CULMINATING PROJECT Mission 26 Unit 10
6.RP.A.3 6.NS.B.3 6.EE.B.6 6.EE.C.9 6.G.A.1 6.G.A.2 6.G.A.4 6.SP.B.5

Dream Space Design Lab

6.G.A · 6.EE.C · Unit 10
Today's objective: Apply ratios, area, volume, and expressions to a multi-step design.
Need a hint?
Re-read the problem and underline the numbers and the question. Pick one representation (model, table, or equation), show your steps, and check that your answer makes sense for the situation.

Your team has been hired as junior architects to design a Dream Classroom or Community Space for your school. You have a $5,000 budget and a 40 ft x 30 ft rectangular room. Your design must include furniture layout (area), storage units (volume and surface area), a materials budget (ratios and rates), a data display showing class preferences, and an equation that models at least one relationship. This is your chance to use ALL the math you learned this year in one real project.

Dream Space Blueprint 40 ft 30 ft Group 1 Group 2 Group 3 Reading Nook Storage Unit 4x2x3 ft Maker Station 12x8 ft Teacher Hub Math Domains Used Area (seating: 10x6 ft each = 60 ft²) Triangle Area (reading nook: ½ x 8 x 8) Volume (storage: 4 x 2 x 3 = 24 ft³) Ratios + Equations (budget: c = 150n + 800)

The Design Challenge

Design your dream classroom or community space! Your room is 40 ft x 30 ft (1,200 sq ft total). Your budget is $5,000. Your design must use math from at least 5 different units you studied this year. The final product is a scale blueprint, a budget spreadsheet, a data display, and a 3-minute team presentation.

Required Math Connections

Your design must include at least one calculation from each of these domains:

Area Calculate the floor area of at least 3 zones in your room. (Units 5, 10)
Volume Calculate the volume of at least 1 storage unit or planter. (Unit 5)
Ratios & Rates Use unit rates to compare material costs. (Unit 3)
Equations Write an equation for cost vs. quantity. (Units 6-7, 9)
Data & Statistics Survey classmates and display results. (Unit 8)
Coordinates Use a coordinate grid for the floor plan. (Unit 7)

Multi-Day Project Timeline

  • Day 1: Dream & Plan (Full Lab Cycle) Brainstorm your space. Survey 10+ classmates on what features they want most (reading nook, maker station, gaming corner, music area, etc.). Assign team roles. Sketch rough ideas. Decide your room zones.
  • Day 2: Design & Calculate Draw the scale floor plan on graph paper (1 square = 2 ft). Calculate area of each zone. Calculate volume of at least one 3D object (bookshelf, cabinet, planter). Write your cost equation.
  • Day 3: Budget & Data Research material costs (desks: $150 each, chairs: $45 each, paint: $35/gallon, shelving: $80/unit). Build your budget spreadsheet. Create a data display (bar graph, dot plot, or box plot) from your survey. Make sure you stay under $5,000.
  • Day 4: Polish & Present Finalize the blueprint. Label all measurements. Prepare the 3-minute presentation. Practice answering defense questions. Every team member must speak.

Investigation Guide

  1. Survey your classmates. Ask at least 10 students: "What is the most important feature in a dream classroom?" Give 5 choices. Record and display the data. What type of data display best shows the results? Why?
  2. Sketch the floor plan. Use graph paper. Each square = 2 ft. The room is 20 squares x 15 squares. Draw at least 4 zones (seating, workspace, storage, a special feature). How do you make sure your zones do not overlap and still leave walking space?
  3. Calculate areas. Find the area of each zone. Include at least one non-rectangular shape (triangle, trapezoid, or composite shape). Show that all zones plus walkways equal the total room area (1,200 sq ft). What fraction of the room is seating? What fraction is walkway? Do those ratios make sense?
  4. Design a 3D object. Choose a bookshelf, supply cabinet, or planter. Give it dimensions. Calculate its volume (how much it holds) and surface area (how much material to build it). If you need 3 of these, how do you find the total volume and total surface area?
  5. Write a cost equation. Example: If desks cost $150 each, the equation is c = 150d where d = number of desks. Use the equation to find the cost for different quantities. Which variable is independent? Which is dependent? What is the rate?
  6. Build the budget. List every item, quantity, unit cost, and total. Add everything up. Are you under $5,000? If not, what do you cut or change? What is the ratio of furniture cost to total budget? Is that reasonable?

