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Functional Question Foundation and Higher (Algebra 2) For the week beginning ….

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5 1212 9 11 8 1010 6 3 2 1 7 4 Here are 12 cards numbered from 1 to 12. Sequences Starter (Foundation/ Higher) Make as many sequences of numbers as you can. · You must use each card once only in a sequence · A sequence must have at least four terms Possible questions · What is a sequence? · What is a term? · What is a rule? · How can a sequence be described? · Why do the numbers generated in a National Lottery draw not form a sequence? · Why does the formula for the nth term give more information than the term-to-term rule? · Give me an example of when knowing a sequence might be useful. · Tell me …… sequences you know and their rules. (Term-to-term or nth, depending on level.)

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Activity 1 (Foundation or easy Higher) Mirrors Sasha uses tiles to make borders for square mirrors. The pictures show three different sized mirrors, each with a one centimetre border of tiles around. She only uses 1 by 1 tiles. 1 Investigate the total number of 1 by 1 tiles that are needed to make borders for different sized square mirrors. Draw some different sized mirrors and try to predict how many tiles will be needed for each mirror. A table of results could be useful. Try to be systematic. Find a formula for T, the total number of tiles. 2 Why does your formula work for these mirrors? 3 Investigate square mirrors surrounded by wider borders and try to predict the number of tiles needed for each width of border. 4 Link all your formulas together. 5 Why does your formula work for all square mirrors?

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Activity 1 (Higher) Sasha uses tiles to make borders for square mirrors. The pictures shows three different sized mirrors, each with a two centimetre border of tiles around. She only uses 1 by 1 tiles. 1 Investigate the total number of 1 by 1 tiles that are needed to make borders for different sized square mirrors. Draw some different sized mirrors and try to predict how many tiles will be needed for each mirror. A table of results could be useful. Try to be systematic. Find a formula for T, the total number of tiles. 2 Why does your formula work for these mirrors? 3 Investigate square mirrors surrounded by wider borders and try to predict the number of tiles needed for each width of border. 4 Link all your formulas together. 5 Why does your formula work for all square mirrors?

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AO3 question (Foundation/Higher) (a) Here are the first four terms of a sequence and its nth term. 90 85 80 75 …… 5(19 – n) Show how Jayne can find the position in the sequence of the term that has a value of 0. [2] (b) Jayne creates these patterns by shading squares. Show how Jayne can work out the number of squares in a pattern in any position in the sequence. [3]

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