Related addition and subtraction facts | Year 2

01 / LEARN

Understand the idea.

Parts and a whole

A fact family uses the same whole and two parts. In $5 + 8 = 13$ , five and eight are the parts. They can swap places when adding; taking either part away from thirteen leaves the other part.

A fact family
Addition	Subtraction
5 + 8 = 13	13 − 5 = 8
8 + 5 = 13	13 − 8 = 5

Use the correct starting number

For these whole-number subtraction facts, begin with the whole. From $12 + 7 = 19$ , write $19 - 12 = 7$ or $19 - 7 = 12$ . If the two parts are equal, swapping them gives the same addition, so some family facts repeat.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Use a whole and two parts

Write a fact family using 9, 4 and 13.

Worked solution

1
Identify the two parts and their whole.
$9 + 4 = 13$
Nine and four join to make thirteen.
2
Swap the parts for another addition fact.
$4 + 9 = 13$
Changing the order of the parts does not change the whole.
3
Remove the part nine.
$13 - 9 = 4$
Starting with the whole and taking one part leaves the other.
4
Remove the part four.
$13 - 4 = 9$
Each of the two parts can be removed from the same whole.

Answer

9 + 4 = 13; 4 + 9 = 13; 13 − 9 = 4; 13 − 4 = 9.

EXAMPLE 02

Use a known two-digit fact

You know 32 + 15 = 47. Find 47 − 32.

Worked solution

1
Identify the whole and the parts.
$32 + 15 = 47$
Forty-seven is the whole; thirty-two and fifteen are its parts.
2
Remove the known part.
$47 - 32 = 15$
Removing thirty-two leaves the other part, fifteen.

Answer

03 / YOUR TURN

Try it yourself.

Check your understanding

Use 8 + 7 = 15 to find 15 − 8.

Show answer & reasoning

The fact $8 + 7 = 15$ says eight and seven are the parts of fifteen. Removing eight leaves seven, so $15 - 8 = 7$ .

Keep practising

6 worksheet questions

Open worksheet Worked solutions

Read the questions online

Complete: $6 + 9 = 15$ , so $9 + 6 =___$ .
Use $11 + 5 = 16$ to find $16 - 5$ .
Write one subtraction fact for $7 + 4 = 11$ .
Use $23 + 14 = 37$ to find $37 - 23$ .
Write two addition facts using $8, 12 and 20$ .
Tom writes $10 - 6 = 4$ and says $6 + 4 = 10$ is related. Explain why.

Read the worked solutions

Complete: $6 + 9 = 15$ , so $9 + 6 =___$ .
Swapping the parts does not change the whole.
15
Use $11 + 5 = 16$ to find $16 - 5$ .
Taking away 5 leaves the other part.
11
Write one subtraction fact for $7 + 4 = 11$ .
The whole is 11; remove either part.
For example, $11 - 7 = 4$ .
Use $23 + 14 = 37$ to find $37 - 23$ .
The other part is 14.
14
Write two addition facts using $8, 12 and 20$ .
Both facts join the same two parts.
$8 + 12 = 20$ and $12 + 8 = 20$ .
Tom writes $10 - 6 = 4$ and says $6 + 4 = 10$ is related. Explain why.
Subtraction undoes the joining shown by addition.
Both use the parts 6 and 4 and the whole 10.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Facts within 20; one-/two-digit calculations; partitioning; related facts; missing numbers; checking.

Official curriculum source ↗

In this lesson

Understand the idea.

Parts and a whole

Use the correct starting number

See the method in action.

Use a whole and two parts

Identify the two parts and their whole.

Swap the parts for another addition fact.

Remove the part nine.

Remove the part four.

Use a known two-digit fact

Identify the whole and the parts.

Remove the known part.

Try it yourself.

Check your understanding

Keep practising