Before You Begin
When solving math word problems with students, teachers often use the following three steps:
- Read the problem closely to determine the appropriate information and procedure needed to solve the problem.
- Model the problem mathematically; extract the numbers; set up an equation.
Solve the equation.
- After finding the solution to a problem, teachers tend to move on quickly without much discussion of what the solution means.
When this happens, the meaning of math is reduced to simple correctness and overtime this can lead students to struggle to find meaning in math beyond whether or not they can solve a problem. Research finds that this can lead students to disengage from math as it feels irrelevant to their lives.
To better support students, teachers help students to “finish” a problem by adding the following step to the above method.
- Re-insert the answer into the word problem and work with students to interpret the conceptual and contextual meaning of the solution.
In June, 2007 Steve Jobs introduced the first version of the iPhone for $499. This was the first smartphone ever released by Apple. In 2017, the iPhone 7 Plus is the latest model and is priced as $769. Since the iPhone was introduced in 2007, what has been the percent increase on the price?
The solution to the problem is 54%. To help students connect the problem to their lives, ask the following kinds of questions:
- What does a 54% increase in the iPhone actually mean? Is that fair?
- What might be some reasons for the increase?
- Would you buy this product? Why or why not?
- Given your understanding of the change in price would you recommend this product to others? Why or why not?
Three potential interpretations include:
- Inflation: Money is worth less than it was in the past, therefore you need more money to buy the same things now.
- Apple markup: Apple realized that they have a really popular product so now they are able to charge more money for it. But is that fair? Why or why not, discuss?
- Better product: Maybe today’s iPhone is actually 54% better than it was 10 years ago (e.g., faster, more options, more storage space).
The purpose is not to find the correct interpretation for the occurrence, but to give students the opportunity to discuss the answer with depth and to see how the answer and math is relevant to everyday life and decisions.
Jamaal Sharif Matthews, Ph.D., University of Michigan School of Education