1. Problem Solving What do you do with the information?

2. Read Carefully Too many times students read the entire problem quickly with little understanding about what is being said. Slow down and attack the problem one sentence at a time. Pay close attention to what the question is asking.

3. Try this one out. The local property tax is $212.50 per thousand dollars of assessed value. How much tax must be paid on a property that has an assessed value of $9,000? Do you know what property tax is? Do you need to know what it is to solve this problem? Do you know what assessed value is? Do you need to know what it is to solve this problem?

4. Problem Solving in Number and Number Relations Addition (amount in problem increases) Multiplication (same as addition because it is repeated addition) Subtraction (amount decreases because it is the opposite of addition) Division (same as subtraction because it is repeated subtraction)

5. Problem Solving in Number and Number Relations (Continued) Comparison (difference-subtraction) Fractions, decimals, and percentages may make the problem look harder, but the operation and strategies for solving are the same. Focus on what is happening to the amount.

6. What can you do with money to increase your amount? You can save money. You can earn money. You can find money. Someone can give you money. You can steal money. You can win money. All of these can increase your amount of money. Can you think of any more?

7. Now, what can you do to have less money? You can spend your money. You can lose your money. You can have your money stolen. You can owe/pay someone money. You can give your money away. You can burn or destroy your money. All of these things make you have less money. Can you think of anything else?

8. What can happen to increase or decrease something other than money? Marbles? Frogs? Dishes? Food? Clothes? People?

9. Comparison Telling how something is alike and how it is different. To find the difference we subtract. Example: John is 6 feet tall. Sarah is 5 feet tall. How much taller is John than Sarah? Clue: How much taller, how much older, how much shorter, how much longer, etc.

10. There are many strategies to help you solve problems. Drawing a picture Making a chart or graph Looking for a pattern Estimating Logical reasoning Acting it out Removing extraneous information

11. Other Problem-solving Strategies (to be discussed later) Translating into an equation Using a formula Applying a rule or definition Substituting numbers that make sense Working backward

12. Drawing a Picture The Johnsons are planning to put a fence around their backyard. The fence will extend 10 feet from each side of the house, then 87 feet toward the back of their yard, and 125 feet across the end of the yard. How much fencing do the Johnsons need?

13. Making a chart or graph At a local store, 3 pounds of peanuts and 2 pounds of cashews are mixed together and sold. If peanuts cost 50¢ per pound and cashews cost 80¢ per pound, what should be the price per pound of the mixture?

14. Looking for a pattern Find the units digit for the problem indicated. 8 13 =? 8 1 = 8 8 2 = 64 8 3 = 512 8 4 = 4096 8 5 = 32768 8 6 = 262144 8 7 = 2097152 8 8 = 16777216.. 8 13 = ?

15. Sorting the data The following are grades for the students in Ms. Smiths 9 th grade Spanish class. Find the median and the mode for the following grades: 65, 73, 89, 92, 70, 77, 78, 99, 100, 74, 73, 77, 82, 81, 89, 90, 91, 90, 69, 100 You can sort all of the grades in the following manner: 100s: 100, 100 90s: 99, 92, 91, 90, 90 80s: 89, 89, 89, 82, 81 70s: 78, 77, 77, 74, 73, 73, 70 60s: 69, 65 The median score is the score that is in the middle: 82 The mode score is the score that appears the most: 89

16. Estimating Which answer below is the product of 1.98 x 82.1? A.1625.58 B.162.558 C.16.2558 D.162558 It is not always necessary to calculate an exact answer. 1.98 can be rounded to 2 and 82.1 can be rounded to 82. 2 x 82 = 164 which is closest to B.

17. Logical Reasoning Mary was 1 st in line. Dave was not last. Joe was after Dave. Sue was last in line. What place in line was Dave? Using what you know to figure out what you dont know. Mary = 1 st Dave had to be 2 nd Joe is 3 rd because he is after Dave. Sue = Last

18. Acting it out Many problems can be solved by acting them out. We usually use physical objects (manipulatives) to show what is happening in the problem. Example: In the problem where the students lined up in a certain order, you could use objects to represent each student.

19. Removing extraneous information At the store, Mom bought bread for $1.19, a baking pan for $3.49, a pair of gloves for $4.99, and cheese for $2.89. How much money did Mom spend on food? Locate and remove the extraneous information: The baking pan and the pair of gloves. What is left? Bread ($1.19) and Cheese ($2.89) $1.19+$2.89=$4.08

20. Make sure that your answer makes sense There were 248 seats on the 203 flight to Los Angeles. The airline had sold 178 tickets. How many seats will be empty on the flight? Some students will take 248, 203, and 178 and add them for a total of 629. Some students will add 248 and 178 for a total of 426. Can you have this many seats empty if there are only 248 seats on the plane?