For problems that have multiple solutions, the best way to solve them is to write down all the combinations or possibilities in an organized list. That way, you can clearly see the answer and be sure not to forget any parts! Making an organized list helps problem solvers organize their thinking about a problem. Recording work in an organized list makes it easy to review what has been done and to identify important steps that must yet be completed. It also provides an easy way of recording calculations.
Example Problem:Doug has 2 pairs of pants: a black pair and a green pair. He has 4 shirts: a white shirt, a red shirt, a grey shirt, and a striped shirt. How many different outfits can he put together?
Understanding the Problem
· How many pairs of pants does Doug have? (2)
· How many shirts does Doug have? (4)
Planning a Solution
· Suppose Doug wears his black pants. What color shirt can he wear? (white, red, grey, or striped)
· If Doug wears his striped shirt, how many different outfits can he wear? (2: striped—black and striped—green)
· If Doug wears the green pants, can he wear all 4 shirts? (yes)
Finding the Answer
Make an Organized List
Black—White
Black—Red
Black—Gray
Black—Striped
Green—White
Green—Red
Green—Gray
Green—Striped
Answer: Doug can make 8 different outfits.
Understanding the Problem
· How many pairs of pants does Doug have? (2)
· How many shirts does Doug have? (4)
Planning a Solution
· Suppose Doug wears his black pants. What color shirt can he wear? (white, red, grey, or striped)
· If Doug wears his striped shirt, how many different outfits can he wear? (2: striped—black and striped—green)
· If Doug wears the green pants, can he wear all 4 shirts? (yes)
Finding the Answer
Make an Organized List
Black—White
Black—Red
Black—Gray
Black—Striped
Green—White
Green—Red
Green—Gray
Green—Striped
Answer: Doug can make 8 different outfits.