Nuffield Mathematics teaching resources are for use in secondary and further education

# Level 2 Algebra and graphs

## Modelling a test drive

Students fit functions to graphs (linear and quadratic). They compare models and comment on their suitability.

This activity is about using graphical and algebraic methods to solve problems in real contexts that can be modelled using quadratic expressions. There are different uses depending on student needs.

## Hire a coach

Introducing linear graphs: this shows how to draw a graph using formulae in Excel. The activities then introduce the concepts of gradient and intercept, and ask students to relate these to the values in the formula and the initial information.

## Factor cards

Learners practise expanding brackets and/or factorising quadratic expressions.
Slides
Student cards set
Student cards set pdf
Student sheets
Student sheets pdf
Teacher notes
Teacher notes pdf

## Hot water tank: formulae

Students learn to substitute values into formulae, and to use a calculator to evaluate expressions.
Slides (1.5 MB)
Student sheets Word
Teacher notes Word

## Goldfish bowl: rearrange formulae

Students practise rearranging formulae. There is a worksheet for individual work, or a set of cards for group work to develop this skill.

## Plumbers' prices

Introduces simultaneous equations and their solution using a graph. The worksheet gives instructions for drawing graphs using formulae in Excel and solving simple simultaneous equations by finding the point of intersection.

## Speed and distance

Students explore the idea that the area under speed-time graphs can be used to find the distance travelled.

Students use acceleration and braking data from a car road test to draw graphs.Students then interpret the graphs and make predictions about values which have not been plotted.

This activity introduces the shape and main features of proportional, linear, inverse proportional, and quadratic graphs.

## Large and small

This activity introduces standard form and shows students how to use it in real life contexts.
Slides LARGE FILE SIZE (3.3 MB)
Student sheets Word (557 KB)
Student sheets pdf (638 KB)
Teacher notes Word (81 KB)
Teacher notes pdf (457 KB)

## Linear graphs

An introduction to linear graphs, leading to the link between the constants in the standard form of the equation (y = mx + c) and the gradient and position of the line.