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Backtracking

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Backtracking lesson for a year 9 maths class.
Used as an introduction to algebra.

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Backtracking

1. 1. Backtracking
2. 2. Volunteer from the audience• Write a number on the board so wholeclass except the teacher can see it.• Class remember the number• Erase it before teacher can see.• Class to perform the following operations,keeping the answers to your self.
3. 3. Multiply the number by 2x 2
4. 4. Now add 3x 2 + 3
5. 5. Now multiply the number by 2x 2 + 3 x 2
6. 6. Finally, take away 1x 2 + 3 x 2 - 1
7. 7. What is your final answer?x 2 + 3 x 2 - 1I will now be able to figure out the starting number
8. 8. How did I do it?x 225+ 3 x 2 - 1Suppose the final number was 25
9. 9. Work backwardsx 2255 261310+ 3 x 2 - 1
10. 10. A mathematician could summarise this storywith algebrax 2255 261310+ 3 x 2 - 1•Start with a number: n•Which becomes 2n•Which becomes 2n + 3•Which becomes 2(2n + 3)•Which becomes 2(2n + 3) -1
11. 11. A mathematician could summarise this storywith algebrax 2255 261310+ 3 x 2 - 1So the above expression can be written2(2n + 3) -1 = 25
12. 12. Your turn!• Teacher has number• Members of class to suggest someoperations• Teacher tells answer• Class must work out original number• Then write the equation
13. 13. Your TurnSo the above expression can be written:
14. 14. Another!• One group has a number• Members of class to suggest someoperations• Group tells answer• Class must work out original number• Class must write the equation
15. 15. Class create the story and find thestarting number for2(3n – 1) + 1 = 47