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