Sunday, February 24, 2008

How to Write Better Word Problems

If you really want your students to grow as a mathematician and have them succeed on standardized tests as an added bonus, incorporating more thought-provoking, relevant word problems can make a huge difference. By challenging them to read, write, think, and relate classroom lessons to their lives, you'll both increase their ability and their investment in your classroom.

Before you can start, you have to know what not to do: don't rely on questions from textbooks, released tests or state-issued material. You can use them if they fall into one of the categories below, but if you look at the examples you'll see why they may not be as beneficial as you think.

Guidelines for Writing Better Word Problems
  1. Have them do something. Ask them to figure out something that would force them to get up and/or look around the room to find or get closer to an answer. This gets them involved and engaged immediately, because it's not something they would be asked to do on a standardized test question.
  2. It's all about them. As I've said many times, all teenagers have one thing in common: they want you to think about them. Sometimes this means demonstrating your keen awareness of them through the relevant questions you ask. This can take on many forms, but you can start with what their concerned about in their lives: school, cell phones, music, cars, movies, their boyfriend/girlfriend, other friends, etc.
  3. Spark a discussion. Don't shy away from a challenging or controversial topic if it will get them thinking mathematically. That discussion might make your lesson one of the more memorable ones of the year, and that's rarely a bad thing.
  4. Money, money, money. The easiest connection to make with most math topics is to money issues. Textbook and test makers rely on this as well, so its up to you to differentiate your questions from theirs by applying the other guidelines here.
  5. Connect math to the real world. Just keep in mind that their world and your world aren't really the same thing, so think about things from their perspective (see #2). Make references to local people, places and things or situations they themselves or their family currently or will soon face.

Here are some examples that apply to some or all of the guidelines above, marked with the Algebra I topic they addressed.
Count the number of girls in this class right now. Then count the number of boys. Subtract the number of girls - the number of boys. Finally, subtract the number of boys - the number of girls. What's the difference between the two answers? [adding and subtracting integers]

Juan makes $1200 a month working full time at Wal-Mart. If his bills are $400 for rent, $150 for electricity, $35 for water/garbage and $50 for his cell phone, how much does he have left for himself and his family? [solving one-step equations with adding and subtracting]

A new 19 inch TV costs about $200. At Rent-a-Center, you pay $12 a week for 78 weeks for the same TV. What's the total cost at Rent-a-Center? [solving one-step equations with multiplication and division]

For every hour she works at Dollar General, Veronica makes 6 dollars. Make a table and a graph showing the hours she works and the money she makes (up to 8 hours). [creating and connecting tables and graphs of a relationship]

The cost of a Whataburger meal is $3.99 each. Write a function for the total cost, c, in terms of the number of meals you buy, m. Use your function to find out how much 8 meals would cost. [writing equations and functions]

A student has six weeks grades of 75 and 50. If you need at least 210 points to pass the semester, what grade does he or she need this six weeks? [measures of central tendency, inequalities]

The yearbook staff sells about $150 of snacks at lunch every day. How long would it take to raise at least $10,000? [inequalities]

Working as a waiter at the new Chili's in Mission will earn you about $2 an hour plus tips. If you work 40 hours per week, at least how much do you need in tips to makes $250 a week? [inequalities]

A subscription to Netflix costs $18 per month for unlimited DVD rentals. If you rented DVDs from a local store, it would cost about $3.50 each. How many DVDs would you have to rent each month for you to SAVE money using Netflix? [systems of linear equations]

The population of Mission in the 2000 census was about 45,000. If the population is increasing by about 3,000 people a year, what should the population be by the end of this year? [rates, ratios, and proportions]

Verizon Wireless charges $0.49 per minute for calls to Mexico. Write an equation to find m, the number of minutes a person can call Mexico for $20. [writing equations and functions]

Mr. D walks 8 miles north and 3 miles west. How far is he from where he started? [Pythagorean theorem]

Mr. D stands on top of a building 250 meters tall. If he jumps off and falls at a rate of 9.8 meters per second, what equation could you use to show how long it will take him to hit the ground and DIE? [writing equations and functions]
Many of these questions led to relevant discussions, usually touched off by a student asking, "Is that true, sir?" More students were engaged in trying to figure out the problem than if I would have had them do something from the textbook or merely given them wordless problems to solve. They were used mostly as "Do Now" activities that would introduce the objective we would cover that day and hook students attention right away.

More Info

For more ideas like this, read my earlier article Reading and Writing in Math Through Journals. Click the literacy tag for even more.