This problem solving activity has a number focus.
Jack says, “Did you know that today is my three sons’ birthday?”
“How old are they?” asks Ollie.
Jack gives him a hint. "The product of their ages is 36 and the sum of their ages is 13.”
“That’s no help,” says Ollie.
Jack gives him another clue. “O.K. My youngest son is very naughty.”
“Nothing to it,” exclaims Ollie, and he tells Jack the correct ages of his sons.
How does Ollie figure out the correct answer and what are Jack’s sons’ ages?
The subtle logic of this problem places it at this level.
Students are given three pieces of information which must be synthesised in order to find a solution. They must be attuned to the semantics of one piece of information, and find the right combination of factors for a given product, while looking for addends of a given sum.
Jack says, “Did you know that today is my three sons’ birthday?”
“How old are they?” asks Ollie.
Jack gives him a hint. "The product of their ages is 36 and the sum of their ages is 13.”
“That’s no help,” says Ollie.
Jack gives him another clue. “O.K. My youngest son is very naughty.”
“Nothing to it,” exclaims Ollie, and he tells Jack the correct ages of his sons.
How does Ollie figure out the correct answer and what are Jack’s sons’ ages?
Work with the three pieces of information separately.
A’s age | B’s age | C’s age | Sum of their ages |
36 | 1 | 1 | 38 |
18 | 2 | 1 | 21 |
12 | 3 | 1 | 16 |
9 | 4 | 1 | 14 |
9 | 2 | 2 | 13 |
6 | 6 | 1 | 13 |
6 | 3 | 2 | 11 |
4 | 3 | 3 | 10 |
From the table we can see that there are two lots of ages (factors of 36) that add up to 13. These are 9, 2, 2 and 6, 6, 1.
It’s not surprising that there are two answers. If there was only one, Ray would have been able to solve the problem without any further clues. But what possible help can it be to know that Jack’s youngest son is very naughty?
The point here is that Jack has a youngest son! He doesn’t have two sons that are the same age. So 9, 2, 2 can’t be the answer. The answer has to be 6, 6, 1, where there is a youngest son whose age is 1.
Ray correctly identified the ages of Jack’s sons as 6 years, 6 years and 1 year.
Printed from https://meaningfulmaths.nt.edu.au/mmws/nz/resource/my-son-naughty at 8:58pm on the 26th February 2024