Maths - How to get more pizza
Here is an exam question from a recent mechanics module paper: "A particle is moving in a straight line from O to P with a constant acceleration of 4ms-2. Its velocity at P is 48ms-1 and it takes 12 seconds to travel from O to P. Find (a) the particle's velocity at O and (b) the distance OP."
Is this a good question? It tests pupils' knowledge of kinematics and their use of the SUVAT equations. But three figures are given in the question, and these are the same three figures that are required to answer both parts of it.
When, in real life, are we confronted with problems where we are given the exact information required to solve them? If we do not expose our pupils to more realistic problems at school, how are we preparing them for adult life?
Step forward Dan Meyer, a former high-school maths teacher from the US currently studying at Stanford University. In a very popular TED talk, he makes this point, but more importantly he offers a solution: three-act maths.
In Act 1, pupils are presented with a "hook", usually a photo or video, and crucially it is a real-life problem. One nice example is Pizza Doubler, where pupils are shown a picture of a slice of pizza alongside two coupons, one offering to double the sector angle of the pizza and one offering to double the radius. Act 1 concludes: "If you are feeling hungry, which coupon would you choose?" And that's it. The pupils are waiting for more - but this time they are not going to get it.
And so begins Act 2: information seeking. Only after some discussion is the image of the pizza menu revealed. The slice in question was from a 12-inch pizza cut into eight slices. When the problem is solved, Act 3 can begin: the sequel. Would the best coupon for the slice in question work for all slices or just some slices? The possibilities for extension work are endless and pupils are hooked.
Meyer's bank of three-act maths problems is not limited to pizzas. Problems such as Lucky Cow, 25 Billion Apps and Nanna's Chocolate Milk intrigued me as much as my learners. I'm not promising you will never again be asked, "Sir, when will I use this in real life?", but this might just be one step in the right direction, and your pupils will be all the better for it.
Access Dan Meyer's materials by searching for "Dan Meyer three-act maths" on the internet. Craig Barton is an advanced skills teacher at Thornleigh Salesian College in Bolton. He is the creator of www.mrbartonmaths.com and is a TES secondary maths adviser. Find him on Twitter: @TESMaths
Use Teach First's scheme of work to help pupils understand why maths is important in everyday situations. bit.lyEveryDayMaths
Give graphs a real-life context in thecardinal's lesson on racing tracks and school journeys. bit.lyRacingMaths.