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2.09 Story problems


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Sometimes we have written problems, where we need to know how to  read and write numbers  .


Example 1

Write the number that is ten more than sixty one thousand, five hundred and ninety seven.

Worked Solution
Create a strategy

Use a place value table.

Apply the idea

Convert the word number into numerals using a place value table:

Ten thousandsThousandsHundredsTensUnits
6159 7

To find ten more than this number we need to add 10. We can do this in a place value table by adding the numbers in each column and carrying to the next column where necessary:

Ten thousandsThousandsHundredsTensUnits
615 \text{ }^19 7
+ 10

So the number is 61\,607.

Idea summary

We can use place value tables to write numbers as numerals, and to add numbers.

Add and subtract in story or word problems

Sometimes we need to read written or story problems, and work out what we need to solve. In this video, we have to find out what our problem is.

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Example 2

Gwen has 37 raffle tickets to sell. She is able to sell 4 tickets to Luke and 9 tickets to Kate. If James now wants to buy all of her remaining tickets, how many are left for him to buy?

Worked Solution
Create a strategy

The word "sell" here indicates subtraction.

Apply the idea

\text{Remaining tickets} = \text{Total number of tickets} - \text{Total number of tickets sold}

The total number of tickets sold is the equivalent to the total tickets sold to Luke and Kate. So \text{Total number of tickets sold} = 4 + 9 = 13

Substitute known values to the formula above: \text{Remaining tickets} = 37 - 13

Use the number line to carry out the subtraction. Locate 37 and jump back by 13:


So: \text{Remaining tickets} = 24

There are 24 tickets left for James to buy.

Idea summary

Key words in a word problem help us know which operations we need to use to solve the problem.

Write number sentences

In this story problem, we find out how to write out the number problem, with both addition and subtraction.

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Example 3

There were 13 flowers in Pauline’s garden. 2 more flowers grew, then Pauline picked 8 flowers to put in a vase.

Which number sentence matches the word problem for the number of flowers left in the garden?

Worked Solution
Create a strategy

The words "more" and "grew" mean addition because the number of flowers got bigger. The word "picked" means subtraction because the flowers were taken away.

Apply the idea

The number of flowers left in the garden matches the number sentence: 13 + 2 - 8 So the answer is option C.

Idea summary

When we have a word problem, we need to think about the story and use the keywords to work out which operators to use. Some words that we may find in a story could be:

give totake away



uses mental and written strategies for addition and subtraction involving two-, three-, four and five-digit numbers


generalises properties of odd and even numbers, generates number patterns, and completes simple number sentences by calculating missing values

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