LESSON ON Productivity Graphing Linear and Quadratic Functions

Let’s Watch AND CONSIDER THE FOLLOWING Where was Mo producing his bow ties before the factory?   Why did Mo want to move production to a manufacturer like Robert Stuart Inc.?   What do you predict is the relationship between number of workers in the manufacturing facility and the number of bowties produced?

Along the Y- Axis place the output variable: Working with your group members:(4-6 students). Name Your Group (each group is a manufacturer) Draw a graph of your prediction about the relationship between the number of workers in a manufacturing facility and the number of bow ties produced. Along the X- Axis place the input variable: WORKERS Along the Y- Axis place the output variable: NUMBER OF BOW TIES PRODUCED Have each group to describe their group’s graph to the class.

Activity 2: Bow Tie Template 1) Cut out one bow tie Activity 2: Bow Tie Template 1) Cut out one bow tie. 2) Decorate the tie with 6 diagonal stripes in alternating colors of marker/pen. 3) Fold the tabs at the end in to the middle and staple or tape Use the paper bowties to test your predictions

Some Vocabulary that can be discussed: What does the word “Marginal” mean? What do you think the words “Marginal Physical Product” mean?   An equivalent word would be "additional." Something that will be added to whatever was there before. The additional quantity produced when the use of a resource increases by one unit while all other resources are held constant.

Activity 3: 4 Rounds Each group will represent a different bow tie manufacturer One copy per group: Production Recording Sheet In Each round students will have 2½ minutes to “manufacture their bowties

Analyze the data collected What happened to the number of bow ties produced as you added workers?   2. What was the resource that increased by one unit in our bow tie manufacturing?   3. What were the resources that were held constant?   4. Why would an entrepreneur like Mo care about marginal physical product? 5. Why would an entrepreneur like Mo care about the total product produced?

Working in your groups: CREATE TWO GRAPHS One Graph of the relationship between Total Product and Number of Workers Another Graph of the relationship between Marginal Product and the Number of Workers Create these graphs on the back of Activity 3: Recording Sheet.

Analyze the Two Graphs Made Answer the following questions for each of your graphs: a) Label the intercept, maxima, and minima. b) What is the intercept? c) What is the maximum? d) What is the minimum? e) What are the periods where the graph is increasing? f) What are the periods where the graph is decreasing? g) What are the domain and range? How do you know?

Continue to Analyze Information: Consider the following questions: What features of your graphs are similar?  What features of your graphs are different?  What was accurate about your original prediction What parts of your prediction do you need to revise? When you graphed your prediction graph, did you graph total production or marginal product?  Was your prediction linear or non-linear such as a quadratic? How do you know? Was your marginal production graph linear or quadratic? How do you know?

Continue to Analyze Information: Continue to Consider the following questions: g. Why is the marginal product graph not linear? The Law of Diminishing Marginal Returns. h. What was accurate about your original prediction? i. What parts of your prediction do you need to revise?

ACTIVITY 5: PRODUCTION DATA IS IT LINEAR OR QUADRATIC? Activity 5 – this activity uses two datasets. (One is linear and one is cubic, resulting in a constant and quadratic marginal product respectively.) Calculate the marginal product and describe the features of the graph. Decide which of the two graphs is a more realistic representation of production in the real world and explain your reasoning.

CONCLUSION: 1) What is the relationship between the number of workers and amount of a good or service produced?  2) What is the definition of marginal product?  3) What is the law of diminishing marginal returns? 4) Why is the relationship between labor and marginal output quadratic (all else constant) and not linear?

Assessment