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

1. Backtracking

2. Volunteer from the audience
• Write a number on the board so whole
class 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. Multiply the number by 2
x 2

4. Now add 3
x 2 + 3

5. Now multiply the number by 2
x 2 + 3 x 2

6. Finally, take away 1
x 2 + 3 x 2 - 1

7. What is your final answer?
x 2 + 3 x 2 - 1
I will now be able to figure out the starting number

8. How did I do it?
x 2
25
+ 3 x 2 - 1
Suppose the final number was 25

9. Work backwards
x 2
255 261310
+ 3 x 2 - 1

10. A mathematician could summarise this story
with algebra
x 2
255 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. A mathematician could summarise this story
with algebra
x 2
255 261310
+ 3 x 2 - 1
So the above expression can be written
2(2n + 3) -1 = 25

12. Your turn!
• Teacher has number
• Members of class to suggest some
operations
• Teacher tells answer
• Class must work out original number
• Then write the equation

13. Your Turn
So the above expression can be written:

14. Another!
• One group has a number
• Members of class to suggest some
operations
• Group tells answer
• Class must work out original number
• Class must write the equation

15. Class create the story and find the
starting number for
2(3n – 1) + 1 = 47