Multiplication and Division

Lesson

Watch this video to learn about number sentences for problem solving.

Mathematical problems can be represented in words, pictures and symbols. Understanding each representation and how it links is important for solving problems. This chapter will look at solving problems with multiplication and division.

When the problem involves equal groups and we want to know the total, we can represent this with a multiplication number sentence. Let's look at some examples to show how the number sentences are formed.

If three friends went fishing and they each caught two fish, how many fish altogether? Because this problem is 3 equal groups of 2 we can write the number sentence as $3\times2=6$3×2=6

We could also write it as $2+2+2=6$2+2+2=6, but we want to shift our thinking from addition into multiplication to help us solve problems more quickly.

You are baking cakes for the school fete and you need to make five batches of ten cakes, how many cakes will you bake altogether? In this problem there are 5 equal groups of 10 so our number sentence is $5\times10=50$5×10=50. You can see, as the numbers get bigger, shifting from addition to multiplication is very important to solve the problem more quickly.

Some questions may involve pictures as well. When the question requires multiplication you should be able to see equal groups within the picture.

Use the picture to help you answer the questions.

Write a multiplication number sentence that will give the amount of candles there are.

How many candles are there in total?

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.

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?

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.

Use simple additive strategies with whole numbers and fractions

Communicate and interpret simple additive strategies, using words, diagrams (pictures), and symbols.