ALGEBRA I Unit 1 Section 2 Translating Problems

– ALGEBRA I – Unit 1 – Section 2 Translating Problems into Equations and Solutions Solving word problems can be one of the trickiest processes in Algebra. The key lies in having a solid approach and plan to attacking word problems.

– ALGEBRA I – Unit 1 – Section 2 Translating Problems into Equations and Solutions We will be using a FIVE-STEP approach for solving word problems in this class… 1 2 3 4 5

FIVE-STEP Problem Solving Plan STEP #1 – GET ORGANIZED This step involves several things: 1. Figure out what you know. 2. Figure out what you DON’T know. 3. Draw a sketch (if necessary). Getting organized is the key to success. Take the time to sort through the information and develop a game plan.

FIVE-STEP Problem Solving Plan STEP #2 – PICK A VARIABLE Choose a letter that makes sense to you. Pick something that reminds you of what you are solving for. For instance, “t” may stand for time. Write any “unknowns” in terms of your variable.

FIVE-STEP Problem Solving Plan STEP #3 – WRITE AN EQUATION Remember that if you write one equation and want to be able to solve it, you can only have one variable in it. GOOD EXAMPLE: w + 6 = 20 BAD EXAMPLE: w + l = 20

FIVE-STEP Problem Solving Plan STEP #4 – SOLVE THE EQUATION I think that this step is pretty self explanatory. Until we officially start solving equations, you will be given possible answers to guess and test with.

FIVE-STEP Problem Solving Plan STEP #5 – CHECK YOUR ANSWER There are several things to do: 1. Check your math and labels. 2. Make sure that you are answering the question. 3. Make sure your answers make sense in the context of the problem.

FIVE-STEP Problem Solving Plan Let’s recap. 1. ORGANIZE The five steps are: 2. VARIABLE 3. EQUATION 4. SOLVE 5. CHECK

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) ORGANIZE What don’t you know? 1. Perimeter = 38 in 2. Length is 5 inches more that the width 3. Add all sides to get the perimeter 1. Length 2. Width Draw a sketch length width What do you know? p = 38 in

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) VARIABLE Width = w Length = w w Since the two unknowns are length and width, make one of them your variable and write the other one in terms of that variable. Edit your sketch as you go… w+5 +5 p = 38 in

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) EQUATION w Write the equation that will allow you to solve for the variable. w+5 p = 38 in w + 5 + w + 5 = 38

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) SOLVE w = 7 inches w If you can solve the equation algebraically, the go ahead. Otherwise, guess and test with the possible choices. w+5 p = 38 in

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) CHECK w The question is asking for the dimensions. Thus, we need to know the width AND length. w+5 p = 38 in w = 7 inches l = 12 inches

Example Problem A rectangle is 5 inches longer than it is wide. What are the dimensions of the rectangle if the perimeter is 38 inches? (Choices for w: 5, 7, or 8) CHECK w Do the answers make sense? Do the sides of the rectangle add up to 38 inches? If yes, then we are done! w+5 p = 38 in w = 7 inches l = 12 inches

Try This Problem… Use the problem solving plan to solve the following problem. Be sure to show your work. Possible answers for the shorter piece have been provided. 1. Suppose that a 2'× 4' piece of lumber is originally 16 feet long, but it is cut into two pieces. The longer piece is three times as long as the shorter piece. How long is each piece? (Possible answers for short piece: 4, 5, or 6) **The answers can be found at the end of the Power. Point.

ALGEBRA IS FUN AND EASY! **Answers: 1) 4 feet and 12 feet