Topics
2. Addition and subtraction
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Australia
Year 5

2.05 Apply addition and subtraction

Lesson
Practice

Are you ready?

Let's try a practice problem to remember how patterns can help us with addition and subtraction.

Examples

Example 1

Fill in the boxes with the missing numbers.

a

14+5=⬚

Worked Solution
Create a strategy

On a number line, start with the bigger number and count to the right by the smaller number.

Apply the idea

Locate where 14 is on the number line, we can find 14 + 5 by jumping from 14 to the right by 5:

1112131415161718192021

14 + 5 = 19

b

24+5=⬚

Worked Solution
Create a strategy

Compare this sum to the sum in part (a).

Apply the idea

24 is 10 more than 14. This means that 24+5 will be 10 more than 14+5=19.

So we can just add 10 to 19.

\displaystyle 24+5\displaystyle =\displaystyle 19+10Add 10 to 19
\displaystyle =\displaystyle 29
c

34+5=⬚

Worked Solution
Create a strategy

Compare this sum to the sum in part (b).

Apply the idea

34 is 10 more than 24. This means that 34+5 will be 10 more than 24+5=29.

So we can just add 10 to 29.

\displaystyle 34+5\displaystyle =\displaystyle 29+10Add 10 to 29
\displaystyle =\displaystyle 39
d

84+5=⬚

Worked Solution
Create a strategy

Use a number line.

Apply the idea

Locate where 84 is on the number line, we can find 84 + 5 by jumping from 84 to the right by 5:

8081828384858687888990

84 + 5 = 89

e

What is the pattern? Choose the correct answer:

A
When you add one number to another, the answer becomes smaller.
B
When adding 5 to a two-digit number that ends in 4, we get a two-digit number that ends in 9.
Worked Solution
Create a strategy

Use the results found from parts (a) to (d). Look for a pattern in the answers.

Apply the idea

In parts (a) - (d), the result was always bigger than the number we added 5 to, and each answers ended in a 9. So, the correct answer is Option B.

Idea summary

We can use number lines and patterns to add numbers together.

Addition and subtraction using patterns

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Examples

Example 2

12-4=8. Use this to find:

a

22-4=⬚.

Worked Solution
Create a strategy

Compare this subtraction to the first subtraction we were given.

Apply the idea

22 is 10 more than 12. This means that 22-4 will be 10 more than 12-4=8. So we just need to add 10 to 8.

\displaystyle 22-4\displaystyle =\displaystyle 8+10Add 10 to 8
\displaystyle =\displaystyle 18
b

32-4=⬚.

Worked Solution
Create a strategy

Compare this subtraction to the subtraction from part (a).

Apply the idea

32 is 10 more than 22. This means that 32-4 will be 10 more than 22-4=18. So we just need to add 10 to 18.

\displaystyle 32-4\displaystyle =\displaystyle 18+10Add 10 to 18
\displaystyle =\displaystyle 28
c

42-4=⬚.

Worked Solution
Create a strategy

Compare this subtraction to the subtraction from part (b).

Apply the idea

42 is 10 more than 32. This means that 42-4 will be 10 more than 32-4=28. So we just need to add 10 to 28.

\displaystyle 42-4\displaystyle =\displaystyle 28+10Add 10 to 28
\displaystyle =\displaystyle 38
d

72-4=⬚.

Worked Solution
Create a strategy

Compare this subtraction to the subtraction from part (c).

Apply the idea

72 is 30 more than 42. This means that 72-4 will be 30 more than 42-4=38. So we just need to add 30 to 38.

\displaystyle 72-4\displaystyle =\displaystyle 38+30Add 30 to 38
\displaystyle =\displaystyle 68
Idea summary

To add or subtract using patterns, compare the calculation that you are trying to work out to another calculation that you already know. If you can see a pattern between the numbers, then you can use that to find the answer.

Addition and subtraction using story problems

Sometimes our problem is in the form of a story, or sentences. In this video, we see how to work out our number problem from the key words, or clues.

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Examples

Example 3

Four friends are picking fruit in an orchard. Tricia picks 16 apples, Ryan picks 29 peaches, James picks 23 pears and Laura picks 15 plums.

How many pieces of fruit were picked in total?

Worked Solution
Create a strategy

Add the amount that each person picked together to get the total. Use the standard algorithm method.

Apply the idea

First, we can find 16+29 by writing it in a vertical algorithm. In the ones column we get 6+9=15. So we bring down 5 and carry 1 to the tens place.\begin{array}{c} & &\text{}^1 1&6\\ &+ & 2&9\\ \hline & &&5 \\ \hline \end{array}

In the tens place, we have 1+1+2=4:\begin{array}{c} & &\text{}^1 1&6\\ &+ & 2&9\\ \hline & &4&5 \\ \hline \end{array}

Next, we can find 45+23 by writing it in a vertical algorithm. In the ones column, we have 5+3=8:\begin{array}{c} & &4 &5\\ &+ & 2&3\\ \hline & &&8 \\ \hline \end{array}

In the tens place, we have 4+2=6:\begin{array}{c} & &4 &5\\ &+ & 2&3\\ \hline & &6&8 \\ \hline \end{array}

Lastly, we can find 68+15 by writing it in a vertical algorithm. In the ones column we get 8+5=13. So we bring down 3 and carry 1 to the tens place.\begin{array}{c} & &\text{}^1 6&8\\ &+ & 1&5\\ \hline & &&3 \\ \hline \end{array}

In the tens place, we have 1+6+1=8:\begin{array}{c} & &\text{}^1 6&8\\ &+ & 1&5\\ \hline & &8&3 \\ \hline \end{array}

83 pieces of fruit were picked in total.

Idea summary

There are some words we might come across that mean we will be using addition whereas other words may suggest subtraction. This is not a complete list, so we need to understand the context of the question, to work out whether to add or subtract.

additionsubtraction
moreless
longershorter
laterearlier
boughtsold
joinedleft

Outcomes

AC9M5N09

use mathematical modelling to solve practical problems involving additive and multiplicative situations including financial contexts; formulate the problems, choosing operations and efficient calculation strategies, using digital tools where appropriate; interpret and communicate solutions in terms of the situation

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