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# Linear functions

The linear functions curriculum unit uses the context of designing games for mobile phones - mathematics is needed to analyse and create new simulated motion games for different characters.

In Part 1, it introduces the following 'hard to teach' mathematical ideas:

• Coordinating algebraic, graphical, and tabular representations
• y= mx+c as a model of constant velocity motion - the meaning of m and c in the motion context
• Piece-wise linear functions

Part 2 extends these ideas to introduce:

• The meaning of negative values for m and c
• Velocity and average velocity

The software has been designed to offer:

• dynamic simulation and linking between mathematical representations (graphs, tables and equations)
• control of the simulation from the graph or the function
• representations that can be shown/hidden, as appropriate

Resources for school based PD

The following resources are provided to support schools to involve more teachers in the department to teach the Cornerstone Maths linear functions unit with confidence.

• A 3 minute introductory video about the linear functions unit

• ## The lesson planning proforma (PDF)

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• Examples of pupils' work  (

and

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## The complete set of PD resources (ZIP)

Landmark activity - Controlling characters with equations

Widget Placeholderhttp://mediacentral.ucl.ac.uk/Player/6538

Landmark activities are those in which the use of the technology prompts pupils (and teachers) to have an 'aha' moment about the mathematics.

In the linear functions unit, the landmark activity relates to the first time that pupils see and work with the equations of straight lines - Investigation 4, Controlling characters with equations (Shakey the robot).

However, pupils will often need some careful support to use the software productively - and have a personal 'aha' moment.

Watch the following video clips to see how different teachers have used the software to support this dialogue. In each case the teacher is using the software for the first time with their pupils. As you watch, think about what you would say and do (possibly involving the software) to support pupils' learning.

### Example 1

A teacher leads a whole class discussion about Question 2 - 'Investigate how time, speed and position are represented in the graph, table and equation.'

### Example 2

A teacher supports an individual pupil who is having problems editing the graph to change Shakey's speed as instructed in Question 1C.

## Some examples of pupils' written work from the landmark activity (PDF)

Designing school-based assessments

The nature of the Cornerstone Maths activities results in some rich opportunities for accurate assessment of pupils' mathematical understanding.

The following Investigations (and particular questions) are especially effective:

• Investigation 2, Question 1d "What is speed?"
• Investigation 3, Question 1c "Explain how fast the car is going in two ways."
• Investigation 4, Question 1a "How fast is Shakey going? How do you know?"
• Investigation 4, Question 1d "Compare the equations of Fast Shakey and Slow Shakey, Describe any differences"