Lesson 5: Solving Word Problems with Algebra

Please go through the following steps to complete Lesson 5.


STEP 1. Watch this short video from Mr H.

STEP 2. Read the following:

Now that you have learned how to solve many types of equations--good work by the way--you're ready to apply your skills to real world problems. Do you remember trying to solve those two word problems in Lesson 1? You used other strategies besides algebra. Was your strategy successful? Was it efficient? Were you frustrated at all? While there are often many ways in math to solve problems, algebra is one of the most efficient and accurate. It can be a very useful and powerful tool!

Since you now know how to solve many types of equations, the learning challenge you now face is this: turning words into an equation. As I said in the video, mathematicians need to turn English into Mathish. Here are a few different kinds of word problems that algebra can solve.
  • Eric has four more than double the number of Facebook friends Jenn has. Eric has 54 friends. How many does Jenn have? 
    • Write "let statements" - mathematical expressions to represent the information and what you're looking for 
      • Let x = the number of Jenn's friends (what you're looking for)
      • Let 2x + 4 = the number of Eric's friends (Info you need) 
    • Write an equation to solve for x 
      • 2x + 4 = 54 
      • 2x + 4 - 4 = 54 -4 
      • 2x/2 = 50/2 
      • x = 25 
    • Answer 
      • Jenn has 25 Facebook friends
    • Check
      • 2(25) + 4 = 54 (It works!)
  • Brooke is 15 years younger then Josh. In 5 years Josh will be twice as old as Brooke. How old are Brooke and Josh? 
    • Write Let statements 
      • Let j = Josh's age (What you're looking for)
      • Let j + 5 = his age in 5 years 
      • Let j - 15 = Brook's age (What you're looking for)
      • Let j - 10 = her age in 5 years 
    • Write an equation to solve for j 
      • 2(j-10) = j + 5 (Double Brooke's age in five years is equivalent to Josh's age in 5 years) 
      • 2j - 20 = j + 5 
      • 2j - 20 + 20 = j + 5 + 20 
      • 2j = j + 25 
      • 2j - j = j - j + 25 
      • j = 25 
    • Answer 
      • Josh is 25 and Jenn is 10 
    • Check 
      • 2(25-10) = 25+5
      • 30 = 30 (Correct!)
  • Petra has six times as many dimes as quarters in her piggy bank. She has 21 coins in her piggy bank totaling $2.55. How many of each type of coin does she have? 
    • Write Let statements 
      • Let q = the number of quarters; Let 0.25q = the value in quarters 
      • Let 21 - q = number of dimes; Let 0.10(21-q) = the value in dimes 
    • Write an equation to solve for q 
      • 0.25q + 0.10(21-q) = 2.25 
      • 0.25q + 2.10 - 0.10q = 2.25 
      • 0.15q + 2.10 - 2.10 = 2.25 -2.10 
      • 0.15q = 0.15 
      • 0.15q/0.15 = 0.15/0.15 
      • q = 1 
    • Answer
      • Petra has one quarter and 20 dimes
    • Check
      • 0.25(1) + 0.10(21-1) = 2.25
      • 0.25 + 2 = 2.25 (Right!)
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You may notice that the math part is stuff you know! These are just equations to solve. The trick with word problems is putting words into an equation of numbers and symbols--turning English into Mathish. Getting good at translating into Mathish comes with seeing lots of examples and doing lots of practice. So take your time learning this skill.

To succeed in this lesson, correctly solve 4 out of 6 word problems on the lesson quiz. Once again, please show your work. Check out the test rubric again, specifically the section on problem solving.


STEP 3. Watch several of the following instructional videos on solving word problems. Once you've watched one, try to solve the problem presented on your own. Then compare your solution to the video's.

STEP 4.
Create several word problems of your own or find some examples in your textbook or online. Create, or find, at least one of each of the following categories: age, coin, integer, and geometry. (The unit test will focus on word problems in these four categories). Now solve them. Do extra practice on the kinds of questions that are most challenging.

If you have questions or want me to check your work, please contact me! I'd be happy to answer any questions.

Remember to show all work--let statements, equation, steps to solve, answer, and check.


 STEP 5. Reflect. How did you do on the practice exercises? Solving word problems can be quite challenging. Don't feel bad about taking extra time learning this skill. Review more instructional videos as needed, try solving a few more problems, or ask me any questions.


STEP 6. Write the Lesson 5 Quiz. Answer on paper, then compare your work to the answer key on the bottom of the quiz. If you get at least 3 correct and show the correct steps, you are ready for the unit test. If you get less than 3 correct and/or do not show correct steps to solve, please redo steps 3 to 5. Then retry the quiz.




STEP 7. Please email me with your quiz score and any questions you still have. Remember, it's okay to do the quiz more than once.
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