Working Backwards Notes
Working backwards is another strategy that falls under the theme of _____________ focus.
With most other strategies, you work ____________ through the information in a problem. To
successfully work backwards, you need to change your focus and consider the whole problem
in ___________. This is a very useful strategy in certain situations. Much of ______________ is
based on working backwards.
Do these three problems:
1. I’m thinking of a number between 1 and 10. If I multiply by 4 and then subtract 3, my
answer is 25. What is my number?
2. I’m thinking of a number between 1 and 30. I add 22. I divide by 3. My answer is 12.
What is my number?
3. I’m thinking of a number. Divide it by 2, then subtract 1. The answer is 7 ½ . What is the
number?
One of the most difficult aspects of working backwards is keeping track of a problem’s
________________ and organizing it in a meaningful way.
When solving a problem by working backwards, always write down the actions in order in
which they appear in the problem. Then ___________ the solution by working forwards.
Ex) The Stolen Pigeons
Bad Bargle sneaked into Homer’s pigeon loft one day. He took half of the pigeons. He decided
that wasn’t bad enough, so he took one more and left. Later, Homer opened the door of the
loft to exercise his prize possessions. Half of the remaining flock flew out, leaving six inside
the pen. How many pigeons did Homer have before Bad Bargle did his dirty deed?
This problem is called ________________________________. It is about __________________
_____________________________________________________________________________.
I am expected to find ___________________________________________________________.
I solved this problem by working backwards. First I wrote down the actions in the order in
which they appeared in the problem. Then I started with the answer and worked backwards. I
multiplied by 2, then subtracted 1, and multiplied by 2 again. I finally got my starting number
of pigeons.
My answer is _______________. I think my answer makes sense because _________________
______________________________________________________________________________
______________________________________________________________________________
______________________________________________________________________________
_____________________________________________________________________________.