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.
Rules and Guidelines Activity Sheet
Building Costs, Tax, and Income Activity Sheet
Scoring Activity Sheet
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
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:
first hotel is balanced on the edges of the cubes, rather than the faces.
picked up the second hotel, one cube would be left behind.
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
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.
Make Sure You…Activity Sheet
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
As students do this, walk around the room and make note of
good suggestions. After ten minutes, choose those students to share their
Scoring Excel Spreadsheet
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.
This lesson was recreated with
permission from Fawn Nguyen fawnnguyen.com.
- Formative: while they are working, ask student groups to
“think out loud” as they experiment.
- Randomly check methodology for student groups calculating
- Summative: Have students calculate the profit or loss from
3D pictures of smaller hotels.
- Have students explain how they systematically determined
per-cube costs based on location of each cube in the hotel.
There are lots of ways in which you can adapt this
lesson to fit your students’ levels. Here are a few suggestions:
- Change the number of cubes, as few as 10-15 cubes for
younger kids, and maybe up to 100 cubes for high school students.
- 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.
- Older students can create the spreadsheet; it's
great practice for understanding how cells work and formulating equations.
- Adjust the time for individual and group work based on
- Modify, take away, or add to the rules and guidelines.
- Change any of the costs/income/tax numbers.
- Change how you reward accuracy or penalize mistakes.
- 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).
- 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?"
- 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.
- 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.
Common Core State Standards – Mathematics
Grade 6, Geometry
Represent three-dimensional figures using nets made up of rectangles and triangles, and use the nets to find the surface area of these figures. Apply these techniques in the context of solving real-world and mathematical problems.
Grade 6, The Number System
Fluently add, subtract, multiply, and divide multi-digit decimals using the standard algorithm for each operation.