Name ______ ________
Modeling Module (Module M) Culminating Activity: The Benefits of Making Coffee at Home
Citizenship, Personal Finance
PROBLEM SITUATION: ESTIMATING THE COST OF COFFEE
Suppose you are an avid coffee drinker who always buys a cup of coffee on your way to class. You have been considering purchasing a coffee maker for some time now. You would like to make a good financial decision based on how much coffee you drink and the relative price of buying coffee at a coffee shop versus making coffee at home. How much coffee would you need to drink to justify the purchase? In other words, when is it worth it?
How much coffee would you need to drink to justify the purchase of a coffee maker? In other words, when is it worth it?
Part 1: Research
(1) Select a popular coffee maker (Mr. Coffee, Keurig, etc.) and determine the price that it would cost you to buy. Also list where you found the price (so you can cite your sources).
Name of coffee maker: Keurig
Cost: $109.99
Source: Taken directly from the Keurig website: https://www.keurig.com/Home-Coffee-Makers/Keurig®-K-Select®-Coffee-Maker/p/K-Select-Coffee-Maker:Matte%20Black_color
Module M Culminating Activity: Part 1
- Select a popular brand of coffee for your maker above and determine the price that it would cost you to buy. Don’t forget to indicate about how many cups of coffee the package will make. Also list where you found the price (so you can cite your sources).
Name of coffee: The Original Donut Shop Coffee, regular medium roast- Keurig brand
Cost of one package of coffee: 24 count box is $17.49 for a one-time purchase
Number of cups of coffee the package will make: K-cup box of a 24 count of total K-cups. Will make 24 cups of a standard 8 ounce cup of coffee
Source: Taken directly from the Keurig website: https://www.keurig.com/Beverages/Medium-Roast/The-Original-Donut-Shop®-Coffee/p/Original-Donut-Shop-Extra-Bold-Coffee-K-Cup-CP:24_CT
- Select a coffee shop and determine the price that it would cost you to buy a cup of coffee. Don’t forget to indicate what type of coffee you are purchasing (large house coffee, medium latte, small mocha, etc.). Also list where you found the price (so you can cite your sources).
Name of coffee shop: Starbucks
Type of coffee: Grande (Medium) Starbucks Vanilla Blonde Latte
Cost of one cup of coffee: $5.54
Source: Taken directly from the Starbucks website: https://www.starbucks.com/menu/product/2122164/hot?toCart=true
You will need all of this information for the rest of the activity.
M.CA.1 | 2
| Name: |
Modeling Module (Module M) Culminating Activity: The Benefits of Making Coffee at Home
Citizenship, Personal Finance
PROBLEM SITUATION: ESTIMATING THE COST OF COFFEE
Suppose you are an avid coffee drinker who always buys a cup of coffee on your way to class. You have been considering purchasing a coffee maker for some time now. You would like to make a good financial decision based on how much coffee you drink and the relative price of buying coffee at a coffee shop versus making coffee at home. How much coffee would you need to drink to justify the purchase? In other words, when is it worth it?
How much coffee would you need to drink to justify the purchase of a coffee maker? In other words, when is it worth it?
Part 2: Linear Equations
Fill in the information below from Part 1.
Cost of coffee maker: $109.99
Cost of one package of coffee: $17.49
Number of cups of coffee the package will make: 24 cups of coffee
Cost of one cup of coffee at coffee shop: $5.54
- Fill in the table. Use the prices given in Part 1.
| Number of cups (c) | Price for coffee at coffee shop (S) |
| 1 | $5.54 |
| 2 | $5.54 x 2= $11.08 |
| 3 | $5.54 x 3= 16.82 |
| 4 | $5.54 X 4= $22.16 |
| 5 | $5.54 X 5= $27.70 |
| 6 | $5.54 X 6= $33.24 |
| 7 | $5.54 X 7= $38.78 |
| 8 | $5.54 X 8= $44.32 |
| 9 | $5.54 X 9= $49.86 |
| 10 | $5.54 X 10= $55.40 |
- Use 𝑐𝑐 to represent the number of cups of coffee and use 𝑆𝑆 to represent the total cost of purchasing coffee at a coffee shop. Create a linear model to find the total cost of purchasing 𝑐𝑐 cups of coffee shop coffee. Show how you created the linear model (i.e. explain what each part of the model is being used to represent).
SS= cc x 5.54
- Fill in the below table. Use the prices given in Part 1. Make sure to include the price of buying the coffee maker in the table and remember that you cannot purchase individual cups of coffee but you must purchase the coffee in packages:
| Number of cups (c) | Price for coffee at home including price of coffee machine(H) |
| 1 | |
| 2 | |
| 3 | |
| 4 | |
| 5 | |
| 6 | |
| 7 | |
| 8 | |
| 9 | |
| 10 |
- Use 𝑐𝑐 to represent the number of cups of coffee and use 𝐻𝐻 to represent the total cost of purchasing a coffee maker and coffee. Create a linear model to find the total cost of purchasing 𝑐𝑐 cups of coffee and the coffee maker. Keep in mind that you cannot purchase individual cups of coffee but must purchase the coffee in packages. Show how you created the linear model (i.e. explain what each part of the model is being used to represent). Hint: You will need more than one equation.
