Finding unknown values | Year 6

01 / LEARN

Understand the idea.

Keep equality true

An unknown stands for a value still to be found. The equals sign says both sides have the same value. In $□ + 7 = 19$ , remove seven from both sides to leave the unknown equal to twelve.

Inverse operations undo each other: subtraction undoes addition, and division undoes multiplication by a nonzero number. After finding the unknown, replace it in the original statement to check that both sides really are equal.

Undo the last step first

For a two-step number machine, undo the final operation first. If a number is multiplied by four and then three is added, first subtract three from the result. Then divide by four to recover the starting number.

Take care when the unknown is the value being subtracted or the divisor. In $30 - □ = 12$ , the missing value is what was removed from thirty. Use the complete relationship and check the original order instead of applying an inverse mechanically.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

Worked example 1

Find the missing number: box×6=42.

Worked solution

1
Use the inverse of multiplication.
$□ = 42 \div 6$
Dividing the total by six finds the factor that was multiplied by six.
2
Calculate the missing factor.
$42 \div 6 = 7$
Seven equal groups of six make forty-two.
3
Check in the original statement.
$7 \times 6 = 42$
The two sides agree when the unknown is replaced by seven.

Answer

EXAMPLE 02

Worked example 2

A number is doubled and then 5 is added. The result is 21. Find the number.

Worked solution

1
Undo the final addition.
$21 - 5 = 16$
Removing the added five leaves twice the unknown number.
2
Undo doubling.
$16 \div 2 = 8$
Dividing by two recovers the original number.
3
Check the full original process.
$2 \times 8 + 5 = 16 + 5 = 21$
Doubling eight and then adding five gives the stated result.

Answer

03 / YOUR TURN

Try it yourself.

Check your understanding

Find the missing number: box÷5=9.

Show answer & reasoning

45.

If dividing the unknown by five gives nine, undo the division by multiplying: $9 \times 5 = 45$ . Check that $45 \div 5 = 9$ .

Keep practising

6 worksheet questions · 8 marks

Open worksheet Worked solutions

Read the questions online

Find the missing number: $□ + 9 = 25$ .
1 mark
Find the missing number: $□ - 12 = 18$ .
1 mark
Find the missing number: $7 \times □ = 56$ .
1 mark
Find the missing number: $□ \div 4 = 11$ .
1 mark
Find the missing number: $□ \times 3 + 4 = 25$ .
2 marks
Find the missing number: $50 - □ = 17$ . Explain the check.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Find the missing number: $□ + 9 = 25$ .
1 mark
$25 - 9 = 16$ .
16.
Find the missing number: $□ - 12 = 18$ .
1 mark
$18 + 12 = 30$ .
30.
Find the missing number: $7 \times □ = 56$ .
1 mark
$56 \div 7 = 8$ .
8.
Find the missing number: $□ \div 4 = 11$ .
1 mark
$11 \times 4 = 44$ .
44.
Find the missing number: $□ \times 3 + 4 = 25$ .
2 marks
$25 - 4 = 21$ ; $21 \div 3 = 7$ . Check $7 \times 3 + 4 = 25$ .
7.
Find the missing number: $50 - □ = 17$ . Explain the check.
2 marks
$50 - 17 = 33$ ; replacing the box gives $50 - 33 = 17$ .
33.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Growing rational patterns; rules; brackets/order of operations; unknowns; algorithms.

Official curriculum source ↗

In this lesson

Understand the idea.

Keep equality true

Undo the last step first

See the method in action.

Worked example 1

Use the inverse of multiplication.

Calculate the missing factor.

Check in the original statement.

Worked example 2

Undo the final addition.

Undo doubling.

Check the full original process.

Try it yourself.

Check your understanding

Keep practising