This activity contains three levels of pattern cubes with 5 of the 6 sides filled out with letters, numbers, and shapes in some sort of predictable pattern. Students must make observations about the sides that they have access to and figure out what needs to go on that missing side.
There are 3 levels of progressing difficulty for the cubes. Each design has five different patterns that need to be solved for. Some of the patterns require comparisons relative to adjacent or opposite sides so it is important that the puzzle is assembled into a cube shape.
To assemble the cubes, you can either use the tabs to fold and tape/glue your cube together or you can cut out the squares and tape/glue them to the sides of boxes or cubes that you already have.
The answers with explanations of each pattern are included.
How I run this task:
As a class, we start out with the “Level 0” cube (essentially a standard 6-sided die with the 4 removed). Most everyone is familiar with this pattern, and they typically just compare this cube against their memory of a die to determine the missing side. After they guess correctly that the missing side should have 4 dots on it, we discuss if there is another way that they could determine the answer besides looking for the missing number between 1-6. Often, somebody will remember that opposite sides of a die always add up to 7. We test out the theory and sure enough, the blank is exactly opposite from the 3 on this cube so the new pattern further supports our theory. This idea that the values can interact is extremely important and it’s useful to help students “unlock” this possibility before they get to the other cubes.
After the introduction, I explain the other three levels of difficulty and let the students work with a partner to decode the missing sides. My role from this point on, is simply as a checkpoint. Students are allowed to present their predictions to me up to 3 times but I will only tell them whether or not they have completed the task 100% correctly or not. Many times, they are only missing one or two small details, but they have recheck all of their work because they don’t receive any clues about where their prediction isn’t matching. This can be very frustrating for anyone but given enough time to struggle through it, every group completes at least one cube before class is over.
- Don’t allow students to touch the cube once it is one the table. This gets the cube out of hands of a single group leader and requires the group to work together to share information
- Don’t tell them the answer. Scientists never truly know if they have come up with the correct conclusion
- Encourage groups to come up with their own designs and challenge their classmates