Click to return to Geri Ashley's Homepage

UPS CHECK

Understand

Before you can solve a problem, you must first understand it. Read and re-read the problem carefully to find all the clues, and determine what the question is asking you to find.

What is the unknown?
What data is available?

 Circle what you know and underline what you need to know.

Plan

Once you understand the question and the clues, it's time to use your previous experience with similar problems to look for strategies and tools to answer the question.

Do you know a related problem?
Look at the unknown! Try to think of a familiar problem having the same or a similar unknown?

Draw a picture.

Some, Some More (+)         Some Went Away(-)

Try It

After deciding on a plan, you should try it and see what answer you come up with.

Can you see clearly that the step is correct?
But can you also prove that the step is correct?

Look Back

Once you've tried it and found an answer, go back to the problem to see if you've really answered the question. Sometimes it's easy to overlook something. If you missed something, check your plan and try the problem again.

Can you check the result?  - Inverse Operation
Can you check the argument?
Can you derive the result differently?
Can you see it at a glance?

Methodologies for Processing Problems

Make a Table

Make an Organized List

Look for a Pattern

Guess and Check

Make a Picture or Graph

Work Backwards

Solve a Simpler Problem

Example of each methodology:

1. Make a Table -

Holly checked a book out of the library and read this notice about fines: It a book is 1 day overdue, the fine is 1¢, 2 days overdue, 2¢, 3 days overdue, 4¢, and so on. It Holly's book is 7 days overdue, how much is her fine? (Hint: Complete this table.)

2. Make an Organized List

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? (Hint: Complete the organized list.)

Pants           Shirts                              Pants           Shirts

Black           White                              Green          White
                   Red                                                    Red
                   Grey                                                  Grey
                   Striped                                               Striped

3. Look for a Pattern

A man was very overweight and his doctor told him to lose 36 kg. If he loses 11 kg the first week, 9 kg the second week, and 7 kg the third week, and he continues losing at this rate, how long will it take him to lose 36 kg? (Hint: Look for a pattern. Then complete the table.)

4. Guess and Check

Marty did 2 of these activities. He paid for them with a $10.00 bill. His change was $3.75. What 2 activities did Marty do? (Hint: Make a guess. Then check your guess.)

5. Draw a Picture or Graph

Janet and Vicki put up a rope to mark the starting line for the sack race. The rope was 10 meters (m) long. They put a post at each end of the rope and at every 2 m. How many posts did they use? (Hint: Finish drawing the picture to help you )

6. Work Backwards

Phil was given his allowance on Monday. On Tuesday he spent $1.50 at the fruit stand. On Wednesday, Jed paid Phil the $1.00 he owed him. If Phil now has $2.00, how much is his allowance? (Hint: Using the facts given, start with the amount Phil has now and work backwards.)

Understanding the Problem

· How much money did Phil have after Wednesday? ($2.00)
· Do you know how much Phil's allowance is? (no)
· How much did Phil spend at the fruit stand? ($1.50)
· Was Phil given any money after he got his allowance? (Yes, Jed gave him $1.00.)

Planning a Solution

· Did Phil have Jed's $1.00 on Tuesday night? (no)
· How much money did Phil have at the end of Tuesday? ($2.00 - $1.00 = $1 00)
· Did Phil spend money on Tuesday? (yes, $1.50) How much money did Phil have before he spent the $1.50? ($1.00 + $1.50 = $2.50)

Finding the Answer

Work Backwards   

Phil's allowance is $2.50. 

7. Solve a Simpler Problem

Tony's restaurant has 30 small tables to be used for a banquet. Each table can seat only one person on each side. If the tables are pushed together to make one long table, how many people can sit at the table?

Strategies involved

• Simplify the problem
• Draw a picture
• Make a table
• Look for a pattern

Pattern: 2 times the number of tables plus 2  ===>  2 x 30 = 60  ===> 60 + 2 = 62

Answer:  Sixty-two people can sit at the table.