Rotational Symmetry STEAM Project
This rotational symmetry art project is a gorgeous and creative way for kids to explore how mathematical concepts and art work together!
This rotational symmetry art project is a gorgeous and creative way for kids to explore how mathematical concepts and art work together!
Did you know art is often made using math? Today's project is called Rotational Symmetry. What does that mean?
For a shape to have rotational symmetry, it must be able to rotate onto itself in less than one full turn.
- Rotation is the process or act of turning or circling around something. like the earth's orbit around the sun.
- Something is symmetrical when it is the same on both sides. A shape has symmetry if a central dividing line (a mirror line) can be drawn on it to show that both sides of the shape are exactly the same.
- Therefore, a shape has Rotational Symmetry when it still looks the same after some rotation.
For a shape to have rotational symmetry, it must be able to rotate onto itself in less than one full turn.
Let's say this arrow is our original shape..
If we rotate the arrow 1/4 of a turn, we have made a 90 degree turn.
If we rotate the shape 1/2 of a turn, we have made a 180 degree turn. Because it is less than one full turn, and it appears exactly the same as the original shape, this shape has rotational symmetry.
Does this shape have rotational symmetry?
Let's find out!
Let's find out!
 1/4 (90 degree) turn |  1/2 (180 degree turn) |  3/4 (270 degree turn) |
Do any of these rotations look exactly like the original shape?
Does this shape have rotational symmetry?
Nope! It takes one full 360 degree turn for this shape to look like the original!
Does this shape have rotational symmetry?
Nope! It takes one full 360 degree turn for this shape to look like the original!
KeAre you having a hard time imagining this? Let's do an art project using this mathematical principle to get a closer look!
In this project, you will create some shapes of your own and find out if they have rotational symmetry!
Here's what you will need:
STEP 1: GATHER
Gather your supplies!
In this project, you will create some shapes of your own and find out if they have rotational symmetry!
Here's what you will need:
- Cardboard or cardstock (try using an old cereal or tissue box)
- Drawing paper
- Colored pencils
- Scissors
- Tumb tack
STEP 1: GATHER
Gather your supplies!
STEP 2: DRAW
Draw a fun and random shape on one piece of cardboard. Keep in mind that the more symmetrical your shape is, the more likely it will have rotational symmetry!
STEP 3: CUT
Cut our your shape the best you can.
STEP 4: PIN & TRACE
Lay down a larger sheet of cardboard, with your drawing paper on top. Place your cut out shape on your paper. Place your thumb tack right in the center of your shape. Your shape should rotate without sliding around. Trace your shape!
(I laid my drawing paper on a paper plate that help the tumb tack still)
Draw a fun and random shape on one piece of cardboard. Keep in mind that the more symmetrical your shape is, the more likely it will have rotational symmetry!
STEP 3: CUT
Cut our your shape the best you can.
STEP 4: PIN & TRACE
Lay down a larger sheet of cardboard, with your drawing paper on top. Place your cut out shape on your paper. Place your thumb tack right in the center of your shape. Your shape should rotate without sliding around. Trace your shape!
(I laid my drawing paper on a paper plate that help the tumb tack still)
STEP 5: ROTATE
Rotate your shape 90 degrees (1/4 turn) from the original and trace again.
Rotate your shape to 180 degrees (1/2 turn) from the original and trace again.
Rotate your shape to 270 degrees (3/4 turn) from the original and trace again.
Did you retrace your original outline at any point? If you did, then your shape has rotational symmetry!
STEP 6: FILL
Fill in the new smaller shapes on your paper with colored pencils, starting with the largest and most obvious shapes and move to the smallest. Try to fill like shapes with the same color!!
Rotate your shape 90 degrees (1/4 turn) from the original and trace again.
Rotate your shape to 180 degrees (1/2 turn) from the original and trace again.
Rotate your shape to 270 degrees (3/4 turn) from the original and trace again.
Did you retrace your original outline at any point? If you did, then your shape has rotational symmetry!
STEP 6: FILL
Fill in the new smaller shapes on your paper with colored pencils, starting with the largest and most obvious shapes and move to the smallest. Try to fill like shapes with the same color!!
For more artistic results, try some more crazy shapes! They are not likely to have rotational symmetry, but they sure will be fun and beautiful to color in!
You can leave your finished project on your paper or cut it out!
Thank you for learning with us today!
See you tomorrow!
Parents: One thing to keep in mind as you are doing this project is that the object kids create will have rotational symmetry, meaning that it will have the same shape after a certain degree turn. But because we are not using compasses and rulers and are generally being free-handed in our drawings, these shapes are not exact examples of objects with rotational symmetry.
You can explain that a circle has infinite rotational symmetry, but that a shape created by tracing and rotating a shape four times as this project demonstrates will have only 4th degree rotational symmetry. As the object makes one full turn, it will be an exact replica of itself four times.
have the kids try it and see how exact their shapes are! It’s all a learning process and the degree (pun!) to which you want to delve into mathematical concepts is up to you.
You can explain that a circle has infinite rotational symmetry, but that a shape created by tracing and rotating a shape four times as this project demonstrates will have only 4th degree rotational symmetry. As the object makes one full turn, it will be an exact replica of itself four times.
have the kids try it and see how exact their shapes are! It’s all a learning process and the degree (pun!) to which you want to delve into mathematical concepts is up to you.
