Year 10 Conjecturing and generalising

problem

Arithmagons

Age

11 to 16

Challenge level

Can you find the values at the vertices when you know the values on the edges?

problem

Take three from five

Age

11 to 16

Challenge level

Caroline and James pick sets of five numbers. Charlie tries to find three that add together to make a multiple of three. Can they stop him?

problem

More twisting and turning

Age

11 to 16

Challenge level

It would be nice to have a strategy for disentangling any tangled ropes...

problem

Differences

Age

11 to 14

Challenge level

Can you guarantee that, for any three numbers you choose, the product of their differences will always be an even number?

$Who \is the \fairest of \them \all ?$

problem

Who is the fairest of them all ?

Age

11 to 14

Challenge level

Explore the effect of combining enlargements.

problem

Hollow squares

Age

14 to 16

Challenge level

Which armies can be arranged in hollow square fighting formations?

problem

Pair products

Age

14 to 16

Challenge level

Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

problem

Speeding boats

Age

14 to 16

Challenge level

Two boats travel up and down a lake. Can you picture where they will cross if you know how fast each boat is travelling?

problem

Circles in quadrilaterals

Age

14 to 16

Challenge level

Explore when it is possible to construct a circle which just touches all four sides of a quadrilateral.

problem

A little light thinking

Age

14 to 16

Challenge level

Here is a machine with four coloured lights. Can you make two lights switch on at once? Three lights? All four lights?

problem

Which is cheaper?

Age

14 to 16

Challenge level

When I park my car in Mathstown, there are two car parks to choose from. Can you help me to decide which one to use?

problem

Filling the gaps

Age

14 to 16

Challenge level

Which numbers can we write as a sum of square numbers?

problem

Plus minus

Age

14 to 16

Challenge level

Can you explain the surprising results Jo found when she calculated the difference between square numbers?

problem

Of all the areas

Age

14 to 16

Challenge level

Can you find a general rule for finding the areas of equilateral triangles drawn on an isometric grid?

problem

Fair shares?

Age

14 to 16

Challenge level

A mother wants to share a sum of money by giving each of her children in turn a lump sum plus a fraction of the remainder. How can she do this in order to share the money out equally?

problem

What's possible?

Age

14 to 16

Challenge level

Many numbers can be expressed as the difference of two perfect squares. What do you notice about the numbers you CANNOT make?

problem

Attractive tablecloths

Age

14 to 16

Challenge level

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

problem

Pick's theorem

Age

14 to 16

Challenge level

Polygons drawn on square dotty paper have dots on their perimeter (p) and often internal (i) ones as well. Find a relationship between p, i and the area of the polygons.

problem

Painted cube

Age

14 to 16

Challenge level

Imagine a large cube made from small red cubes being dropped into a pot of yellow paint. How many of the small cubes will have yellow paint on their faces?