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

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 the most exciting, hands-on, integrative subject in your homeschool.

Setting up various math and science (notice I added in science next to math) learning centers around your house, can entice your learner to dive deep into math. Especially, when they see the rich and beautiful connections math has with the sciences and found as geometric patterns right in your own back yard. 

In my 1 year access to my NatureGlo's eScience math and natural sciences course bundle, I teach a year long course called MathArt. In MathArt, learners dive deep into ancient maths history and see the connections there are with marth art, architecture, music and literature.

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 astonishing, beginning with the Golden ratio and Fibonacci numbers found in botany, animal body and human body proportions. The golden ratio can also be found in ancient architecture such as the Great Pyramid of Egypt and the Greek Parthenon. This is a natural lead into ancient history studies. These connections are like searching for hidden treasure which makes learning fun rather than a chore.

Want to learn how to create your own math-themed unit studies like I do? Grab my free unit study planer below and get started today! 

Want me to teach your kids math and science unit studies online for you? You'll be hearing from me soon about when registration is open to join NatureGlo's eScience 1-year MathArt and Natural Science 30+ course bundle.

In my MathArt courses, I did all the hard work and years of research making it easy for you to learn the inter-relationships and connections there are between math and our world. You and your child can go through the courses together or your child can go through them independently. Some children may need more assistance from parents than others.

You both can do the learning, while I teach it. If you want to join in with us, sign up for my free unit study planner above. You will then hear from me about when my registration is open next.

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 by 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, Goldennumber.net

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° (divided by) 1.618033 = 222.5°!

My Personal Journey of Creating the MathArt Online Course for kids 10 - 18

There has been an ongoing almost underground revolution studying this type of "living" math. It still has not been re-embraced by mainstream education. The whys of that are a mystery to me as the math relationships across the curriculum would truly excite mainstream education students.

Even though there are rich mathematical connections all around us, it takes pointing out these numbers for people to really see AND ENJOY 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. I was never taught the entirety of my K - 12 education, neither college, where to see  mathematical connections around me in real life. 

In grade school and college I struggled and was perpetually bored in math classes. I barely pulled 70% in my upper maths algebra and geometry classes. Why? It was lifeless and meaningless to me. I saw no connections between the numbers and diagrams on my papers with the world around me. That all changed.

It was 1993. I was a college student in my early 20's at a flea market. I picked up and perused a hardback Time Life book entitled Mathematics. For the very first time in my life, this book introduced me 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 bought the book, brought it home, and read it.  I wanted to find out more about patterns in nature and beautiful connections there are with math, ancient history, and architecture. I became obsessed with seeing math in ancient cultures.

I 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 about connections with math in nature, history, and science. There wasn’t a lot of information available, but enough to whet my appetite.

This epiphany and discovery of the “Living Math” sent me on a 7-year journey researching and getting outdoors in nature photographing and videoing as many examples of patterns, shapes and numbers as I could find in nature. These mathematical connections are literally everywhere!

This journey led me to create my year long online course, MathArt. MathArt is an accumulation of my research and resources that I've been gathering since 2003. It has grown into a full-year 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 in the course, especially when they do projects with their older siblings. 

What Academic Subjects Fit with MathArt?

What subjects DON’T fit in with MathArt is the real question! Really, everything around us can be described by pattern, shape, and number. Academics that go extremely well with mathematics includes but is not limited to: 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: steemit.com

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

Get outdoors starting right in your own backyard with your family. 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 - butterfly 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 to learn how to create your own math-themed unit studies like I do? Grab my free unit study planer below and get started today! 

Want me to teach your kids math and science unit studies online for you? You'll be hearing from me soon about when registration is open to join NatureGlo's eScience 1-year MathArt and Natural Science 30+ course bundle.

My 1-year MathArt and science membership will give you access to 25+ online courses for kids ages 10 - 18. Younger siblings typically like to participate too.

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 also have 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 and science membership learning journey. The membership includes a community of learners via a forum, a private Facebook for members only called Liberate Your Homeschool Learning Mentorship.

I hope you got a TON of value from this post. Scroll down below and share any comments or questions about this topic. I love to here from you.

Check out: How to Create Rich and Engaging Math Unit Studies Part II

Check out: How to Create Rich and Engaging Math Unit Studies - Circular Patterns Part III

Check out: How to Create Rich and Engaging Math Unit Studies - Hexagons Part IV


Gloria Brooks aka NatureGlo


Hi, I'm Gloria Brooks! I'm into education reform! Since 2011, I've had the privilege of teaching/facilitating thousands of faith-based and secular homeschool and unschool families around the globe. I hold a BA in K - 12 education, certificates from the Wilderness Awareness school, and over 20 years of eclectic teaching and child self-directed learning experiences in private schools, and homeschool online courses with NatureGlo's eScience. NatureGlo's eScience is a one-stop nature-based eLearning center for kids ages 10 - 18  helping them fall in love with the natural world while covering their other academics.

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