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Home | Activities and links

Geometry Activities for Educators

These hands-on activities will help spark students' interest in geometry. They're designed for classroom use but can also be done by families or other groups. ESPAÑOL indicates activities that are available in Spanish.

Grade level Title Description

K-2

Put triangles together to make patterns.

Pon triángulos juntos para hacer patrones.

3-5

Combine polygons to make larger shapes.

Combina polígonos para hacer formas más grandes.

3-5

Build repeating patterns, both 2D and 3D.

Construye patrones que se repiten, tanto en dos dimensiones como en tres dimensiones.

Outdoor Activities for Educators

This set of activities is written for a class, after school, or other group to do on a playground. They can easily be adapted to be done by families, however, and they can be done at other outdoor locations. Physical exercise and the gamelike nature of the activities make learning geometry fun.

ESPAÑOL indicates activities that are available in Spanish.

Geometry Playground is made possible by the National Science Foundation and the Gordon and Betty Moore Foundation.

Any opinions, findings, conclusions, or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

Credits

© 2010 Exploratorium | The museum of science, art and human perception
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Home | Activities and links These hands-on activities will help spark students' interest in geometry. They're designed for classroom use but can also be done by families or other groups. ESPAÑOL indicates activities that are available in Spanish. Grade level Title Description K-2 Put triangles together to make patterns.

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Carol - Photos that Inspire Math Conversations

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Carol - Photos that Inspire Math Conversations

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This is an excellent website that I wanted to share, photos to inspire math conversations.  In kindergarten it is all about the conversations you have with your students.  The math is all around them, we as teachers need engage the students in the purposeful conversation.  Here is the link Pictures to inspire math conversations

The author Deanna McLennan also has an excellent set of books that I love to use to explore math in nature.  It is geared toward early years and primary.  I highly recommend them!

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75 new photos · Album by Deanna McLennan

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Read this article and watch the video about bees honeycombs and hexagons.

This video would be a great one to show in class when discussing different shapes and where we see them in nature. It is also perfect for discussing area of shapes and comparing different shapes based on their size and area and how easily they connect to one another.

Too often I hear “why do I have to learn this” in math, so this is an excellent way to express the importance of shapes in helping bees to produce and preserve their honey. This is a great lesson to cross with Science as well!

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Premier Bee Products | Beekeeping Supplies & Bee Products

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By now, it's pretty clear that honeybees are tiny math geniuses.

The precision seen in nature is no accident - they are methodical in their approach to survival.

Studying honeybees and their comb is partially what drove our team to venture down the path of manufacturing premier foundation .

As we dove into biological and engineering research around honeycomb, we discovered that current foundations were not nearly as precise as what we see in nature. Cell walls were too thick, which resulted in more work for the bees and less honey produced.

Unfortunately, it made sense why this occurred. Most of this neglect was in an effort to save costs, but this failed to account for the loss in honey production through wasted bee energy and space.

Thanks to our team of engineers and our unique manufacturing process, we were able to create a more precise foundation with up to 10% more cells per sheet.

This, we believe, only honors our fellow insect engineers.

You can read more in , but this story is not about us. It's about the mind-blowing bees we work with daily.

For a visual representation of the geometry behind honeycomb, watch this TED-Ed video on why bees love hexagons.

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By now, it's pretty clear that honeybees are tiny math geniuses. The precision seen in nature is no accident - they are methodical in their approach to survival. Studying honeybees and their comb is partially what drove our team to venture down the path of manufacturing premier foundation .

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Mackenzie - Measurement/Science - How old is this tree?

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Mackenzie - Measurement/Science - How old is this tree?

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Read the lesson above to introduce circumference in the measurement unit. I love that you are able to alter this activity for many different grade levels. For my students I would use a measuring tape instead of just a piece of tape.

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#1459. How Old is that Tree

Science, level: Elementary
Posted Mon Dec 27 19:39:53 PST 1999 by Cindy Roter ( rgilcin@aol.com).
Hebrew Academy , Nassau County New York
Materials Required: A cross section of a tree or large branch. Masking tape, ruler
Activity Time: 20 minutes
Concepts Taught: Annual Rings, Tree growth rate ,environmental science

Explain to students the concept of annual rings. The rings are really a tubular system that carries water from roots to
top of tree. For every year the tree is alive it has another outer ring. In years with great precipation the ringd are further apart.
Also, if you measure the circumference of a tree in inches, one inch is approximately one year of age for the tree. 30
inch bark is about 30 years old etc.

