In a previous article, we discussed the best strategies for students to learn addition and subtraction number facts. Now let’s take a look at strategies for multiplication and division.
Foundations
First, it’s important to remember that long-term math learning is achieved through guided exploration, handling objects in different contexts, and mathematical discussions in class. This way, students will develop better conceptual understanding and be more inclined to use mathematical reasoning when needed.
Number sense
Multiplication can be introduced in the classroom in the form of repeated addition so that students can fully understand how the operation works. Similarly, division is a form of repeated subtraction. Young learners will turn to multiplication and division when looking for a more efficient process.
Multiplication can be represented to students in many ways: repeated addition, times tables, or sets of elements. By examining all of these representations, students will be able to observe that the commutative property of multiplication requires elements to be rearranged.
In addition, when children first start learning math, they’re taught to skip count in ascending and descending order. This may seem like a trivial skill, but it is very useful for understanding multiplication and division.
Recall strategies
It’s a good idea to start with 0, especially by involving objects. Any number multiplied by 0 makes 0, and it’s impossible to divide by 0.
Students can quickly learn the multiples of 1, 2, 5, and 10 using objects and prior knowledge (doubles and skip counting).
When doing multiplications involving the number 9, students will notice a regularity. It is strongly recommended not to point this out to them, but rather to put them in situations where they can make this observation themselves:
- The sum of the digits that make up the product is always 9. (18: 1 + 8, 27: 2 + 7, etc.)
- The product’s ten is always 1 less than the factor that is not 9. (9 × 5 = 45. 4 is 1 less than 5.)
By combining these ideas, it’s possible to find the quotient of a multiplication involving the factor 9. Other students may prefer using the 10 times table and subtracting the other factor to find the answer.
This will also help students learn other strategies and use the distributive and associative properties to solve operations. It also means that students do not need to memorize the times tables up to 9, since they will develop strategies to find the answers.
There are no universal strategies. Learners use the strategies that make the most sense to them, depending on their skills and the problems they have to solve. Throughout their learning, students will stop using certain strategies as they discover other ones that work better for them.
Mastering number facts
Remember that the long-term learning of number facts isn’t achieved through memorization or the ability to find the answers quickly. It’s important to realize that setting a time limit doesn’t encourage the students to review their answers nor allow them to validate their strategies. It can even diminish students’ confidence in their abilities when they actually have good processes. Fortunately, you know the best ways to help your students develop skills they will not lose over time.
