Waldorfish Blog
Why Seventh Grade Geometry in Waldorf Education is So Much More Than Math
In Waldorf education, seventh grade marks a time of profound transformation. The child is entering adolescence - curious, questioning, and more emotionally aware than ever before.
Example work from Grade Seven Geometry curriculum.
It’s a phase where students begin to look both inward and outward with new intensity, seeking meaning, structure, and truth in the world around them.
This is precisely why the seventh grade geometry curriculum is such a perfect fit: it weaves together logic and beauty, discovery and structure, the artistic and the analytical.
Geometry in seventh grade builds on the strong foundation laid in earlier years. In fifth and sixth grade, students explored the natural forms of geometry - think of the hexagons in a beehive or the spirals of a sunflower - while gaining comfort using a compass and straightedge. They practiced freehand constructions that mirrored the work of the Ancient Greeks, and they learned to appreciate geometry not as abstract math but as a living language of form and proportion.
Now, in seventh grade, the curriculum deepens and expands. Geometry becomes a journey of exploration - across time, culture, and perspective. Students revisit Ancient Greek ideas through the lens of Renaissance artists and architects. They investigate how geometry shows up in the human body (like in Leonardo da Vinci’s Vitruvian Man), in Gothic cathedrals, and in the natural world through phenomena like the Fibonacci sequence. Geometry becomes a kind of time travel - linking the student with thinkers and creators across history.
For example, rather than simply memorizing formulas, a seventh grader might explore area by constructing a golden rectangle using only a compass and straightedge, then identify the golden ratio in pinecones, flower petals, or seashells.
Or they might discover the value of Pi not by being told it's 3.14159… but by physically measuring circles in nature - wrapping string around a tree stump or tracing circular stones - and calculating the ratio of circumference to diameter.
The moment they realize that the answer is always just a little bit more than three is a revelation, especially when they learn that this irrational number continues forever without repeating - just like some of life’s biggest questions.
In Waldorf education, we understand that seventh graders are beginning to see themselves as separate individuals.
They want to test what is true. So it’s no surprise that they take real delight in uncovering geometric truths. Proving the Pythagorean Theorem using ancient visual methods - like drawing squares on the sides of a triangle and physically rearranging them to prove equivalence - gives students a hands-on way to engage in abstract thinking. It shows them that some things can be known, that there are universal laws, and that their own reasoning and observation can uncover them.
Geometry at this stage also encourages discernment and builds trust in one’s own inner capacities. Adolescents are often swimming in a sea of emotion and change, but patterns like those in sacred geometry or the Fibonacci sequence offer grounding and reassurance. Amid the swirling questions of identity and belonging, geometry quietly says: “Some things are constant. Some things make sense.”
And perhaps that’s the greatest gift of seventh-grade geometry in the Waldorf curriculum.
It’s not just about mastering content; it’s about helping students feel connected - to truth, to history, to the natural world, and to their own sense of wonder.
About the Authors
Robyn Beaufoy is Waldorfish’s CEO, and also a course instructor for Simple Season, Waldorf Art for Beginners, and Weekly Art Foundations. You’ll find her intuitive touches and influences throughout everything Waldorfish offers. Robyn has been in the world of education for over 25 years, with an MA in Education and a certification in Waldorf teaching - she also homeschooled both of her children for some of that time. In 2012 Robyn co-founded Waldorfish.com, creating it with the vision of making Waldorf inspired-art and pedagogy more accessible, joyful, and doable for homeschoolers all over the world.
Caitlin Amajor is Waldorfish’s course instructor for Geometry grades 5 & 6, and Botany, as well as our Administrative Assistant. From a young age, Caitlin has been immersed in Waldorf education, attending a Waldorf school from K-8. After receiving a BA in History, Caitlin gained her certification in Waldorf teaching, and spent seven years as a Waldorf class teacher in the upper grades. With a special fondness for watercolor painting and geometry, Caitlin loves bringing Waldorf education to her students all over the world, and seeing their own individuality and style bloom from the curriculum!
Waldorf 5th Grade: Weaving Geometry Throughout the Curriculum
“The Crown” form found in our grade five geometry course.
Waldorf fifth grade curriculum includes a variety of subjects to explore.
It is particularly exciting because it is the first year history and science are introduced as stand-alone areas of study. Ancient Civilizations, Greek Mythologies and History, Botany, Decimals, and much more are explored using a variety of approaches, including (but not limited to!) art, music, and story.
One of our favorite aspects of the fifth grade curriculum is Geometry. Through a freehand approach, the fifth grader builds a strong relationship to geometry within their own bodies, and is prepared for the more complex work with tools that they will experience in sixth grade.
