IN CLASS WORD PROBLEMS



Chapter 1 Notes and In-class problems

I. Polya’s four steps for problem solving

A. Understand the problem

B. Devise a plan

C. Carry out the plan

D. Look Back

II. Some strategies to use for problem solving

A. Guess and Check

B. Use a variable (write an equation and solve)

C. Draw a picture

D. Make a table

E. Work Backward

F. Solve a simpler problem

G. Look for a pattern

H. Use a formula

1) For his wife's birthday, Mr. Jones is planning a dinner party. There will be 22 people attending. Mr. Jones plans to form one large, rectangular table using card tables, the size that seats one person on each side. Assuming he doesn't own any card tables, what is the smallest number of tables he needs to borrow to do this? What other arrangement of card tables would seat 22 people? What if the guest list grows to 38 people?

2) Sue and Ann earn the same amount of money, although one worked 6 days more then the other. If Sue earned $36 a day and Ann earned $60 a day, how many days did each work?

3) A business woman goes to a bank and sends half of her money to a stock broker. Other than a $2 parking fee before she entered the bank and a $1 mail fee after she left the bank, this was all she spent. The next day she returns to the bank, pays the $2 parking fee, then sends one half of her remaining money to the stock broker. She again spends $1 for a mailing fee. If she has $182 dollars left, how much money did she have before the trip to the bank on the first day?

III. Other problems to practice with

4) An office building has 33 floors, each 10 feet high, and elevators that travel at a constant speed. If it takes 10 seconds for an elevator to go from the first floor to the fifth floor, how long will it take and elevator to go from the fifth floor to the middle floor?

5) After the first two terms in the following sequence, each number is the sum of the preceding two terms. Find the missing numbers.

4 ___ ___ ___ ___ 67

6) Fencing is sold in 8 foot sections at $15 per section. Fence posts cost $4 each. How much will it cost to build a fence around a square field which is 240 feet on each side?

7) In a game of chips, Pauli lost half of her chips in the first round, won 50 chips, then lost half her total and finally won 80 chips. She finished with 170 chips. How many chips did she have at the beginning of the game?

8) The surface of Big Lake is 31 feet above the surface of Long Lake. Long Lake is half as deep as Big Lake and the bottom of Long Lake is 8 feet below the bottom of Big Lake. How deep is each lake?

9) Tom and Barb have only nickels and dimes. Barb has 75 cents and Tom has 90 cents. Both have the same number of coins and Tom has the same number of dimes as Barb has nickels. How many nickels does Barb have?

10) A "Superbounce" ball rebounds half the height it drops. The ball is dropped from a height of 176 feet. How far off the ground is the ball when it has traveled a total of 500 feet?

11) On a certain 20 question test, a student receives 4 points for each correct answer, loses 3 points for each incorrect answer, and loses 2 points if no answer is given. Todd took the test and scored 34 points. How many problems did he answer correctly?

12) Is the sum of four consecutive counting numbers ever divisible by 4? If so, when? IF not, why?

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