SOLVING PROBLEMS USING ORGANIZED LISTS

 Another way of figuring outcomes and calculating probability is to use an organized list/table

 Use table format and list each possible combination when given a question  For the table make a heading for each option  Go through each option systematically to start listing possibilities based on the limits set in the question  You should be able to see a pattern in each category of your table

SAMPLE QUESTION  Sara has 36 cents. If she only has dimes and pennies, how many different combinations can you make?

UNDERSTAND THE PROBLEM  Given: Sara has 36 cents; only dimes and pennies  Required: How many combinations can there be

MAKE A PLAN  I’ll make an organized list of all the possible combinations  Since the number of dimes has a bigger effect on the number of combinations, I’ll start by having the number of dimes be zero and count up from there, while changing the penny column to equal 36

CARRY OUT THE PLAN ComboDimesPenniesTotal

SOLUTION  I see a pattern in my list, so I’m sure that I’ve found all the combinations. The dimes category starts at 0 and counts by 1s up to 3. 3 is the maximum number of dimes she can have because 4 dimes would make 40 cents, which is more than she has. The penny column drops by 10 for every increase in the number of dimes. It can’t drop any more once there are only 6. Therefore, if Sara has 36 cents in total, and only has dimes and pennies, there are only 4 possible combinations.