Problem Solving Strategies

“Buffet of Strategies”

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.

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

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.

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.

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?

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?

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?

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?

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

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?

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?

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?

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?

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?

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!!

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

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

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?

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.