angles of reflection

To begin their study of angles of incidence and reflection, the Hawks asked, “Does a ball bounce off of a wall the same way light bounces off of a mirror?”

They made a couple hypotheses and came up with an experiment to test them using a ball dipped in paint that would trace its path. They compared the path of a laser pointer with the orange paint ball paths.


As Mackenzie writes, “The group started to see some patterns emerging between the path of the ball and the path of the laser beam. They also began to be able to predict where the ball would bounce to. A new question emerged: ‘What is the relationship between the angle at which light hits the mirror and the angle at which it leaves?’ To answer this we traced the path that a laser beam travels as it enters and leaves a mirror then measured these angles.”

After they measured several angles, the Hawks began to see that the angle of light entering a mirror is the same as the angle at which it leaves!


With this knowledge, the Hawks were given a laser game provocation where they had to orient mirrors precisely enough to hit a fixed target. They had to use what they’d learned about angles of incidence and reflection being equal, and used a protractor to be as precise as possible.




Despite the fact that a traditional trajectory of math doesn’t introduce such skills until the seventh grade, the eight-year-old Hawks used pre-algebra skills to solve the angle challenges in the game, since they only knew the value of one angle. They turned to angle challenges in the abstract – on paper! – and loved wrestling with these problems.


To connect these ideas to a real-world situation, the Hawks visited the Billiards Palacade. Mackenzie writes, “In small teams the Hawks solved problems involving bank shots that put their understanding of angles of reflection to the test.” They used protractors, rulers, and ball launchers to experiment with distances and angles of reflection that would get a ball to bounce right into a pocket







They had some help with queues from a local pool shark!


Their experiments continued with further provocations back at school. Mackenzie writes, “The Hawks were put in pairs each with a covered mirror and a designated spot. Each team had to figure out where their partner had to stand in order to see each other in the mirror.”


They also took inspiration from the Ancient Egyptian pyramid builders who used polished metal to light the tomb walls for painting their murals. Mackenzie placed targets throughout the school and challenged the kids to use mirrors to hit the targets with sunlight, which they traced on blueprints of the school.

The Hawks have been so impressive in their understanding of these concepts and their ability to translate what they’re learning to new situations!