1) A volunteer from the class chose a secret number and performed a series of operations on it without revealing the number. 2) The operations were: multiply the number by 2, add 3, multiply the result by 2, and subtract 1. 3) The teacher then revealed the final result was 25 and used algebra to work backwards and determine the secret starting number was 5.

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