Last Landing

Junior (Age 9 – 12)

Curriculum Goal

Junior: Geometry and Spatial Sense

  • Describe and perform rotations and translations on a grid in various contexts.

Context

  • Students will be in groups of two to four with a chess board or any 8 × 8 grid. Students should have prior experience with translations, reflections, and using cardinal directions (e.g., translate one space west).

Materials

  • A chess board or any 8 × 8 grid
  • Paper to mark which parts of the board are north, south, east, and west (Appendix A)
  • Two to four L-shaped pieces (landing strips), and markers (Appendix A)

Lesson

  • Begin by placing the pieces of paper with directions (i.e., north, south, east, and west) in their respective positions around the board.
  • There are two moves that players can make:
    • 1) Players can translate their piece one space in any direction, or
    • 2) Reflect their piece in any direction.
  • Players must ensure their entire landing strip always stays on the board.
  • Players begin by placing their landing strips in any direction, anywhere on the board.
  • Players then place a marker on the board underneath the x that is on their landing strip. This spot becomes their first no-landing zone spot (neither players’ x can land on this spot).
  • The first player begins by announcing how they will move their landing strip (e.g., I am going to reflect north). When moving their landing strip, the player must also ensure their x does not land on a no landing zone. The player places a marker wherever their x lands.
  • The next player does the same, marking wherever their x lands and ensuring their landing strip does not land on a no-landing zone.
  • Players landing strips may overlap if it does not overlap at the no landing zone.
  • Players are eliminated if they land on a no-landing zone.
  • Players continue taking turns, filling up the board, until they are eliminated.
  • The last player to make a successful landing is the winner.

Look Fors

  • Do students successfully describe and preform reflections and translations?
  • Are students able to successfully predict the result of their transformations?
  • What strategies do students use to predict the results of their transformations?

Extension

  • Use different shaped pieces as landing strips. • Add more x’s onto the landing strips, to create more no-landing zones.
  • Each player is given multiple landing strips.
  • Players rotate pieces by a certain amount (e.g., 90 degrees).
  • Increase the number of spaces a player can move (e.g., translating piece two spaces).
  • Increase the number of movements a player can make (e.g., player has two moves, can reflect once, and translate once).
  • Use a cartesian plane instead of an 8 × 8 grid, and have players announce the landing strips’ coordinates.

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