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Exploring Wild & Wonderful Number Patterns

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Sending Cards

This challenge asks you to investigate the total number of cards that would be sent if four children send one to all three others. How many would be sent if there were five children? Six?

1, 2, 3, 4, 5

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

1, 2, 3, 4, 5

Using the numbers $1, 2, 3, 4$ and $5$ once and only once, and the operations $\times$ and $ \div$ once and only once, what is the smallest whole number you can make?

example: 132 divided by 4, multiply by 5 equals 165. Is this the smallest number you can make?

Why do this problem?

This short problem could be used to start a lesson or fill a gap made by those who finish early. It will promote thinking about numbers and offers opportunities to practise multiplication and division.

Key questions

What results can you find obeying these rules?
Why don't you put all your answers in order?
What things do you notice about your different results?
Why do you not get any divisions by $5$?
Does it help to multiply by $1$? If not, why not?

Possible extension

Learners could make the largest number that they can using the same rules, and then as many results in between as possible.

Possible support

Using a calculator will help some children.