Christmas Tree Tessellations (No Printable Needed!)

Christmas tree tessellations are a unique holiday activity that combine math and art. You can adapt the large Christmas tree tessellation as a collaborate classroom STEAM project, or individual artists can experiment with triangular shapes to make a variety of tessellated patterns.

Best of all, we show you how to make several different Christmas tree tessellations without the need to fire up the printer to print out a template. With our method, kids learn how to graph and draw their own shapes, enhancing the learning process.

Quick review: A tessellation is a repetitive patterns of shapes that fit perfectly together across a 2-dimensional plane of space. The tessellated shape can be regular, as are these Christmas tessellations, or irregular, as are the shapes in our original tessellations activity post and video.

We made Christmas tessellations using simple triangles, as well as traditional fir or pine tree shapes. The concept of how to tessellate each pattern is the same, so once kids understand how it works they will want to experiment!

Materials

• Graph paper
• Plain white paper, such as art or construction paper
• Scissors
• Pencil
• Ruler
• Markers, colored pencils, crayons, for coloring and decorating the trees

Simple Triangle Tessellations

Making Christmas tree tessellations with an isosceles triangle is the easiest way, so we will start with that.

On the graph paper, draw an isosceles triangle. An isosceles triangle has two equal sides. In our photos you can see examples of two different isosceles triangles we used as our pattern.

To form an isosceles triangle, draw a rectangle or square on the graph paper. Any size will do; it can be tall or squat, your choice. The top point of the triangle starts in the midpoint in the top side of the rectangle. Draw two lines, one each from the top point to each of the bottom corners of the rectangle. Ta da!

Now, cut out the triangle. This will be the template for the tessellation. If you wish, glue it to a piece of heavy paper or card stock and cut on the outline to have a sturdier template.

Place the triangle template on your white paper and draw the outline of the triangle. Then, move the template over and line up the bottom edge with the triangle you just drew. Continue in this manner until you have a line of triangles.

At this point, savvy kids will realize that the space between the triangles is exactly the same shape as their template, only upside down. They will be quick to understand how to fill the paper with this new, groovy tessellation pattern.

Christmas Tree Shape Tessellations

This slightly fancier tree shape based on fir or pine tree shapes takes a bit more skill to draw, but it's still easy!

Begin by counting out a rectangle on graph paper with an x-axis of 10 squares and a y-axis of 12 squares. Make a dot at the mid point of the top line (5,12). That is the tippy top of the tree.

Draw lines from:

• (0,0) to (2,3)
• (2,3) to (1,3)
• (1,3) to (3,6)
• (3,6) to (2,6)
• (2,6) to (4,9)
• (4,9) to (3,9)
• (3,9) to (5,12)