Mathematical Programming Challenges

Some starting points for pupils (and teachers)

Notes

Part 1

SQUARES

Start with a square.

How many different programs can you write that will draw a square?

Write a program that will give you variable sizes of squares.

Your last program might help you to draw some of the following challenges. Write programs for as many as possible.

Square steps

Nested squares

More nested squares

Growing squares

Growing, rotating, nested squares

Tessellated squares

A square with diagonal lines inside

Squares inside squares

Square curves of pursuit

Four squares with a diagonal pattern

More squares inside squares

Can you use your program to work out the area of the centre square in each of these?

What happens if you start the drawing from a different place along the edge?

Draw a square and then draw a circle inside it that touches each edge

Draw a circle with the largest possible square inside it

Draw a square with the largest possible equilateral triangle inside it

Draw an equilateral triangle with the largest possible square inside it!

Draw a square with four arcs of circles inside it

A square with a star

A large and small square pattern

Patterns with squares

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