Searching for SolutionsChoosing an Operation/Multi-Step Problems
Searching for Solutions
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Strategy 6 - Choosing an
Operation/ Multi-Step Problems
Many multi-step problems require more than one operation to be used when solving the problem. In the next series of examples, you will need to read carefully so that you understand what the question is really asking. Remember that extra information in the problem could lead you off track, so be sure to use only the information needed when solving.
Activity 1: Example Problems:
 | Sarah is on her way to the mall. She wants to buy a new sweater for $25, a CD for $15 and an anniversary present for her parents for $28. Since she'll be there in the early afternoon, she may want to buy lunch. Her lunches are usually around $8. How much money should Sarah take with her to the mall? |
| The PTA created a fund-raiser to pay for new curtains for the stage area. They ran a car wash over the weekend and charged $2.50 for each car. On Saturday, 87 cars came through the car wash and on Sunday, there were 106 cars. How much money did the PTA raise over the weekend? |
| Lori wants to invest $20 in stock that shows a steady increase in price per share. Her broker listed the original price of two stocks and their gains and losses over a four-year period. Which stock should Lori choose? (Mathematics Plus 6, Harcourt Brace & Company, 1989, p. 436) |
|
Stock A - Price Per Share | ||||
| Original Price | Year 1 | Year 2 | Year 3 | Year 4 |
| $15 | +5 | -6 | +10 | -4 |
|
Stock B - Price Per Share | ||||
| Original Price | Year 1 | Year 2 | Year 3 | Year 4 |
| $10 | +1 | +1 | +1 | +2 |
| What if Lori wants to by stock that will give her the highest return on her money in one year? How will this affect her choice? |
| Michael has some loose change in his pocket. He has a combination of dimes and quarters that total $2.10. How many quarters does Michael have in his pocket? |
| Lauren's parents went on vacation. While they were away, they sent many postcards from various places. They sent twice as many postcards from New York than from New Jersey. They sent three less postcards from Maine than from New York and three more postcards than from Vermont. Lauren received eight postcards from New Jersey. How many postcards did her parents send in all? |
Activity 2: Here's a chance to use some logical reasoning and problem solving.
Peggy has a piggy bank filled with coins. She empties the bank on her desk and sees pennies, nickels, dimes, and quarters. Use p to represent the number of pennies, and n to represent the number of nickels, and d to represent the number of dimes, and q to represent the number of quarters. Write equations for what Peggy sees.
| She sees 8 more pennies than nickels. |
| She sees half as many dimes as pennies. |
| She sees 4 times as many pennies as quarters. |
| She sees twice as many dimes as quarters. |
| She sees 6 fewer dimes than nickels. |
| The sum of the number of nickels and quarters is 27. |
| The number of dimes less the number of quarters is 7. |
| The number of nickels plus the number of dimes is 34. |
| The number of nickels is 8 less than the number of pennies. |
| The number of nickels is 1 less than 3 times the number of quarters. |
| The number of pennies divided by the number of dimes is 2. |
| Five times the number of nickels is 100. |
Solve the equation in the last problem. Use your solution and any other information to find how much money Peggy has in all.
| COIN | Pennies | Nickels | Dimes | Quarters | Total |
| Number | |||||
| Value |
(Mathematics Plus 7, Harcourt Brace & Company, 1989, Enrichment 9.14)
Activity 3: Let's solve some problems on the Internet. Go to Levering's Puzzling and Perplexing Problems at: http://www.fi.edu/school/math/index.html and choose a month to investigate. Each month's activities rely on your application of a variety of problem-solving strategies, so don't forgot those skills learned in previous lessons!
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© Searching for Solutions - A Web-Based Problem-Solving Unit - Developed by Judy Campf, e-Learning Specialist.
