### Why do this problem?

This problem offers an opportunity to combine skills from
mathematics and science. It can be solved numerically,
algebraically or graphically, so can offer a useful opportunity for
discussing the merits of different methods.

### Possible approach

Introduce the boiling and freezing point of water in Celsius
and Fahrenheit.

"What other information can you deduce from these temperature
facts?"

Give the class some time to discuss in pairs, then bring the
class together to collect ideas on the board. Possible responses
might be:

"$50^\circ C = 122^\circ F$ because it's halfway
between."

"$200^\circ C = 392^\circ F$ because it's another $180^\circ
F$."

"A temperature increase of $100^\circ C$ is the same as a
temperature increase of $180^\circ F$."

"Can you use everyone's ideas to deduce any more information
about the temperature scales?"

Again, give the class some time to discuss in pairs, and then
collect ideas once more.

"Is there a temperature where the reading in Celsius is the
same as the reading in Fahrenheit?"

Give the class plenty of time to approach this problem. Most
students are likely to use a numerical approach. If some
students use algebraic or
graphical methods, ask them
to share their approaches with the rest of the class.

If nobody uses algebra or graphs, ask the class to consider
first how a graph might help:

"Can you represent the original information graphically in a
way that could have helped you to solve the problem?"

The graphical method can then lead on to a discussion of the
algebraic representation of the straight line graph and hence
algebraic methods of solution.

Take time to discuss the merits of the different methods and
then challenge students to show how to use each solution method to
solve problems such as:

"Is there a temperature at which the Fahrenheit reading is 20
degrees higher than the Celsius reading?"

"Is there a temperature at which the Celsius reading is 20
degrees higher than the Fahrenheit reading?"

### Key questions

Does every method give the same answer?

What are the merits of the different methods?

### Possible extension

See the extension challenge introducing the Kelvin scale of
temperature in the problem.

### Possible support

Spend lots of time discussing how to deduce information from the
initial temperature facts given. Perhaps it would help students to
suggest new values if the information is presented in a
table.