# Problem Solving

## CONTENTS OF CURRICULUM UNIT 80.07.04

## Logic and Set Theory

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## Sample Lesson Plan 2:

to solve problems.

Motivation: Take the pretest problem 1 and write it on the board. Discuss methods used in solving.

The problem was as follows: There are 20 children at a party; 13 had cokes; 7 had sandwiches; and five had

both. How many did not eat or drink?

A Venn diagram consists of a rectangle which represents the universe, and circles within the rectangle representing the sets involved.

Draw a Venn diagram for the above.

(figure available in print form)

Begin with those that had both. It is placed where the circles intersect. How many people then had only cokes? 135=8. How many had only sandwiches 75=2. The Venn diagram now appears as follows:

(figure available in print form)

The total of those who had something to eat or drink is 15 leaving 5 who had nothing to eat or drink.

Try the following problem:

A survey of 100 students at Sheridan gave the following data:

41 students taking Spanish

29 students taking French

26 students taking Italian

15 students taking Spanish and French

8 students taking French and Italian

19 students taking Spanish and Italian

5 students taking all three languages

Find the number of students among the 100 that are not taking any of the 3 languages. How many take just one of the languages?

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Solution:
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(figure available in print form)

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Solution:
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41 Children are studying no foreign language. 27 children are studying only one language.