Modeling Prompt 9

Planning a Concert

Algebra 1

Standards Addressed

Student Handouts

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In-Class Launch

Ask students if they have been to a concert or a similar event before. Invite students to share what the experience was like. For example, where was the event? Were there a lot of other people? Who was performing?

Then ask students what they would need to think about if they were planning a concert. After some quiet think time, ask students to share their ideas with a partner. Then invite students to share their thoughts, and record the ideas for all to see. Possible responses include:

Which band or performer to have
How much to charge for tickets
Whether to charge for parking
How many people to expect
Where to have the concert
What kinds of food and drink to sell
Whether to sell backstage passes or other special add-ons

For each item that students suggest, ask whether it represents something that costs the organizers money or makes the organizers money. Some items may do both—for example, the organizers need to pay the band, but the band is also the reason the audience is paying money for tickets. In this case, the band probably brings in more money than they are paid so, overall, paying the band is not a cost. Remind students that profit is the amount the organizers make minus the amount they pay out. Tell students that, in this task, they plan a concert themselves.

Task Statement 1

Teacher Instructions

Students need to think carefully about the survey results in order to use them to decide on a ticket price. A helpful first step is to figure out how many of the people surveyed would buy a ticket for \$10, how many would buy a ticket for \$20, and so on. Students should remember that if someone says, for example, that they would pay \$30, this means they also would buy a ticket if it was less than \$30. Students graph the number of people, willing to buy a ticket for each price, to see how the ticket price affects the number of tickets bought, and they find a linear equation that describes how the number of tickets depends on the price. This helps them create an equation for the amount of money the charity makes by selling tickets at each price, as shown in the sample response.

The amount of detail students put into their plan is limited only by the amount of research they are willing to do. To find a place to have the concert, students search terms such as "rent event space," and search engines will show nearby venues. If students have trouble finding local spaces, they can pretend the concert is in the nearest large city instead.

A charity is raising money by having a concert. You are helping to plan the concert. You need to decide where the concert should take place and how much the tickets should cost. You also need to predict how much profit the charity makes from the concert.

The charity collected data about ticket prices. They chose 100 people at random and asked them, “What is the most that you would pay for a ticket to a charity concert?” Here are the responses:

ticket price (\$)	number of people who would pay this amount
10	15
20	22
30	13
40	15
50	17
60	15
65	3

Here are some questions to guide you as you make your plan:

Based on the information from the survey, how much should tickets cost?
What kind of performer do you want to have at the concert—a local band? A famous singer? An orchestra? A “battle of the bands,” featuring many different groups? Well-known performers may draw a larger crowd, but they also may charge more money. Research the current rates of different performers.
Research possible concert venues. How much would they cost to rent, and how many people can they hold?
If the tickets are sold at the price you recommend, which venue creates the most profit?
Should the charity also sell items at the concert, such as food or T-shirts? If you think so, recommend this also to the charity, and predict how much profit they’ll make.

Create a presentation to explain your plan and your reasoning to the charity’s directors. Include an estimate of the costs and the profit.

Task Statement 2

Teacher Instructions

Although this version of the task gives students some guidance about how to decide on a ticket price, using the survey information, they have not done this sort of work before and may struggle. If they are unsure how to begin or how the hints are supposed to help, try asking them to look at problems they have seen before that involve equations for income or profit. These equations can be factored into the form $x(\text-ax+b)$. Ask students how this relates to the fact that $\text{amount of money made}=\text{price}\boldcdot \text{number of things sold} $. (The price is $x$. The number of things sold is a linear equation that depends on $x$, because the more something costs, the fewer people buy it.)

The amount of detail students can put into their plan is limited only by the amount of research they are willing to do. To find a place to have the concert, students search terms such as "rent event space," and search engines will show nearby venues. If students have trouble finding local spaces, they can pretend the concert is in the nearest large city instead.

The charity has collected some data about ticket prices. They chose 100 people at random and asked them, “What is the most that you would pay for a ticket to a charity concert?” Here are the responses:

ticket price (\$)	number of people who would pay this amount
10	15
20	22
30	13
40	15
50	17
60	15
65	3

You can use this information to find out which ticket price brings in the most money. Here is how:

First, figure out how many people would buy a ticket for \$10, how many would buy a ticket for \$20, and so on.
Then create a graph with the ticket price as the independent variable and the number of people who buy tickets as the dependent variable. Plot the points you found in the first step, and then find a linear equation that shows how the number of people depends on the ticket price.
The amount of money that the charity makes from ticket sales is the ticket price multiplied by the number of people who buy tickets. Use the linear equation you found to create a quadratic equation that shows how the ticket price affects the amount of money the charity makes from ticket sales.

After you have decided on a ticket price, here are some other questions to think about:

What kind of performer do you want to have at the concert—a local band? A famous singer? An orchestra? A “battle of the bands” featuring many different groups? More famous performers may draw a larger crowd, but they also may be paid more. Research the current rates of different performers.
Research possible concert venues. How much would they cost to rent, and how many people can they hold?
If the tickets are sold at the price you recommend, which venue creates the most profit?
Should the charity also sell items at the concert, such as food or T-shirts? If you think so, recommend this also to the charity, and predict how much profit they’ll make.

Create a presentation to explain your plan and your reasoning to the charity’s directors. Include an estimate of the costs and the profit.

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Planning a Concert

Standards Addressed

HSA-CED.A.2

HSA-REI.B.4

HSN-Q.A

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Task Statement 1

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Audience

Assessment Access

Planning a Concert

Standards Addressed

HSA-CED.A.2

HSA-REI.B.4

HSN-Q.A

Student Handouts

In-Class Launch

Task Statement 1

Teacher Instructions

Task Statement 2

Teacher Instructions

Prompt 9

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Lift Analysis ⓘ

Lift Analysis

Lift Analysis