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. Here are some of my favorite methods for teaching multiplication facts.
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.
One Factors
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 easily; however, you will want to look out for students who are adding instead of multiplying. Remind them that they are to count the other factor zero or one time.
You can use this multiplication and division game to practice these factors.
Multiplication Strategies for Twos Factors
Learning about factor two is fun! I teach students that the product is the same as the sum of a double 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.
Three’s Facts
Three’s facts are when we begin diving into the distributive property of multiplication. Students learn that they can split a factor into two addends. In the case of threes, we can split it into one and two. Then, you can multiply the factor by one and again by two and add the two products.
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 or an abacus for your students while they are learning this strategy. Teach them how to use it, and let them explore to find all the factors. Eventually, they will begin to make a visual in their mind and complete threes facts without manipulatives.
Multiplication Strategies for the Factor Four
Double – double anyone? Teaching fours facts are always fun. Again, we use the distributive property of multiplication to teach this strategy. Students should be familiar with their twos facts.
For this strategy we use a similar example as we did for the threes 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 twos 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 fours facts with this game.
Five’s Facts
We usually teach fives 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.
If you have students struggling to skip count by 5’s, try refreshing their skills with this math game.
Multiplication Strategies for 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 as, (8 x 1) + (8 + 5). The products become 8 + 40, which equals 48. You can also say multiply the factor by five and then add the factor one more time.
Look for students who are struggling with the distributive property. Use an abacus or counters to assist students in understanding how to use the distributive property.
Strategies for Sevens
Sevens facts are moderately tricky for most students. I like to use other strategies if the other factor has an easier 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?
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 support with manipulatives and extra practice.
Eight’s Facts
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 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. Double the sum to get 6 + 6 = 12. 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 Nine’s Facts
Nifty nines are my most 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 notice seven fingers to the right of my middle finger are 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.
Give your students time to practice. They may have trouble using their fingers, so use a printable of hands to give them practice.
Ten’s Facts
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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