Rhombus Hexagons
How it works
Imagine you're trying to cover a hexagon with rhombus pattern blocks. Can you always do it, no matter the size and shape of the hexagon, or are there some hexagons that are impossible to cover with these rhombi? What if you are allowed to use a single triangle pattern block in addition to the rhombus pattern blocks? Does it matter where you place the triangle? What if you have 2 triangle pattern blocks?
In this activity, students first try to cover a variety of different hexagons with rhombus pattern blocks. In doing this, they discover that some are possible and some are impossible. Then they try to cover some of the impossible ones with rhombi and one triangle, exploring when this is possible or impossible depending on the position of the triangle. They also explore additional challenges where they must place 2 triangles in specific positions and then try to cover the rest of the hexagon with rhombi.
Why we like this activity
It’s fun! Students enjoy using the pattern blocks and trying to figure out when it's possible or impossible to cover the hexagons with pattern blocks.
It helps to develop spatial reasoning.
It helps to develop logical reasoning.
It requires students to engage in mathematical habits of mind:
- Finding and using strategies, looking for patterns, and making and testing predictions when trying to determine which challenges are possible and which are impossible
It has a low floor and a high ceiling: Students can start trying to cover hexagons by trial and error, but finding ways to more efficient ways to determine when it's possible and when it's impossible requires more advanced reasoning and strategy.
