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# 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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### Large and small

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

This activity introduces standard form and shows students how to use it in real life contexts.* *

### Linear graphs

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

The resource is an introduction to linear graphs, leading to the link between the constants in the standard form...

### Modelling a test drive

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

The resource asks students fit functions to graphs (linear and quadratic). They compare models and comment on...

### Plumber's prices

The ‘Plumbers' prices’ resource introduces simultaneous equations and their...