Multiplication can be a daunting task for students of all ages. However, with the right multiplication strategies in place, it can become a fun and easy process.
In this article, we will discuss 7 multiplication strategies that will help students understand the why behind multiplication before learning how to do it.
With these strategies in place, students will be able to confidently approach multiplication problems and succeed before learning multiplication facts.
The importance of understanding the why before learning how to multiply
It can not be understated. multiplication is a fundamental building block for many mathematical concepts.
If students do not have a strong foundation in multiplication, they will likely struggle with more complex topics down the road.
Therefore, it is essential that students understand the why behind multiplication facts before moving on to learning how to do it.
What are the 7 strategies for multiplication?
In my 14+ years as a high school mathematics teacher, I have noticed that many students have gaps in their knowledge about multiplication strategies.
Once they are allowed to use a calculator they rely on this heavily and forget the mental math strategies they used in primary and middle school.
Knowing the times tables becomes assumed knowledge in high school to be able to readily apply them to algebra, measurement and other topics quickly. So these multiplication strategies are extremely useful to all students.
Commutative property
If you know that 4 x 7 = 28, then 7 x 4 also equals 28 because the commutative property of multiplication states that the order of numbers does not affect the product.
This is a key multiplication strategy for students to understand because it can help them save time and effort when multiplying large numbers.
It also means students only need to memorize half of the times tables.
x4 = Double double
If you know that doubling a number and then doubling the result is the same as multiplication by four, then you can use this strategy to solve multiplication problems quickly.
For example, if you need to calculate 28 x 4, you can first double 28 to get 56. Then, double 56 to get 112. Therefore, 28 x 4 = 112
Doubling and halving
This multiplication strategy is great when multiplication by a large even number is required.
For example, if you need to calculate 16 x 3, you can first halve 16 to get 8. Then, double 3 to get 6. Therefore, 16 x 3 = 8 x 6 = 48
This diagram shows two rectangles of dimensions 16 x 3 and 8 x 6.
You can see that they have the same area.
9 times tables on fingers
This multiplication strategy is one that students often learn in primary school.
To use this strategy, you hold up your hands and put down your finger that you are multiplying by 9.
For example, if you are finding 9 x 7, you put down your 7th finger like this.
This leaves 6 fingers to the left of the finger that was folded down and 3 fingers to the right.
So 9 x 7 = 63
Try it with your fingers and 9 x 8. Hold down your 8th finger and you should have 7 fingers to the left and 2 to the right, so 9 x 8 = 72
Repeated addition
This multiplication strategy is often used with young students who are just learning to multiply.
It is a helpful strategy for them to understand that multiplication is simply repeated addition.
For example 4 x 3, can be thought of as 4 + 4 + 4 = 12
Skip counting
Skip counting is a strategy that can be used with any number. It relies on multiplication facts that have already been learned to skip count by the number being multiplied.
For example, if you need to calculate 5 x 13, you can start by skip counting by 5’s like this:
5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60, 65
Skipping count by the number that you are multiplying to find the answer.
Equal groups
When we group objects into equal sets, we can add them up to find the total number of objects.
This is a strategy that is often used with young students who are just learning to multiply.
For example, 4 x 3 can be represented by equal groups of 3.
This can be represented with a diagram with 4 plates of cookies with 3 cookies on each plate. Then we can count the cookies.
So 4 x 3 = 12
Arrays
Whole number multiplication can also be thought of as repeated addition with an array.
An array is a rectangular arrangement of objects. The number of rows in the array tells us how many times we need to add.
The number of columns tells us what number we are adding.
For example, this array has three rows and four columns
There are 12 dots altogether so 3 x 4 = 12
What order do you teach multiplication strategies?
There is no definitive answer to this question as different students will learn multiplication strategies at different rates. However, it is generally recommended that students learn repeated addition and skip counting first. Then the commutative property before moving on to more difficult strategies such as doubling and halving.
What is a multiplication fact strategy?
Using the commutative property is the simplest multiplication fact strategy.
The commutative property is when the order of the numbers being multiplied does not affect the answer.
So this means you only need to learn half of the multiplication facts since
5 x 4 = 4 x 5
The benefits of using multiplication strategies
There are many benefits to using multiplication strategies.
Some of these benefits include:
– Students will develop a deeper understanding of multiplication concepts.
– Students will be able to approach multiplication problems with confidence.
– Students will be better prepared to tackle more complex mathematical concepts in the future.
Final thoughts and my experience of using multiplication strategies in the classroom
These multiplication strategies are essential for students to understand the multiplication facts which are often rote learned. They can then be applied to any multiplication, even if it is for the multiplication of decimals or algebraic terms.
In my teaching experience, the students who were able to apply these different strategies had better success solving unfamiliar problems and were faster, allowing them more time to think about harder questions.
