Geometry is my favorite thing to teach in math and that's probably because I can turn anything geometry related into an art project!
To help kids understand measuring angles, we start with quarter turns. Since I teach it after a unit on time measurement, I make the connection to starting at 12:00, and the minute hand stopping at 15, 30, 45, and back to 1. I explain that one difference between the angles and the clock is the hour hand moves slightly, while the angles stay at multiples of 90 degrees.

Measuring Angles Art
Paper or plastic cups are good options for tracers. I tend to have plenty of plastic takeout containers on hand so we can reuse them for painting from year to year and those work great for this project as well. By filling in the arcs, kids can see that even though the arcs can vary in size, they have a defined start and end point if it is 90, 180, 270, or 360 degrees.
For our second art project, I give students two "lines" (strips of paper) and we practice rotating one of them around in a clockwise direction. Once they are glued we trace the the arcs again, and this time we label the degrees after measuring angles.
By introducing these 4 angle sizes, students were able to make pretty good initial estimates about angles that were "near 90," "near 180," "near 270" and "near 360." Before I even started teaching them how to line up and read a protractor, they were getting a sense of reasonable measurements of angles.
Measuring Angles Task Cards for Additional Practice

These cards are great for measuring angles in isolation as well as within polygons. I even threw in a bonus for students to "discover" when it comes to adding up all the angles of like colors (hint: each set of like colored angles form a complete circle). I've had great success with these task cards since there are lots of examples for kids who need repeated practice, and adding up to 360 degrees is engaging enrichment for students who need more stimulation.

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