June 2004 Tip
Ah, June has finally arrived! Whether you are just winding down school or have already begun your summer break, it’s a great feeling to renew, isn’t it! This month is just a little thoughtful piece for those few months ahead. For you can, without having to really work at it, collect word problems and problem solving scenarios in the world around you while you enjoy your well-deserved break.
First of all, let’s talk about “Word Problems” versus “Problem Solving.” Regardless of your grade level, the definitions and intent remain the same.
Word Problems are those problems which students can solve using arithmetic as part of a problem solving plan. The plan can be any variation of:
- 1) read and understand the problem
- 2) determine the solution strategy (operation) and find the important data
- 3) solve the problem
- 4) check the answer for reasonableness.
Problem Solving or Non-routine Problems are those problems which require a strategy other than arithmetic as part of a problem solving plan. Problem-solving strategies include:
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1) draw a picture
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2) act it out
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3) look for a pattern
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4) systematic guess and check
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5) solve a simpler problem
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6) make a chart, table, or graph
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7) work backward
Certainly a problem can be both a simple “word” problem as well as a true “problem solver” depending upon the age and mathematical ability of the student, as is the case for the following problem. “Ariana had 8 bags of fruit. Each of the bags contained 4 apples. How many apples did she have?”
For an end-of-the-year third grader, this should be a “word problem,” because third graders are expected to solve word problems using multiplication. But for a primary student, this would be a true “problem solver.” The primary student would be expected to draw a picture, or act out the problem, or use a strategy other than the multiplication algorithm in order to find the solution.
A non-routine word problem usually expects students to work in groups to find a strategy for solving the problem. Obviously the more mathematical knowledge students have the more complex a problem solver needs to be. Many of the Ms. Fritzie problems are “problem solvers.”
Word problems that are meaningful for your grade/aged students are difficult to find. Meaningful Problem Solvers are even MORE difficult. As you travel, rest, interact with people this summer, think about the mathematics around you. What are you seeing that would be interesting for your students? How can you create meaningful problems for them, both word and non-routine? Generate a set of these problems and keep them handy to use anytime during the day when there is down time, or when your math class needs a little refreshing boost. There’s nothing like a teacher telling her students, “You know, this summer when I was vacationing I saw…..” Kids pick up on it, too, and begin bringing in their own math tales.
Happy Mathematics and have a wonderful summer break!
