# Algebra

This collection of Nuffield Maths resources explores Algebra. The demand is roughly equivalent to that in GCE A level.

They include slide shows to introduce the topics, student sheets and teacher notes, as well as spreadsheets and other relevant resources.

The teachers' notes start with a short overview of the activity, who and what it is designed for, and lists the necessary resources. The student sheets have background information where needed, and tasks for the students to work and reflect on. Extensions and solutions are included in the teachers' notes.

The collection contains the following resources:

Maximum and minimum problems Using graphical methods to solve maximum and minimum problems in industry and in working life, using a spreadsheet or graphic calculator.

Climate prediction   There are two versions of this activity.
Students create (A) spreadsheets or use (B) graphic calculators to model what would happen to the temperature of the Earth if there were to be a sudden change in the amount of radiation entering or leaving the planet. Then they investigate polynomial and exponential functions to find the best model.

Gas guzzlers  Students use graphical methods to find a suitable model to connect two sets of data. Students can use their model(s) to make predictions. They should also be encouraged to work out percentage errors to test and compare the accuracy of their model(s).

Coughs and sneezes  Students use polynomial and trigonometric functions to model the number of people suffering from a cold over several weeks.

Cup of coffee  Students model data from measuring how long caffeine from tea, coffee or cola stays in the human body’s bloodstream. This involves drawing graphs, then finding functions and parameters to fit different models to the graphs.

Smoke strata  Practice in using logarithmic graphs to check that a power law is a good model for data and find the associated parameters.

Water flow  Students use linear and quadratic functions to model data, and calculate percentage errors.

Test run   Students interpret a speed–time graph for a car during a test run, and fit linear and quadratic models to the graph.

Completing the square  Students match cards to practise completing the square and relating the competed square form to the graph of the function.

Ozone hole  Students suggest types of function to model ozone hole data (given in a table and also a graph) before using a graphic calculator or spreadsheet to find at least two particular models.  They then consider how well their functions model the data and what they predict for the future.

## Resources

### Climate Prediction

The Nuffield Foundation provides this activity which students use to create spreadsheets that model what would happen to the temperature of the Earth if there were to be a sudden change in the amount of radiation entering or leaving the planet. Students then investigate polynomial and exponential functions to find...

### Gas Guzzlers

The Nuffield Foundation provide this activity which uses graphical methods to find a suitable model to connect two sets of data. There are a variety of ways in which the data could be used, depending on the focus required. It is possible to use a log graph to find an exponential model, which is the intended focus...

### Ozone Hole

The Nuffield Foundation provides this activity where students suggest types of function to model ozone hole data, before using a graphic calculator or spreadsheet to find at least two particular models. They then consider how well their functions model the data and what they predict for the future. The slideshow...