Would You Rather?
1 out of 3
Would you rather: Have 10% of £5 or 75% of 80p? Be given 60% of 2 pizzas or 26% of 5 pizzas?
Problem
Would You Rather? printable sheet
Would you rather...
Be given 60% of 2 pizzas or 26% of 5 pizzas?
Have 10% of £5 or 75% of 80p?
Be bitten by 15% of 120 mosquitoes or 8% of 250 mosquitoes?
Skip using a rope which is 54% of 105cm long, or 88% of 2.75m long?
Sit in a traffic jam for 33% of 2 hours or 44% of 1hr 40mins?
Make sure you explain your reasons clearly.
Perhaps you'd like to make up some of your own questions like these and send them to us.
There is also a version of this problem using US units.
Getting Started
It's hard to give hints to this problem but here are a few things to think about:
- Try estimating which you think will be the answer first
- Linking percentages to fractions often helps
Student Solutions
Marion at Tattingstone School and Aditya, who is from Bristol Grammar, both calculated these percentages carefully and came to sensible conclusions!
- Have 10% of £5 or 75% of 80p. 10% of £5 is 50p:
10% of £5 = (10/100) * 500 = 5000/100 = 50
and 75% of 80p is 60p. I'd rather have the latter. - Have 60% of 2 pizzas or 26% of 5 pizzas. 60% of 2 is 1.2 and 26% of 5 is 1.3. Again, I'd rather have the latter.
- Get bitten by 15% of 120 mosquitoes or by 8% of 250 mosquitoes. 15% of 120 is 18 and 8% of 250 is 20. I'd prefer the first.
- Skip with a rope 54% of 105cm long or with one 88% of 2.75m long. 54% of 105cm is 56.7cm, and 88% of 2.75m is 2.42m = 242cm. I'd prefer using the longer rope.
- Get stuck in a traffic jam lasting 33% of 2 hours or 44% of 1 hr 40 mins. 33% of 120 minutes is 40 minutes, and 44% of 100 minutes is 44 minutes. I'd prefer neither!
Teachers' Resources
Using NRICH Tasks Richly describes ways in which teachers and learners can work with NRICH tasks in the classroom.
Why do this problem?
This activity would be a good start to, or could follow on from, work on finding percentages of quantities. In whichever context it is used, it will provide a good assessment opportunity for you to find out what your pupils understand well and what they have difficulties with.
Possible approach
These problems are probably best tackled as a group activity with children working in threes or fours. Give each group a set of these cards, five of which contain one each of the scenarios and one of which is blank. Challenge each group to decide which situation they would prefer and say that you will want them to explain how they came to their decisions.
Having given them a suitable length of time to work on the problems, bring everyone together. You could take a vote on each one to start with and then ask one group to explain how they came to that conclusion. Invite other groups to contribute different ways of working out the solution as well so that a range of methods are discussed.
You could then ask each group to make up their own question in a similar style which they could write on the blank card. These could then be swapped. Of course the group which poses the problem must have also worked out the solution!
Key questions
How will you compare these two scenarios?
Can you express this percentage in any other way?
What do you estimate this percentage to be?
Possible extension
Making up a similar problem (with its solution!), whose answer is not immediately obvious, will challenge many learners.
Possible support
Calculators may be useful.