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### Number and algebra

### Geometry and measure

### Probability and statistics

### Working mathematically

### For younger learners

### Advanced mathematics

# Real-life Equations

### Why do this problem?

This
problem encourages students to get into the real meaning of
equations and graphical representation without getting bogged down
in algebraic calculations or falling back into blind computation.
It will help to reinforce the differences between different 'types'
of equation.
### Possible approach

### Key questions

### Possible extension

### Possible support

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Age 16 to 18

Challenge Level

- Problem
- Teachers' Resources

Note the difference between showing that an equation
is a possibility and
showing that it is not a
possibility. In the first case, students need only give a single
example of a curve with certain paramaters which passes through a
point of the required type. To show that an equation CANNOT pass
through a point of a certain type requires more careful
explanation. Hopefully students will work this out for themselves,
but prompt them if necessary.

- How can you tell if a certain point will match a certain equation type?
- How can you tell if a certain point will not match a certain equation type?

You might naturally try Equation
matching next.

Give concrete examples by labelling the points $(1, -1), (-1,
1), (-1, -1), (1, -1)$

Alternatively, try the easier non-algebraic question Bio-graphs

Make a functional window display which will both satisfy the manager and make sense to the shoppers