• Approach word problems with a positive attitude
  • Use a problem-solving strategy for word problems
  • Solve number problems

Assignment

How to Approach Word Problems

I strongly recommend you read the opening part of this section in the book. Many students shut down when presented with word problems, and you are likely one of them. And nearly all of those students are perfectly capable of solving those problems, but they can’t get over that initial shock of “math but words”.

Approaching something with an open mind really does go a long way. Take it from someone who is more cynical and sarcastic than he should be.

Use a Problem-Solving Strategy for Word Problems

Before jumping into any kind of word-problem strategy, let’s get something out of the way: the best way to get good at solving problems is by just solving problems. Experience beats education, so you should be going through every example problem in the text so you can see all the different problems you’ll encounter. Then, you can use that knowledge to solve similar problems, and then knowledge from those to some similar ones, and so on.

The text provides a nice outline for approaching any kind of problem.

Use a Problem-Solving Strategy to Solve Word Problems.

  1. Read the problem. Make sure all the words and ideas are understood.
  2. Identify what we are looking for.
  3. Name what we are looking for. Choose a variable to represent that quantity.
  4. Translate into an equation. It may be helpful to restate the problem in one sentence with all the important information. Then, translate the English sentence into an algebraic equation.
  5. Solve the equation using good algebra techniques.
  6. Check the answer in the problem and make sure it makes sense.
  7. Answer the question with a complete sentence.

I’m going to go through some of the book’s examples and do the translation step. Make sure you can find the path from the text of the problem to the equation.

Pilar bought a purse on sale for $18, which is one-half of the original price. What was the original price of the purse?

$18 is one-half of the original price.

\[\begin{align} 18 = \frac{1}{2}p \end{align}\]

Ginny and her classmates formed a study group. The number of girls in the study group was three more than twice the number of boys. There were 11 girls in the study group. How many boys were in the study group?

The number of girls in the study group was three more than twice the number of boys.

\[\begin{align} g = 2b + 3 \end{align}\]

The difference of a number and six is 13. Find the number.

\[\begin{align} n - 6 = 13 \end{align}\]

The sum of twice a number and seven is 15. Find the number.

\[\begin{align} 2n + 7 = 15 \end{align}\]

One number is five more than another. The sum of the numbers is 21. Find the numbers.

One number is five more than another.

\[\begin{align} x = y + 5 \end{align}\]

The sum of the numbers is 21.

\[\begin{align} x + y &= 21 \\ (y + 5) + y &= 21 \end{align}\]