Stacking Toy

Contributed by
Ashlie Arkwright and Macy Reed

Topic: Applying Surface Area and Volume Concepts to Design a 3D Printed Child’s Stacking Toy


Objectives:  During this lesson, students will explore 3D printing by completing a design challenge. Students will use Tinkercad and Cura software programs to design and print a child’s stacking toy. Related mathematical and problem solving objectives include applying an understanding of surface area and volume during the design process.

NGSS Science Standard:

  • MS-ETS1-1: Define the criteria and constraints of a design problem with sufficient precision to ensure a successful solution, taking into account relevant scientific principles and potential impacts on people and the natural environment that may limit possible solutions.

Common Core Mathematics Standards:

  • CCSS.Math.Content.6.G.A.2: Find the volume of a right rectangular prism with fractional edge lengths by packing it with unit cubes of the appropriate unit fraction edge lengths, and show that the volume is the same as would be found by multiplying the edge lengths of the prism. Apply the formulas V = l w h and V = b h to find volumes of right rectangular prisms with fractional edge lengths in the context of solving real-world and mathematical problems.
  • CCSS.Math.Content.6.G.A.4: 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.


  • Enough computers (each preferably with a mouse) with internet access for students to work in groups of two to four students
  • Tinkercad access (internet-based)
  • Cura software installed on each student computer
  • SD cards
  • 3D printer and filament (Note: We use an Ultimaker2 3D printer in our classroom. Procedural changes may need to be made if you use a different type of 3D printer.)

Safety Considerations:  Students should be instructed about potential hazards when using a 3D printer. Since the printer’s nozzle heats up to over 200 degrees Celsius and the platform heats up to over 100 degrees Celsius, students should wear gloves and avoid touching these parts of the printer. In addition, safety glasses should be worn, particularly when removing objects from the printer platform.



  1. Prior to introducing this project, students should have a basic understanding of what 3D printers are and how they can be used to create solutions for a variety of problems, such as designing custom-fit prosthetic limbs for amputees.

  2. It is recommended that you work with your math teacher to teach students the geometric concepts of surface area and volume. At our school, our two sixth grade science and two sixth grade math teachers worked together to implement the project with our entire sixth grade. The math teachers taught students the relevant geometry concepts, and the science teachers instructed students on the 3D printing process and the use of Tinkercad and Cura.


  1. Introduce students to computer-aided design (CAD) software. Explain to students that for this project they will be using Tinkercad, an internet-based CAD software program, to design a 3D model of a child’s stacking toy. Note that other CAD software programs may be used. We prefer Tinkercad because it is internet-based (thus, students may work on their projects at home if they so choose) and free. Additionally, Tinkercad offers numerous tutorials that are appropriate for middle school-aged students to learn the basics of computer-aided design.

  2. Assign groups of two to four students (we assigned groups of three students). Ask each student to create an account on Tinkercad, and then allow one to two class periods for students to work on Tinkercad tutorials. You may choose to assign specific tutorials (“Die from Scratch” is a great choice), or allow students to choose tutorials that they feel are best suited for the design challenge they have been given. Some students will quickly pick up on the skills needed to be successful, whereas others will need help from teachers or other students. Encourage students to work on tutorials at home if they need extra practice.

  3. Once students are feeling confident with their ability to use the Tinkercad program, allow them to begin designing their stacking toys. We asked each team to submit their “Project Design” and “Permission to Construct” worksheets (see attached worksheets) to show their plans for their stacking toys, which we then approved before teams were allowed to start creating the digital versions on Tinkercad. Depending on students’ skill level and their level of experience with CAD software, you may choose how rigorous to make your design constraints. For example, for less experienced students you can instruct them to just make the stacking toy shapes and then they could decorate them by hand with permanent markers. For more experienced students you can ask them to increase the dimensions of their pieces by a certain ratio (e.g., 1:2:3 and then calculate how this would affect the volume of the stacking pieces). For our students, we allowed them the option of decorating the pieces by hand or designing them on Tinkercad, but every team chose the Tinkercad option and was successful with doing so. Although all three stacking pieces can be created on one Tinkercad file, we recommend creating three separate files so that team members can each work on a piece simultaneously and so that the pieces can be printed in different colors, if desired. See the included scoring guide for the specific scoring criteria we used.

  4. Once teams have successfully designed their stacking pieces, they will need to transfer their files from Tinkercad to the Cura software program in order to save the files to the correct format for 3D printing. Instruct teams on how to do this. See the included “What to do when you have successfully created your stacking toy on Tinkercad” handout for specific instructions, and provide a copy of this handout to each team. In addition, provide enough SD cards for the class for teams to save their files for 3D printing. We recommend a minimum of one SD card per 5 teams in order to facilitate this process.

  5. In addition to creating their stacking toy models on Tinkercad and completing the individual and team assignments in their team folder, ask each team create a poster that includes a rationale for their choice of theme and toy, a mock-up drawing of their toy, and a net (labeled with dimensions and surface area and volume calculations for each piece) of their toy.



  6. After all digital models, posters, and assigned handouts are finished, allow class time to conduct a gallery walk and give students the opportunity to provide feedback to other teams about their designs and calculations. We also asked each student to submit an individual “Calculations Worksheet” (see attached) to assess their understanding of the relevant mathematical concepts and to complete a daily journal reflection of their progress for the individual portion of his/her grade.

  7. You may then either choose to print every team’s design, or ask the class to vote on their favorite designs. We recommend the latter option since the time and materials investment involved in printing every project is significant. We gave each student a ballot and asked them to vote on their favorite projects. Since we have two classes of students, each student voted on the projects in the other class to avoid voting for their own projects. We then printed the winning designs (two per class) and held a short “unveiling” ceremony where we brought both classes together, revealed the winners, and presented printed stacking toys to the baby of one of our teachers, who visited school especially for the ceremony. The kids loved this part because they got to see the beneficiary of their hard work actually enjoy the toys they designed.


    stacking toy

Closure:  Wrap-Up Discussion

  1. During this wrap-up discussion, ask students questions such as:  

    • Which aspects of this design challenge were easiest, and which aspects were most difficult?
    • What specific skills did you gain during the course of this design challenge, and where else might you use these skills?
    • How was this challenge similar to and different from design challenges that scientists might face in the real world?
    • Can you give specific examples of problems that could be solved using 3D printers that you thought about during the course of completing this design challenge?

  2. Possible math extension activities include asking students to calculate how many of their group’s toys would fit into a box of a particular size, or asking students to calculate the volume of the smallest possible box in which all pieces of their toy would fit.