Module M Culminating Activity: Part 3
| Name: Sarah Schweiner |
Modeling Module (Module M) Culminating Activity: The Benefits of Making Coffee at Home
Citizenship, Personal Finance
PROBLEM SITUATION: ESTIMATING THE COST OF COFFEE
Suppose you are an avid coffee drinker who always buys a cup of coffee on your way to class. You have been considering purchasing a coffee maker for some time now. You would like to make a good financial decision based on how much coffee you drink and the relative price of buying coffee at a coffee shop versus making coffee at home. How much coffee would you need to drink to justify the purchase? In other words, when is it worth it?
How much coffee would you need to drink to justify the purchase of a coffee maker? In other words, when is it worth it?
Part 3: Comparison
- Fill in all the information from Part 2 below. Remember these should be equations. Linear model for total cost for 𝑐𝑐 cups of coffee at coffee shop:
Linear model for total cost for 𝑐𝑐 cups of coffee at home (should include coffee maker and coffee): (Hint: Remember this may require more than one equation.)
- Use the equations above or the tables from Part 2 to graph each of the models. Be sure to include scales and labels on the axes. Let the horizontal axis be the number of cups of coffee purchased and the vertical axis be the total amount of money each cost. Also include a meaningful title for the graph. Make sure to label the two different models.
M.CA.3 | 1
Module M Culminating Activity: Part 3
- Using your graph, ESTIMATE how many cups of coffee you would need to drink at your coffee shop to justify the purchase of a coffee machine. Remember that you cannot purchase a fraction of a cup of coffee nor can you purchase individual cups of coffee at home (coffee comes in packages). Explain how you determined your answer using your graph.
- Use the models from Question 1 to algebraically find how many cups of coffee would you need to drink to justify the purchase of a coffee machine. (Hint: Use your algebraic models to write one equation, using only the variable c, which represents this situation.) How does this answer compare to your answer in Question 3? Remember that you cannot purchase a fraction of a cup of coffee nor can you purchase individual cups of coffee at home (coffee comes in packages). Show your work.
- Explain at least two limitations of the linear models.
- Over-simplifies problems by assuming linear relationship among the variables
M.CA.3 | 2
Module M Culminating Activity: Part 4
Modeling Module (Module M) Culminating Activity: The Benefits of Making Coffee at Home
Citizenship, Personal Finance
PROBLEM SITUATION: ESTIMATING THE COST OF COFFEE
Suppose you are an avid coffee drinker who always buys a cup of coffee on your way to class. You have been considering purchasing a coffee maker for some time now. You would like to make a good financial decision based on how much coffee you drink and the relative price of buying coffee at a coffee shop versus making coffee at home. How much coffee would you need to drink to justify the purchase? In other words, when is it worth it: How many cups of coffee does it take before making it at home becomes cheaper than buying it at the coffee shop?
How much coffee would you need to drink to justify the purchase of a coffee maker? In other words, when is it worth it?
Part 4: Limitations of Linear Models
(1) At the end of Part 3, you were asked to consider some limitations of the linear models. One issue is that a coffee maker will not last forever.
If you were interested in modeling the value of your coffee maker in the future, knowing homemade appliances lose 25% of their value each year, It makes sense to use an exponential model rather than a linear model because… (circle all that apply)
- a linear model would imply that at some point the Keurig machine would have 0, and then negative worth.
- we cannot determine a linear equation without a set of data points.
- the percentage change tells us that we will be multiplying in each step and repeated multiplication is exponentiation.
- the resale value of most products drops sharply after purchase but decreases less and less as time goes on.
- exponentials always increase.
M.CA.4 | 1
Module M Culminating Activity: Part 4
- Write an exponential model to represent the decrease in value of your coffee maker. Show how you created the model (i.e. explain what each part of the model is being used to represent).
- Using your exponential model, approximately how long before your coffee maker will need to be replaced? Assume your coffee maker will need to be replaced when it’s worth approximately 10% of its original value. Explain your calculations and interpret your answer.
- Consider your answers to all four parts of this activity. Type a paragraph that answers the main question. Use the Writing Principle with complete sentences. Remember that the reader should be able to read your paragraph without knowing what the main question is and be able to understand what you are trying to answer. Include enough information to support your answer, including your sources. Type your paragraph below.
How much coffee would you need to drink to justify the purchase of a coffee maker? In other words, when is it worth it?
M.CA.4 | 2
Academic Honesty Statement
By submitting this assessment for grading I am certifying that it is entirely my own work, with any words and/or ideas from other sources properly cited.
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