First have students count the number of rings they see. Instruct them move to the widest areas if the rings has an indented circumference. Let each group come up with the number of rings.

Then to confirm the number of years, have students take masking tape and tape the entire perimeter of the treering. Cut the tape where the end meets the beginning. Carefully remove the tape and place it up on the black board. (using different colors keeps students awake, is more lively as and keeps the groups separate). Have students come up to the board and measure the tape with a ruler in inches. Every year a tree is alive is approximately one inch of circumference. How close were the annual ring count to the circumference measurement. Usually they are pretty close.
Look at the spacing between the rings and ask the children
where it rained the most. The students enjoy this truly hands on activity. Once you locate the wood rings you can use them for years.

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Science, level: Elementary Posted Mon Dec 27 19:39:53 PST 1999 by Cindy Roter ( rgilcin@aol.com). Hebrew Academy , Nassau County New York Materials Required: A cross section of a tree or large branch. Masking tape, ruler Activity Time: 20 minutes Concepts Taught: Annual Rings, Tree growth rate ,environmental science Explain to students the concept of annual rings.

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The above video I've used when working our way through op art ideas for my visual arts block. I've also used that video as an extension when discussing drawing circles, given three points. Similar to this video here. It used to be a Grade 8 expectation in the 2005 curriculum, but has since been removed. I don't see anything similar in the 2020 version.

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How to Draw a Perfect Circle (with straight lines)

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Carleigh is excited to draw circles with straight lines.

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Carleigh is excited to draw circles with straight lines.

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Love this activity! I love the art component! I think a nice connection to the art of drawing a circle using only straight lines, would be to introduce the idea of Pi. Way back when, Archimedes found a very close approximation for Pi using straight lines. He drew a 48 and 96 sided polygon to come up with the circumference of a circle. Straight lines to make a circle!

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Each student gets one of these cards and we ask ourselves these questions:

What kind of pattern do you have? How do you know? What attributes/elements are in your pattern?

Then we try to find others who might have the same type of pattern some how and compare!

I LOVE THIS ACTIVITY! It is so fun for them to see math in everyday things!

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STEM Series - Math in Nature - Part 1

https://www.youtube.com/watch?v=yN-sPN3aWqk

STEM Series - Math in Nature - Part 2

https://www.youtube.com/watch?v=EMogHILVOm0&t=126s

I haven't had too much experience teaching math in nature but I found the following videos which I thought were pretty interesting and a great hands on activity for students to identify math in nature.

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It's interesting that we are discussing this at the moment, because I JUST finished using a Jo Boaler video and lesson to teach about patterns in nature. Although we did not go into Fibonacci much, it was touched on and the Grade 5/6 students thoughts it was fascinating. They enjoyed finding all the patterns in Pascal's triangle and some started looking around in their backyards for similar patterns in nature.

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Adding to the discussion.... I thought I'd talk about the human face as an example of math in nature.

In Carol Dweck's book Mindset, she writes about a book that teaches people how to draw, with amazing results. It's called Drawing on the Right Side of the Brain by Betty Edwards. I have this book and it's very good! Here is a link to the Before and After pictures people did after only a few weeks of classes:

One of the techniques Betty Edwards teaches is that faces are mathematically proportional.

This is something Leonardo da Vinci experimented with. He measured a large number of people to come up with the proportional measurements of peoples faces, and bodies. In his notebooks he writes:  ‘The space between the mouth and the base of the nose is one-seventh of the face. The space from the mouth to the bottom of the chin is one-fourth of the face and equal to the width of the mouth. The space from the chin to the base of the nose is one-third of the face and equal to the length of the nose and to the forehead.’ (You can see this in the Vitruvian Man).

If you do teach this lesson, students might be interested to know that the animation studio, Pixar, also teaches a class on drawing to its employees (Note: They are not all artists--although many are). They use the Betty Edwards technique. They say that it doesn't teach people to draw--as much as it teaches them a new way to see.

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Before & After Student Drawings - Drawing on the Right Side of the Brain

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Examples of recent works by students in workshops taught by Brian Bomeisler. The "before" drawings are made on Day 1, the "after" drawings on Day 5 of the 5-Day Workshops. None of these individuals are professional artists. All drawings are done with

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This idea is connected to the lesson put forward by Carleigh.