Language Support: Key Vocabulary

Blueprint
A detailed plan or drawing that shows measurements and layout.
Scale
A ratio that compares a drawing size to real size. Example: 1 square = 2 feet.
Budget
A plan for how to spend money. Lists items, costs, and a total.
Zone
A separate area in the room for a specific purpose (reading, working, etc.).
Unit Rate
Cost for 1 item. Example: $150 per desk. Helps you compare prices.
Composite Shape
A shape made of two or more simpler shapes combined.
Survey
Questions asked to a group of people to collect data about their opinions.
Presentation
Sharing your work with an audience. Explain your design and math clearly.
Sentence Frames for Presentation:

"Our dream space includes ___ because the survey showed ___."

"The ___ zone has an area of ___ ft² because we calculated ___."

"Our storage unit holds ___ ft³, which is enough for ___."

"We stayed under budget by ___. Our total cost is $___."

"The equation c = ___ shows that for every ___, the cost increases by ___."

Sample Calculations

Room: 40 x 30 = 1,200 ft² total

3 Group seating areas: 10 x 6 = 60 ft² each, 3 x 60 = 180 ft²

Reading nook (triangle): 1/2 x 8 x 8 = 32 ft²

Maker station: 12 x 8 = 96 ft²

Teacher hub: 10 x 6 = 60 ft²

Storage area: 12 x 5 = 60 ft²

Walkways & open space: 1,200 - 180 - 32 - 96 - 60 - 60 = 772 ft²

Walkways are 64% of the room -- plenty of space to move!

Bookshelf: 4 ft long x 2 ft wide x 3 ft tall

Volume = 4 x 2 x 3 = 24 ft³ of storage space

Surface area = 2(4x2) + 2(4x3) + 2(2x3) = 16 + 24 + 12 = 52 ft² of material

If we need 3 shelves: Total volume = 3 x 24 = 72 ft³

Item Unit Cost Qty Total
Student desks $150 12 $1,800
Chairs $45 24 $1,080
Bookshelves $80 3 $240
Paint (gallons) $35 6 $210
Beanbag chairs $60 4 $240
Maker supplies -- -- $500
Whiteboard $200 2 $400
TOTAL $4,470
Remaining Budget $530

Equation: Desk cost = 150d. For d desks: c = 150d. If d = 12, c = $1,800.

Survey: What Feature Do You Want Most? Reading Nook 10 votes Maker Station 8 votes Gaming Corner 6 votes Music Area 3 votes Quiet Zone 3 votes n = 30 students surveyed

Reading nook got the most votes (10/30 = 1/3 of students). We included it in our design!

Team Roles (Extended)

Facilitator / Project Manager
Keep the team on the timeline. Check off deliverables each day. Make sure every team member contributes equally. Run the survey on Day 1.
Model Builder / Architect
Draw the scale floor plan. Create the 3D object sketches. Build the coordinate grid layout. Make sure all measurements are labeled.
Precision Checker / Accountant
Verify every calculation. Build the budget spreadsheet. Check that area totals equal room area. Ensure the budget stays under $5,000.
Reporter / Presenter
Create the data display from survey results. Write the presentation script. Make sure every team member has a speaking part. Time the presentation (3 min max).

Day 1: Lab Cycle Timer

Ready
Use on Day 1 for the initial planning cycle.
03:00
  • Read the entire design challenge.
  • Assign roles for the project.
  • Brainstorm: what kind of space do you want?
  • Checkpoint: Does everyone know their role and the 4-day timeline?
  • Write survey questions (5 feature choices).
  • Sketch 2-3 rough floor plan ideas.
  • List the math domains you will use.
  • Start identifying which calculations go where.
  • Checkpoint: Do you have a survey ready and at least one rough sketch?
  • Pick your best design from the sketches.
  • Start assigning zones to the floor plan.
  • Make a list of items you want to buy and estimate costs.
  • Checkpoint: Does your plan have at least 4 zones?
  • Share your plan with the class (quick 30-second pitch).
  • Write down what you need to finish on Days 2-4.
  • Identify who does what tomorrow.
  • Checkpoint: Can every member explain the plan in one sentence?

