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A Math lesson on Symmetry





Summer Jett

Tricia Whitney

TOPIC: Symmetry
OBJECTIVES: Students will recognize symmetrical and non symmetrical designs. Students will create symmetrical and non symmetrical patterns with bandannas.


A. Anticipatory Set – Teacher will ask, “What is a cowboys best friend?” Take suggestions from class. Finally, tell class that a bandanna is a cowboy’s best friend. Then talk to class about “Cowboy Math”, a cowboy who likes to be perfect, so insists that when he wears a bandanna it must be symmetrical. The class will be helping out Cowboy Math today.

B. Conceptual Development/Activity – We’ve talked about symmetry in the past, ask class for examples, point out certain things that have symmetry throughout the room (face, piece of paper). Students will then break up into groups of two.

      1) First they will do the “Square Meal, Square Deal”, folding their bandanna’s in half making a fine napkin or a crumb catcher. Does this new design have a line of symmetry?

      2) A cowboy’s food, or “grub” was piled onto a tin plate. Fold your bandanna in half again. Now you can put those hot plates right on your lap when you eat. Is this design symmetrical?

      3) You’re full and need a hot drink for the cold, chilly night. Fold the bandanna in half and put it around you cup of hot chocolate. It will keep you hand from being burned. Is this design symmetrical?

      4) Cowboys spent their days outdoors. Bandannas helped them look cool and keep cool in hot weather. Make a triangle with your bandanna. You could dampen this triangle with cold water and put it under your cowboy hat to keep cool. You could also put it around your neck to mop your face when you sweat. Is this design symmetrical?

      5) A bandanna comes in handy when you need a bag. Or when you need a tent for you pet snake. Fold the bandanna to make a triangle. Is this design symmetrical?

      6) Fold it again. Tie both ends in a knot. (You can open the “bag” so that one side has three layers of cloth and the other only one.) Is this design symmetrical?

      7) Say you’ve found some chunks of gold. Or maybe you’re carrying a pocket watch your great grand – daddy gave you. Wrap your keepsakes in your bandanna by folding each corner into the middle. Place your precious loot in the first layer of folds. Is this design symmetrical?

C. Practice – Have the students find other ways to fold the bandanna symmetrically. Share the discoveries with the entire class. Then ask class to find ways to fold the bandanna that aren’t symmetrical. Share that with the entire class.

D. Assessment – Teacher will walk around the room observing each of the groups, asking each team questions pertaining to the lesson (Why does/doesn’t that have symmetry?). When students come up with own symmetrical and non symmetrical designs, teacher will evaluate.

E. Closure – Class will discuss other places that we see symmetry. Then class could move into actual geometric shapes.

MATERIALS: Bandanna (one per two students), paper, pencil

SOURCE: Durkin, C. (1994). “On the Trail with Symmetry”. DynaMath. Volume 13, Number2, October 1994. Scholastic: New York. p. 6 – 7.

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