The Brown Family
The Brown Family printable sheet
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?
We had a few correct answers for this challenge. Firstly Alex from Branchburg Central Middle School in USA said:
There are seven children in the Brown family: three boys and four girls.
Julian from the British School Manila in the Philippines, gave this mathematical explanation:
Number of male children: b
Number of female children: f
b=f-1
f=2(b-1)
b=f-1
f=2b-2
b=2b-3
b=3
f=b+1
f=4
b=3. f=4
7 children
From Moonstone at the Hammond Academy we had this:
We think that there are 7 children in the Brown family altogether. Sally has 3 sisters and Mark has 2 brothers.
Finally Katie at Raysfield Infants School, wrote this excellent explanation as to one way of solving the challenge.
We read the instructions and logged on to the website. There were three 'questions'.
Q1. Sally had equal numbers of brothers and sisters.
She did not have an equal amount of brothers and sisters so we made it equal by adding a sister.
Q2. Mark has twice as many sisters as brothers.
He now had 2 sisters and no brothers so we added a brother to make Q2. Correct.
We checked Q1 again to see if it was true. It was not so we added another sister to make Q1. correct.
We checked Q2 to see if this was correct still, it was not so we added another brother to make Q2. correct.
We went back to Q1. To see if that was correct, it was not so we added another Sister.
Now Q1. is correct, we checked Q2. and that was correct too.
We then added up all the children to see how many there were.
There were 7 children.
Thank you for those results of your work, well done in persevering.
The Brown Family
The Brown Family printable sheet
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?
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.
Children could then work in pairs on the problem either 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 a table of results 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 Mark got 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 something to represent the boys and girls, for example counters in two colours.