# Algebra and Maths

This collection of Nuffield Maths resources explores Algebra and Maths. The demand is roughly equivalent to that in Higher Level GCSE and Level 2 Functional Mathematics.

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

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

Road tunnel  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.

Hot water tank: formulae Students learn to substitute values into formulae, and to use a calculator to evaluate expressions.

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.

Road test  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.

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

Spreadsheet graphs  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.

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.

## Resources

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### Modelling a Test Drive

This resource from the Nuffield Foundation provides the opportunity for students to fit functions to linear and quadratic graphs. It is assumed that students will already have some knowledge of linear and quadratic functions and their graphs, which are used to compare models and comment on their suitability. A...