These challenges are perfect as a mini-lesson or an extension activity to what the students are already learning about congruence, slope, and graphing coordinates. I've also included black-and-white copies of the reindeer and elf tessellations which can be used as coloring pages for early finishers or during a holiday movie.
Holiday Tree Challenge
Students are challenged to create a tree that can be repeated in order to create a tessellation. Using graph paper and trial and error, students will work together to create their tree and prove that it tessellates. The challenge worksheet includes an example of tessellating trees, graph paper, a space to list out coordinates, and extension questions.
Elf and Reindeer Tessellation Challenge
Students are given a worksheet with a square broken up into four different sections. The challenge is that the students must cut out the square and rearrange the sections in order to create the tessellation sample pattern already provided on the worksheet. Students then explain how they rearranged the pieces and why it works to create the repeating pattern.