Triangle Cat

This activity will bring math to life by using triangles to create actual art! This activity is perfect for 4th graders and above who are learning to connect the material they are learning at school with the real world. We’ll use the three angle-based triangles to create the head, and the three side-based triangles to create the body and tail. Let’s bring math out of the abstract and into the practical!

Supplies:

2 pieces of printer paper

Colored pencils, crayons, or markers

Pen or pencil

Glue

Ruler

Optional Activity Modification: If you aren’t as interested in the math concepts behind this activity, please feel free to ignore steps 1 and 5. This will turn Triangle Cat into more of a diy puzzle rather than an art/math hybrid.

Step 1: Triangle Key

First, take one of your pieces of paper and turn it so it is in landscape view (horizontal). In the top left corner, Write a title called Angle-based triangles, write out the names of the three angle-based triangles (right, acute, and obtuse) below the title, and assign them a color. You may also want to draw a small picture to identify them as shown.

Step 2: Creating the Head

We will now use the second piece of paper to draw, color, and cut out the triangles that will create the head of our kitty. First, draw two right triangles that are 1 inch by 1 inch. A right triangle is defined by having a right angle (90 degrees).

Next to the right triangles, draw an obtuse triangle with one side being 2 inches long and the obtuse angle centered above the 2-inch-long side. An obtuse triangle is defined by having an obtuse angle (greater than 90 degrees).

After that, draw two acute triangles with one side being 1.5 inches long. The acute angle directly above the 1.5-inch-long side should be .5 inches from the right on the first triangle, and .5 inch from the left on the second triangle. This will create the effect of the triangles looking like they are mirror images, or a reflection, of each other rather than being direct copies like the others. An acute triangle is defined by having all angles be under 90 degrees.

Finally, we will create the ears by drawing two more right triangles. These triangles should be 1 cm by 1 cm.

Helpful tip: The triangles don’t need to be perfect (mine certainly aren’t!). If the triangles don’t fit together exactly right once cut out, it is perfectly acceptable to layer them on top of each other or leave a bit of space in between them.

Step 3: Coloring and Cutting

Next, color in all the triangles using the colors that you chose at the beginning of the activity and cut them out. If you have modified this activity, feel free to use whatever colors you’d like!

Step 4: Putting the Head Together

Now we’ll be able to put the head together just like a puzzle! The head will be glued down to the first piece of paper with the key on it in the top left section.

The large right triangles will form the center of the head. Place them back-to-back so that the right angles are touching.

The obtuse triangle will form the chin. Flip it upside down and attach it under the right triangles.

The two acute angles will form the top and sides. Place the largest sides against the right triangles with the angle sticking out closest to the chin.

Finally, place the two smallest right triangles on top of the acute triangles to form the ears. They should be facing away from each other on opposite sides.

After gluing down all triangles, add some eyes and a mouth.

Step 5: Triangle Key

We will now make another key for the side-based triangles (isosceles, equilateral, and scalene). Place it underneath the key for the angle-based triangles and be sure to assign them a new color each!

Step 6: Creating the Body

Next, use what’s left of the second piece of paper to create the body using the side-based triangles.

First, we will create a tall and skinny isosceles triangle. Draw a 1-inch long line to create the base. In the middle of this line (.5 inches), draw a 5-inch-tall line extending upwards and draw two diagonal lines from the top all the way to the ends of the 1-inch line. Isosceles triangles have two identical sides.

Next, we will make a scalene triangle. The base should be 5 inches long. The other two sides can be as long as you’d like, just as long as one side is shorter than the other. A scalene triangle is defined by having three sides of different lengths.

We will now create 7 equilateral triangles. To do this, first draw one triangle with all sides being 1 inch long. Next, color it in and then cut it out (The reason why we are coloring this one before the others is because I’ve found that it’s easier to color in the triangles when they are still a part of the page). Then, trace it 6 times.

Lastly, we’ll make the tail by creating a smaller

isosceles triangle. Make the base .5 inches long

with each side being 2.5 inches long.

Step 7: Coloring and Cutting

Color and cut out all remaining triangles either using the key made during step 5 or using whatever colors you would like if the activity has been modified.

Step 8: Putting the Body Together

We’re in the homestretch now! We can now put the body together.

Glue the highest point of the biggest isosceles triangle directly underneath the center of the chin. This will create the middle of the body.

The scalene triangle will form the right side and chest area. Place the 5-inch side of the scalene triangle against the right side of the isosceles triangle with the outward facing angle closest to the head.

The 7 equilateral triangles will form the back. Place four of them side by side down the left side of the isosceles triangle, starting from the top. The remaining three will fit in between them just like shark teeth.

Finally, the smallest isosceles triangle will

form the tail. Place it sideways on the bottom

part of the left side of the isosceles triangle.

Step 9 (optional): Give the kitty a background!

I decided to place my kitty in a flower field near a tree, but you can place your kitty wherever you’d like! Congratulations on creating a cat out of triangles!