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Launch

Explain to students that the cost of food is only one expense for running a restaurant. Ask students to brainstorm other things restaurant owners need to spend money on. From their list, decide as a class which of these depend on the number of meals ordered and which are ongoing expenses. Tell students that restaurants charge more for their meals than just the cost of the ingredients in order to pay for these expenses. This increase in price is called “markup.”

Tell students they will predict if a restaurant will make a profit. Display the Info Gap graphic that illustrates a framework for the routine for all to see.
Remind students of the structure of the Info Gap routine, and consider demonstrating the protocol if students are unfamiliar with it.

Arrange students in groups of 2. In each group, give a problem card to one student and a data card to the other student. After reviewing their work on the first problem, give students the cards for a second problem and instruct them to switch roles.

Action and Expression: Internalize Executive Functions. Check for understanding by inviting students to rephrase directions in their own words. Keep a display of the Info Gap graphic visible throughout the activity or provide students with a physical copy.
Supports accessibility for: Memory, Organization

Activity

None

Your teacher will give you either a problem card or a data card. Do not show or read your card to your partner.

If If your teacher gives you the problem card:

Silently read your card and think about what information you need to answer the question.
Ask your partner for the specific information that you need. “Can you tell me ?”
Explain to your partner how you are using the information to solve the problem. “I need to know because . . . .”

Continue to ask questions until you have enough information to solve the problem.
Once you have enough information, share the problem card with your partner, and solve the problem independently.
Read the data card, and discuss your reasoning.

If your teacher gives you the data card:

Silently read your card. Wait for your partner to ask for information.
Before telling your partner any information, ask, “Why do you need to know ?”
Listen to your partner’s reasoning and ask clarifying questions. Only give information that is on your card. Do not figure out anything for your partner!

These steps may be repeated.
Once your partner says they have enough information to solve the problem, read the problem card, and solve the problem independently.
Share the data card, and discuss your reasoning.

Student Response

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Building on Student Thinking

2.2

Activity

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

MLR8: Discussion Supports Notice and Wonder

Materials

None

Activity Narrative

The purpose of this activity is for students to write and solve equations as a strategy to compare the projected costs of using reusable versus disposable plates and forks. First, students examine dot plots representing the average number of customers served per day at a sample of restaurants to make a prediction about how many customers they might serve per day. Then, students see that the cost of buying disposable plates and forks can be modeled with a proportional relationship, while the cost of buying and washing reusable plates and forks can be modeled with an equation in the form . Finally, students construct arguments about which type of plates and forks would be better depending on the number of days the restaurant is open (MP3).

Launch

Tell students to close their books or devices (or to keep them closed). Display the dot plots about the number of customers served per day for all to see. Give students 1 minute of quiet think time and ask them to be prepared to share at least one thing they notice and one thing they wonder. Record and display responses without editing or commentary for all to see. If possible, record the relevant reasoning on or near the dot plots.

Students may notice:

Many of the fast-food restaurants serve more customers per day than the full-service restaurants.
There is a lot of overlap between the two distributions, from 300 to 600 customers.

Students may wonder:

Were the restaurants included in the samples selected at random?
Is there a meaningful difference between the average number of customers served at these two types of restaurants?
About how many customers would my restaurant serve per day?

If the difference in the number of customers at each type of restaurant does not come up during the conversation, ask students to discuss this idea.

Tell students to open their books or devices and give students quiet work time followed by whole-class discussion.

Activity

None

A sample of full-service restaurants and a sample of fast-food restaurants were surveyed about the average number of customers they serve per day.

Two dot plots.

How does the average number of customers served per day at a full-service restaurant generally compare to the number served at a fast-food restaurant? Explain your reasoning.
Estimate how many customers you think your restaurant will serve per day. Explain your reasoning.

Here are prices for plates and forks:

	plates	forks
disposable	165 paper plates for \$12.50	600 plastic forks for \$10
reusable	12 ceramic plates for \$28.80	24 metal forks for \$30

Using your estimated number of customers per day, write an equation for the total cost, , of using disposable plates and forks for every customer for days.
Is proportional to ? Explain your reasoning.
Use your equation to predict the cost of using disposable plates and forks for 1 year. Explain any assumptions you make with this calculation.

1. How much would it cost to buy enough reusable plates and forks for your predicted number of customers per day?
2. If it costs \$10.75 a day to wash the reusable plates and forks, write an expression that represents the total cost, , of buying and washing reusable plates and forks after days.
3. Is proportional to ? Explain your reasoning.
4. How many days can the reusable plates and forks be used for the same cost that you calculated for using disposable plates and forks for 1 year?

Activity Synthesis

Ask the class how many days they can use the reusable plates and forks for the same cost as using disposable plates and forks for 1 year. Select students to share what this reveals about the situation. (If their answer is greater than the number of days they planned for their restaurant to be open during the year, then this means that buying and washing reusable plates and forks is cheaper than using disposable plates and forks.)

Select students to share their reasoning about whether or not there is a proportional relationship between the cost of using disposable or reusable and the number of days.

Students might share the following ideas:

The relationship for the cost of using disposable looks like it is proportional, because it is written in the form .
- The relationship for the cost of using disposable is not exactly proportional, because the equation is assuming an average number of customers per day, and in real life the restaurant serves a different number of people each day.
The relationship for the cost of using reusable is not proportional because:
- There is a start-up cost of buying the reusable plates and forks.
- The equation cannot be written in the form . There has to be a term that is added that represents the start-up costs.
- If the relationship was graphed, it would not go through the origin, but it would cross the y-axis at a point that represents the start-up costs.

MLR8 Discussion Supports. Display sentence frames to support students’ reasoning about whether there is a proportional relationship between the cost of using disposable or reusable and the number of days: “The relationship between the cost of using disposable dishes is/is not proportional because .” “I agree because . . . .” “I disagree because . . . .”
Advances: Speaking, Conversing