Box or Not?

Curriculum Goal

Identify two-dimensional shapes and three-dimensional figures and sort and classify them by their geometric properties.
Compose and decompose two-dimensional shapes and three-dimensional figures.

This activity strengthens visualization skills, mental rotation skills, and supports a child’s ability to imagine transformation from a 2D to a 3D structure.
Children look at pre-arranged square frameworks to determine whether the frameworks will create an open box or not.

Square-shaped Polydron frameworks (if not available, cardstock paper can be used)

Facilitate a discussion with students about 2D and 3D shapes, their properties, similarities, differences and how they are related.
Lay a framework flat on the ground and allow students to imagine how it will transform into an open box.
Carefully fold the sides of the box to show students how the box is created.
Allow students’ turns to hold, flatten and re-create the box for several minutes.
Show students a different framework and have them imagine how they could fold it into a box (or not).
Invite students to verbalize their explanations using spatial language to share their predictions of whether an open box can be formed or not.

Can the child articulate the properties of the 2D and 3D shapes (e.g. number of sides, number of vertices)?
Can the child articulate the difference between 2D and 3D shapes? Can they categorize them?
Can the child clearly articulate with words and gestures how the frames can be folded into boxes?
Does the child use spatial language?
Observe: gesturing, embodied cognition, and language as students reason about their conclusions.

After children have become familiar with this activity, it can be extended to include different 3D structures (e.g. pyramid, rectangular prism).
Eventually, have students create their own framework sets and challenge their classmates.
Show the children a constructed 3D structure and have them create all possible nets.

A possible extension, students transform 3D figures into 2D drawings.