Geometry can be taught in block form in fifth grade (where the lessons are taught every school day over a three or four week period) and/or can also be sprinkled in throughout the school year - it is an ideal subject to be woven into other aspects of the curriculum.
Geometry fits in just about everywhere in the fifth grade year- here are several suggestions if you’re interested in weaving it all together:
Javelin throwing is a big part of the Pentathlon and can be a full-body way of exploring parallel lines, angles, arcs, and much more from the geometry curriculum!
Greek history: Greek architecture and art is filled with familiar forms that are found all throughout geometry in fifth grade and will also bring back an opportunity to review form drawing as well.
Movement: As students prepare for the Waldorf Pentathlon (a common activity for fifth graders), students and educators can explore the geometry behind movement. Angles of the javelin throw, symmetry in running strides, and the circular motion in discus throwing all connect back to geometry in a real-world way.
Botany: Flowers and leaves unfurl, bloom, and structure themselves in beautiful patterns naturally! Take the time to find these patterns through nature sketching, or on a hike, and discover just how orderly nature really is.
Ancient Civilizations: Mandalas evoke the beauty of Ancient India, the sculpture and carvings of Ancient Persia have repeating patterns- there is endless inspiration here for things to be created on main lesson book pages and other artwork!
Map drawing: Fifth grade is a wonderful time to bring in a more strategic and skillful approach to map drawing by using freehand grids. Maps can be drawn of students’ home towns, countries, ancient kingdoms, and much more.
One of the most beautiful aspects of Waldorf Education is how various subjects seamlessly weave into each other, and geometry is no exception!
Math into art, history into nature studies, music into movement- the possibilities are endless when it comes to creating a rich tapestry with the fifth grade curriculum.
Explore our blog!
About the Authors
Robyn Beaufoy is Waldorfish’s CEO, and also a course instructor for Simple Season,, Waldorf Art for Beginners, and Weekly Art Foundations. You’ll find her intuitive touches and influences throughout everything Waldorfish offers. Robyn has been in the world of education for over 25 years, with an MA in Education and a certification in Waldorf teaching - she also homeschooled both of her children for some of that time. In 2012 Robyn co-founded Waldorfish.com, creating it with the vision of making Waldorf inspired-art and pedagogy more accessible, joyful, and doable for homeschoolers all over the world.
Caitlin Amajor is Waldorfish’s course instructor for Geometry grades 5 & 6, and Botany, as well as our Administrative Assistant. From a young age, Caitlin has been immersed in Waldorf education, attending a Waldorf school from K-8. After receiving a BA in History, Caitlin gained her certification in Waldorf teaching, and spent seven years as a Waldorf class teacher in the upper grades. With a special fondness for watercolor painting and geometry, Caitlin loves bringing Waldorf education to her students all over the world, and seeing their own individuality and style bloom from the curriculum!
Waldorf Geometry: How it Meets the Sixth Grader
A running theme of the sixth grade Waldorf curriculum is the phrase “cause and effect.”
A twelve pointed circle becomes something beautiful with some color and shading!
Students at this age are ready to experience and observe more on their own than ever before, which is why we introduce the formal study of science, history, and more (and if you’re interested in learning more about the middle grades science, click here!)
My favorite subject to teach in sixth grade is geometry (not a big surprise to you, I’m sure!) It’s a block I look forward to, and deeply love, and not just because it speaks to me personally, but because I truly enjoy watching the transformation the materials create space for within the young middle schoolers.
The students have experienced geometry in fifth grade, so the subject isn’t completely new to them. They are familiar with the vocabulary, and have discovered and experienced the balance, symmetry, and beauty that freehand geometry provides.
In sixth grade, the geometry block brings a new experience for the student, and it's one that doesn’t always get the credit it deserves! But in my experience, it is perhaps the most important and developmentally appropriate block of sixth grade: it is all about cause and effect, the beauty of order, and the laws of nature.
So, how does the geometry curriculum reinforce the sixth grade theme of “cause and effect”?
If we’re constructing a six pointed form, the compass point must lay on the intended point as perfectly as possible. If it’s a little off, then the whole form will be a little unbalanced.
If we are constructing parallel lines and don’t use our straightedge accurately, then we simply won’t end up with parallel lines when we are done.
If we construct six equidistant points on a circle’s circumference, and connect them one by one with straight lines, then we’ll create a hexagon.
We include a string form lesson in our sixth grade geometry course!
Notice the “if….then…” wording?
If this, then that.
