## Doctor, Doctor, Give Me the News, I've Got a Bad Case of Loving Math

### Becca Childress

#### Description

Tired of hearing, “When are we ever going to use this again?” Students will use their knowledge of graphing inequalities to solve this real world problem. Students will have to figure how many doctors and nurses can be hired within budget and building constraints

#### Objectives

Uses systems of equations and inequalities to solve real world problems graphically, algebraically, and with matrices.

#### Materials

-Real world worksheet
-Graph paper copied on front and back
-Colored pencils

#### Preparations

1. Prepare transparencies of blank graphs (if a teacher uses an overhead)
2. Have overhead markers in 5 different colors
3. Straight edges for students.
4. Worksheets of real world problem for each student.
5. Copy of full page graph for each student. (Have a graph on both sides of the paper in case of mistake.
6. Have sharpened colored pencils for the students’ use.
7. Copies of the review sheets if you are going to use them.

#### Procedures

Students should have prior knowledge of graphing systems of inequalities and solving systems of inequalities. There are practice worksheets as review.

1. The teacher uses examples of greater than, less than, greater than and equal to, and less than and equal to discuss the different types of inequalities. Be sure to emphasize solid/dashed lines and shading. (Practice Worksheet #1 is graphing inequalities. Practice Worksheet #2 is graphing systems of inequalities). Use the prepared overhead graph transparency.

2. Discuss the problems from the attachments and answer any questions.

3. Pass out the attachment entitled, “Doctor, Doctor, give me the news, I’ve got a bad case of loving math. Write an equation describing the problem.

6. Students use the Doctor, Doctor….. worksheet to write appropriate inequalities for the conditions listed in 1-5. There should be six inequalities. Number 5 has 2 inequalities.

7. Teacher walks around to check the inequalities.

8. Pass out the graph paper.

9. Students label the X axis D (for doctor) and the Y axis N (for nurse). Number both axes in increments of 5. (0, 5, 10…95,100)

10. Pass out the colored pencils

11. Students use one color per inequality that is graphed. Graph the inequalities. Remember to shade.

12. Teacher walks and checks the students as they are graphing the inequalities.

13. When all inequalities are graphed, students find the intersection of the shaded area. Make this a bold color.

14. Students use their graph to find the boundaries (intersection points). There will be 5. (Hint- one of the ordered pairs will have a fraction for the d and n value).

15. Student uses the intersection points to solve the equation they wrote in the 3rd step by substituting the ordered pair for d and n respectfully.

16. After substituting, students will find the minimum cost. The numbers used to solve for this minimum cost will be the number of Doctors and Nurses hired.

#### Assessments

Students use the information given to create a graph and use the graph to solve the real world problem.
Provide corrective feedback as needed. Collect the graphs and check for accuracy.
Criteria Use the checklist to check the students’ work. (see attached)
Students use the created graphs to answer the real world problem

#### Attached Files

Graphing Worksheet 1     File Extension: pdf

Graphing worksheet 2     File Extension: pdf

Assignment Sheet     File Extension: pdf

Checklist     File Extension: pdf