Year 10 Being resourceful

Imagine you were given the chance to win some money... and imagine you had nothing to lose...

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

Construct two equilateral triangles on a straight line. There are two lengths that look the same - can you prove it?

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A dot starts at the point (1,0) and turns anticlockwise. Can you estimate the height of the dot after it has turned through 45 degrees? Can you calculate its height?

Why does this fold create an angle of sixty degrees?

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

Watch the video to see how Charlie works out the sum. Can you adapt his method?

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?

Where should runners start the 200m race so that they have all run the same distance by the finish?

When two closely matched teams play each other, what is the most likely result?

Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Is it the fastest swimmer, the fastest runner or the fastest cyclist who wins the Olympic Triathlon?

How can we make sense of national and global statistics involving very large numbers?

Match the cumulative frequency curves with their corresponding box plots.

Surprising numerical patterns can be explained using algebra and diagrams...

Which armies can be arranged in hollow square fighting formations?

Is it possible to find the angles in this rather special isosceles triangle?

Can you match these calculations in Standard Index Form with their answers?

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?

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?

What do you notice about these families of recurring decimals?

Given an equilateral triangle inside an isosceles triangle, can you find a relationship between the angles?