How to Create Rich and Engaging Homeschool Math Unit Studies – Part II

Creating rich, engaging math themed unit studies can be incredibly gratifying to you as a homeschool parent curriculum creator and inspiring for your learner's experience across the curriculum.

In part I of this series, I introduced you to the famed yet mysterious Golden ratio and Fibonacci numbers found in art, architecture, and nature. I'm not going to re-teach the same things about these numbers, so, if you have not read the post about them, please read that post here.

The wonder and beauty of studying nature's patterns, shapes and numbers is truly astonishing. So astonishing are these maths to me, in fact, that I've been studying them since 2003. So great was my excitement about the connections there are with mathematics and the world around us, that I just had to create my MathArt curriculum to tie in cross-curricular connections there are with art, architecture, nature, science, history and even literature. I just know that I will continue to revise and make this curriculum better and better, most likely for the rest of my working career.

What about your own family's math unit studies? It's pretty rare to find unit studies centered around math. I'm privileged to make a stamp on this topic within the worldwide Web. Have I got a GREAT activity to help you get started and on a roll with creating these fascinating unit studies.

Backyard Patterns in Nature Treasure Hunt Activity

One of the things that enthralled me the most when I first discovered maths found in nature, were the repeating patterns and shapes found everywhere! It became a treasure hunt for me looking for them. With my camera and journal in hand, I'd take off down a trail sweeping from side-to-side looking at plants, trees and even animals. I'd stop and observe a wild flower, bird or tree, take photographs, draw the specimen and mathematically describe the numbers, shapes and patterns I saw. Have a look at a real life example from my MathArt journal below.

Pictures Including Math Journal Showcasing the Trout lily

Be sure to Zoom in to see the details!

This is a Trout lily I found in the forest at Ashland Nature Center in central DE.

NatureGlo's Trout Lily Math Journal Entry

Here I created a journal entry about the Trout lily wildflower. I wrote up mathematical descriptions about this beautiful wildflower in my journal.

Some of the most common patterns found in nature

  1. Circular - spirals, spheres, circles - flowers, leaves, planets
  2. Hexagons - look for bee honeycomb or wasps' nests
  3. Lines - straight, curved, waves or meanders - rivers, ocean waves, wind-blown sand 
  4. Fractals - branching as in lightening bolts and veins of a leaf
  5. Symmetry - butterfly wings, flowers
  6. Five-pointed star - flowers have these many times in their petal arrangement or found within male and female parts.

The template below addresses: lines (waves), spirals, hexagons, five-pointed start and fractals

Below you can get my free helpful template that will guide your learner in looking for some of the most common patterns found in nature. The template is appropriate for students approximately ages 8 and up. I suggest modifying it for younger students, if necessary.

Tips for using the Backyard Patterns in Nature Template

After your learner completes searching for and drawing one example of each type of patterns found in your backyard, they'll answer the final questions. The questions are:

What is its relationship to math? Hint:Include its shape(s) and numbers.

At first, this might boggle you and your learner. I'll offer a few examples to hopefully give you the aha you need to finish section c.

Say, for example for the wave/meander, you select ripples found in their sandbox. If you look down at sand after a rain or a strong wind storm, you can notice varying wave patterns. This would be a perfect example (if you have access to sand in your backyard) for the wave/meander example.

How would waves/meanders found in sand be related to math? You don't have much space to express it, so, I'd put, any number of the following:

  1. Formed by wind blowing at say 15 mph or...
  2. Formed by thousands of rain drops.

The numbers you can come up with related to the sand waves and how they got there, is math! It's just a matter of putting on your "math glasses" and seeing with a mathematical eye.

Using the Backyard Patterns in Nature Treasure Hunt Template to further your Math Unit Study

After your learner completes the activity, each pattern can become the starting point for a separate unit study. You can of course do this how you want according to the amount of time you have. However, I have dedicated a single one-hour lesson to each pattern. 

Unit Study Building Resources for the Wave Pattern

Here's a link to a page of resources I've used over the years for the curved lines study.  I include connections with science, art and even music. The video about cymatics is really AWESOME!

Cymatics is a relatively new branch of science. It is basically the science of sound vibration's rhythmical effect on matter such as water, sand or powder. For example, the surface of a plate, diaphragm or membrane is vibrated in some way  whether it be through music or some other sound. Different geometric patterns emerge in the materials used and can be seen depending on the geometry of the plate and the driving frequency of sound.

Have a look at musician Nigel Stanford's illustrative video of what cymatics can look like below. 

I hope you enjoy the study in your homeschool!

Until next time!