1 Understanding the problem
- What are you asked to find?
- What information do you have?
- What do you need to find out? (the unknows)
2 Devising a plan
- How to use given data to find missing data?
- Decide what steps you need to take to solve the problem
- Write an equation
3 Execute the plan
- Use your mathematical tools
- Check each step of the plan as you proceed.
4 Check your answer
- Did you answer the questions asked?
- Does your answer makes sense ? Why?
- Substitution (Check the solution in the original equation to catch errors)
- Can you solve it another way?
(George Polya, 1945)
Example:
Diana went shopping at a department store. She bought a bottle of shampoo for $3, one hair brush for $6, and a bottle of nail polish for $4. When she paid for her purchases, the cashier gave her $7 in change. How much money did she give the cashier?
We know that she spend: 3 + 6 + 4 (13 dollars)
The cashier gave her $7 in change
We need to find X, the total amount she give the cashier
X – (3 + 6 + 4) = 7
X – 13 = 7
X = 7 + 13
X = 20
Check:
20 – (3 + 6 + 4) = 20 – 13 = 7 OK