Mathematical Programming Challenges

Some starting points for pupils (and teachers)

Notes

Part 2

CIRCLES

(or parts thereof)

Symmetrical Growing Circles

Is one half higher than the other?

If so, why?

Concentric Circles

Petals from arcs

More Arcs

RECTANGLES

(and other shapes!)

Halves and quarters

......(or are they?)

Triangles and diamonds

How many triangles?

How many rectangles?

How many octagons?

What else?

How on earth do I draw it?

SEEING STARS

Explore ways of drawing stars.

How many different types of star can you draw? How many different ways can you find to make them?

The stars below all use rotating squares. But what is the angle that the square rotates and has this anything to do with the number of sides?

5 points

6 points

7!

Mind Bogglers

Circles in squares

Circles in circles

These two lines are the same length.

Interlocking triangles and squares (thanks to Pythagoras)

MATHEMATICAL PROGRAMMING CHALLENGES

Computer programming offers pupils unique opportunities for exploring and developing important mathematical concepts. Ideally, pupils should be encouraged both to set and find their own solutions to practical problems as this provides greater motivation to achieve success.

Solving problems can challenge pupils’ mathematical abilities and often provides opportunities for the teacher to extend learning because there is a real need to learn more mathematics in order to solve a problem.

Teachers often ask what the pupils should do once they can draw the regular polygons in different sizes and use them to create rotating patterns. This series of ‘Challenges’ has been compiled as an answer to this question. It should be realised though that it can be very challenging to draw a house with a right-angled triangle for a roof, or even different sized houses.

Pupils often have very imaginative ideas for tasks that can be tackled with programming languages. Generally speaking tasks that pupils set themselves are the most rewarding and provide suitable mathematical experiences for the child.

No procedures for drawing any of the ‘Challenges’ have been given. An enhanced learning situation is provided if pupils analyse the problem for themselves, break it down into smaller units, then test, and if necessary modify, their solutions.The ‘Challenges’ allow for differentiation even if a whole class works on the same problem, as some pupils may use a mathematical solution, whereas others will work mostly by trial and improvement.

It is not intended that the Challenges should be worked through sequentially, but that either pupils, or teachers, should select those suggestions which will interest or challenge them.

Ideas by Diana Cobden - originally published in book form 1993

Additional material : Martin Longley

©Diana Cobden 1993 and Lexicon Learning Ltd 2014

This resource may be freely used and adapted for educational purposes but may not be used for financial gain.

A number of the ideas for these challenges are taken from the ATM Mathematical activity tiles