Building Complex, Colorful Polyhedrons

Abigail Simpson, Middle Grades Math Teacher

In this final project for one of our units, 7th graders went beyond simple polyhedrons such as cubes or triangular prisms, and created complex, colorful, novel 3D shapes out of chipboard.

Students began the unit with little to no direct instruction, except for how to put pieces together and what makes a polyhedron. From there they had a few class periods for open exploration and question formulating. During the process, students dove into the concepts of nets, identifying 3D shapes by name, edges, vertices, faces and cross-sections. The hands-on, open-ended approach led to interesting discussions about angles, patterns, similarities and differences between groups, and how certain shapes came together.


Next, students started creating a net of their polyhedron and calculating the surface area. A challenge for some groups that had created complicated polyhedrons was creating their net and working backwards. It was great seeing students think critically to tackle creating a net, and then watching the process of students starting from scratch to put their shapes back together from the net. Once they completed the process, students were quite satisfied. 


From there, students moved on to a sturdier material for their second drafts. Using chipboard, they re-created their shapes using their net, now having a better understanding of how they folded back together.


Next, we moved on to volume. Nearly all students were familiar with the concept of volume, and how to find it for basic prisms (length x width x height), but once students were tasked with finding the volume of their own polyhedrons, it became quite the challenge! They first estimated the volume of their 3D shapes based on how much sand fits in one cube, then went from there to calculate the volume of the entire polyhedron.


Throughout the whole unit, the groups kept a log of their progress in a journal where they could make observations about their and each other's work, record their ideas of the difference between surface area and volume, upload pictures of their polyhedrons, nets and calculations and even take on the challenge of exploring tessellations.

Finally, students finished off the unit with a personal touch. The students painted their polyhedrons and described how the hands-on aspect of this project helped them understand the concepts of 3D shapes, volume and surface area. 


According to one group, Renee and Mya, the project "helped us better understand the difference between surface area and volume, as well as how to find the volume in complex shapes. We liked how this project showed our creativity—how it was very open."


Another group, Dasha and Liv, said, "I liked how we used a hands-on project that was also fun and interesting to help us better understand surface area and volume."

Lastly, Ana and Ana raved, "We loved how interactive this project was! It helped us understand more about 3D shapes by showing how a visual structure can affect our learning."




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