Great Problems for New Classes - September 2010, All Stages

This month we have chosen a selection of problems ideal for beginning problem-solving at the start of a new school year. These tasks help to break the ice and stimulate mathematical discussions. We hope they will help new classes to develop good mathematical habits of mind.

Problems

Why not send us your solutions?

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Lots of Biscuits!

Stage: 1 Challenge Level: Challenge Level:1

Help share out the biscuits the children have made.

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Ip Dip

Stage: 1 and 2 Challenge Level: Challenge Level:1

"Ip dip sky blue! Who's 'it'? It's you!" Where would you position yourself so that you are 'it' if there are two players? Three players ...?

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Triple Cubes

Stage: 1 and 2 Challenge Level: Challenge Level:1

This challenge involves eight three-cube models made from interlocking cubes. Investigate different ways of putting the models together then compare your constructions.

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Follow the Numbers

Stage: 2 Challenge Level: Challenge Level:1

What happens when you add the digits of a number then multiply the result by 2 and you keep doing this? You could try for different numbers and different rules.

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Gran, How Old Are You?

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

When Charlie asked his grandmother how old she is, he didn't get a straightforward reply! Can you work out how old she is?

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Next Size Up

Stage: 2 Challenge Level: Challenge Level:2 Challenge Level:2

The challenge for you is to make a string of six (or more!) graded cubes.

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Shady Symmetry

Stage: 3 Challenge Level: Challenge Level:1

How many different symmetrical shapes can you make by shading triangles or squares?

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Diminishing Returns

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

In this problem, we have created a pattern from smaller and smaller squares. If we carried on the pattern forever, what proportion of the image would be coloured blue?

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An Unusual Shape

Stage: 3 Challenge Level: Challenge Level:2 Challenge Level:2

Can you maximise the area available to a grazing goat?

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Triangles and Petals

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

An equilateral triangle rotates around regular polygons and produces an outline like a flower. What are the perimeters of the different flowers?

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L-triominoes

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

L triominoes can fit together to make larger versions of themselves. Is every size possible to make in this way?

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Curvy Areas

Stage: 4 Challenge Level: Challenge Level:2 Challenge Level:2

Have a go at creating these images based on circles. What do you notice about the areas of the different sections?

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Interactive Workout - Core

Stage: 5 Short Challenge Level: Challenge Level:1

An interactive workbook which randomly generates questions on core post-16 mathematics. Give yourself a mathematical workout!

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Curvy Catalogue

Stage: 5 Challenge Level: Challenge Level:1

Make a catalogue of curves with various properties.

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Turning to Calculus

Stage: 5 Challenge Level: Challenge Level:1

Get started with calculus by exploring the connections between the sign of a curve and the sign of its gradient.

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A Function of Gradient

Stage: 5 Challenge Level: Challenge Level:1

Find curves which have gradients of +1 or -1 at various points

Elsewhere...