Challenge Extensions

Gold Level: Add a coordinate grid to your floor plan. Place furniture using ordered pairs. Create a legend so anyone can read your blueprint.
Platinum Level: Compare two different furniture options using unit rates. Example: Store A sells desks for $150 each with free delivery. Store B sells desks for $130 each but charges a $200 delivery fee. Write an equation for each store and find the break-even point.
What If...?
  • What if your budget were only $3,000? What would you cut?
  • What if the room were L-shaped instead of rectangular? How would your calculations change?
  • What if you had to design for 40 students instead of 24?

Presentation Guide (3 Minutes)

Opening: The Vision30 sec

"Our team designed a ___ because our survey showed ___. We used math from ___ different units."

The Blueprint Tour60 sec

Walk the audience through your floor plan. Point to each zone and give its area. Show the reading nook triangle or any non-rectangular shape calculation.

The 3D Object30 sec

Show your bookshelf/cabinet sketch. State the volume and surface area. Explain why these measurements matter (how much it holds, how much material to build).

The Budget30 sec

Show the budget table and equation. State the total and remaining funds. Mention one trade-off your team made.

Closing: What We Learned30 sec

"The most important math we used was ___ because ___. If we had more time, we would ___."

Project Rubric

Category Exceeds (4) Meets (3) Approaching (2)
Math Accuracy All calculations correct with units. Uses 6+ math domains. Most calculations correct. Uses 5 math domains. Some errors or missing units. Uses 3-4 domains.
Blueprint & Scale Floor plan is to scale with grid, all zones labeled with dimensions. Floor plan has most measurements. Scale is consistent. Floor plan is rough or missing some measurements.
Budget Complete budget table with equation. Under $5,000 with trade-offs explained. Budget table complete. Under $5,000. Budget is incomplete or over $5,000 without explanation.
Data Display Survey results displayed with title, labels, and interpretation. Data displayed with title and labels. Data collected but display is incomplete.
Presentation All members speak. Clear explanations with math vocabulary. Under 3 minutes. Most members speak. Explanations are clear. Only 1-2 members speak or math is not explained.
Teamwork All roles fulfilled. Evidence of revision and collaboration. Roles mostly filled. Team worked together. Uneven contribution or roles not clear.

Total possible: 24 points. 20-24 = Exceeds, 15-19 = Meets, 12-14 = Approaching, Below 12 = Not Yet.

Defense Preparation

  1. How did your survey data influence your design? "The survey showed that ___ was the most popular, so we included ___."
  2. Show one area calculation and explain why it matters. "The ___ zone is ___ ft² because we calculated ___. This matters because ___."
  3. What equation did you use and what does each part mean? "Our equation is c = ___, where ___ represents ___ and ___ represents ___."
  4. How did you stay under budget? What trade-offs did you make? "We chose ___ instead of ___ because ___. This saved us $___."
  5. What math skill from this year was most useful for this project? "The most useful skill was ___ because without it we could not have ___."

Exit Product: Final Deliverables

Your team submits a project folder with:
  • Scale floor plan (graph paper or digital) with all zones labeled
  • Area calculations for at least 4 zones (including one non-rectangle)
  • Volume and surface area of at least 1 storage/furniture item
  • Cost equation with table showing at least 3 input-output pairs
  • Budget spreadsheet with all items, quantities, and totals (under $5,000)
  • Survey data display (bar graph, dot plot, or box plot) with labels
  • 3-minute team presentation where all members speak
Team Self-Assessment:
  • We used math from at least 5 different units
  • Every calculation has correct units (ft², ft³, $)
  • Our budget is under $5,000
  • Our data display has a title, labels, and interpretation
  • Our floor plan is to scale and labeled
  • Every team member contributed and can explain the math
  • We can answer 3+ defense questions with evidence
Individual Reflection (each student writes):
  • "The math concept I used most was ___"
  • "One thing I learned from my teammates was ___"
  • "If I did this project again, I would change ___"

Work Space

Survey Data:



Floor Plan Sketch:




Area Calculations:



Volume / Surface Area:



Budget Table:



Equation:


Presentation Notes: