New
New
Year 5

# Use a complete list of factors to explain when a number is a square number

I can use a complete list of factors to explain when a number is a square number.

New
New
Year 5

# Use a complete list of factors to explain when a number is a square number

I can use a complete list of factors to explain when a number is a square number.

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## Lesson details

### Key learning points

1. A square number has an odd number of factors.
2. A square number is the product of multiplying a number by itself.

### Common misconception

Pupils record the number of factors for a square number as even as they record the same number twice when writing down the factors of the square arrangement.

Highlight the need to only record each number as a factor once. You may like to record this on the tail of the factor bug to help emphasise this.

### Keywords

• Factor - Factors are whole numbers which exactly divide another whole number.

• Square number - A square number is the result of multiplying an integer (not a fraction) by itself.

In this lesson, time should be given over to allow pupils to explore and investigate the factors in square and composite numbers. Encourage additional exploration into larger integers and promote further pattern seeking opportunities.
Teacher tip

### Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

## Starter quiz

### 6 Questions

Q1.
Which factor is missing from the factor bug?
Q2.
What number has only the following factors: 1, 2, 11, 22
Q3.
Which factor is missing from the factor bug?
Q4.
Which of these is the correct full list of factors of 26?
1, 2, 6, 10, 13, 26
2, 13
Correct answer: 1, 2, 13, 26
1, 2, 4, 13, 6.5, 26
Q5.
What is the missing factor of 54 from this list? 1, 2, 3, 6, 18, 27, 54
Q6.
What is the missing factor of 69 from this list? 1, 23, 69

## Exit quiz

### 6 Questions

Q1.
Which multiplication is shown by this array?
4 × 4 =
4 × 1 =
2 × 4 =
Correct answer: 2 × 2 =
Q2.
What square number is represented by this incomplete factor bug?
Q3.
Tick the square numbers.
48
110
200
Q4.
Tick the lists which show factors of a square number.
1, 2, 3, 4, 6, 8, 12, 24
Correct answer: 1, 2, 3, 4, 6, 9, 12, 18, 36
1, 2, 5, 10, 25, 50
Q5.
Match the expression to the correct square number.

9

49