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

Teaching math as a unit study can be a daunting task. Much of modern mathematics curriculum treats math as a separate subject from the rest of academics. I don’t kid you when I say that math can become a most exciting, hands-on, integrative subject in your homeschool.

I teach a course called MathArt where my students and I delve deep into ancient maths history and bring in connections with art, architecture, music and literature. Since ancient civilizations, it is believed in some mathematics circles that the Golden ratio (1.618) and Fibonacci numbers (0, 1, 1, 2, 3, 5, 8, 13...etc.) were taught to young children but were removed from our current curriculum only 100 years ago. Our mathematics education has been replaced with a dry factory-like manufactured view of mathematics, stripped of numbers true beauty, wonder and connections with the natural and human-made world. The connections there are with the natural world and mathematics is truly astounding, beginning with those two numbers I introduced to you, the Golden ratio and Fibonacci numbers. These numbers are found in art, architecture and nature.

​​​​I did all the hard work and years of research making it easy for you to learn the interconnections there are between math and our world. You and your child can go through the courses together. You both can do the learning, while I teach it. If you decide not to join us this year for the membership, there are oodles of resources out there on the Internet about seeing the connections between math and the real world. However, my MathArt courses will definitely save you hours, days and weeks of prep and research.

What is the Golden ratio?

It is called many names including:

  1. The Divine Proportion
  2. Phi (pronounced Fi when in upper case and phi (fee) in lower case)
  3. Golden mean
  4. Divine section
  5. Golden cut
  6. Tau(t)

The Golden ratio is an irrational number, 1.618.. It embodies what is known as the most beautiful proportion. These proportions have been found in Leonardo da Vinci’s most famed works of art including the Mona Lisa and the Last Supper. Rembrandt used the proportion frequently in his paintings. His most famous self-portrait is found to be within the golden ratio.

The image on the left shows the entire canvas within the golden ration. The Golden rectangle is also drawn about Mona Lisa's face. The image on the right shows that her eye is aligned with the center of the canvas. Golden ratio lines from the center of the painting to the sides of the canvas align nicely with the width of her hair. There may also be golden ratios in the vertical dimensions of the painting. Photos credit: Gary Meisner,

Rembrandt's self-portrait here is within the golden triangle. The golden triangle, also called the sublime triangle, is an isosceles triangle wherein the ratio of the hypotenuse a to base b is equal to the golden ratio, a/b=phi.

What are the Fibonacci Numbers and how are they used?

The Fibonacci numbers are a series of numbers (0, 1, 1, 2, 3, 5, 8, 13, 21...etc.) wherein the subsequent two numbers are added to give you the next two numbers. They are popularly found in the numbers of spiral turns found in sunflower and daisy seed heads, pine cones, aloe plants and well, all throughout the plant and animal kingdoms and strongly possible in the newly discovered mineral, quasicrystals atomic make-up. Even tree branches grow from their trunks at a consistent 222.5° or 360° ➗ 1.618033 = 222.5°!

My Personal Journey Creating MathArt

There has been an ongoing almost underground revolution studying this type of math. It still has not been re-embraced by mainstream education. The why’s of that are a mystery to me as the math relationships across the curriculum would truly excite mainstream education students. Even though it’s all around us, it takes pointing out these numbers for people to really see them. I didn’t realize much of any relationships between mathematics and the natural world, art, architecture and science until I was in my early 20’s. It was never taught!

I always struggled and was perpetually bored in grade school and college math classes. I barely pulled 70% in my algebra classes. I did okay in geometry. Why? It was lifeless to me. It bore no connection with the world around me. That all changed.

It was 1993 and I was a college student in my early 20's at a church flea market. I picked up and perused a hardback Time Life book entitled Mathematics. It introduces to the Golden Ratio, Fibonacci numbers, geometric shapes and patterns found in nature, art and architecture. I was baffled, amused, awe-stricken and inspired. A fire was lit under me. I of course bought the book and searched high and low for as much supporting information as I could and devoured it. It was like a real treasure hunt to find books in the library in 90’s around this topic. There wasn’t a lot of information but enough to wet my appetite. The discovery of the “Living Math” sent me on a 7-year personal journey researching and getting outdoors in nature photographing and videoing as many examples of patterns, shapes and numbers as I could find. They’re literally everywhere!

