Snowflake math naturally includes geometry, symmetry, patterns, angles, basic shapes, and fractals.
Scientific America: Why are snowflakes symmetrical? – This is where science and math come together! Read about the science behind the symmetry of snowflakes.
Symmetry of Snowflakes offers another explanation of how a snowflake is formed.
Bridges in Mathematics: Snowflake Symmetry – This site offers a video link that helps make learning about symmetry more interesting with Lego bricks, and information about different types of symmetry: rotational symmetry and reflection symmetry. Plus it offers a few links for learning more about symmetry online and how to make snowflakes from paper.
NOTE: For this link to work, choose the option for, “The Way Back Machine” and it will take you to the original activity.
The Spruce Crafts: Magical Paper Snowflake Craft Projects & 9 Amazing Snowflake Templates – This site is filled with a wide variety of paper snowflake activities for the beginner and for anyone looking to challenge their paper snowflake making skills. Classic snowflakes, animal snowflakes, 3-D snowflakes and much more can be found on this site.
When it comes to learning math, we enjoy exploring it in fun and challenging ways and do our best to turn simple items into cool, useful things. Making 3-D ornaments from paper and/or recycled cardboard is a great way to do this.
3-D Geometric Shapes
3-D Geometric shapes make really nice tree ornaments. When I did craft programs for kids and families, the kids really enjoyed the challenge of making these and had a lot of fun decorating them.
Octahedrons have 8 equilateral triangles, they look like two pyramids put together.
Enchanted learning has a printable octahedron that can be used to make this 3-D shape. Just follow the directions on the page to put it together. Decorate the triangles before or after folding and gluing it.
Sphericons are an unusual 3-D shape, and a bit of challenge to make, but look really nice once you get them together. Print these sphericon templates to make them.
Print out, make and decorate a cube, dodecahedron and a tetrahedron too.
We made ours by printing out a template, making a pattern out of it by gluing it to a piece of cardboard, cutting that out carefully and tracing it onto construction paper or a piece of festive paper. Once we cut out our pattern, we carefully folded the edges, glued it together, decorated them with stickers, and put ribbons on them.
3-D Basic Shapes
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| 3-D Star by Fran W |
Another way to make 3-D ornaments is to take two identical shapes, that are the same size, and put them together by cutting one shape from the bottom to the middle and the other from the top to the middle, then sliding them together. A small amount of tape may be needed to keep them in place.
We cut our shapes from cardboard, covered them with festive paper, put them together and added ribbon. We used our own stencils to do this project, but if you don’t have any, you can use the suggested templates below, or trace around cookie cutters.
Hang these on the tree, in corners or along the tops of door jams.
Tip: 3-D ornaments can be made from construction paper, card stock, and recycled cards as well.
Suggested templates…
Tree, star, bell, round ornaments, gingerbread man and snowman
Origami Projects
Some origami projects make really nice tree ornaments as well.
We made our origami ornaments with foil origami paper that we purchased in a craft store, but copy paper can be decorated and used and so can wrapping paper, if it is cut into even squares.
A sticker or a picture can be put in the middle of the star box and the paper balloon can be wrapped like a present.
Suggests for origami ornaments…
Crane, star box, paper balloon, star and stocking
Click here for more holiday origami projects.
More holiday activities can be found here on FranW.com.
3-D Ornaments by Fran W
We started having fun folding paper when my oldest child was about 6 years old and we’ve been finding ways to incorporate it into our lives ever since. One year we added origami presents and cranes to a Christmas tree, another we offered a bunch of holiday related folding projects for a craft program to those who wanted something different to do.
Here are some of the other ways we have used the paper folding projects…
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| Tree Forest by Fran W |
Origami for Winter
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| Stars by Fran W |
This star activity can be very simple to make but if you are up to a little challenge there’s a suggestion for one below!
