2D to 3D Draw String Shapes 

This page gives ideas for making 2D cut-outs that transform via draw strings into 3D shapes. You can either trace a shape multiple times on card stock, then cut out, or you can digitally design the 2D version and use a paper cutter. 

This activity can be adapted for a variety of age levels. Younger students can be given more guidance and a project that is farther along. Older students can be tasked with designing their shape from the ground up. Those who finish early could even be asked to engineer improvements like devising ways for the shape to spring back to 2D more effectively, or programming a servo motor to activate the draw string. In either case, students can make calculations and observations about area, volume, and other attributes. 

To see some basic shapes that I 3D printed for tracing, search for "Shapes to Trace for 2D to 3D" in Tinkercad. Change their sizes, or have your students design their own.

For paper cutting on a Cricut or Silouhette, you can use any program that will produce a SVG (scalable vector graphic) file. 

Here, I used Tinkercad to plan out 2D shapes for cutting. I sank the designs slightly into the workplane to ensure proper export as SVG. 

When open, students can write the areas and dimensions of different elements of the shapes. 

When drawn closed, the 2D view becomes a 3D shape. Card stock paper works well. 

Here, a square and a matching equilateral triangle have been 3D printed to allow a student to plan and trace the sides of a four sided pyramid. Note the position of the holes for the string to be cut.

The square base of the pyramid has been glued to a piece of cardboard, which has an exit hole for the drawstring.

Directions for making a draw string dodecagon

Here's a dodecagon, the end product the next series of steps is headed toward.

The first step is to use a shape to trace and plan the sides. Note the positioning of the holes for the draw string. 

Once the shape is traced and cut, use a straight edge to help you crease the corners in. Here I used the shape I traced. 

I wanted the draw string to move easily from under the model. I made a top piece with two small holes for the string to exit, then a middle piece with larger cuts for the string to move out through, and then a large cardboard base. 

I made the mistake of gluing everything together before threading the string, so I had to help the string with a paperclip. A better plan is to use hot glue to join the two small pieces of cardboard, and then glue stick to attach the base of the model. Thread the string (making sure it's long enough), and then hot glue the small cardboard to the large (avoid getting glue on the strings). 

Thread the string as shown and your dodecagon is ready for action.