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Great Squares

Investigate how this pattern of squares continues. You could measure lengths, areas and angles.

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Walk and Ride

How far have these students walked by the time the teacher's car reaches them after their bus broke down?

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Rolling Around

A circle rolls around the outside edge of a square so that its circumference always touches the edge of the square. Can you describe the locus of the centre of the circle?

N Is a Number

Stage: 3 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

Why do this problem?

This problem, which does not need the use of algebra, is nevertheless, quite tricky to do and does require clear logical thinking. Learners will need to understand the properties of numbers and the relationships between speed, time and distance.

Key questions

Is N odd or even?
What sort of speed would you expect the walkers to do?
How long do the walkers take to reach B?
How large can N be?
How many minutes are there in an hour? Does this make a difference?
How can the distance of road be related to the speed of car and the time taken travelling?

Possible extension

Learners who found this problem easy could try Four on the Road.

Possible support

Suggest trying Bike Ride which is an easier problem instead.