I had students bring in their favourite action figures/dolls to class. We took measurements of their feet, calves, legs, waist, arms...etc. We then took Canadian averages and scaled the action figures to size. Once we scaled all of our measurements, we created a visual representation of our "life-like" action figures and dolls on butcher paper. The proportions were ridiculous! This lead to some excellent conversations around media and body image.

I didn't use this video in class, but it describes a similar exercise with Barbies.

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Ken: Hiya, Barbie!

Barbie: Hi, Ken! You're looking unrealistically thin today!

Ken: Funny, I was going to say the same about you.

Narrator: Barbie is one of the most popular dolls in America. But that doesn't mean that she's loved by everyone. For years, women advocates have criticized the doll for her proportions, which they say set unrealistic and damaging body expectations for young girls.

In response, her maker, Mattel, created a handful of new sizes in 2016, including Curvy Barbie. But how unrealistic is Barbie really? Is Curvy much better? And where does Ken fit into all of this? That's what we set out to discover.

Benji Jones: Hello, and welcome to our Barbie experiment. Today, we're going to open up each of these three dolls and do a little bit of math to try to figure out what they would look like if they were life-size. We have your more typical Barbie over here. We've got a Curvy Barbie, which is kind of a newer doll. And then, of course, we also have a Ken doll because I couldn't not get Ken. So let's get started.

Narrator: First, we measured each of the dolls, their height, waist, and so on, and used some high-school algebra to figure out their life-size measurements. Then, we compared them to a real-life woman for comparison: our colleague Jensen.

Jones: So Jensen, how tall are you?

Jensen Rubinstein: I am 5-3 and a half.

Jones: So you are the average height of an American woman, congratulations.

Rubinstein: Wow, thank you!

Jones: First thing we're gonna do is take some of your measurements.

Rubinstein: OK.

Jones: And then we're gonna compare that to Barbie. Will you point to your belly button for me?

Rubinstein: Right here.

Jones: OK.

Narrator: Although Jensen is the average height of an American woman, she has a smaller-than-average waist. But still, it's not nearly as thin as Barbie's. If we scale Barbie to life-size, her waist would be a mere 50 centimeters, and her hips, just 71 centimeters. And if Jensen had Barbie's proportions, this is what she would look like. She'd have shorter arms, a longer neck, and tiny feet. In fact, they'd be so small that she'd have trouble balancing and would be forced to walk on all fours.

And what about Curvy Barbie? Is she any more realistic? Actually, yes, at least relative to Jensen. Her waist would be around 63 centimeters and her hips around 90, the same as Jensen's. Now, here's Jensen with Curvy Barbie's proportions. Not that different. Though, of course, she still wouldn't be able to walk upright.

Now, we can't forget about Ken. This time, I stood in for comparison. If we scale Ken up to my height, his waist would be just 63 centimeters, and he would also have unusually small feet, long legs, and larger calves. But his biceps, well, mine are actually bigger. Uh, Ken, you better watch out.

So as you might expect, most Barbies look nothing like average Americans, as fit as they may be. In fact, researchers found that the chance of a woman having traditional Barbie's proportions is less than one in 100,000. And that's a problem.

Deborah Tolman: My name's Deborah Tolman. I'm a professor of critical social psychology and women and gender studies at Hunter College at City University of New York.

Narrator: And according to Tolman:

Tolman: Dolls actually have an enormous effect on girls' and boys' sense of themselves, their ideas about body, particular thin-body ideals. If you have an ideal, and you're never able to achieve it, you don't need a psychological study to show that it makes you feel bad.

Narrator: But there are plenty of studies that do. A study published in 2006, for example, found that young girls who are exposed to Barbie-doll images had more body dissatisfaction and lower body esteem compared to girls who were shown similar pictures of a larger-sized doll. But fortunately, it goes both ways.

Tolman: Playing with a more, I guess, quote, chubby doll actually suppresses the desire for a thin body. So thinking about it only as negative really doesn't tell the full story because there are ways that we can introduce dolls and play that will actually yield protective effects.

Narrator: And that's why some experts applaud Mattel for creating Curvy Barbie. But it's also led to a whole new business for people who want to make even more realistic dolls because let's face it, Curvy Barbie still doesn't depict the average American woman.

