Name: ______Class: ______Student #: ______
Task: A new pizza restaurant is opening up in Shanghai. The store management is trying to figure out how much of a profit it can make from each individual order. Help them figure out a way to find the cost. It is essential you show as much of your work as possible!
When making and delivering a pizza there are three things to consider as seen below. When you determine the equations for these three things, make sure to put it in algebraic form and use product notation!
- The size (area) of the Pizza in terms of cm2.
- The weight (kg) of toppings on a pizza.
- How far (distance) the deliveryman must travel to deliver the pizza in km.
This assessment will be graded on criterion B, C, and D.
Expectations for each criterion is as follows
Criterion B (Investigating Patterns)
· Understand the problem, select, and apply a mathematical problem solving technique
· Describe the pattern between variables
· Workout a general formula for patterns.
· Draw a conclusion and make predictions from findings.
· Justify the formulas completely using logical arguments.
Grade: ______(Maximum: 8)
Criterion C (Communication in Mathematics)
· Uses algebraic form and notation
· Uses formulas, diagrams, tables, and graphs, for representation to communicate his/her understanding of the problem and uses them accurately.
· Student moves effectively through different forms of representation
· Presents the report of investigation in a coherent manner by logically explaining and reasoning the calculations.
Grade: ______(Maximum: 6)
Criterion D (Reflection in Mathematics)
· Explain why the results are correct and make sense in context to the problem.
· Explain the importance to their findings.
· State and justify the degree of accuracy of their results where appropriate.
· Suggests improvement to the methods wherever applicable.
Grade: ______(Maximum: 6)
Teacher’s comments: ______
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1. The size of the Pizza in terms of area (cm2). If there is an initial fee to make the pizza of 9RMB and it costs an extra 4RMB for every cm2 in additional size (a), what is the equation to determine cost (C1)?
2. The weight (kg) of toppings on a pizza. On each pizza you can get a variety of toppings like cheese, peperoni, pineapple, mushrooms, etc. Some toppings are heavier than others, so the following table was created to determine cost based on weight (w) of the toppings. Use the table to find the equation to determine cost (C2).
Weight (kg) / 2.5 / 2.75 / 3 / 3.25 / 3.5Cost (RMB) / 12.5 / 13 / 13.5 / 14 / 14.5
3. How far (distance) the deliveryman must travel to deliver the pizza. A business graph was made to determine how much it would cost in terms of distance. Use the graph to determine an equation based on distance (d) and cost (C3).
a. Setup an equation that can determine the total cost of making and delivering a pizza.
b. If a student at school made an order for a pizza that was…
-25cm2 in area
-weighed 1.75kg
-and the school was 2.75km away
how much did the student pay for the pizza?
c. Choose any of the three equations you found and explain why it works. Use mathematical words as much as possible.
d. Draw a graph to represent either pattern 1 or pattern 2 from the investigation. (Your choice).
*You only need to graph a few points!
**Make sure to write the coordinates next to each point you graph.
Reflection
You must answer the questions in complete sentences. Not doing so will hurt your grade!!! Try writing more than 1 one sentence.
1. Is there any way that student might be able to save money? Try thinking of a way and explain it.
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2. Why do you think it was important for the pizza restaurant to make equations for how things cost?
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3. How do you know the equations you found were correct?
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4. What mistakes did you make and how can you prevent them from happening next time? (Complete this section AFTER the investigation is graded and handed back to you)
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