Many of our schools have the brightly coloured flat plastic pentominoes tucked away in storage cupboards. I have always like pentominoes due to their affordances for puzzles, problem-solving and spatial reasoning.
One thing I’ve noticed is that they have not been particularly appealing to our younger learners and I wondered if it was because of their two-dimensionality. I thought something that was more tactile for them and that they could build with might be more appealing.
When I saw these cubes at the dollar store, my mind went to building pentominoes based on a task I had read about in the Taking Shape book by Joan Moss et al.
How many different ways can 3 blocks be put together, with all edges and faces flush? How will you know if you have found all the ways? Are two objects congruent if their orientation is different?
With 4 blocks?
With 5 blocks? (pentominoes)
I have done this task with teachers, both as part of our BCAMT Reggio-Inspired Mathematics Collaborative Inquiry Project and as part of a session on the mathematics curricular competencies at our district conference.
Teachers have found this task touches upon so many areas in our curriculum – spatial reasoning, geometry, problem-solving, visualizing, reasoning and analyzing, communicating, etc.
As an extension to the building task, using the little wood cubes, I glued sets of pentominoes together, using an image of the 12 pentominoes I found online to help me as a guide. I also left lots of blocks not glued to be used for building the different arrangements.
Pro-tip – don’t use liquid white glue on the coloured blocks….the dye runs and you’ll have a mess on your hands and elsewhere!
One of the unique aspects of pentominoes is that they are able to fit together to form various rectangles. How many different rectangles can you make using some or all of the pentominoes?