Cherries Come in Twos

'Cherries Come in Twos' printed from https://nrich.maths.org/

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Cherries Come in Twos

Susie had a large bowl of cherries.

Bowl of Cherries

They were all in pairs.

4 pairs of cherries

Susie took out a pair, she ate one cherry and put the other one back. She took out another pair and did the same again.
Then she helped herself to one of the single cherries in the bowl.

Susie continued helping herself to the cherries in this way (pair, pair, single - pair, pair, single - ...)

two pairs and one cherry

After she had done this lots of times, there were just $14$ single cherries left.

How many cherries had there been in the bowl to start with?

Why do this problem?

This problem provides practice in addition and subtraction and in an arithmetic sequence. Learners will need to use a systematic approach of trial and improvement. Although the problem does not require the use of symbols it does encourage the use of generalising patterns.

Key questions

Is there and odd or even number of cherries?

What would be a good number to try for a start?

How many cherries does Susie eat during each round of helping herself to pair, pair, single cherries?

How many extra single cherries are there in the bowl after each round?

Can you think of a good way of recording what you have done?

Can you see any patterns in it?

Possible extension

Learners could try Magic Vs .

Possible support

Suggest using some pairs of multilink cubes (or counters) to represent the cherries. Start with a low even number and continue with increasingly higher even numbers until it works out.