When the problem involves equal groups and we want to know the total, we can represent this with a multiplication number sentence. We could also write a number sentence with repeated addition, however we want to shift our thinking to multiplicative ways to solve as they are much more efficient.

QUESTION 1

Use the picture to help you answer the questions.

Write a multiplication number sentence that will give the amount of precious stones there are.
How many precious stones does this give?

Array diagrams

Another way to represent a mathematical problem is with array diagrams. This is where items are ordered in equal rows. Can you imagine an array with two rows of five dots? This array is representing $2\times5=10$2×5=10.

This type of picture makes seeing equal sharing much easier. I can see how to share 10 into 2 equal groups by looking at the rows or $10$10 ÷ $2=5$2=5. And I can see how to share 10 into 5 equal groups or $10$10 ÷ $5=2$5=2 by looking at the columns. Take a look back at the video above if you aren't sure what an array diagram looks like.

QUESTION 2

Use the pictures to help you answer the questions.

Fill in the blanks:

There are $\editable{}$ rows of $\editable{}$ boxes.
How many boxes are there altogether?
The boxes are packed into the trucks so that there is the same amount in each.

Write a division number sentence for the number of boxes that will go into each truck.
How many boxes will go into each truck?

division

When a problem involves equal sharing then we can use division to solve it. Using array diagrams to organise our thinking makes the problem easier to solve.

QUESTION 3

A teacher wants to divide up her class of $24$24 students evenly onto $3$3 tables.

Write a division number sentence for this word problem.
How many students will there be at each table?

summing up

Mathematical problems can be represented with words, pictures and symbols. If the question involves equal groups and finding a total then multiplication is the strategy we use to solve the problem. If the problem involves sharing into equal groups then we use division.

Remember!

Organising our thinking into arrays is a powerful way to help us solve mathematical problems.

Worked Examples

Question 1

Use the picture to help you answer the questions.

Write a multiplication number sentence that will give the amount of precious stones there are.
How many precious stones does this give?

Question 2

Use the pictures to help you answer the questions.

Fill in the blanks:

There are $\editable{}$ rows of $\editable{}$ boxes.
How many boxes are there altogether?
The boxes are packed into the trucks so that there is the same amount in each.

Write a division number sentence for the number of boxes that will go into each truck.
How many boxes will go into each truck?

Question 3

A teacher wants to divide up her class of $24$24 students evenly onto $3$3 tables.

Write a division number sentence for this word problem.
How many students will there be at each table?

Problem solving with multiplication and division (1,2,3,5,10)