Rule, order, and natural consequences that exist without opinion or judgement- kind of perfect for a sixth grader, who probably feels judged often, unsure of where they stand in the world, and feels change all around them and in their physical body.
Truly feeling the reality of cause and effect, as well as the challenges and satisfaction that come with the experience of using tools and constructing complex forms, is deeply important for the student.
So what then is the significance of the next step, which is shading and using color to finish the final form?
This second step of using color and shading techniques, is a critical piece for the student to experience to truly get the benefits that this block provides. Now is the time to give them choice - what colors will they use? Bright, soft, bold, dark? Will the form be darker on the outer edges and get lighter as it moves in?
The choices are endless. When my students came to the point that a final form was ready to be finished with color, it never failed that the room would become quieter, students would arrange their pencils in possible color combinations, and careful, intentional work would begin. Beauty would begin to bloom around the classroom!
Student work displayed from a sixth grade classroom- every form and drawing is unique and beautiful!
Within the laws of nature, there is space for the beauty of the individual.
Isn’t that amazing, and so important for an-almost-teenager to experience?
For a sixth grader (or perhaps everyone?) it is important to hear and experience the comfort and structure that comes with knowing the laws of nature. We can count on these truths, and know that they will not waver, no matter how chaotic the world may seem. And within these laws, there is space for one to create beauty, and express their individuality in important and impactful ways.
I know these are big and lofty things to say about just one 3 or 4 week block, but I don’t say them lightly!
Geometry really is that powerful, meaningful, and just plain amazing.
Bring your homeschool curriculum to the place where art meets math! Our courses for grades 5-8 provide a full year’s worth of curriculum, instructor support, step-by-step instructions, and so much more.
About the Author
Caitlin Amajor taught in the Waldorf middle school for seven years, and was also a Waldorf student herself! She currently works as an administrative assistant for Waldorfish, and is also the instructor for the grades 5 and 6 geometry courses. Caitlin enjoys baking, gardening, and spending time with friends and family.
Waldorf Geometry :: Math in the middle grades
Ge•om•e•try | noun
Origin:
Middle English- via Old French from Latin “geometria”, from Greek, gē ‘earth’+ metria ‘measurement’.
Earth Measurement. This sounds like something entirely different from most of our own experiences with Geometry in school, yes?
Over thousands of years, geometry has become a standard part of math class and yet it sits in the modern math curriculum isolated from its true origin.
Ancient scholars, the first geometers, understood geometry to be the act of measuring the complete human experience of living on Earth. They set out on this study in order to understand the design behind everything they were experiencing in the physical world. In ancient Greece, the latin word “Mathematikos” meant “desire to learn” and the latin word “mathema” meant “knowledge/study.” In other words, the measurement and study of the physical world in order to understand the human experience on earth and how everything around us is created.
“Inspiration is needed in Geometry, just as much as in poetry.”
Rudolf Steiner and Waldorf education place the utmost importance on Geometry in the Waldorf curriculum, and have created a different path for students than the typical math curriculum offers.
In truth, in Waldorf schools children begin their study of “earth measurement” with their first lesson on the first day of first grade - by drawing straight lines and curved lines. Straight lines and curved lines are nature’s design tools and they will become the essential building blocks of writing and drawing.
Printing, cursive, numbers, and music notation are constructed with lines and arcs. As the students progress through the early grades, patterns of lines and arcs are part of almost every lesson. Where there are patterns, there is geometry. Clapping games establish rhythm and order. Eurythmy and dance involve expression by way of patterns in movement. Students sit in rows, circle up, and line up.
Waldorf geometry curriculum evolves as the child grows through grades 5-8!
Music and geometry go hand in hand as well. Rhythm, intervals, and patterns are the geometric design of music and poetry. As the students learn more about music, they can observe how different geometric patterns in music have unique qualities that induce a particular mood or feeling. Major chords sound “happy” and minor chords sound “sad.” The interval between a root note and the 5th sounds and feels much different than the interval between the root note and the seventh. Music is a great example of geometry as the tool behind the expression through sound. The idea of math as a universal language actually goes much deeper than numbers and calculations on paper being the same everywhere in the world. Ideally, a child’s education in the early grades is full of geometry.
Early experiences with Waldorf Geometry
In grades one through four, there is no formal geometry class. Geometry comes by way of everyday school life (music, writing, movement, etc) and Form Drawing class. Forms are patterns of straight and curved lines that become more complex as the children advance through the grades. Simple repeating forms in grades one and two help with the development of coordination for printing and cursive writing. More complex forms in grades three and four help to develop a sense of spatial awareness and symmetry. In the fourth grade, students practice forms that are also symbols from different cultures (i.e. Nordic symbols) and learn how to tie knots - a three dimensional version of the form drawings.
