Think of two whole numbers under 10, and follow the steps. I can work out both your numbers very quickly. How?
There is a particular value of x, and a value of y to go with it, which make all five expressions equal in value. Can you find that x, y pair?
A circle of radius r touches two sides of a right angled triangle, sides x and y, and has its centre on the hypotenuse. Can you prove the formula linking x, y and r?
What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
This task, written for the National Young Mathematicians' Award 2016, invites you to explore the different combinations of scores that you might get on these dart boards.
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
Can you prove that twice the sum of two squares always gives the sum of two squares?
Can you decide whose drink has the strongest blackcurrant flavour from these pictures?
The challenge for you is to make a string of six (or more!) graded cubes.
Can you place the blocks so that you see the reflection in the picture?
