# Bee Engineering with Polygon Tessellations

All Subjects

Not only are bees master engineers, but they are also mathematicians. Learn more about bee engineering by exploring 2D and 3D polygons and tessellations.

## LEARN:

Show your kids a honeycomb. Have them make and share their observations. (Good scientists always make observations.)

Your children might observe that the honeycomb is three-dimensional, the shapes are hexagons, and that there are no gaps between the shapes. No gaps mean the bees use their storage space very efficiently!

All honeybees build equal-sided polygons to store their honey. Bees must know that there are only three equilateral shapes that can fit together like a puzzle, without leaving gaps in between. The shapes are triangles, squares, and hexagons. Bees use hexagons. Other shapes, such as circles, leave gaps.

### STEM ACTIVITIES:

1. Build your own 2D and 3D paper models to demonstrate the bee’s math and engineering skills.

You’ll need strips of paper, a ruler, scissors, tape, and a pencil. Make circles, triangles, and squares first.

If your shape has vertices, divide the length by that number. So for a triangle, it has three vertices. Divide your length (10” by 3 = 3.33”). Now mark with a pencil your 3.33” measurements. Fold on those marks. Tape ends together. You will have three equal (3.33”) sides.

A circle has no vertices so you just tape the ends together. Look at the circle model. Have your kids observe the gaps. Would this be an efficient storage system or would it waste space?

Now, make 3D triangles or squares. Would bees use these for storage? Maybe. There are no gaps so it would be efficient.

A bit harder to make are hexagons – but try it with your older, elementary-aged kids. It’s worth it! By making 3D hexagons, you will make a honeycomb structure just like a honeybee’s.

Remember to measure and divide so you get equal length sides. To make a 3D hexagon tube, cut long strips of paper. Measure the length. Divide. These equal measurements will be the vertices, or folds, of your shape. Fold on your marked measurements. Tape together.

So far your kids are practicing geometry and measurement. Now let’s make it a bit harder by adding in art and engineering.

2. Make tessellations.

Introduce another mathematics concept called tessellations. Tessellations are polygons that fit together like puzzle pieces –without gaps or overlaps. So the equilateral triangle, square, and hexagon are tessellations.

Now, make your own simple 2D tessellations. Cut a square. (Remember that squares are equal lengths on all four sides.)

On one side of the square, cut out an angular shape. Don’t use curvy lines if you want to make a 3D tessellation later. You might try cutting out a triangle, for example.

Slide that shape to the opposite side of your square. Tape down.

Now you have a 2D shape that will tessellate. Trace around the shape so it interlocks with itself. Color to make beautiful art.

To make a 3D tessellation, get a strip of paper and your 2D shape. You’ll need to measure each side of your 2D shape on the strip of paper using a rotating method. Measure the first side of the tessellation on the strip of paper. Rotate the shape along the top of your strip of paper to the next side and mark. Continue until you’re done with the entire shape. Fold on your marks. Tape the ends together. (The photos below show each step of this process.)

Learning about bees, tessellations, and polygons will help kids see how much math and engineering are in nature and real life. Have fun!