(7 minutes)Explain how to solve a word problem.
Many students find solving word problems difficult. Especially when they are asked to explain their thinking. Some teachers give students a "weekly problem" that they are expected to solve during the week, explaining their reasoning and presenting their solution. This exercise directly addresses the problem solving requirements of the WASL and prepares students for the Washington State Math Olympiad Session I problem.
Before you present this lesson, you should become familiar with what is meant by the terms UNDERSTANDING, STRATEGY, COMMUNICATION and REASONABLE RESULT in the context of solving a word problem. Here are some practical definitions:
You will also be required to become THOROUGHLY familiar with the Peanuts problem and be able to evaluate a student response on-the-spot. So read it, make a table yourself, try guess-and-check and work the problem backwards to become familiar with the problem.
- UNDERSTANDING - showing by written sentences or calculations that the team understood the problem. This is not a very difficult determination. It should be easy to see if the team is "on the right track".
- STRATEGY - This means that the team must convey to you HOW they solved the problem (what way did they use?). This does not have to be described in words (although sentences are a good way to describe a strategy). The strategy could be a table, a relevant picture, guess-and-check, working backward or the discovery of a numerical relationship. In the Peanuts problem, working backward, guess-and-check and making a table are reasonable strategies.
- COMMUNICATION - This means that the team described in clear sentences what they were doing and that you did not have to discern that they understood the problem by examining random scribblings on the paper. The writing should be clear, orderly and not have "holes". Whole sentences count here. It is possible for a team to get 4 points for UNDERSTANDING and 4 points for STRATEGY and 0 points for COMMUNICATION if they showed by calculations that they understood the problem, clearly used a valid strategy (for example, made a table) but wrote no sentences about their solution (other than "The answer was 11", for example).
- REASONABLE RESULT - This means that the team wrote a sentence or sentences describing how they checked their work. Teams achieve a 4 for REASONABLE RESULT only if they solve the problem by another method.
- Organize students into teams of 4 (3 or 5 are OK). Assign a captain
to each team.
- (No more than 10 minutes!)Explain how a word problem is solved:
- Read the problem to UNDERSTAND what is being asked for
- Figure out a STRATEGY for working the problem
- COMMUNICATE by showing your work and telling us what you were thinking
- Check your answer to see if you have a REASONABLE RESULT. Try a
different way of working the problem.
- Write these rules on the board (ahead of time):
- The team turns in 1 paper
- All writing is in complete sentences.
- Neatness counts.
- Show your work!
- (40 minutes)Work the Peanuts problem
- Hand out the problem and the answer sheet (one for each student).
- Read and explain the problem. Tell students that they can bring their paper to you (complete or not) for an INSTANT grade. Use the rubric to evaluate their paper. You must thoroughly understand the rubric (for example how a Strategy score of 2 differs from a 4) to do this. Tell them that they can bring their paper to you multiple times until they get the best score they can achieve. When students bring you a paper and you grade it, tell them WHY they didn't get a top score in each category.
- Give HEAVY coaching and advice throughout. Make sure every team
succeeds. If they can't think of a strategy, suggest making a table.
- (10 min) Ten minutes before class end ask for all papers to be turned in. Quickly evaluate all responses using the rubric. Explain to students what made some papers good. You may want to award prizes for, say, papers with grades of 16 or above.