# Geome-Tree – A Christmas Math Project

Christmas is just around the corner, and it is a great time to make some new ornaments to hang on the Christmas tree and create a unique table decoration for your home or classroom. In this fun and easy Christmas Math project, you will do just that! We will be exploring geometry, 3D nets and Sierpinski Triangles, all while making fun Christmas crafts, ornaments and decorations.

## CHRISTMAS GEOME-TREE DIY PROJECT

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Geometry is the part of Math that helps us understand all these shapes. How do you pronounce geometry… well it is ‘je-aa-ma-tree’. That tree sound at the end was the perfect inspiration for us to make this Geome-Tree project for the holidays. We will be using different shapes to create unique Christmas ornaments and decorations. All while learning a little math, which makes this the perfect project for the classroom.

## Check out the Video Tutorial

If you can’t see the video, find it on the STEAM Powered Family YouTube Channel.

## What is Geometry?

OK, so the name is cool, but what is geometry in math?

Geometry helps us understand shapes, their sizes and how they are constructed. Think of your classroom: the rectangular desks, the round clock on the wall, and the parallel lines on your notebook paper. Geometry is everywhere! But it’s not just about identifying shapes. It’s also about understanding the “rules” that govern them. Like, did you know that the angles in a triangle always add up to 180 degrees? Cool, right?

### Vocabulary

In geometry, you will learn many new words to help you make sense of the different shapes and how many of the same shapes put together can create an entirely new shape or object.

Let’s look at some of the words that will help us do this:

Lines – Lines can be straight or curved.

Angles – Angles show us how and where lines meet each other.

Points – A point is where two lines meet or cross each other.

Rays – A ray is a straight line that starts at a point and can go on and on in one direction.

Planes – A plane is an invisible, flat surface that can go on and on in two directions. A plane does not have any thickness. It is always flat. The top of a table is a plane. A door, a piece of paper, a wall, a window, and a TV screen are planes, too.

Plus of course all of the names of shapes from squares (2D) to cubes (3D), circles (2D) to spheres (3D). Let’s learn about dimensions now.

### 2D vs 3D Shapes

Shapes also have dimensions, they can be 2D (two-dimensional) or 3D (three-dimensional).

2D shapes are flat and do not have volume. It means that they cannot be filled with anything. Think of a circle. If you tried to pour water into a circle… it would make a big mess.

3D shapes have length, width and height, meaning they have volume and can be filled. You can walk around them and see their form from any angle. Think of a cylinder, like a glass. It has a circle bottom but because it has curved sides all the way up, you can fill the inside with water.

The 3D shapes we will use in this Christmas math project are a tetrahedron, a cube and a cone.

These 3D shapes all began as 2D shapes â€“ a cube (made up of six square faces), a tetrahedron (made up of four triangular faces), and a cone (made up of a triangle and a circle).

### The Sierpinski Triangle

In this fun math project, we will make ornaments for the Christmas tree using 3D nets and create a fantastic centrepiece for our Christmas dinner table called a Sierpinski Triangle which we are turning into a festive maths tree.

This intricate triangle is named after a Polish Mathematician called Waclaw Sierpinski. The shape comprises many triangles (we use tetrahedrons) stacked on each other in a particular way to create a really cool and intricate triangle.

## Christmas Geome-Tree Project

In this Christmas Math project, we will be making Christmas decor using cones, squares and tetrahedrons, plus using Sierpinski triangles we will make a cool maths Christmas tree.

For this activity, we have a printable that is available to our STEAM Powered Family mailing list members. Enter your email to unlock the printable.

### Materials & Tools

The Christmas Geome-tree Templates (see form above)
White and coloured cardstock
Cello tape
Glue gun
Glue stick
White craft glue
Ruler
Scissors
Glitter
Thin ribbon, string or wool
A screw (optional, but helpful for scoring the cardboard/paper)
Printer

## Directions

### Making Geometry Shapes

This first step is making plain shapes for students to explore and learn before we make our Christmas Ornaments and Sierpinski Triangle Tree.

Print the templates on regular paper and cut out the tetrahedron, cone and cube as shown on the templates.

Using a ruler and a screw, lightly score all the dotted lines and fold inward on all the dotted lines. You do not want the text on the outside of your 3D shapes.

