Hello, my name is Kiley, and welcome to Problem Solving Strategy 9: Work Backwards.
I bet adults often tell you to look ahead when you're walking or running, right?
What if I tell you that you can look backwards for a few minutes right now?
Well I'm not recommending that you walk or run backwards,
but solve a math problem by working it from the back end first.
Don't believe me?
Let's look at a word problem together.
"Paul has money in his piggy bank.
His mom adds $5 to the bank.
Paul takes out $2 to buy an ice cream,
but adds $10 his grandmother gave him for his birthday.
At the end of the day, Paul empties his piggy bank to count his money and finds he has a total of $20.
How much money did Paul have in his piggy bank at the start of the day?"
This is a great problem because there are a lot of things happening.
Money is being added and subtracted and taken out of Paul's piggy bank.
What are we looking for?
Right.
How much money did Paul have in his piggy bank at the start of the day?
Most math problems give you starting information and ask what you end with,
but this one gives us what we end with and asks us to find what we started with.
So, the best way to solve this problem is to work backwards, or work in reverse,
first using the amount we have at the end of the problem
to find out what we had originally at the beginning of he problem.
We know that at the end of the day Paul has $20.
At one point his grandmother gave him $10.
Since we're working backwards, we'll do the opposite, and take that $10 away
from his $20 at the end of the day.
So, we will subtract $20 - $10 = $10.
This is how much money Paul had before he took out money for ice cream.
Paul took out $2 to buy ice cream, but that means he had $2 more than $10.
Remember we're thinking backwards.
That's $10 + $2 = $12.
Wait, there's one more step.
Remember, Paul had $5 added by his mother in the beginning of the day.
That means he had $5 less than $12.
So $12 - $5 = $7.
Guess what?
That's our answer.
Paul started with $7 in his piggy bank.
It is always best to check your answer, especially when you've worked backwards to solve it.
The best way to check is to now solve it by working forward.
Let's do it quickly together.
If Paul starts with $7 and his mom adds $5, that gives him $12.
Check!
He takes out $2 for ice cream.
That means he then had $10.
Check!
He adds the $10 his grandmother gave him.
That makes $20.
Check!
That's correct.
Paul definitely had $7 when he started his day.
Great job!
The working backwards method doesn't work for every problem,
but it does work when there are multiple steps to solving a problem.
When you work through word problems on our online games and quizzes,
see if you can find when to use the working backwards strategy.
Have fun and always be clever.