Math Concepts: Symmetry, Reflection, Angles, Patterns

What You Can Do: Symmetry occurs in natural environments, such as the bilateral symmetry of
the human body or the rotational symmetry of a starfish, and it can also be explored in many human creations, such as the
arrangement of tiles on a floor, the blades of a fan, the pattern of a tapestry, or even the drawing of a five-point star
by your child.

One fun activity to do with young students is to investigate the symmetry of the letters of the alphabet. The letter A
has vertical symmetry, the letter D has horizontal symmetry, the letter N has rotational symmetry, and the letter X has
all three types of symmetry. The words NOON and OBOE naturally exhibit symmetry — NOON can be rotated 180° and it will
look the same, and OBOE reads the same when reflected over a horizontal axis.

Artists like Scott Kim and John Langdon use some of these symmetric properties of letters to create inversions,
words or names that can be read in more than one way. Your child might enjoy learning more about these artists or trying
to write their own name so that it reads in more than one way.

Math in the Game: Students with an aggressive trigger finger like to shoot quickly. But encourage
them to take some time to think about the path of the ball. Students may quickly choose a path that will hit a 250-point
token, but that may not be the best shot if the ball slams off a wall and immediately disappears into a hole. Maybe there’s
another path that would hit three 100-point tokens? That would be a better shot.

Students should consider the location of the wall. The dimensions of the board are very important to the path that the
ball takes. Changing the location of the wall just one click will sometimes alter the path of the ball so that it hits
multiple tokens instead of just one.

Related Resources:

Paper Pool Lessons

In the game of Paper Pool, students investigate the results of rolling a ball around pool tables of various sizes.
As in Slam Ball, the ball caroms at a 45° angle and stops when it reaches a pocket.

Paper Pool Tool

This applet allows students to investigate the Paper Pool game.

Paper Pool

Provide opportunities for students to develop their understanding of ratio, proportion, greatest common factor and least common multiple by playing Paper Pool.

Paper Pool: Analyzing Numeric and Geometric Patterns

Provide opportunities for students to develop their ability to analyze numeric and geometric patterns by playing Paper Pool.