3D Printing in The Classroom: Matter and Shape

Integrate geometry and physics by exploring form, volume, density, and weight in a problem-based scenario.


Students who participate in this project will gain hands-on experience using mathematical models to predict the weight, volume, and density of an undefined quantity of pre-defined substances, and will have the opportunity to design a rocket fuel tank for NASA. Drawing from both geometry and physics, this project requires participants to conduct scientific investigation to determine the values for specific variables, then employ geometric formulas in order to hypothesize either the volume, density, or weight of a particular quantity of a substance.


1) Explain volume formulas and use them to solve problems

CCSS.MATH.CONTENT.HSG.GMD.A.1 - Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid, and cone. Use dissection arguments, Cavalieri's principle, and informal limit arguments.

CCSS.MATH.CONTENT.HSG.GMD.A.2 - Give an informal argument using Cavalieri's principle for the formulas for the volume of a sphere and other solid figures.

CCSS.MATH.CONTENT.HSG.GMD.A.3 - Use volume formulas for cylinders, pyramids, cones, and spheres to solve problems; visualize relationships between two-dimensional and three-dimensional objects

CCSS.MATH.CONTENT.HSG.GMD.B.4 - Identify the shapes of two-dimensional cross-sections of three-dimensional objects, and identify three-dimensional objects generated by rotations of two-dimensional objects.

2) Modeling with Geometry

CCSS.MATH.CONTENT.HSG.MG.A.1 - Use geometric shapes, their measures, and their properties to describe objects (e.g., modeling a tree trunk or a human torso as a cylinder).

CCSS.MATH.CONTENT.HSG.MG.A.2 - Apply concepts of density based on area and volume in modeling situations (e.g., persons per square mile, BTUs per cubic foot).

CCSS.MATH.CONTENT.HSG.MG.A.3 - Apply geometric methods to solve design problems (e.g., designing an object or structure to satisfy physical constraints or minimize cost; working with typographic grid systems based on ratios).

Tools & Materials:

  • Dremel 3D45 3D Printer (or comparable 3D printer).

  • Dremel PETG filament material (or comparable material).

  • Digital scale capable of measuring up to one hundredth of a gram (for example, a one-dollar bill should read “1.00” or “1.00 g” when placed onto the scale.

  • Graduated cylinder measuring at least 500 cubic centimeters (cc) in increments of 50 cc or less (one per student or pair of students).

  • Instrumentation used for placing liquid into the 3D-printed shapes (e.g. teaspoon or baster).

Click the button below to download this lesson plan.

3 Reasons to Use a 3D Printer in Your Classroom

I get incredibly excited whenever I see new examples of educators using makerspace tools, such as 3D printing, as a teaching aid — not because I believe that more technology (or more advanced technology) is inherently better for all students. After all, a 3D printer cannot drag a classroom into the 21st century on its own, nor can it magically reconfigure education policy to resolve systemic issues related to school funding. What a 3D printer can do, however, is transform the way educators teach and the way students approach learning. If you teach geometry or introductory physics and are interested in incorporating 3D printing into your classroom, be sure to download our free “Matter and Shape” lesson, which includes 3D files, objectives, an overview, concept-checking questions, sample questions, a cheat-sheet for instructors, and more! This lesson was made possible by Dremel Digilab.

#1 - Hands-on, experiential learning can play a democratizing role in education.

Whether it is a district-wide effort to establish a makerspace or a single teacher creating their own lessons to be used with a 3D printer purchased out-of-pocket, integrating 3D printing into the classroom helps students develop a more tactical, personal relationship with the content they’re expected to learn. Our best students have gotten good at learning things by consuming information from books, screens, following precise instructions, and answering test questions, at following along precisely with their teachers’ expectations; meanwhile, a significant portion of students in every classroom struggle to demonstrate mastery not because they’re not smart enough, but because they struggle to form a meaningful connection with what they’re learning, often because they play the role of passive recipient rather than active participant. By using 3D printing to make everyday classroom activities more tactile and experiential, we provide our students with newer, more exciting ways to engage with the same old content. More importantly, 3D printing makes it easier to provide more avenues toward understanding and mastery.

#2 - Personalized, open-ended lessons can elicit greater student engagement.

With the exception of basic arithmetic, having every single student follow the same steps in order to achieve the same result is not good for student engagement. If every single aspect of a lesson or project has already been spelled-out for the student and they must simply follow along a predetermined path, the classroom becomes a little less colorful and students become a lot less engaged. Alternatively, engagement levels soar when students are given the opportunity to make a project their own. Thankfully, 3D modelling and 3D printing offer countless opportunities to do so. Incorporate a little bit of mystery and an abundance of student choice in your next lesson, and your students will likely thank you with better attitudes, better classroom behavior, and higher rates of retention.

#3 - 3D printing makes it easy to incorporate Problem-Based Learning into classroom instruction.

To make this point clear, let’s consider the traditional word problem. Can you remember being in high school and getting excited to solve a word problem in a textbook? If you can, consider yourself lucky. Traditional word problems often posit what-if scenarios that place students on the sidelines rather than at the center of the situation and, in doing so, they can fail to authenticate the problem and the urgency with which the students should solve it. As an example, consider the inner voice of the student in response to the following question:

Question - “How can Suzy use principles of trigonometry to harvest an apple from the nearby apple tree?”

Answer - “Sorry Suzy, but I would rather design and build a device to harvest apples in my own backyard rather than help solve your imaginary problems. I may eventually discover that my design process is made easier using principles of trigonometry to reach my goal, but I care more about creating a solution than helping somebody who lives on a screen or on a worksheet.”


From traditional STEM- and STEAM-oriented curricula at the primary and secondary levels to prototyping, research, and service-learning at the secondary and university levels, additive manufacturing has proven itself to be widely adaptable and relevant in education, just as it has done throughout the last decade in R&D labs, design studios, and factory floors throughout the world. If you’re an educator who believes that 3D printing in education is just a fad, it is my hope that this article helps you see this so-called trend in a more positive light.

Owen Schoeniger