Problem Solving Using our friends the EQUATIONS Lesson

Problem Solving Using our friends the EQUATIONS!!!!! Lesson Objective: To take a word problem and define a variable, write an equation, solve the equation, and interpret the solution.

PROBLEM SOLVING STRATEGIES Use a graph Write an equation Find a pattern Use reasoning Make a table Use formulas Make a list Work backwards Draw a picture Act it out

Problem Solving is easy if you follow these steps What Am I Trying to Find Out ?

Step 1 – What am I trying to find out? • Read the problem carefully. • Find the important information. • Identify what the problem wants you to solve.

Step 1 - What am I trying to find out? Read the problem carefully. • Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?

Step 1 - What am I trying to find out? Decide what the important facts are? • Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week? Total = 31 1 st week =14 2 nd week = ?

Define a Variable for what is unknown

Step 2 – Define a variable for what is unknown Total = 31 1 st week =14 2 nd week = ? Let “s” represent the number of points earned for the second week.

Decide what operation to use

Step 3 – Decide what operation to use. Remember the verbal phrases for each operation. They are clues! • Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week?

Write the Equation

Step 4 – Write the equation Total = 31 1 st week =14 2 nd week = ? Since I know both weeks total 31 I write 14 + s = 31

Solve The Equation

Step 5 – Solve the equation Total = 31 1 st week =14 2 nd week = ? I can use the inverse operation to solve for “s” 14 + s = 31

Step 5 - Solve the problem I can use the inverse operation to solve for “s” 14 + s = 31 s + 14 = 31 - 14 s = 17

Answer question using a complete sentence. Luis earned 17 points during the second week.

Does the solution make sense? Substitute your new number • Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week? Total = 31 1 st week =14 2 nd week = 17

Does the solution make sense? Substitute your new number • Luis earned 14 Accelerated Reading points the first week of November. At the end of the following week he had a total of 31 points. How many points did he earn the second week? 14 + 17 = 31 Yes!

Write an equation to solve this problem. Nine less than a number is 23. What is the number? Let “n” represent the unknown number. Less than means SUBTRACTION n – 9 = 23 +9 +9 n = 32

Write an equation to solve this problem. Cindy has 25 CD’s which is nine more than David has. How many CD’s does David have? Let “d” represent David’s CD’s & let “c” represent Cindy’s CD’s More than means ADDITION c = 25 d + 9 = 25 -9 -9 d = 16

Write an equation to solve this problem. Vicki baked 90 cookies. If there are 15 cookies in each batch. How many batches were baked? Let “b” represent the number of batches. In each batch means ? ? ? How many batches means? ? 15 b = 90 15 d = 90 15 15 (1)d = 6 d= 6

Write an equation to solve this problem. Navneet has 3 times as many Facebook friends than Arlene. If Navneet has 360 friends, how many does Arlene have? Let “a” represent the number of friends Arlene has 3 times as many means ? ? 3 a = 360 3 3 (1)a = 120

Do the You Try’s • The difference between two numbers is 5. The lesser number is 8. What is the greater number? • The sale price of a sweater is 7 dollars less than the regular price. The sale price of the sweater is 48 dollars. What is the regular price? • Lisa scored 8 points less than Terry. Lisa scored 30 points. How many points did Terry score?