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# Doubling Fives

## Doubling Fives

This challenge is about doubling multiples of 5.

Pick a multiple of 5. Double it.

What is your answer? How many 10s is this?

Can you spot any patterns?

Can you explain the patterns?
#### Why do this activity?

This activity provides a context for doubling multiples of 5. The children will also be noticing and describing patterns.

#### Possible approach

It would be good to start the lesson by counting in 5s and reminding the class that multiples of 5 end in a 5 or 0.

A possible starting point for the activity is looking at doubling single-digit numbers. The children could try numbers of their choice and record them on whiteboards. As you collate the ideas, you could record the responses systematically using a table like this one:

What do children notice about all of the answers? Can they spot any patterns? Can they come up with a rule? "Whenever we double a single digit number ..." They then might conjecture that this will also be true for two-digit numbers and might test this.

Explain to the class that they will be looking at doubling multiples of 5. Do they think the answers are going to be odd or even? This time, they will be exploring the number of 10s that are created when multiples of 5 are doubled. You might encourage systematic recording in a table like this:

Some children start at or move onto the extension tasks (below).

#### Key questions

What is double this multiple of 5?

How many 10s is this? Is it an odd or even number of 10s?

Which numbers end up with an odd/even number of 10s?

Can you record your work systematically?

What is the same about these numbers? Can you spot a pattern?

Why does this happen?

#### Possible extensions

*Extension 1*: How about this time you start with a multiple of 10 and then halve it? Can you come up for a rule for when the answer will end in a 0 and when it will end in a 5?

*Extension 2*: Have a go at the original activity or the extension for other numbers. You could try starting with multiples of 3 and see what happens when you double them. What happens to multiples of 6 when you halve them?

#### Possible support

Base 10 apparatus or similar may help children to reason about the halves and doubles.

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Age 5 to 7

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Pick a multiple of 5. Double it.

What is your answer? How many 10s is this?

Can you spot any patterns?

Can you explain the patterns?

A possible starting point for the activity is looking at doubling single-digit numbers. The children could try numbers of their choice and record them on whiteboards. As you collate the ideas, you could record the responses systematically using a table like this one:

Single digit number |
Double the single digit number |
Odd or even? |

1 | 2 | even |

2 | 4 | even |

What do children notice about all of the answers? Can they spot any patterns? Can they come up with a rule? "Whenever we double a single digit number ..." They then might conjecture that this will also be true for two-digit numbers and might test this.

Explain to the class that they will be looking at doubling multiples of 5. Do they think the answers are going to be odd or even? This time, they will be exploring the number of 10s that are created when multiples of 5 are doubled. You might encourage systematic recording in a table like this:

Multiple of 5 |
Double the multiple of 5 |
How many tens? |

5 | 10 | 1 |

Some children start at or move onto the extension tasks (below).

How many 10s is this? Is it an odd or even number of 10s?

Which numbers end up with an odd/even number of 10s?

Can you record your work systematically?

What is the same about these numbers? Can you spot a pattern?

Why does this happen?