Why do this problem?

This problem can be solved in a variety of ways (trial and improvement, graphically, algebraically) so can offer a useful opportunity for discussing the merits of different strategies.

Possible approach

Write the formula on the board: F= 9 5 C+32

"Does anyone recognise this formula?"

"Water freezes at 0∘ Centigrade.
Can you use the equation to work out what this is in Fahrenheit?"

"Water boils at 100∘ Centigrade.
Can you use the equation to work out what this is in Fahrenheit?"

"We are sometimes given temperature in Fahrenheit, can you convert into Centigrade?

Take for example 80∘ F. What would this be in Centigrade?"

Give the students a few minutes to answer the question.

Can they suggest more than one strategy?
Compare their efficiency.

Give them another temperature in Fahrenheit to convert into Centigrade, this time using all the strategies that have been suggested.

Pose the problem:
" Is there a temperature at which Celsius and Fahrenheit readings are the same?"

Again, set aside some time to compare strategies.

Key questions

Does every method give the same answer? Which methods are most accurate?
Which method is most efficient?

Possible extension

When is the temperature in Fahrenheit double the temperature in Centigrade?
When is the temperature in Fahrenheit treble the temperature in Centigrade?
When is the temperature in Fahrenheit half the temperature in Centigrade?

Is it always possible to find a temperature that fits a relationship of this sort?
When is the temperature in Fahrenheit 9 5 ths the temperature in Centigrade?

Possible support

Suggest that students tackle this graphically.