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Year 8 Spring 2 Lesson 8: Fibonacci SequenceObjectiveTo continue Fibonacci style sequencesAimThe optional literacy exercise ‘Collective Memory’ is one that focusses on the skill of memorizing. This is something that will be built in lessons throughout school to help with this skill that is required now at GCSE. It also brings in a bit of History of Maths for the students.The main objective is addressed through the activity at the end of the lesson.ResourcesPowerpointCollective memory sheetCollective memory mark schemeBlank Paper to recreate posterExcel Fibonacci question generatorActivity 1: Remind students about the Fibonacci sequence from last lesson. They answer questions from the first two slides on their mini whiteboards.1008380885825The nth term in question is Questions for progressionCan you write down the first 5 numbers in the Fibonacci sequenceHow is it different to sequences we have looked at in the sequences unit of work?Why can't we find the nth term with the methods we know so far? Activity 2: (Optional)Collective memory:Print out the Fibonacci information? onto 4 A3 posters to be displayed in four places areound the classroom.In groups of 3 or 4, students must recreate the poster.Rules:Person 1 from each group goes up to a poster and studies it for 1 minute (make sure this is timed).They return to their group and either write the information on the sheet or tell someone else what to write.Person 2 comes up to the poster for a further 1 minute try to fill in the gaps.?They return to try to add to their poster.Repeat for further members of the group.Display the?mark scheme?on the board.Groups exchange posters and get marks for keys words and phrases (highlighted here). 1 mark for the word or phrase; 2 marks for correct spelling.Questions for progressionWhat strategies did you use to memorise the facts?How did you choose what to memorise?Activity 3: Show slides 3 and 4 for students to answer on their mini whiteboards.Show the Excel question generator – ensure that content is enabled.Cllck on the ‘add’ tab at the bottom of the spreadsheetStudents find the missing numbers from the sequence on their whiteboards. Missing answers can be shown by clicking the yellow show/hide button.Questions for progressionWhat if you had a different pair of starting numbers?What if you started with 2, 1 instead of 1,1. How do you think this will alter the sequence?Can you write the first 10 numbers in the sequence?What if you added the first three numbers?Activity 4: What if you don’t know both of the starting numbers/ How can you go backwards?Click the ‘solve’ tab at the bottom to show questions of this type. You can 'switch on' or off any of the cells in the sequence by clicking on it.Students to solve in pairs on their whiteboards. Students will probably use a range of trial and improvement methods here.Once they have investigated for a while, if nobody suggests using a letter for a missing number, then ask the following questions to help them solve.They can them form and solve equations to find the missing numbers. Link back to previous work on equations.If they know the first term, they can substitute this into the other term they know to make an equation to find b, and hence the rest of the sequence.Questions for progressionWhat do we usually call a missing number in maths?If the first term is a, and the second is b, then what is the third term? (a + b)What is the 4th term in terms of a an b? (a + 2b)What is the 5th term? (2a + 3b)Acknowledgements:M Warden ................
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