My journey led me to create a year long course called MathArt of which I piloted with my students every year since 2003. It has grown into a full online course. The class has been taken by students as young as 8 but I suggest it for students 10 and up. Younger advanced students also do well with the course.

What Academic Subjects Can Fit with this Ancient/New MathArt

What subjects DON’T fit into a scope with MathArt is the real question. Really, everything around us can be described by either or all of the above: pattern, shape, and number. Academics that go extremely well with mathematics including history/geography, literature, poetry, art, science, architecture, and nature connection, and even spirituality. Interesting math connections such as the Flower of Life symbol have been found in many countries across the religions around the world. How’s that for mind boggling?

What is the Flower of Life?

The flower of life is a geometrical shape composed of multiple evenly-spaced, overlapping circles arranged in a hexagonal flower like pattern with six fold symmetry. Many religions consider it to be sacred geometry containing ancient religious value showing the foundational forms of space and time.

Here we see the Flower of LIfe found worldwide at: Scotland (1), Israel (2), China (3), Turkey (4), Egypt (5), India (6), Germany (7), Bulgaria (8), Sweden (9), France (10), Czech (11), Greece (12) Image credit:

What's the Easiest Way to Start Incorporating Math Unit Studies?

Bring your family outdoors and look for patterns and numbers in nature. Start with the most common patterns in nature including:

  1. Circular - spirals, spheres, circles
  2. Hexagons - look for bee honeycomb or wasps' nests
  3. Lines - curves and straight
  4. Fractals - branching as in lightening bolts and veins of a leaf
  5. Symmetry - buttefly wings, flowers

Look for Fibonacci numbers (1, 1, 2, 3, 5, 8, 13, 21, 34...etc.) in:

  1. Numbers of spiral turns in pine cones.
  2. Numbers of flower petals
  3. Tree branches

Want me to Teach for you? Which MathArt Course Should My Child Begin With?

My 1-year MathArt and science membership will give you access to over 25 courses. Students can begin any of the courses in any order, however, I suggest starting with Math Connections with the Real World. This course introduces students to the Golden ratio and Fibonacci numbers. Have a look at the topics below.

Math Connections with the Real World Topics:

Lesson #1 - Introduction & History of the Golden Ratio and Fibonacci Numbers

Lesson #2 - The Golden Number & Fibonacci in Art, Architecture & Nature

Lesson #3 - Fibonacci Numbers - Flower Petals, Seed heads and More!

Lesson #4 - History & Golden Ratio of the Great Pyramid of Egypt

Lesson #5 - Quasicrystals & the Golden Ratio

Lesson #6 - The Mathematics of Music

What is NatureGlo's Homeschool Math and Science Facebook Group?

I'm also starting a homeschool math and science Facebook group for parents here. This group will be for homeschool parents that are looking for math and science support. This can include:

1). Looking for out-of-the-box resources and methods for improving your learner's math and science learning including more hands-on and outdoor nature experiences.

2). Interested in learning and or gaining more resources and methods for math and science-centered unit study style teaching and learning.

The group is a place to discuss all things homeschool math and science. This includes: gain support, share what's working, isn't working with your current math and science curriculum, you and your learners' struggles, wins, and questions you have about improving your children's learning.

This is a closed but free group. It was created to give you access to other homeschoolers and myself as resources to each other. Its main focus is to share each other's current struggles, wins and exchange resources, ideas, and methods about hands-on, outdoors, and online math and science education across the curriculum (unit studies).

Consider joining the one-year MathArt membership learning journey. The membership includes a community of learners via a forum, a Facebook as mentioned above, for parents, email or chat support from me and much more. Check it out below!


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