Thought for the day: There are many ways to use Creative Math Prompts: (1) just notice and wonder, (2) create conversation around a concept, (3) create a full lesson, (4) as the starting point for a long-term project, (5) as a tool to discover creative mathematical talent in students who do not perform as well on traditional assessments, (5) other….

Concepts: recognizing cubes, spatial visualization, nets, open and closed shapes, edges of solids (possibly flips and turns)

Beginning

I notice that the bottom shape looks like a solid (a cube).
I notice that the two shapes on top each have 6 squares.
I notice that a real cube is also made of 6 squares. (Suggestion: you might want to have some cubes handy for kids to look at.)
I notice that one of the shapes on top looks like a cross.
I notice that one of the shapes on top looks like stairs.

Exploring

I wonder if I can make a cube by cutting out one of the shapes on top and folding it.
i wonder how I can tell which direction to fold the paper.
I wonder how i can tell how far to fold each edge.
I wonder how I can hold my folded shape together. (Students may need help connecting the edge with tape or something other method.)
I notice that I can fold both of the shapes into a cube.
I wonder if I can make other 3-dimensional shapes from the 6 squares.
I notice that some 3-dimensional shapes might not close up.
I wonder if I can make other shapes (from 6 six squares) that fold into a cube.
I wonder if I could make the flat shapes and the cubes out of toothpicks.
I notice that it takes more toothpicks (15) to make the “nets” than it takes to make the cube (12).
I wonder why this happens.

Creating

As they notice and wonder, students may create nets, cubes, and other shapes The things that they create may come from what they have noticed and wondered. For example, they may:

Create a cube from the “cross” net.
Create a cube from the “stairs” net.
Try to create other shapes from the nets (including some that may not close).
Create other nets from six squares.
Try to create cubes (or other 3-dimensional shapes) from their new nets.

Reflecting and Extending

I notice that I can make solids (3-dimensional shapes) out of flat (2-dimensional) shapes.
I notice that some shapes will close up (to make an inside and an outside), and some won’t.
I notice that it matters which way I fold the paper.
I notice that sometimes I can look at two folds at a time to see where they will meet.
I notice that when I fold a net, two edges on the net meet to turn into one edge on the cube.
I wonder how many different nets I can draw that will make a cube.
I notice that two nets that look different might really be the same (because I could flip or turn one of them to make the other one).
I wonder if I can make a flat shape out of six squares that will not fold into a cube.
I wonder if there is a quick way to look at a net and see if it will make a cube.

Notes

A net for a 3-dimensional shape (a solid) is a 2-dimensional shape that can be folded to make the 3-dimensional shape. You can decide whether or not to share and use this vocabulary with your students. There are 11 nets that will make cubes. They look like this:

There are lots more things to notice and wonder:

All of them except the one on the bottom right would fit very nicely inside a 3 by 4 rectangle.
Not all of the nets would be made from the same number of toothpicks.
You can often change one net into another by moving just one square. (This might help you keep track of what you have tried!)
Is there a flat shape made of six squares that will not fold into a cube? (Try making one that has five squares lined up in a row.)
Is there any easy way to tell if a shape can be folded into a cube (without actually folding it)?
How can you tell when you have found all of the possible nets (if no one had told you that there were 11 of them)?
Could you make nets for other 3-dimensional shapes?