Fun time
On Saturday, Asha and Kishan's grandad took them to a theme park. Use the information to work out how long they were in the theme park.
Problem
On Saturday, Asha and Kishan's grandad took them to a theme park.
In total, they spent $\frac{1}{5}$ of the day queuing for rides.
They worked out that $\frac{3}{4}$ of the rest of their time there was spent enjoying the rides.
Of the time left, $\frac{1}{2}$ was spent having lunch.
The 3D cinema show took up $\frac{2}{3}$ of the rest of the day.
Finally there were $10$ minutes left to go to the gift shop before they went home.
How long were Asha and Kishan at the Theme Park?
Getting Started
Try working backwards:
What fraction of the total time for the cinema and shopping is the $10$ minutes of shopping?
So how long did they spend in total watching the film and shopping?
Continue like this....
Student Solutions
You all realised that you need to work backwards, or from the end of the question, to answer this problem. Thomas, Serge, Runi and Sam from Newberries Primary School all found the correct length of time that Asha and Kishan spent at the fair to be five hours. Sam explains how he worked this out:
Lucy from St John's R. C. Primary School used a pie chart to calculate the answer:
Alice and Gwen, who are both from The Downs C.E.P School, represented their solution as a rectangle:
After we've counted queuing for the rides, they have $\frac{4}{5}$ of the day left.
After we've counted the rides themselves, they have $\frac{1}{4} \times \frac{4}{5} = \frac{1}{5}$ of the day left.
After we've counted lunch, they have $\frac{1}{2} \times \frac{1}{5} = \frac{1}{10}$ of the day left.
After we've counted the cinema, they have $\frac{1}{3} \times \frac{1}{10} = \frac{1}{30}$ of the day to spend in the gift shop.
Teachers' Resources
Fun Time
On Saturday, Asha and Kishan's grandad took them to a Theme Park.
In total they spent $\frac{1}{5}$ of the day queuing for rides.
They worked out that $\frac{3}{4}$ of the rest of their time there was spent enjoying the rides.
Of the time left, $\frac{1}{2}$ was spent having lunch.
The 3-d cinema show took up $\frac{2}{3}$ of the rest of the day.
Finally there were $10$ minutes left to go to the gift shop before they went home.
How long were Asha and Kishan at the Theme Park?
Why do this problem?
This problem gives practice in calculating with fractions and encourages different ways of representing and recording.
Key questions
Possible extension
Andy's Marbles is a similar problem which might make a good follow-up activity.
Possible support
Fair Feast would be a good problem to try first if children find calculating with fractions difficult.