TS-9.3

teachwire.net/secondary WHY TEACHTHIS? This lesson invites students to make sense of a counting-out game to predict who will be the winner. KEY CURRICULUM LINKS • Make and test conjectures about the generalisations that underlie patterns and relationships; look for proofs or counter-examples; begin to use algebra to support and construct arguments • Select appropriate concepts, methods and techniques to apply to unfamiliar and non- routine problems A counting-out game provides a context for students to apply knowledge of sequences, multiples and powers, says Colin Foster COUNTING OUT Lesson plan: MATHS KS4 In this lesson, students analyse a counting-out game, known as the Josephus problem , in which people are excluded one at a time until the person left at the end is the winner. Students explore which person will be the winner with different numbers of starting people and find connections with arithmetic sequences and powers of 2. In a counting-out game, how can you predict who will win? Q teachwire.net/ maths-data DOWNLOAD a FREE KS4 lesson plan on real-world data analysis 70 STARTER ACTIVITY Q Imagine 10 people sitting in a circle numbered 1 to 10 in order. You go round the circle counting ‘out’ every other person, starting with person 1, until there is just one person left. Who will be left? Students may get different answers depending on how they interpret the instructions. They need to completely ignore anyone who is already out. Go through this together until everyone agrees that the answer is person 4. then then red crossings out starting with person 1 1, 3, 5, 7, 9 purple crossings out starting with person 2 2, 6, 10 green crossings out starting with person 8 8