Spirograph Activities to Spark Math Wonder - Play Discover Learn 24/7

Spirograph Activities to Spark Math Wonder

spirograph math art

Spirographs are a great way to break up the monotony of any math schedule and see the artful and playful side of math.  

We needed this shake up our in homeschool routine.  I found it a great way to strengthen the habit of observation. We took a closer look at cause and effect as we played with spirographs. 

I used 3 essential elements with the Spirographs to spark math exploration: story, constraints and great questions.

Spirographs and Stories

I probably sound like a broken record but I believe storytelling is essential to making any activity successful. To be truly effective teachers, we must recognize that we are salespeople.  We have great ideas that we want to connect our children to, but we need to sell them on the greatness of these ideas.

To be truly effective teachers, we must recognize that we are salespeople.

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The greatest sales people connect people to the greatness of their ideas through stories.  They tell those stories in a way that connects the heart to the mind.  But why are stories so effective?

Science Tells Us

  • We are drawn to stories.
  • We organize information and experiences into stories.
  • We are built to remember stories easily.
  • Stories simulate multi-sensory experiences. 

Spirographs remind us of the beautiful spirals found in nature. I read a beautiful story on spirals found in nature to draw at the my children's natural desire to tell stories. 

spirograph art

I suggest to pick a book that is more artistic and less literal, so that students feel free to create in their own artistic style.  I love just about every Van Gogh picture book.  He incorporates a lot of spirals in his art. Of course, you can't go wrong with a book on the Fibonacci Sequence either. At the end of the blog, there are some suggestions. 

Use the story as an inspirational background for free play.  Have students start creating spirographs with no constraints. We used colorful gel pens to create our Spirograph pictures.  

Our Spirograph set came with just 3 gel pens that worked great, but that is just not enough for my colorful crew.  We also got a gel pack with 60 pens, but I wasn't too happy with it.  Half the pens didn't work. Sigh, so I can't recommend any.  Can you? 

Spirographs with Constraints

After a day of free play creating stories with the Spirographs, it is time to introduce constraints. An activity with constraints is an activity that balances freedom of expression with a task designed to achieve a specific discovery.


Ancient Hebrew wisdom reveals to us the very word engrave "Cherut" was also understood as freedom.  This is peculiar because the one time it is mention is when God engraves the Law into the stone tablets.

What connects freedom and the Law? Ancient Hebrew Wisdom saw that there is freedom found in loving and obeying the law.  I see this in math too. Constraints can free us from the distraction of too much information and allow us the freedom to look closely at something. 

This is why unschooling can fail a child. A student surround by too much may struggle to find their way through the noise to effectively learn anything. Guided discovery by a mentor offers to students freedom to see ideas for themselves. Yet, the mentor is able to construct an environment that let's the child see through the noise of information. 

In all history, every great person had a mentor, a guide, a story, that persuaded their hearts and moved them to actionable discoveries. Whatever schooling you chose, you must recognize the power of constraints to free a child to deepen their insights and discover for themselves great ideas. 

In the Spirograph box, there are instructions on how to create specific designs. This is a great place to start with constraints. The student can freely choose a design they want to do. You can also encourage them to continue telling a story with their art.

Spirographs and Great Questions

Connecting with your child is important throughout this exploration. Asking them what they notice is a great place to start, but we can also provide specific tasks to help them discover more math in their art.

Activity Ideas

spirograph lesson ideas

Using the inside track of 150/105, create a shape using hole #1 of wheel #42. How many times around the ring did you go before completing the shape and returning to your starting point?

It is easy to get lost in the Spirograph and forget where you begin. In this activity, we are asking the student to attend to this, so that they notice how many times they go around before completing the structure. Encourage the student to try a different hole in the wheel and see if they go around the same number of times.

Spirograph activities

Using inside track of 150/105, create a shape using hole #1 of wheel #63. What shapes do you see? Now use hole #2. How does the shape change? What about when you use hole #3, #4 and so on?

In this activity, we are drawing the student’s attention to the shapes being made and how they change as you move from hole to hole.  This is important observation of cause and effect.

The habit of observation is a life skill that will take your child far.  A child with the strong habit of observation will use that skill to help solve problems whether in science, math, finance, bible study or daily interaction between people. 

Using Graph Paper with Spirographs

Spirographs are much prettier on plain white paper especially when you use colorful gel pens, but graph paper gives students ability to compare more easily. Use graphing paper when you want to draw the student’s attention to size and shape change.

Spirograph activities

Using the inside track of 150/105, create a shape using hole #1 of wheel #45. Then using the outside track of 150/105, create a shape using the same hole #1 of wheel #45.

In this activity, students are drawn to observe the impact the inside and outside of the track have on the size and form of the shapes. Using the graph paper, they can count roughly the difference in size.

Such a habit of observation helps children to look for ways to quantify their observations. Quantifying observations give students a tool to make useful comparisons on cause and effect. 

Comparing in Math Art

During all these activities, have the student talk about their artwork and then have them compare shapes, sizes and patterns found in each other’s artwork. Leave room for them to make their own activities and discoveries.

No matter what job or career your child chooses in his life to serve others, the ability to share and articulate ideas will take him far.  Too often, we just listen and articulate the ideas of others.  It is very different to articulate one's own ideas, so it is a good habit for children to practice articulating their own ideas.

Don't Miss the Wonder of Spirographs

activities for Spirographs

Spirographs leave us to wonder a lot, and it’s important to get children to articulate what they wonder about as they make spirographs. I had wondered how to express these mathematically.  My kids had wondered, "How does it do that?"

I didn't have the answer to these questions, but we don’t have to have the answers for the questions we wonder about or the questions our kids wonder about.

The point is building the habit of wondering and questioning things.  In wondering, a curiosity can be lit, and that is when learning really takes off. 

In all these activities, focus on training them up in the habit of observing. 

Observing is key to discover.  We all see the same thing, but it is those that look closely that make discoveries.

We spent an entire week on Spirographs and barely covered the surface of all that could be observed.   Be sure to follow me on Instagram for daily math ideas and inspirations. 

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Lacy | Play Discover Learn 24/7

Knowing the best kind of learning comes from a highly motivated internal drive, Lacy Coker cultivates tools and resources that help to make learning for young children playful and self-directed.

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