1. Ancient Arab and Roman mathematicians were
Ratio
N4.3 Core Plenary
Ancient Arab and Roman mathematicians were
very interested in solving problems like this.
A man dies. He leaves a pregnant wife and silver coins.
He wanted the money shared out between his wife and baby like this:
■ If the baby is a boy, shared between mother and son in the ratio 1 : 2.
■ If the baby is a girl, shared between mother and daughter in the ratio 2 : 1.
Twins are born – a boy and a girl!
How would you divide up the money to carry out the man’s will in the best way possible?
Preamble
This sort of problem really did engage Ancient Arab and Roman mathematicians. After allowing pupils a few minutes to understand the problem, take explanations from the whole group about how to approach it. Initially attention should be focused on producing ratios which are ‘fair’ according to the will conditions – or at least do not contradict them. The actual sums of money are not important. Pupils may need to be reminded of the initial conditions. Any alternative answers must be fully defended.
Possible content
Using ratio in a practical context, making decisions and giving reasons for them, dividing a sum of money into a given ratio.
Resources
None.
Solution/Notes
The son gets twice as much as the mother and the daughter gets half as much as the mother so the ratio son : mother : daughter is 4 : 2 : 1.
This ratio has 7 parts; each part is ÷ 7 =
The son gets 4 × coins = coins.
The mother gets 2 × coins = coins.
The daughter gets 1 × coins = coins.
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Original Material © Cambridge University Press 2009