## Snap Hotel

Sometime ago I stumbled on an amazing lesson plan from Fawn Nguyen where students design a hotel using unifix cubes.^{[6]}NCTM loved this lesson so much that they put it on their illuminations website. Also, it sounds like Andrew Stadel has been involved with this, so I want to give him his props as well. I loved the idea of the lesson, but it didn't really overlap with the content I was covering in fifth grade. Now that I am teaching sixth grade and the content I cover aligns with the project, the lesson is on!

**Background Knowledge**

My sixth graders are finishing up a unit on 2D and 3D measurement. Here's a quick hit list of what was covered earlier in the unit: units; iteration; area and perimeter of rectangles, triangles, parallelograms, and different polygons that can be decomposed; measuring angles with angle rulers; interior angle sums; exterior angle sums; non-polygons vs. simple polygons vs. complex polygons; concave vs. convex; regular vs. irregular; surface area; volume; nets; polyhedra; prisms; and pyramids. Outside of this unit they have covered fraction operations, but not operations with decimals, percents, or integers.

While we tackled the 2D topics in depth, I am beginning this project after only about three 45 minute class periods exploring 3D shapes and properties. The idea is that, before this project, my students have some basic understanding of what surface area and volume represent and can find those properties for a given rectangular prism. Though not all can do so easily or consistently.

**Basics of the Hotels**^{[7]}I have modified this pretty extensively from Fawn's set up. She had a percentage tax structure that my students do not have the background to make use of. The room conditions and values, however, are copied and pasted straight from her website.

The students will be designing a hotel which is constructed out of unifix cubes. The goal is to construct a hotel with greatest value possible. A hotel's value comes from the number of rooms it has and the quality of each room. Each room is represented by one unifix cube. A room's value increases when more of its sides are open and when it has a roof (no cube directly above it):

Room Conditions |
Value |

4 windows, 1 roof | $600 |

4 windows, 0 roof | $500 |

3 windows, 1 roof | $300 |

3 windows, 0 roof | $250 |

2 windows, 1 roof | $200 |

2 windows, 0 roof | $175 |

1 windows, 1 roof | $150 |

1 windows, 0 roof | $125 |

We all know that running a business is not all profit. So, many aspects of the design and construction process come with costs. First, the students need to buy the cubes (raw materials). The first 10 cubes they purchase cost $5 each, the next 10 are $10 each, the next 10 are $20, and the price continues to double for every 10 cubes that are purchased.^{[8]}This is supposed to simulate the idea of supply and demand and limit the total number of cubes they can reasonably purchase. The most profit that can come from a single cube is $600 but the 81st cube they purchase will cost $640. Additionally, students have to purchase the land the hotel rests on. Every unit of land the hotel occupies costs $400.^{[9]}No more than 60 units of land can be purchased. Finally, there is a tax of $500 per floor above the 6th floor.^{[10]}In general, I wasn't sure where the students' designs would head, so I put it some natural barriers to keep them from becoming too massive.

Finally, to simulate the nature of government bureaucracy, I added some building requirements. Each hotel must have a 12 cube rectangular lobby on the ground level, and 6 units of land must be left open as parking structure. I presented this information in the form of a government regulations handout and asked the students to parse it on their own. I am tweaking it based on their feedback, so I will share that document in a later post. Shoot me a note on twitter if you just can't wait.

**Project Structure**

I expect the project will take about six classes to complete. It could probably be finished in as few as four, but I want to mix in a few other things. First, I want to use the project as an opportunity to learn some basic spreadsheet skills. During the beginning of this project, their homework is going to be to write some equations in google spreadsheets.

I am having students work on their own to begin the project. I am giving them two classes to parse rules and regulations and then construct a "rough draft" hotel of 30 cubes or less. I am going to have them use this "rough draft" to practice calculating the value using a spreadsheet template I made. Then, finally, I will put them into mixed-ability groups and have them work on their final hotel and supporting documents.

Each group will turn in a final hotel design and completed budget spreadsheet which will include finding the volume and surface area of the hotel. I will also have each group member complete a separate reflection that will force some meta-cognition.

I'll share more as we go. This is going to be fun!

**Update 2/6/16: **I posted about how the project was going.