Year 10 Conjecturing and generalising

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

Explore the effect of combining enlargements.

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

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?

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

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

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

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

Imagine a room full of people who keep flipping coins until they get a tail. Will anyone get six heads in a row?

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?

Which armies can be arranged in hollow square fighting formations?

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

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

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

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

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.

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?

Pick a square within a multiplication square and add the numbers on each diagonal. What do you notice?

Position the lines so that they are perpendicular to each other. What can you say about the equations of perpendicular lines?

Charlie has moved between countries and the average income of both has increased. How can this be so?

Can you decide whether two lines are perpendicular or not? Can you do this without drawing them?

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

Use the animation to help you work out how many lines are needed to draw mystic roses of different sizes.

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

Can you see how to build a harmonic triangle? Can you work out the next two rows?

Can you work out which spinners were used to generate the frequency charts?