#### Folding the 3D shapes

Starting with the cube, glue one of the flaps to a corresponding side and hold it down for a few seconds. Do this with all the flaps until the cube is complete.

Next, glue the tetrahedron together like you did the cube, one flap and side at a time.

The cone is a little tricky. Put some glue on the extended flap, take the opposite side, gently curve it, bend it up to meet the flap, and stick it down. Please do not push it flat. If you do, gently make it round again by pushing down on the glued flap.

If you have not lined it up perfectly, trim the bottom edge so the two sides are the same length.

Put glue onto each flap of the bottom piece, fold each flap upward, close the “lid”, and turn the cone the right side up and hold it down for a few seconds. This helps to hold each of the little flaps in place.

Your 3D shapes are now done! This is a great time to explore the number of points, angles, lines, etc. that make up the shapes.

### Making the Sierpinski Triangle Tree

#### Preparing the tetrahedrons

Using cardstock, print and cut out eight pages of the smaller tetrahedron (this will give you 16 tetrahedrons) you will use for your centrepiece. I printed mine on green cardstock. You may use one or multiple colours.

You also need to print and cut out the star on page 7 of the template for the top of the centrepiece.

Get your ruler and a screw, score all the pieces, then fold and glue all 16 tetrahedrons together.

This would be an excellent time to get some helpers or have students work in teams to make the Sierpinski Triangle. It can be tricky and time-consuming. Extra hands are helpful!

#### Putting the Sierpinski Triangle together

Now that you have all sixteen tetrahedrons, it’s time to make this fantastic geometrical structure!

The first thing to do is to make four individual mini tetrahedrons made up of four tetrahedrons.

Step 1 – Tape two tetrahedrons together in a straight line.
Step 2 – Tape a third tetrahedron to the back of the second tetrahedron. Ensure the points meet in a straight line.
Step 3 – Tape the third and first tetrahedrons together at the back. Again, ensure the points meet straight.
Steps 4 – Tape the fourth tetrahedron to the top of the three tetrahedrons at the bottom.

###### Sierpinski Triangle Assembly Tips
• Always fold the tape in half. Place one side on the face of the tetrahedron and the other half on the underside.
• Make a small slit in the tape between the two tetrahedrons and tuck the little pieces to the inside with the tip of the scissors.
• It is always easier to turn the pieces you have joined around so that they sit flat on the surface you are working on before placing the tape.

You should now have four groups of four tetrahedrons.

#### Putting Together the Sierpinski Triangle Tree

In the same manner as the process above, you will now tape three groups of tetrahedrons together to make the base of the Sierpinski Triangle.

The fourth group can be a little tricky. Just remember to be very gentle. It is very delicate!

Place the last group on the surface in front of you. Turn the group of three tetrahedrons over until all the pieces fit together. Then, apply the tape. Keep turning it repeatedly until all the sides are joined.

Remember not to apply force when moving the whole triangle or applying the tape as it will break. This is not a train smash, as all you have to do is reinforce the broken pieces of tape!

#### Finishing off the Sierpinski Triangle Tree

Using the glitter you have, cover the star you cut out earlier with white glue and sprinkle the glitter onto the glue. When it is dry, turn it over and repeat the process on the other side.
Use a glue gun to glue the shiny star onto your Sierpinski Triangle.

It’s now time to make some Christmas tree ornaments.

### How to Make Geometry Christmas Tree Ornaments

For this task, you have two options:

You can either use the 3D shapes we made at the beginning of the project and decorate them creatively or print and cut out pages 6-8 of the templates, create the 3D shapes again, and colour them in your favourite colours.

To hang them on the Christmas tree, use the glue gun to glue some ribbon, string or wool to the tops of each shape and tie them onto your Christmas tree.

Who knew Geometry could be so much fun and so festive?

## Extension Activities

Have your kids noticed that inside their shapes it is empty? Why not use these as a fun way to gift small items? Kids can place little letters inside or candies to share with someone they love. If you are doing this, you may want to use a slightly thicker paper stock.

Looking for more math fun for Christmas and the holidays?

Try making MÃ¶bius Strip Ornaments and Garland.

Or test your logic with Sudoku inspired Christmas math problems.

Need more STEM ideas for the holidays? Check out Christmas STEM Activities for loads of inspiration.