1. CONFIDENTIAL1 OBJECTIVE: Problem Solving Plans and Strategies WARM-UP: 1.) 6 ÷ (8 - 5) + 4 x 5 2.) Evaluate 9 - 3x for x = 4; 3.) 4 2 + 3 3 = 16 + 27 = 4.) Is 5,310 divisible by 3?

2. CONFIDENTIAL2 3 + n is an "ALGEBRAIC EXPRESSION" Numbers Operations Variables Algebraic Expressions consist of Numbers, Operations, and Variables.

3. CONFIDENTIAL3 The VARIABLES in an expression can be replaced with any number. 3 + x If I substitute a 5 for the x........... I have 3 + 5 or 8 This is how we Evaluate (or find the value of) the Expression

4. CONFIDENTIAL4 Can you evaluate 3a ÷ b for a = 4 and b = 2 ? Very Good! Let's move on!

5. CONFIDENTIAL5 When solving math problems, it is often helpful to have an organized problem-solving plan. U P S nderstand lan olve

6. CONFIDENTIAL6 U To nderstand the problem, we need to -read the problem carefully -identify the facts that we know -identify what we need to know (WHAT IS THE QUESTION?) -determine if we have enough or too much information (Many students find it helpful to highlight or underline the important facts in the problem.)

7. CONFIDENTIAL7 Next, we must P lan -determine how the facts relate to each other -plan a strategy for solving the problem -estimate your answer Key words play an important role in determining which operations to use. Add plus sum total in all Subtract Multiply Divide minus difference less times product of quotient

8. CONFIDENTIAL8 And finally, we S olve the problem -use your plan to solve the problem -if your plan does not work, revise it or make a new plan -find the solution -make sure the answer makes sense and is close to your estimate Keep in mind that numbers do NOT always appear in a problem in the order in which they should be used to solve the problem.

9. CONFIDENTIAL9 On a beautiful spring day, 525 boys signed up to play baseball. If the league assigns 15 players to each team, how many teams will there be? U P S nderstand lan olve read identify facts estimate strategy use operation(s) find answer

10. CONFIDENTIAL10 Another method to use when problem solving is the... Guess-And-Check Strategy This strategy is an efficient way to narrow down the field of possible answers. Examine the problem carefully, choose a possible answer, and then check to see if it is correct!

11. CONFIDENTIAL11 For example, The sum of four coins is thirty-two cents. What are the coins? To solve 1.Pick any four coins and find their sum. 2.If their sum is NOT 32 cents, choose four more coins. 3.Repeat this process until you have your answer ANSWER: A quarter, a nickel, and 2 pennies

12. CONFIDENTIAL12 I can also use the Guess-And-Check strategy to find solutions for equations. In the equation x + 8 = 12, which value for x would make the equation true? a.)2 b.)3 c.)4

13. CONFIDENTIAL13 Let's try a few practice problems: 1.) An adult male walrus weighs about 2,670 pounds. An adult female walrus weighs about 1,830 pounds. Their tusks measure about 3 feet in length and weigh about 10 pounds. How much less does an adult female walrus weigh than an adult male walrus? 2.)On average, a dog lives 12 years. This is 13 years less than a horse lives. What is the average life span of a horse? 3.)Identify the solution for 9 + x = 17 a.)7 b.)10 c.)8

14. CONFIDENTIAL14 LET US TAKE A SHORT BREAK!!!

15. CONFIDENTIAL15 TRY SOME BRAIN TEASERS!!! What happened in 1961 and will not happen again until 6009? The year reads the same upside down! What letter is next in this sequence? M, A, M, J, J, A, S, O,__ N for November!

16. CONFIDENTIAL16 Explain whether each statement is True or False. 1.) In the expression m + 8, the variable m can have any value. 2.) In the equation m + 8 = 13, the variable m can have any value. (Notice the difference between an EQUATION and an EXPRESSION.)

17. CONFIDENTIAL17 If Jupiter orbits the sun at a rate of 8 miles per second. How far does Jupiter travel in one hour? U P S nderstand lan olve

18. CONFIDENTIAL18 Let's see how well you can solve problem! 1.) In 1990, the population of Sacramento, CA was 370,000. In 2000, the population was 407,000. How much did the population increase? 2.)The Smith family wants to purchase a television set and pay for it in four equal payments of $180. What is the cost of the television set? 3.)Complete the pattern: 6, 11, 16, 21, ___, ___, ___ ? ? ?

19. CONFIDENTIAL19 4.)Brandon is thinking of four different numbers from 1 through 9 whose sum is 23. Find the numbers. 1,5,8,9 5.)Identify the solution of the equation: 66 = z - 23 a.)88 b.)89 c.)90 Answer to #4:

20. CONFIDENTIAL20 Well Done! Let's review what we learned today! An organized problem solving strategy is UPS Understand Plan Solve Another strategy we can use is Guess-And-Check. It is important to check our answer and see if it makes sense. Know the "question" that is being asked. Many times there is more information in the problem than you need to answer the "question"!