Once the template has been printed on cardstock paper or a pattern has been made, cut out stars from construction paper, recycled cardboard cereal/cracker boxes, oak tag, or foam, and pop a hole in the ones you want to hang.  |
| Roasted marshmallow by Fran W. |
Marshmallows were once made from the root of the marshmallow plant and were used to help sore throats!
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| Bird w/flower Made with circles |
Did you know…
The word circle derives from the Greek word kirkos
Activity: Circle scenes
You’ll need:
Round flat objects such as bottle caps, lids, or cups, pencil, colored paper, scissors, and glue
Optional: Ruler
Set up:
Using a variety of round lids and objects, trace around them with a pencil onto colored paper and cut them out. You will want to cut a bunch of circles in a variety sizes and then cut them in the following ways.
Use a ruler when needed:
– Leave some of the circles whole
– Take one section out (any size)
– Cut pie shapes (sectors)
– Cut some circles in half
– Cut some circles into: thirds, quarters, eighths, sixteenths, twenty-fourths, etc.
– Cut arcs and cords from your circles
– Cut squiggly lines
Have fun and be creative with this project.
Note: You can turn this into a recycled project by using old magazines, newspaper, old wrapping paper, cards and junk mail. Decorate your own paper and use that too.
What to do:
Use your circles, and parts of circles, to make a variety of objects and scenes. Lay your pieces out in different ways and then glue them down when you like what you see.
Here are some ideas:
Make an underwater scene, fish, people, birds, flowers, butterflies, trees, animals and all kinds of creative designs.
Question of the day:
Objects in nature are rounded.
Can you find something in nature (not made by man), that is not rounded?
Learn more:
Coolmath.com
Definitions and formulas of a circle
Circle Parts
Word search
Design with circles
Make designs with a compass
Basketball Geometry Learn how to find the circumference of a circle and then play basketball when you get the answer correct.
How is Geometry Used in Everyday Life?
Article about geometry.
Math Warehouse: Geometry: Circle
Circles, arcs, chords, tangents – Interactive & Exploratory Activities
Wholemovement
Find out the benefits of folding circles into 3-D shapes.
Wikipedia: Circle
Explains what a circle is, terminology, history and more
Related posts on FranW.com:
Ways to Celebrate Pi Day
Geometric Designs
Bird w/flower Made with Circles
Did you know…
There are seven game pieces used for tangram puzzles and over 5,900 patterns that can be made from them!
Activity: Make Tangram Puzzles
You will need:
Tangram puzzle pieces
Tangram puzzle patterns
Card stock paper
Pencil
Ruler
Scissors
Colored pencils or crayons – optional
Index cards that will fit the size of your finished puzzles
Print out or construct your puzzle pieces and color them if you want. Use card stock or thick grade paper so that the pieces can be used multiple times.
After cutting your puzzle pieces out carefully, play around with them for a bit to see what they look like when you put the shapes together in certain ways. When you are ready, print out puzzles to solve, but don’t peek at the solutions until you are ready!
Variation #1: Homemade Puzzles: Using smaller Tangram pieces that you make yourself, design your own puzzle cards. To do this, make your puzzle on an index card and trace around your completed design with a pencil, then go over it with a dark colored crayon or marker. Put solutions on the back in pencil and then give your puzzles to someone else to solve.
Variation #2: Tangram Art: Make your own designs from pieces that you make, glue them to a piece of paper, color them in and create a scene around them.
If you would rather play Tangrams online, try this site out:
PBS Kids: Tangrams
Rules: The traditional rules to the game say that you must use all seven pieces, they must lay flat, they must touch one another, and they can not over lap.
Question of the day:
In what year did Tangrams come to America?
Learn more…
abcteach.com: Tangrams
Printable patterns and puzzles
Tangram House
Play an Tangrams online
Tangram Channel
Puzzles, solutions, history, geometry connection and more.
Squidoo: Tangrams Activities
Article about Tangrams filled with links to other sites
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