Nickolay Lamm: So Curvy, Tall, and Petite Barbie, like, I think it sounds good, like, "Oh, Curvy, Tall, and Petite, we're all diverse and everything." But if we actually look at their individual, each doll, each doll is still unrealistic because the Curvy is still like the perfect hourglass shape. The Petite is very extremely slim, and the Tall is basically like essentially the original Barbie, except kind of a little bit taller.

Narrator: That's Nickolay Lamm.

Lamm: I'm the founder of Lammily, which makes dolls with realistic body proportions to promote healthy body image.

Narrator: Lamm competes with Mattel for business, so of course there's some difference in opinion about the perfect doll, but if you look at his dolls, it's easy to see how they differ from Barbie, Curvy or otherwise. And in the end, maybe there is no perfect doll. After all, people come in all different shapes, sizes, and colors, and it's pretty clear that dolls should too.
EDITOR'S NOTE: This video was originally published in June 2019.

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We compared our bodies to Barbie. Here's what the doll would look like in real life.

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How realistic are Barbie and Ken's bodies? If you scale Barbie up to the height of the average American woman, her waist is about half the size.

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This is the art of birchbark biting.

I was drawn to this because of it's any layers connected to nature and the senses. The senses are what connects us to nature. I like to imagine a world beyond covid where people do not have to be afraid of coexisting with each other, and appreciate and respect the human body connection to art, culture,, learning, respect, etc....

It also ties in to the affects of what we eat and how it becomes part of our whole bodies (teeth and saliva too). Inquiry: Why can't most people keep birch biting art that they made for very long? (Our food is impure and interacts with the bark of the tree differently than if we lived purely from the land).

Ojibwe: Mazinibaganjigan, plural: mazinibaganjiganan) is an Indigenous artform made by Anishinaabeg, including Ojibwe people, Potawatomi, and Odawa, as well as Cree and other Algonquian peoples of the Subarctic and Great Lakes regions of Canada and the United States. Artists bite on small pieces of folded birch bark to form intricate designs.

https://youtu. be/bFJaa9ndAts

Students to working in groups will foster more of an Indigenous approach to teaching/learning.

Students use fingertip (or ruler, meter stick) to show where the lines of symmetry are.

Samples or work adapts to the senses and allows students to feel, see, smell the product.

Brainstorm what symmetry, and lines of symmetry are.

Inquiry: Where does mother nature provide us with symmetry, how do we know it is symmetrical? Students can collect symmetrical items from nature and display them around the classroom, store them in a scrapbook, or even make a classroom mural of symmetry.

Where do we see symmetry in other Indigenous art forms where symmetry is evident (Star blankets, moccasins, beadwork, Métis flower beadwork).

http://aboriginalperspectives.uregina.ca/rosella/lessons/math/introduction.shtml

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-Andrew Goldsworthy Nature Mandalas

-Nature Walk Mandala

A few years ago my learners were really interested in mandalas and their passion tied with my recent work facilitating at our boards Arts Camp (where an amazing teacher created an eco art program) led to us making eco-mandalas.

This project was able to hit expectations within the art, math (specifically geometry and measurement) and science curriculum. You can also encourage learners to find mandalas that already exist in nature and really dive into the historical and spiritual significance of them. We spent some time planning our mandalas, a few days travelling around our community and collecting materials (only found material was allowed) and then a morning creating them in the forest behind our school (where a lot of our learners go to learn, FDK goes on regular walks). It was a great community building activity for us as a class and we also hosted a walkthrough for the classes at our school, which was great. Many of the mandalas managed to last for a while (we did this activity in the spring) and lots of members of the community commented on how neat they were!

You can also use this for the younger grades (patterning and symmetry link) and in our current virtual world you can ask learners to create one in their own space using things they found outside or on walks and send you a picture.

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Teaching the younger grades can be lots of fun.  I like going out for nature walks and having the students collect leaves, twigs, etc., and making symmetrical art. The photos are not from my class, but they will help get the idea of what we do with the items we find on our nature walk.

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My class also has outdoor learning in the morning. We start our day at 8:10 and explore our outdoor learning until 9:00.  Students explore their environment, look at bugs, make mud cakes, find sticks etc.  What they really are doing is noticing.  I like to explore their 'notices" with them.

Example:

Which puddle is deeper? How might we use a stick to measure the puddle?

What do you notice about that stump (maybe the size, comparing it to others, the rings)

Do you notice a pattern on that tree, bug, flower?

Here are a few pictures from our outdoor learning where students noticed the math. It is all about exploring and having conversations with our students.