Grades 9-12
Escape Rooms in the Classroom
Presenter: Andrew Menfi
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In this lesson students interpret key features of graphs for both linear and quadratic functions in the context of total and marginal production. The lesson begins with a short video about a young entrepreneur who designed his own line of bowties. Students then predict the relationship between number of workers and production of bowties. Students test their predictions by participating in a production activity making paper bowties. Next, they sketch graphs of their total and marginal product, and describe the key features of their graphs. The lesson closes with students graphing two datasets and deciding which dataset most realistically describes the relationship between number of workers and production.
Approximately 90 minutes (two class periods steps 1–14 on day one, 15–20 on day two.)
“Success Stories: Mo’s Bows ” video clip from ABC’s Shark Tank Season 6, Week 20.
Figure 1: Graph of Marginal Product for a Manufacturing Firm
Sample answer: in order to evaluate Jeremiah’s plan to double production, we would need to know the marginal product of each additional worker. It is not enough to know total production in order to predict the effect of additional workers. While production may double, the increase in production is not linear; it is more likely quadratic. For Jeremiah this means that doubling workers from three to six may result in less than doubling of output. The reason for this is that increasing one input, in this case workers, while holding the other inputs constant, in this case ovens and other baking equipment, will eventually result in decreasing marginal product. The available space in the ovens, or number of mixers may limit production.
Why is the relationship between labor and marginal output quadratic (all else constant) and not linear? (The law of diminishing marginal returns states that as one input is increased while all other inputs are held constant, the additional output per increase in units of input will eventually decrease. We can explain this by imagining more and more workers trying to use the same amount of capital resources, like scissors or table space. Eventually each worker will be less productive than the previous worker, and as they get in each other’s way, may actually result in negative marginal product.)
In this lesson students interpret key features of graphs for both linear and quadratic functions in the context of total and marginal production. The lesson begins with a short video about a young entrepreneur who designed his own line of bowties. Students then predict the relationship between number of workers and production of bowties. Students test their predictions by participating in a production activity making paper bowties. Next, they sketch graphs of their total and marginal product, and describe the key features of their graphs. The lesson closes with students graphing two datasets and deciding which dataset most realistically describes the relationship between number of workers and production.
(1) Round |
(2) Number of Workers |
(3) Number of Bow Ties Produced in the Round |
(4) Marginal (additional) Bow Ties Produced |
(5) Total number of bow ties produced in all rounds |
1 |
1 |
3 |
3 |
3 |
2 |
2 |
6 |
3 |
9 |
3 |
3 |
7 |
1 |
16 |
4 |
4 |
7 |
0 |
23 |
After you complete your graphs, be prepared to describe your graphs to the class. To help you describe your graphs, answer the questions on Activity 4: Features of Graphs.
Grades 9-12
Presenter: Andrew Menfi
Grades 9-12
Grades 9-12
Presenter: Council for Economic Education
Grades 9-12