## Hotel Snap: Building for Profit

• Lesson
3-5,6-8
3

Students will be required to build a high-profit yielding hotel using snap cubes. Building costs, rules and regulations, taxes, and income are all variables that students will be required to take into consideration.

Thorough preparation in this lesson is crucial in order to maximize student work time. Each group should have three students. Depending on the dynamics of your class, you may choose to pre-select teams or have them choose their own teammates.

Make sure that you have enough materials such that each student has:

• 50 snap cubes (stored in zip bags)
• The Rules and Guidelines Reference Sheet
• Building Costs, Tax, and Income Reference Sheet
• Scoring Activity Sheet (one for each student plus one for each group)

To begin the lesson, tell students that they will be working in teams to see who can build the best hotel. The best hotel will be determined by who can make the highest profit. However, there are certain rules and regulations in how the hotel must be built. Distribute the Rules and Guidelines Activity Sheet and the Building Costs, Tax, and Income Activity Sheet.

Display the Rules and Guidelines Activity Sheet with a document camera, or have students follow along while you review each bullet point as a class. Although there are pictures that demonstrate non-examples, displaying physical models using a document camera may be helpful for visual learners. Either way, be sure to check for comprehension by asking students why each non-example is invalid. Here are the answers:

[The first hotel is balanced on the edges of the cubes, rather than the faces.

If you picked up the second hotel, one cube would be left behind.

There is a room in the center of the first floor that does not have a window.

Lastly, all three examples use fewer than 50 cubes.]

Once you review the rules and guidelines, ask students how profit is calculated. [Profit = Income - Expenses.] Display the Building Costs, Tax, and Income Activity Sheet on the document camera (or have students follow along).  Review with students how the expenses and income will be calculated in this lesson.

Once all the information has been shared with students, check for understanding with a few pre-made smaller examples (hotels that use ~10 cubes). Ask students whether or not each structure will work, and why or why not. If you choose to, one of the mini-hotels could be used to perform a sample profit calculation.

Now, distribute the cubes to each student for individual work. Announce that they have 15 minutes to explore by themselves until they are grouped into teams.  Give them verbal cues such that they have enough time to fill out their Scoring Activity Sheet. While students work, walk around to make sure that they are following all the rules and guidelines.

After 15 minutes, group students into their teams, and give them the following instructions:

“Take your hotel and Scoring Activity Sheet with you to your team. You will have 25 minutes to work. During this time, you need to: (1) share and discuss your individual hotel, (2) choose the best hotel and modify it (if you wish). You are also welcome to start from scratch, but be careful of your time! (3) Use a new Scoring Activity Sheet to calculate your team’s profit. (4) Lastly, you will also need to write down why you built you hotel they way you did on the Activity Sheet.”

These set of directions can be printed distributed (or shown on the projector).

Allow students to begin choosing their group hotel. Monitor the groups, checking for understanding, listening for strategies, and reminding them of the time remaining. Once 25 minutes has passed, ask students to break down the hotels that were not selected, put the cubes back into the zip bags, and return them to the front.

Ask student groups to share their hotel designs, their total profit (including their income & expenses), and why they chose to build the hotel that they did. As students present, you will want to write their total profit on the board for reference. Give each team 5 minutes to present.

After all students have presented, ask students to get back into their groups with their hotel. Ask, “If you could relocate just 5 cubes on your hotel, where would you place them?” Allow ten minutes for each group to brainstorm. They should not change their hotel; this is purely a what-if scenario.

As students do this, walk around the room and make note of good suggestions. After ten minutes, choose those students to share their recommendations.

To conclude this activity, collect groups’ Scoring Activity Sheets, and use the Scoring Excel Spreadsheet to give them their final score. Announce the winner during the next class period.

### Credit

This lesson was recreated with permission from Fawn Nguyen fawnnguyen.com.

Assessment Options

1. Formative: while they are working, ask student groups to “think out loud” as they experiment.
2. Randomly check methodology for student groups calculating profits.
3. Summative: Have students calculate the profit or loss from 3D pictures of smaller hotels.
4. Have students explain how they systematically determined per-cube costs based on location of each cube in the hotel.

Extensions

There are lots of ways in which you can adapt this lesson to fit your students’ levels. Here are a few suggestions:

1. Change the number of cubes, as few as 10-15 cubes for younger kids, and maybe up to 100 cubes for high school students.
2. Also for younger kids, have the Excel file (more on this later) readily available on computers so kids can go back and forth between checking their profit margin and tweaking their hotel design — so no calculations are needed on their part, they just need to be able to know how to count the different types of rooms.
3. Older students can create the spreadsheet; it's great practice for understanding how cells work and formulating equations.
4. Adjust the time for individual and group work based on your expectations.
5. Modify, take away, or add to the rules and guidelines.
6. Change any of the costs/income/tax numbers.
7. Change how you reward accuracy or penalize mistakes.
8. Ask each group to estimate and rank the profit margins of other teams' hotels just by looking at them (like on a -5 to +5 scale, -5 for biggest loss and +5 for biggest profit).
9. Ask, "What if all costs and tax stay the same, but now the incomes for the rooms are all reversed so that 4-window-1-roof earns only $125 while 1-window-0-roof earns$600? How would you build your hotel using the same rules?"
10. If I were to do this with my 6th graders, I'd first have everyone build the same 10-cube hotel with me, and then we'd use this hotel to familiarize ourselves with the different types of rooms and tally them up. We could calculate the costs and income together for practice.

Questions for Students

1. What strategy, if any, did you use while you were working by yourself, in order to decide how to start building a hotel?
2. When you were working as a team, what role did each team member play?
3. What strategy, if any, did your team use to design a hotel before building one?
4. What patterns did you see in arranging the cubes for maximum profit?
5. How did you check your calculations for accuracy, in order to avoid a penalty?

Teacher Reflection

• How difficult was it for students to embrace the task at hand?
• How can the teacher encourage systematic and patterned thinking rather than brute force?
• How well did the student teams work when they came together after individual exploration?
• Were students able to explain the reasoning behind their constructions?

### Learning Objectives

• Students will use Snap Cubes® to construct a model of a “hotel.”
• Identify and use variables such as land cost, and taxes to calculate profit/loss.
• Optimize the values of the set of variables to maximize profit or minimize loss.

### NCTM Standards and Expectations

• Develop and use strategies to estimate the results of whole-number computations and to judge the reasonableness of such results.
• Work flexibly with fractions, decimals, and percents to solve problems.
• Describe sizes, positions, and orientations of shapes under informal transformations such as flips, turns, slides, and scaling.
• Recognize and apply geometric ideas and relationships in areas outside the mathematics classroom, such as art, science, and everyday life.
• Make and test conjectures about geometric properties and relationships and develop logical arguments to justify conclusions.
• Describe location and movement using common language and geometric vocabulary.
• Predict and describe the results of sliding, flipping, and turning two-dimensional shapes.
• Build and draw geometric objects.
• Recognize geometric ideas and relationships and apply them to other disciplines and to problems that arise in the classroom or in everyday life.
• Use geometric ideas to solve problems in, and gain insights into, other disciplines and other areas of interest such as art and architecture.