Math Word Problems
Gaining proficiency with mathematical word problems is a crucial skill for your students to master.
By Greg Harrison
Quite often, when math students hear the phrase "word problems" all sorts of negative thoughts enter their heads, then a blank stare appears on their faces as they look at the problem on the paper. I've seen many students who were terrific at math shut down when faced with a word problem that required two or more steps to solve. Why is this? Part of the reason is that word problems require reading, and many students who are incredibly good at math are not as confident or proficient when it comes to language arts. Another part of the reason is that many students have not been taught strategies they can utilize when it comes to solving a word problem. And so, when a word problem comes up on a homework assignment, a quiz, or standardized test, they often feel defeated before they even get started on it.
Like anything else in mathematics, in order to become confident and successful problem solvers, students must be taught problem solving strategies and given many opportunities to put those strategies to use. It's all about the practice! Thus, I have made problem solving a regular part of my daily math class. When math class begins, my students take out their Daily Math books. The students divide a sheet of paper in their books into four sections by drawing a vertical line down the middle and a horizontal line across the middle of the page. I do the same thing up on the whiteboard. Each of the sections contains a math problem. Anything goes! The problems can range from simple calculation problems, to Roman Numerals, to number patterns, to geometry concepts, to beginning algebra problems . . . anything at all. I always reserve the fourth box for a word problem. Here's an example:
I want to put wood tiles on part of the classroom floor. The space is 12 feet long by 10 feet wide. The square-foot tiles come in packages of 25. How many packages will I need to buy in order to cover the space?
This is a classic example of a "two-step" word problem. It requires "two-steps" because it takes two separate calculations to solve it. Here are the strategies I teach my students to solve a problem like this:
1) Take three deep breaths to help you relax, and send lots of oxygen to your brain. (This may sound strange to you, but trust me . . . it works!)
2) Read the problem twice.
3) Circle all of the numbers in the problem.
4) Underline the sentence tells you what you have to figure out.
5) Decide which operations you have to use to solve each step.
6) Perform your calculations and solve the problem.
Most students will realize that they have to figure out how many square feet (how big) the space is that I want to tile. If they multiply 12 X 10, they will come up with 120 square feet and will know that they need 120 tiles to do the job. Now they have some options. Some students will count by 25's to see how many packages are needed to cover the floor. They can count up - 25, 50, 75, 100, 125. Voila! Five packages will be needed. Other students will use division, 120 divided by 25 is 4.8, so a full 5 packages will be needed.
Two-step problems are, of course, more difficult than one-step problems. In the beginning of the year, I would have made this problem a one-step problem by simply asking them how many square feet of floor I wanted to tile. As the year goes on, and as your students get more comfortable with solving word problems, you simply add more steps. To make this example into a 3-step problem, you could tack on the sentence: If the packages of tiles cost $18.00 each, how much money will I have to spend in order to tile the floor?
In this simple way you can incorporate word problems into your daily math lesson plans for your students. You will find that as their confidence grows, they will begin saying "Give us a hard problem!" After all, math word problems are like riddles, and we all know how much children love a good riddle. Additionally, math word problems are a great example of how we, as adults, use math in "real-life" situations - which is another reason why it's so important to give your students guidance and practice in this critical area of mathematics. Here are some other lesson plans which will give you some terrific ideas for teaching and incorporating mathematical word problems into your daily lessons.
Mathematical Word Problem Lesson Plans:
Word problem activities don't have to be boring! Most everyone loves pumpkins, and here is a lesson that should pique your students' interest. They read and analyze a chart about ten of the biggest pumpkins in the world, determine what math operation needs to be used to solve word problems, and complete a worksheet in the plan. A very fine lesson!
In this motivating lesson, students take turns acting as "math coaches" who assist other students in solving word problems by identifying key words that usually indicate specific mathematical operations. This lesson speaks to a very important concept used for problem solving - recognizing the words that often give them clues as to how to proceed when deciding on an operation to use, and solving the problem.
Once your students become more confident and proficient with their problem solving, this very clever lesson will give them some higher-level practice. Students access the Disaster Math website, and select from the following Disaster Math games: Hurricane, Tornado, Wild Fire, Winter Storm, or Flood Math. They work in pairs and attempt to solve a variety of word problems associated with each disaster.
This lesson is geared for upper elementary/middle school students, and provides an excellent opportunity to solve word problems regarding a favorite food for most kids - cereal! Students utilize the nutrition labels on a variety of cereal boxes to solve word problems and, eventually, to create their own cereal. A masterful lesson!