## Who Won the Cross-Country Meet?

### Johnny WolfeSanta Rosa District Schools

#### Description

Using algebraic expressions, the students write a verbal expression into an algebraic expression and then solve the expression. Some of the examples will deal with Who Won the Cross-Country Meet?

#### Objectives

Describes, analyzes and generalizes relationships, patterns, and functions using words, symbols, variables, tables and graphs.

#### Materials

- Overhead transparencies (if examples are to be worked on overhead) for Who Won the Cross-Country Meet? EXAMPLES (See Associated File)
- Who Won the Cross-Country Meet? EXAMPLES (See Associated File)
- Who Won the Cross-Country Meet? WORKSHEET (See Associated File)
- Who Won the Cross-Country Meet? CHECKLIST (See Associated File)

#### Preparations

1. Prepare transparencies (if teacher uses overhead for examples) for Who Won the Cross-Country Meet? EXAMPLES. (See Associated File)
2. Have marking pens (for overhead).
3. Have Who Won the Cross-Country Meet? EXAMPLES (See Associated File) prepared and ready to demonstrate to students.
4. Have enough copies of Who Won the Cross-Country Meet? WORKSHEET (See Associated File) for each student.
5. Have enough copies of Who Won the Cross-Country Meet? CHECKLIST (See Associated File) for each student.

#### Procedures

NOTE: This lesson does not cover patterns, tables and graphs on SSS MA.D.1.4.1.

PRIOR KNOWLEDGE: Students should be familiar with basic operation skills such as addition, subtraction, multiplication, division, exponents, fractions, decimals, solving functions, and the 4-step approach to problem solving.

1. Get students' attention by making the statement, “We are going to determine the winner of a cross-country meet by looking at the way a meet is scored and the position of the runners as they finish.”

2. Ask the students if they have ever been to a cross-country meet. If someone has, have them explain the appearance of chaos at the finish line. If not then the instructor must explain what it looks like with numerous runners crossing the finish line. (It would be good if the instructor could video the finish of a cross-country meet.)

3. Make the following statement, “In cross-country, a team’s score is found by adding the place numbers of the first five finishers. For example, five runners for a team finished 2nd, 6th, 8th, 9th, and 13th. Their team’s score is found as follows: (2 + 6 + 8 + 9 + 13 = 38). The team with the lowest score wins.”

4. Explain the 4-step approach to problem solving. (See Who Won the Cross-Country Meet? EXAMPLES in the Associated File)

5. Work example # 1 from the Who Won the Cross-Country Meet? EXAMPLES. (See Associated File)

6. Work example # 2 from the Who Won the Cross-Country Meet? EXAMPLES. (See Associated File)

7. Emphasize to students the importance of the 4-step approach.

8. Work example # 3 from the Who Won the Cross-Country Meet? EXAMPLES. (See Associated File)

9. Emphasize to students the importance of the 4-step approach.

10. Work example # 4 from the Who Won the Cross-Country Meet? EXAMPLES. (See Associated File)

11. Emphasize to students the importance of the 4-step approach.

12. Distribute the Who Won the Cross-Country Meet? WORKSHEET. (See Associated File)

13. The students correctly use the 4-step approach to problem solving:
a) Explore “Define a variable”
b) Plan “Write a function”
c) Solve “Solve the function and answer the problem”
d) Examine “Check to see if the answer makes sense”

14. The students write their responses on the worksheet showing the 4-step approach to problem solving.

15. The teacher distributes the Who Won the Cross-Country Meet? CHECKLIST (See Associated File) and describes what constitutes an A, B, C, D, and F.

16. Move from student to student observing their work and lending assistance.

17. Students' worksheets are collected and scored. (See the Who Won the Cross-Country Meet? WORKSHEET KEY and CHECKLIST) Grades are posted in the grade book.

18. Students with grades below C will be remediated.

#### Assessments

Use the Who Won the Cross-Country Meet? CHECKLIST. (See Associated File) Grades are assigned for the Who Won the Cross-Country Meet? WORKSHEET and recorded in the grade book. Students who receive a grade below C will be remediated.

#### Extensions

Ask students to pick a team score and then come up with various ways that the members can finish to arrive at that score.