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How many different combinations of two ice-cream flavours are possible on a double cone? Answer: 3 (Flavours used are strawberry and vanilla) 2 scoops of vanilla 1 scoop of vanilla 1 scoop of strawberry 2 scoops of strawberry 1 How many different combinations of three ice-cream flavours are possible be on a double cone? Answer: 6 (Flavours used strawberry and chocolate.) 2 scoops of vanilla 2 scoops of strawberry 1 scoop of vanilla 1 scoop of strawberry are vanilla, 1 scoop of vanilla 1 scoop of chocolate 1 scoop of strawberry 1 scoop of chocolate 2 scoops of chocolate Your task today is to investigate how many combinations there would be for 4, 5 and 6 different flavours of icecream. Record all of your working out on the sheets provided. 2 Name: School: Ice-Cream Up Investigation In the space below, describe the investigation that you are being asked to do. Introduction:………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… Put your results into a table. 3 Name: Number of IceCream Flavours: 1 2 3 4 5 6 School: Number of combinations on a double cone: 1 3 6 10 15 21 Can you see a pattern or rule? Yes / No Describe this pattern or rule in your own words. ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… ………………………………………………………………………………… 4 Name: School: How many combinations would be possible for 7 flavours ? Predict your answer:………………………………………….. How many combinations would be possible for 10 flavours ? Predict your answer:…………………………………………. Can you find a quick way to work out how many combinations would be possible for 20 flavours ? Predict your answer:…………………………………………… Explain what your quick way is: …………………..……………………………………………………………. ………………………………………………………………………………… 5 Answers: The numbers 1, 3, 6, 10, 15, 21, 28, 36, etc are called the Triangular Numbers. In this sequence, the difference between the consecutive numbers gets bigger by 1 each time. e.g. 1 and 3 ………the difference is 2 3 and 6 ………the difference is 3 6 and 10 ………the difference is 4 and so on………………………… 1 3 6 10 15 6 Formula: A quick way to work out the number of possible flavour combinations on a double cone can be made using this formula: Possible combinations = 0.5n2 + 0.5n Where n is the number of ice-cream flavours E.g. for 20 flavours (n = 20) Possible combinations = 0.5 x 20 x 20 + 0.5 x 20 = 200 + 10 = 210 7 Name: School: 8