fancy way of saying you can break a factor into smaller bite-sized parts. In our case with threes, you split 3 into 1 and 2. You multiply those smaller parts and boom– you’ve got your answer when you add ’em up.
For example, 4 x 3 is the same as (4 x 1) + (4 x 2) = 4 + 8 = 12. Students must have a solid grasp on the ones and twos facts before mastering this concept.
An easy way to model this in your classroom is by giving your students counters. Have them create three columns of the same amount. Then, place a craft stick between a set of columns so that you have one column on one side and two columns on the other.
You might want to provide counters, snap cubes, or an abacus for your students while they are learning this strategy. Teach them how to use the manipulatives first, and let them explore to find all the factors. Eventually, they will begin to make a visual in their mind and complete the three’s facts without manipulatives.
Multiplication Strategies for Factors of Four
Double – double anyone? Teaching four’s facts are always fun. Again, we use the Distributive Property of Multiplication to teach this strategy. Students should be familiar with their two’s facts.
For this strategy, we use a similar example as we did for the three’s facts, except we use four columns. So, 4 x 4 is the same as (4 x 2) + (4 x 2) = 8 + 8 = 16. If we’re thinking about the two’s factors being a double, then this is a double-double fact. Because (4 x 2) + (4 x 2) = (4 + 4) + (4 + 4).
You can practice four’s facts with this game.
Factors of Five
We usually teach five’s facts right after 0, 1, 2, and 10. This is such a fun strategy to teach. Students should know that all products of five end with either a 0 or a 5 in the one’s place. We skip count by five to multiply.
This shows up in the real world when we are telling time on an analog clock. Students can see 60 represented in the face of the clock. It also shows up when counting coins. These are two simple supporting standards you can include when teaching five’s factors.
If you have students struggling to skip count by 5’s, try refreshing their skills with this math game.
Multiplication Strategies for Factors of Six
Now that we’re getting up to the higher numbers, the strategies become even more necessary! First, any number multiplied by six will always be an even number. Next, students can use their knowledge of ones, fives, and the distributive property to solve equations.
For example, 8 x 6 can be thought of as, (8 x 1) + (8 x 5). The products become 8 + 40, which equals 48. You can also multiply the factor by five and then add the factor one more time.
Be aware of students who are struggling with the Distributive Property of Multiplication. Use an abacus, counters, or other math manipulatives to assist students in understanding how to use the Distributive Property of Multiplication.
Strategies for Factors of Seven
Sevens facts are moderately tricky for most students. I like to use the Communicative Property of Multiplication to identify other factors with easier strategies if it has one, but it doesn’t always. For this strategy, I ask students what two addends of 7 would make helpful factors to use the Distributive Property of Multiplication.
They usually always say 2 and 5, so again, we model using our counters. Let’s say we have 7 x 7. We can think of it as (7 x 2) + (7 x 5) = 14 + 35 = 49, so 7 x 7 = 49.
This factor takes a lot of practice, so provide lots of opportunities and support with manipulatives and extra practice like these math games!
Factors of Eight
Eights facts are probably the most difficult for students to learn, but there is an excellent strategy for this factor! I call it the “Turkey Factor” because it sounds like I’m gobbling when I tell the students. I ask them to double, double, double!
What does this mean?
Well, let’s say we’re trying to solve 8 x 8. Let’s double the factor eight to get 8 + 8, and our sum is 16. Now, let’s double 16 to get 16 + 16. Our sum is now 32. Let’s double that sum one more time to make 32 + 32. The total is 64. So, 8 x 8 = 64.
This strategy works any time you multiply a number by 8. Here’s another example: 3 x 8. Double three to get 3 + 3 = 6. Next, double the sum to get 6 + 6 = 12. Finally, double the sum once more to get 12 + 12 = 24. So, 3 x 8 = 24.
Model this strategy and allow students time to practice.
Multiplication Strategies for Factors of Nine
Nifty nines are my favorite factors to teach because they are magical!
First, I model on my hands with my palms facing up. Let’s try 3 x 9. Beginning at my left thumb, I count 1 – 2 – 3. My middle finger is down. I notice my thumb and index finger are still up to the left of my middle finger. This represents two tens. Then, I noticed seven fingers to the right of my middle finger were up. This represents seven ones. So, 3 x 9 = 27.
Now, if I were to take the digits of the product and use them as addends, my sum would be nine. For example, 2 + 7 = 9.
Not only that, but two is one less than three. I can find 7 x 9 just by thinking about one less than 7 to get 6. Now, if I put that into an addition equation to equal nine, I’d have 6 + ? = 9. I know that 3 makes the equation true, so the answer is 63.
Try not to teach all these strategies at once to prevent overwhelm. Instead, teach one skill one at a time and give your students time to practice and explore. They may have trouble using their fingers, so use a printable of hands to give them practice.
Factors of Ten
I typically teach the tens facts along with my ones and zeros. They are super easy to teach students. Any number that is multiplied by ten will be in the tens place, and a zero will remain in the one’s place.
For example, for the equation 5 x 10 = 50, the product has a 5 digit in the tens place and a 0 digit in the one’s place. Students pick up on this quickly!
So there you have some of my favorite strategies for teaching students about multiplication. Please know that we practice these strategies a lot. We use these multiplication and division math games to apply these strategies. They are fun for math centers and homework.
I’d love to know which of these strategies you teach your students.
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