In this lesson students will be creating pentominoes and using them to create open boxes. The purpose of this activity and the previous lesson activity is to get students comfortable with composing and decomposing solid figures to build a background for volume.
I begin this lesson by showing students a screenshot from a game of Tetris. In this game all the pieces are polyominoes using four boxes. Once I display the screenshot on the projector I use a See, Think, Wonder approach with the students. I ask them to first silently look at the picture. I then ask them to think about what they see by discussing with their neighbor. And finally, I have them share what they wonder about the picture to the group. I then have students share out some of the responses from their peers as we recap the picture.
As I continue in the lesson students will be creating pentominoes using graph paper. A pentomino is a net with five squares adjoined. Their job is determine how many pentominoes are possible. There are twelve possible pentomino shapes but I am careful not to divulge this information to the students.
Just as in the Tetris pieces you just saw, there were many shapes but they all were made of the same four squares. You are going to be creating your own Tetris pieces today but instead of four squares per shape, you are going to be using five squares which is called a pentomino.
I would like you to work individually but you may discuss with your group during the investigation. Your job is to create as many pentominoes as possible without making duplicates. I will provide you with some graph paper and you may use other resources if you find it necessary.
I allow the students some time to work and I circulate the room and help students who are struggling to make their first pentomino correctly.
To wrap up this lesson I call upon students to share some of the pentominoes they created until all 12 have been displayed. As students are presenting their pentomino on the document camera, I draw quick sketches of the displayed pentomino on the whiteboard.
Once I have all twelve combinations draw on the whiteboard I ask the students one final question for the investigation.
If you were to try and use these pentominoes to create an open box, which of them would work?
I allow students time to discuss in their groups as they think abstractly at home the net could be made into a box. The only directions I give them are that they are not able to cut any part of the pentomino, it just has to have the ability to be folded into an open box.
There are eight of the pentominoes that would fold into a box and four that would not.