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