Try A Free Geometry Lesson
Moving into the middle grades
An example of a fifth grade freehand form with colored pencil.
Grade Five - Freehand Waldorf Geometry
Grade five is a special, transitional year, symbolic of the peek of childhood. The students study great civilizations of the past, including the “Golden Age” of Greece. The students themselves are in the golden age of childhood.
They are at the peak of their development in their child bodies and have gained as much mastery of their physical bodies as they are going to before heading into puberty. Fifth grade also marks the transition from form drawing to geometry. The goal of grade five “freehand geometry” is to lock the archetypal geometric forms into the body by drawing them without the use of tools. Classes also set out to find geometric forms in the world outside of their classrooms.
(Learn more about fifth grade geometry here!)
This form begins with twelve points on a circle- all constructed with a compass and straightedge!
Grade Six - Geometric drawing tools
With the arrival of adolescence, grade six becomes a year of re-birth both physically and in the curriculum. In geometry, we need to go all the way back to the beginning with straight lines and curved lines. This time, however, the children learn to construct lines and arcs with geometric drawing tools. A straightedge (ruler) constructs a line and a compass constructs an arc. The students will now begin a second journey through geometry that mirrors grades 1-5. The three-fold approach to learning (doing, feeling, thinking) is beautifully displayed in the geometry curriculum. In grade 6, the focus is on the physical doing aspect of learning. Learning to use tools to construct and measure is a physical task and it challenges the students as they begin to develop new physical bodies. The focus on “doing” in grade six mirrors the 1st and 2nd grade curriculum where an understanding of lines, arcs, and patterns comes from drawing forms with both the hands and feet, walking patterns, and rhythmic clapping games, etc.
(Learn more about sixth grade geometry here!)
Seventh grade geometry curriculum weaves into history, art, mathematics, human anatomy, and more!
Grade Seven - Inward and outward exploration
Grade Seven in Waldorf schools is generally thought of as “the year of exploration.” A seventh grader, now fully immersed in adolescence, is ready to outwardly explore the physical world and inwardly begin an exploration of the question “who am I?” The feeling life of the seventh grader takes center stage in the curriculum as we use geometry to understand the human body and the natural world we live in. Da Vinci’s Vitruvian Man and the work of Fibonacci give us clues about the mathematical formula behind all that is living on our planet. It’s an incredible moment when students discover that the same ratios and patterns found in pentagrams, roses, apples, insects, hurricanes, and the milky way galaxy, are also found in the structure of our own bodies. The observational studies of nature performed by the likes of Plato, Pythagoras, Eratosthenes, Fibonacci, and Leonardo Da Vinci are mirrored by the observational powers of the seventh grader (they see everything, yes?).
Grade Eight - Digging deeper
In grade eight, the geometry curriculum enters the thinking realm. Armed with knowledge about how to use the tools of the geometer and the experience of searching for one’s self both in nature and the human body, the students are ready to become mathematicians, in the ancient Greek spirit of the mathematician being one who studies all things.
Eighth grade geometry works with 3D forms- both on paper and with hands-on modeling!
We can now venture into the world of abstract thought and theory. The students will grapple with how to measure and study the three dimensional world on the two dimensional surface of the paper. By the 8th grade, it is the hope that students can see that there is always more than meets the eye, and they now have the physical and intellectual tools to dig deeper through observation, making precise measurements and calculations, and articulately describing what they see. They are mathematicians, scientists, and philosophers training to see things on multiple levels.
On one level, numbers define quantities and help us with measurements and calculations. On another level, each number has its own unique set of qualities. Like the circle, the number one represents wholeness and the beginning. Plato called the circle “the mother of all shapes.” When the whole is cut into two, polarities are created (up, down, left, right, life, death, hot cold, positive, negative, male, female, etc.). The number three has a very balanced quality (tripods, tricycles, triangles). This way of understanding the quality of numbers is similar to the phenomenological way of teaching science. When a botany student imagines a plant, the goal of the teacher is to get the child to have a fluid mental picture that includes the entire life cycle of the plant, as opposed to just a fixed image of the plant in a particular moment in time.
With geometry, the goal for the 8th grader is to help them think of numbers not just as quantities but as parts of patterns in nature with their own qualities that shape the world around us and our experience of the world.
“Let no one ignorant of geometry come under this roof.”
•We created a 3 page Qualities of Numbers reference guide for you! Tell us where to send yours in the form below. It’s free!
•We offer a comprehensive Geometry curriculum, covering the grades 5-8.
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