This lesson will help students to see multiplication as more than just an operation to be carried out or to be memorized. It will show how the two factors and their product can be read as a comparison.
Work through the examples and explanations in this lesson with your children and then try the worksheet that you will find at the bottom of this page.
When you multiply, you are often making a comparison between two numbers.
In the equation 7 x 5 = 35, the answer 35 is 5 times as many as 7. It is also 7 times as many as 5.
Let’s use drawings to help us see this relationship a little more clearly.
|When you compare the picture of 7 tiles to the picture of 35 tiles, you can see that there are 5 times as many tiles in the picture of 35. Therefore, you can think of 35 as 5 times as many as 7.|
|Similarly to the above picture, when you compare the picture of 5 tiles to the picture of 35 tiles, you can see that there are 7 times as many tiles in the picture of 35. Therefore, you can also think of 35 as 7 times as many as 5.|
Any two factors and their product can be read as a comparison. Let’s look at another multiplication equation:
3 x 2= 6.
6 is 3 times as many as 2, and 2 times as many as 3.
Again, it’s helpful to see this relationship visually by comparing tiles. See below
6 is 3 times as many as 2:
6 is 2 times as many as 3:
Discuss with your child how the equal sign is like a balance symbol. Both sides of the equal sign total the same value. When you see an equal sign, you should think “is the same as” instead of “put the answer here”.
Although we are used to seeing equations that look like a “problem” followed by an “answer”, for example: 4 x 5 = 20 it is just as correct to say that 20 = 4 x 5 or 20 = 5 x 4.
More Multiplication as Comparison
20 = 4 x 5 Think “20 is the same as 4 sets of 5”.
20 = 5 x 4 Think “20 is the same as 5 sets of 4”.
|When we start from this basic understanding, it is much easier to compare the relationship between the numbers.|
|20 is 4 times as many as 5. |
20 is 5 times as many as 4.
Try to work out what the missing numbers are below (after you have tried you can click on the spaces to see the answers)
|Fill in the missing information about the relationship between the numbers in this equation: 3 x 9 = 27|
27 is _ times as many as _
and is _ times as many as _
Multiplication as Comparison : Recap
Look at the eight multiplications below. Think, or better still, say out loud, the relationship between the numbers. Click the spaces as you work to check each one as you go.
|3 x 6 = 18||6 x 7 = 42|
|2 x 8 = 16||3 x 5 = 15|
|4 x 8 = 32||2 x 4 = 8|
|5 x 6 = 30||9 x 6 = 54|
Multiplicative Comparison Worksheets
Click the link below and get your child to try the worksheet that will allow for practice with multiplicative comparison questions.