Can you sketch triangles that fit in the cells in this grid? Which ones are impossible? How do you know?
If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?
Some people offer advice on how to win at games of chance, or how to influence probability in your favour. Can you decide whether advice is good or not?
Place four pebbles on the sand in the form of a square. Keep adding as few pebbles as necessary to double the area. How many extra pebbles are added each time?
Florence, Ethan and Alma have each added together two 'next-door' numbers. What is the same about their answers?
Square numbers can be represented as the sum of consecutive odd numbers. What is the sum of 1 + 3 + ..... + 149 + 151 + 153?
Can you arrange these numbers into 7 subsets, each of three numbers, so that when the numbers in each are added together, they make seven consecutive numbers?
This page, and the accompanying webinar recordings, draw attention to the value of offering learners opportunities to conjecture and generalise.
Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?
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?
