Edexcel, 2016, Foundation Maths GCSE: A running club has 50 members. 30 members take part in road races, 15 members take part in fell races, 12 members do not run in road or fell races. How many members run both fell and road races?

Start with a Venn Diagram. Ask them to draw it out and put the numbers where they think the numbers should go. Talk about overlapping: e.g. imagine two paper circles that overlap. The middle portion is thicker because two pieces of paper, i.e. double counted. Have to 'remove one layer of paper' - similarly the venn diagram has to add up correctly so take away a number so that you get the correct total:E.G.50 = total30 = road racers15 = fell racers12 = no racers50 = 12 + 30 + 15 - ?? = 7so 7 was double counted! --> 7 is the middle of the venn diagram --> 7 is the answer!12 + 30 + 8 = 50http://www.mathsgp.co.uk/wp-content/uploads/2017/07/badly_answered_2_foundation_1.pdf