# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.05

## Word Problems Solved By S.M.S.

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## Lesson Plans

Our sample lesson plans, discussed separately, will develop a sample twoweek unit for both the Consumer Related Mathematics Curriculum and the Basic Algebra Curriculum. Please note that there may be repetition between the two developments, as we do want to introduce much of the Method similarly. We encourage that these plans be as diversified as possible, leaving judgment on presentation up to the individual teacher.

### Consumer Related Mathematics

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Lesson 1.
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Write a few simple word problems on the board and have the students solve them. Have an extensive discussion after each one about the steps that the class used to solve each problem. Ask for a series of similar steps. This is an introduction of the S.M.S. Method.

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Lesson 2.
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Continue the discussion on how a word problem is solved and list the S.M.S. Method for the class. It would be best if the class could “discover” the method on their own.

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Lesson 3.
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Do a few problems mapped through the S.M.S. Method. Hand out a worksheet asking questions that could relate to any problem. Be sure to state that not all of the questions need to be answered. For homework, have the students solve three or four problems using the worksheet, listing the steps. See Appendix A for a sample worksheet.

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Lesson 4.
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Have the students solve the problems on the board. Discuss any variations to find the solutions to the problems. See if anyone can come up with a few other methods to solve the problems. Make sure to go through all four steps of the S.M.S. Method.

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Lesson 5.
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Have the students write several word problems with the assumption that they will be distributed to the class to be solved by everyone. The teacher should not make any corrections or include the names of the students. Have the class criticize the use of grammar, structure, and vocabulary.

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Lesson 6.
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Give the students a map of the school or any other area. Have the students organize a set of directions to get from one place to another. You might ask for directions from one spot to another and then an alternative route.

Sample Lesson Plans for both Consumer Related Mathematics and Algebra should continue for about a twoweek period. You can use the Science Research Associates Inc. kit for a day of individualized exploration. You may spend one day going over some of the basic ‘skills that seem weak among your students, as evidenced in a diagnostic test.

A typical problem that may take a full lesson would be the following:

A new school needs school colors. The colors have to be chosen from a given list:

light: | dark: |

yellow | blue |

silver | red |

orange | black |

white | green |

purple |

Students will have to vote by picking one light and one dark color from the list. How many different color combinations could be made with one color from each list? A diagram will help. The use of Venn diagrams may be introduced.Many different types of problems can be solved with the S.M.S. Method. The following is a partial list of some concepts that you could include in problem solving units:

- 1. Proportions to compute the rate of heartbeats in humans and animals.
- 2. To interpret scale drawings.
- 3. To figure atmospheric pressure at different depths below sea level.
- 4. Reading maps.
- 5. Comparing consumer prices at different stores.
- 6. Using formulas and writing formulas.
- 7. Completing tables.
- 8. Estimating and rounding off.
- 9. Measuring in English and Metric Units.
- 10. Laboratory activities.
- 11. Career questions; hairstylist, musician, medical researchers, insurance agents, architecture.
- 12. Mechanical comprehension.
- 13. Interest problems including compounded interest.
- 14. Writing checks and keeping an account.
- 15. Discount and commissions.
- 16. Installment payments including interest.
- 17. Making a budget
- 18. Taxes.