Introduction: The Exponential Decay Paper Christmas Tree

About: Hi...I'm a HS Math teacher, STEM Presenter & Podcaster, & all around fixer/builder/maker. Let me know if I can be of help!

Do you have some construction paper, scissors, & glue sticks? That's all you need to introduce an important math idea called Exponential Decay to your kiddos while making a pretty Christmas tree.


1 rectangle of green construction paper

1 small scrap of brown construction paper

1 small scrap of yellow construction paper

1 piece blue construction paper


glue stick

hole punch & scraps of paper for decorations

Step 1: Make a Square

Start with a green square of construction paper (mine was about 6 inches). An easy way to make a square is to fold a rectangle so that one edge is lined up with the adjacent edge. Grab a corner of your rectangle and pull it up so that it touches the top edge. Then cut along the exposed edge.

Step 2: Cut Along the Diagonal

Cut along the diagonal of the square (the line should be visible from when you folded to make the square). Now you have 2 equal size triangles, half the area of the original square.

Step 3: Continue Cutting in Half

Set aside one of your triangles.

Then take the other triangle, fold it in half, then unfold it and cut along the diagonal. You now have 2 equal triangles again, each half the size of the previous one you set aside.

Set one of these aside, and repeat the process of folding in half and cutting the remaining triangle until you've gotten to the smallest triangle you want to make.

This is the basic idea of Exponential Decay, a topic from most High School Algebra classes, but any student can understand it with this easy example of cutting triangles. Exponential decay (& exponential growth) are used in many situations about populations and interest on money. In fact, if you had a pair of tweezers and a microscope, you could continue to cut the triangles in half forever!

Step 4: Make the Tree

Starting with the largest triangle, take each of the triangles you just made and glue them one at a time to the blue construction paper starting near the bottom. Overlap each smaller triangle as you go up the tree.

Step 5: Make the Trunk

Every good Christmas tree needs the typical rectangle shaped trunk. Grab a scrap of brown or black construction paper from your scrap bin (what? you don't have a bin of construction paper scraps & cardboard pieces? shame on you!) and make it a rectangle shape. Put glue on the back of it, and slide it under the bottom triangle.

Step 6: Make the Star & Decorate the Tree

Grab a scrap of yellow construction paper and cut a star shape and glue it to the top of the tree. If you can't reach the top, get an abominable snowman to help (they don't need a ladder to reach).

Feel free to make any other decorations you'd like for your tree:

-circles for balls can be made using a hole punch

-make garland using those stringy bits from spiral notebooks

-grab something fancy from your scrap bin

Step 7: Finished!

Display it proudly...and if you share pics of it on social media, feel free to tag me @dailySTEM

Want to see it in time-lapse?

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