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## 'The Brown Family' printed from http://nrich.maths.org/

## The Brown Family

Sally Brown has an equal number of brothers and sisters.

Mark Brown, her older brother, has twice as many sisters as brothers.

How many children are there in the Brown family?

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### Why do this problem?

This problem requires logical thinking and could be a good way to introduce a trial and improvement approach. Children need to understand the difference between having a certain number of brothers and the number of boys in a family.

### Possible approach

You could start with a discussion on how many brothers and sisters the members of the class have and relate this to the number of boys and girls in their families.

Alternatively, you could use the interactivity on an interactive whiteboard to introduce, but not to solve, the problem. After this, children could work in pairs on the problem either using the interactivity or using paper/miniwhiteboards to make jottings. It would be worth stopping them after a few minutes to see how they are going about tackling the problem and to share some ideas. You
could also draw attention to different ways of representing the problem that you have noticed.

You may wish to introduce the idea of recording in a table. Some children could be challenged to design their own table while you could give others

this sheet to complete. Filling in the first line or two of the table together as a class would give them a
good start.
### Key questions

How many brothers has Sally got now?

How many brothers has Mark got now?

How many boys are there in the family now?

### Possible extension

Children could make up different problems for each other such as "What would the answer be if Mark had three times as many sisters as brothers?" Alternatively, they could make up similar problems about their own, or invented, families.

### Possible support

Some learners would benefit from using the interactivity if possible, or counters in two colours to represent boys and girls.