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## OBJECTIVE: Problem Solving Plans and Strategies

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**OBJECTIVE: Problem Solving Plans and Strategies**WARM-UP: 1.) 6 ÷ (8 - 5) + 4 x 5 = 6 ÷ 3 + 4 x 5 = 2 + 4 x 5 = 2 + 20 = 22 2.) Evaluate 9 - 3x for x = 4; 9 – 3 x 4 = 9 – 12 = -3 3.) 42 + 33 = 16 + 27 = 43 4.) Is 5,310 divisible by 3? Yes CONFIDENTIAL**3 + n is an "ALGEBRAIC EXPRESSION"**Numbers Variables Operations Algebraic Expressions consist of Numbers, Operations, and Variables. CONFIDENTIAL**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 CONFIDENTIAL**Can you evaluate**3a ÷ b for a = 4 and b = 2 ? (3 x 4) ÷ 2 = 12 ÷ 2 = 6 Very Good! Let's move on! CONFIDENTIAL**When solving math problems, it is often helpful**to have an organized problem-solving plan. U nderstand P lan S olve CONFIDENTIAL**To**U 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.) CONFIDENTIAL**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 Subtract Divide Multiply minus difference less quotient plus sum total in all times product of CONFIDENTIAL**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. CONFIDENTIAL**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 Each team has 15 players Total 525 boys read identify facts nderstand Total no of players = No of teams x No of players per team P estimate strategy lan S No of teams = 525/15 = 35 use operation(s) find answer olve CONFIDENTIAL**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! CONFIDENTIAL**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 CONFIDENTIAL**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 CONFIDENTIAL**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? 2670-1830 = 840 pounds 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? Life span of a horse – 13 = Life span of Dog Life span of horse = Life span of Dog + 13 = 12 + 13 = 25 3.) Identify the solution for 9 + x = 17 a.) 7 b.) 10 c.) 8 CONFIDENTIAL**LET US TAKE A SHORT BREAK!!!**CONFIDENTIAL**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! CONFIDENTIAL**Explain whether each statement is True or False.**1.) In the expression m + 8 , the variable m can have any value. True 2.) In the equation m + 8 = 13 , the variable m can have any value. False (Notice the difference between an EQUATION and an EXPRESSION.) CONFIDENTIAL**If Jupiter orbits the sun at a rate of 8 miles**per second. How far does Jupiter travel in one hour? U Speed of Jupiter = 8 miles per second nderstand P In one second Jupiter travels 8 miles In one hour = 60 x 60 seconds lan Therefore, in one hour Jupiter will travel = 60 x 60 x 8 = 28,800 miles S olve CONFIDENTIAL**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? Increase in population = 407,000 – 370,000 = 37,000 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? Cost of TV = 4 times $180 = 4 x 180 = $720 3.) Complete the pattern: 26 31 36 6, 11, 16, 21, ___, __, ___ CONFIDENTIAL**4.) Brandon is thinking of four different numbers**from 1 through 9 whose sum is 23. Find the numbers. 1, 5, 8 and 9 5.) Identify the solution of the equation: 66 = z - 23 a.) 88 b.) 89 c.) 90 Answer to #4: 1,5,8,9 CONFIDENTIAL**Well Done! Let's review what we learned today!**An organized problem solving strategy is UPS Understand Plan Solve Know the "question" that is being asked. Many times there is more information in the problem than you need to answer the "question"! Another strategy we can use is Guess-And-Check. It is important to check our answer and see if it makes sense. CONFIDENTIAL