Problem Solving Strategies

1. Problem Solving Strategies “Buffet of Strategies”

2. What’s the point • This lesson is geared towards introducing you to 10 different types of strategies that you can use to solve word problems and extended constructed response questions. • Think of this like a buffet. When you go to a buffet, you usually take a sampling of everything that looks good! That is what we are doing now, sampling. • When you go up for seconds, you end up picking what you like the best. When given a word problem, you will end up using the strategies you like the most.

3. 10 strategies • Draw a diagram • Make a model • Make an organized list • Make a table of graph • Look for a pattern • Predict and test • Use logical thinking • Work backward • Solve a simpler problem • Write a formula or equation

4. How do I use them? • Draw a diagram- you can use this when you need to see the information given in a problem. • Make a model- You can use this when you need to see the data, and watch how the solution is found. • Make an organized list- You can use this to help you review the information in a problem and organize your thinking. • Make a table of graph- You can use this to organize information in a problem. Tables help you see relationships and patterns in data. • Look for a pattern- You can use this to predict what comes next. If you can find the rules for a pattern, you can use it to solve a problem.

5. 10 strategies • Predict and test- You can use this when it is difficult to work out the answer. You can guess and then test it. • Use logical thinking- You can use this when you need to think about how the information you know fits together. • Work backwards-You can use this strategy when you know the total but need to find a missing part. Start at the end and work back. • Solve a simpler problem- You can use this when the numbers in a problem are very big. Change them to smaller numbers that are easier to work with. • Write a formula or equation- You can use this when you need to find a missing amount to solve a problem.

6. Draw a diagram • A contractor is building steps from a floor to a landing that is 6 feet up. Each step is 8 inches high. How many steps will there be between the floor and the landing? • Mr. Suarez delivers milk to grocery stores. He drives 8 miles north from the plant to Bill’s Market and then 5 miles west to Speedy Stop. From there, he drives 9 miles south to Frieda’s Foods and the 5 miles east to Downtown Dave’s. How far and in what direction does Mr. Suarez have to drive to get back to the plant?

7. Make a model • A soup can is 4 inches tall an 2 ½ inches in diameter. How many soup cans can be packed into a carton that is 15 inches wide, 25 inches long and 1 foot tall • In a cake eating contest, Todd ate 13/16 of his cake. Ralph ate 5/8 of his cake. Edward are 11/12 of his cake, and Oliver ate 5/6 of his cake. Who are the most?

8. Make an organized list • There are 6 players in the violin section of the orchestra. The principal violinist always sits in the first chair. One of the other violinists wears a leg brace and can sit only in the sixth chair. How many arrangements are possible? • Dr. Uri bought 5 different kinds of plants for her office. She wants the tulips to be in the middle. How many arrangements are possible with tulips in the middle?

9. Make a table or graph • A phone company charges $8.99 for the first twenty minutes and the $.07 for each minute after that. Sam makes a 35 minute call. What is his charge? • One day last month, Suzanna has $128. On each subsequent day, she spent half the money she had. On which day did she have less than $1 remaining?

10. Look for a pattern • Ten new students meet at the school office. They each introduce themselves to every other student. How many introductions are there? • What are the next three numbers in this pattern? What is the rule for the pattern? 1/3, 2/9, 4/27

11. Predict and Test • For $50.00 Matt can buy a movie pass that allows him to pay only $1.00 for a matinee. The regular price for a matinee is $4.00. How many times does Matt have to go to a matinee for the pass to be a good buy? • A barrel holds 22 times more rainwater than a bucket. The bucket holds 52.5 fewer gallons of rainwater than the barrel. How much rainwater does the barrel hold?

12. Use Logical Thinking • Betty has twice as many brothers are sisters. Her brother Bert has the same number of brother and sisters. How many boys and girls are in this family? • Nikki’s age is a prime number between 9 and 40. Joe is 6 years older. His age is a perfect square. How old is Nikki?

13. Work Backwards • Mrs. Lee gives piano and violin lessons. Eleven of her students play the piano, and 15 of them play the violin. This includes 8 students who play both instruments. How many students does Mrs. Lee have? • Anita has an average of 89.6 on 5 math tests. Her scores are 85, 89, 90, and 92. What is her score on the fifth test?

14. Solve a simpler problem • A radio station had a contest and 839 people called in to participate. The station manager estimates that this is 4% of all listeners. How many people listen to that radio station? • Dan has $3.70. He has a total of 24 quarters, nickels and dimes. How many of each coin does Dan have?

15. Write a formula or an Equation • Laura had an average grade of 88 over the first 7 tests in History. After the 8th test, her average fell to 86. What was her grade on the 8th test? • In 1864, Abraham Lincoln received 2,218,388 votes. This was about 55% of all the votes cast. How many people voted in the 1864 presidential election?

16. Now… • You have sampled everything the buffet had to offer. It is now time for you to go up and take seconds of what you like the most!!

17. Here we go… • Gina spent half her paycheck on food at the market. She spent 2/3 of the remaining amount on new boots. She spent ¼ of the remainder on lunch. She had just enough left to buy 3 planters of flowers at $9.00 each. How much was her paycheck? Explain you answer

18. Another • One week, the most-watched TV show had a rating of 12.4. A rating point represents 1.07 million homes. The second most-watched program had a rating of 12.0. How many more homes watched the most-watched TV show? Show your work

19. One more • MiChong plays a game where she can move her marker backward or forward on a circular path. After 5 turns, she had moved forward 2 spaces, back 5, forward 4, back 1 and forward 3. Where is her marker now?

20. Ok.. I lied • Marcia earns $6 per hour at her yard cleaning business. Last weekend, she paid her brother $12 to help her. After she paid her brother, she had $66. How many hours did she work? Explain the strategy you used.