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?

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?

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?

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.

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?

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?

What do you notice about these families of recurring decimals?

The area of a square inscribed in a circle with a unit radius is 2. What is the area of these other regular polygons inscribed in a circle with a unit radius?

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?

Manufacturers need to minimise the amount of material used to make their product. What is the best cross-section for a gutter?

How many intersections do you expect from four straight lines ? Which three lines enclose a triangle with negative co-ordinates for every point ?

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

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.

Can you match up these equivalent algebraic expressions?

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