Number sentences and word problems (10x10)
Solving word problems with multiplication and division
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.
Multiplication
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.
question 1
If eight friends went to a party and they each got a lolly bag with ten lollies in it, how many lollies are there altogether? Because this problem involves equal groups and you want to find a total then we can use multiplication to write our number sentence, it is $8\times10=80$8×10=80.
We could also write it as $10+10+10+10+10+10+10+10=80$10+10+10+10+10+10+10+10=80, but we want to shift our thinking from addition to multiplication to help us solve problems more quickly.
Some questions may involve pictures as well. When the question requires multiplication you should be able to see equal groups in the picture.
Question 2
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?
DIVISION
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 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.
Organising our thinking into arrays is a powerful way to help us solve multiplication and division problems.