Tinkercad Volume Project: A 3D Design Lesson on Composite Solids

Engage students with this project-based math lesson plan. Using the free 3D design tool Tinkercad, learners will calculate the volume of rectangular prisms and composite solids to design and build a creative 3D model that meets specific mathematical criteria.

Create Your Own Custom Lesson Plan
PDF

Lesson Plan: Beast Architect's Lair Design Challenge

Materials Needed:

  • Computer with internet access
  • A free Tinkercad account (autodesk.com/tinkercad)
  • Beast Academy Guide & Practice Book 5D, Chapter 12: 3D Solids
  • Pencil and paper (or a digital notepad) for calculations
  • Calculator (optional, for checking work)

1. Learning Objectives (The Goal)

By the end of this lesson, you will be able to:

  • Calculate the volume of rectangular prisms and complex 3D shapes made from them (composite solids).
  • Apply volume formulas to a creative design project.
  • Design a multi-part 3D model in Tinkercad that meets specific mathematical requirements.
  • Clearly explain and document the mathematical process behind your creative design.

2. Warm-Up: Volume Refresher (15 minutes)

Let's get our brains warmed up for 3D thinking!

  1. Review the Formulas: Quickly read through the Beast Academy Guide 5D, Chapter 12 pages on volume. Pay special attention to the formula for the volume of a rectangular prism: Volume = length × width × height.
  2. Practice Problem: On paper, solve Practice 12A, problem #4 from the Beast Academy book. This problem involves finding the volume of a composite solid (a shape made of multiple rectangular prisms). Think about the two main strategies:
    • Addition: Breaking the shape into smaller, simpler prisms and adding their volumes together.
    • Subtraction: Imagining a larger, complete block and subtracting the volume of the "missing" piece.
  3. Check Your Work: Confirm your answer in the back of the book. If you got stuck, re-read the examples of the addition and subtraction methods. The goal is to feel confident with these two strategies.

3. Guided Exploration: Tinkercad Basics (20 minutes)

Now, let's move from the page to the digital world. We'll learn the essential tools for a Beast Architect.

  1. Log in to Tinkercad and create a new "3D Design."
  2. Master the Basics:
    • Create a Shape: Drag a "Box" from the right-hand menu onto the Workplane.
    • Change Dimensions: Click on the box. You'll see white and black squares (handles). Click a white corner handle to see the length and width dimensions appear. Click on a number and type a new value (e.g., change it to 40mm long and 30mm wide). The top center handle controls the height. Let's imagine 1mm in Tinkercad = 1 unit from our math problems.
    • Calculate Volume: If your box is 40mm x 30mm x 20mm, what is its volume in cubic mm? (Answer: 40 * 30 * 20 = 24,000 cubic mm).
    • Combine Shapes: Drag a second box onto the workplane and move it so it overlaps with the first. Select both shapes (drag a selection box over them) and click the "Group" button in the top-right menu. You've just created a composite solid!
    • Create Holes: Drag a "Hole" box (the striped one) and place it inside your solid shape. Select both and click "Group." You've just used the subtraction method to cut a piece out of your shape!
  3. Experiment: Spend a few minutes playing with these tools. Combine shapes, make holes, and change dimensions. Get comfortable building things.

4. Main Activity: The Beast Architect's Design Challenge (60-90 minutes)

Your Mission: The creatures from Beast Academy need a new custom lair, and you've been hired as the lead architect! Your task is to design a lair for a beast of your choice using Tinkercad. However, there are strict building codes you must follow.

The Building Codes (Project Requirements):

  1. Total Volume: The final lair must have a total volume between 75,000 and 80,000 cubic units (mm³). You must prove this with your calculations.
  2. Multiple Rooms/Sections: The lair must be a composite solid, made of at least 3 different rectangular prisms joined together. (Think: a main hall, a sleeping area, and a tower).
  3. A Window or Tunnel: The lair must include at least one "hole" created using the subtraction method. This could be a tunnel through a wall or a window.

Your Design Process:

  1. Step 1: Plan on Paper. Before you build in Tinkercad, sketch a rough design for your lair. Label the different parts (e.g., "Main Hall," "Tower"). Assign target dimensions (length, width, height) to each part.
  2. Step 2: Calculate As You Go. On your paper, create a "Beast Architect's Report." For each part of your lair, write down its dimensions and calculate its volume.
    Example Report Section:
    • Main Hall: 50 x 40 x 20 = 40,000 mm³
    • Tower: 20 x 20 x 50 = 20,000 mm³
    • Entryway: 15 x 20 x 15 = 4,500 mm³
    • Sub-Total Volume: 40,000 + 20,000 + 4,500 = 64,500 mm³
    • Hole (Tunnel): - (10 x 10 x 15) = -1,500 mm³
    • Total Volume: 64,500 - 1,500 = 63,000 mm³ (Oops, too small! I need to adjust my design.)
  3. Step 3: Build in Tinkercad. Use your plan and calculations to build the lair in Tinkercad. Adjust the dimensions of your shapes digitally to match your plan. Group them together as you go.
  4. Step 4: Refine and Finalize. This is a creative math puzzle! If your total volume is too high or too low, go back to your design. Do you need to make a wall taller? A room wider? A tunnel bigger? Keep adjusting your plan and your Tinkercad model until you meet the 75,000-80,000 cubic unit requirement.

5. Assessment & Wrap-Up (15 minutes)

To complete your project, present your findings. This is your chance to show off your brilliant design and your sharp math skills!

  1. Final Tinkercad Model: Make sure your final design is grouped into a single object. Give it a creative name!
  2. Final Architect's Report: Your paper (or digital doc) should be neat and show the final calculations for each part, the subtracted hole, and the final total volume that meets the requirement.
  3. Show and Tell: Explain your design.
    • What beast is this lair for? What are the creative features?
    • Walk through your Architect's Report. How did you calculate the volume of each part?
    • What was the biggest challenge? How did you solve it? (e.g., "My first design was too small, so I increased the height of the main hall by 10 units, which added 10,000 cubic units to my total.")

6. Extension & Further Challenges (Optional)

Feeling like a master architect? Try one of these optional challenges:

  • The Paint Job: Calculate the surface area of your lair. This would tell you how much paint you'd need. Research the formula for surface area and add this calculation to your report.
  • Complex Shapes: Add a new room using a different shape, like a Cylinder or a Wedge. You'll have to research the volume formulas for these shapes!
  • Budget Constraints: Imagine solid parts cost $2 per cubic unit and empty space (holes) costs $0. Give yourself a budget of $155,000 and try to get as close as you can without going over.