Great Problems for New Classes - September 2010, Stage 4&5

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

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Curvy Areas

Age 14 to 16 Challenge Level:

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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Triangles and Petals

Age 14 to 16 Challenge Level:

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

Age 14 to 16 Challenge Level:

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

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Weekly Challenges

Age 14 to 18 Challenge Level:

The NRICH Stage 5 weekly challenges are shorter problems aimed at Post-16 students or enthusiastic younger students. There are 52 of them.

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Interactive Workout - Mathmo

Age 16 to 18 Short Challenge Level:

Mathmo is a revision tool for post-16 mathematics. It's great installed as a smartphone app, but it works well in pads and desktops and notebooks too. Give yourself a mathematical workout!

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Curvy Catalogue

Age 16 to 18 Challenge Level:

Make a catalogue of curves with various properties.

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Turning to Calculus

Age 16 to 18 Challenge Level:

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

Age 16 to 18 Challenge Level:

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