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In the Money
There are a number of coins on a table.
One quarter of the coins show heads.
If I turn over two coins, then one third show heads.
How many coins are there altogether?
Once you have thought about how you would begin to solve this problem, click below to see how other children began to work on it:
Freddie said:
I got some coins to try out ways to make it work.
Vasanthi and Francis said:
We noticed that there were more heads after turning over two coins.
Hussam and Suzy said:
First we thought of what number could have a quarter and a third which are whole numbers.
Did you start the problem in the same way as any of these children?
What do you think about each method?
Now continue to work towards a solution to the problem. You could choose to use Freddie's, or Vasanthi and Francis', or Hussam and Suzy's method.
Why do this problem?
This problem challenges children to calculate with fractions and provides a good context in which to encourage learners to be curious about different methods of approach.
By focusing on the problem-solving journey and not just the answer, learners will become more resilient as problem solvers.
By focusing on the problem-solving journey and not just the answer, learners will become more resilient as problem solvers.
Possible approach
You could set the scene for the problem by having a pile of coins on the table or desk and inviting children to talk about what they see. Take comments and encourage other children to respond.
Present the problem itself and give children a short amount of time to work in pairs on it. Explain that you are not expecting them to reach a full solution in this time, rather you are wanting them to think carefully about how they might approach the task. Mini-whiteboards might be useful at this stage. Listen out for sound reasoning and helpful strategies for getting started on the
problem.
Draw the whole group together again and share 'ways in' to the problem. You could do this by using examples of ways of working that children in your class have used, or you might give the examples in the problem (Freddie, Vasanthi and Francis, and Hussan and Suzy). If you go for the latter, you might find this sheet useful, which is a copy of the problem and each approach. Facilitate a discussion about the different methods, helping everyone understand them, and giving opportunities for learners to talk about the merits of each.
Draw the whole group together again and share 'ways in' to the problem. You could do this by using examples of ways of working that children in your class have used, or you might give the examples in the problem (Freddie, Vasanthi and Francis, and Hussan and Suzy). If you go for the latter, you might find this sheet useful, which is a copy of the problem and each approach. Facilitate a discussion about the different methods, helping everyone understand them, and giving opportunities for learners to talk about the merits of each.
Then allow more time for children to continue working on the task and invite them to choose one of the approaches they have heard about if they wish.
A follow-up question of a similar sort could be useful for a plenary or second activity so that children get chance to practise their strategies. For example: one sixth of the coins are heads up. If I turn over four more, then one fifth are heads. How many coins are on the table?
Key questions
What do you know about the total number of coins?
Have you tried out any possible numbers?
Possible extension
Pupils could be encouraged to create their own version of the problem for a friend to solve.
Possible support
Using coins to try out possibilities will help some pupils.