Transformania: Teacher Guide

Standards

Key vocabulary

• pre-image / image: the figure before a transformation, and the figure after it
• translation: a slide; every square moves the same number of units in the same direction
• rotation: a turn around a fixed point; each quarter-turn is 90°
• clockwise / counterclockwise: the way a clock’s hands turn, and the opposite way
• reflection: a flip across a line; every point lands the same distance from the line, on the other side
• congruent: the same size and shape; every image in the game is congruent to its pre-image

What students learn

Students don’t answer a question and then watch a block fall: they perform each transformation themselves, on the grid, and compare their image with a faint ghost of the pre-image that stays where the figure started. The game checks every square of the image against the correct one, so a figure that looks right but sits one unit off, or turned the wrong way, isn’t accepted.

• Translations: slide left or right a given number of grid units. Students may move back and forth freely; only the final position counts.
• Rotations: the figure sits on tracing paper pinned at a red point. Students turn the paper by dragging its handle or pressing a key, one quarter-turn (90°) at a time, and the red arrow on the paper, which starts pointing up, shows how far it has turned. 180° is two turns, 270° three, 360° four, and the game checks the direction as well as the amount: 180° clockwise and 180° counterclockwise land in the same spot but are different turns.
• Reflections: a pink vertical line and a green horizontal line are both shown. Students choose the right one: left and right flip across the vertical line, up and down across the horizontal line. Each square lands the same distance from the line, on the other side.
• Sequences (Hard): two or three transformations in a stated order, done one step at a time.

How the game works

• A figure made of squares appears in the transform zone above the white dotted line, already turned or flipped at random. Students slide it to a starting spot and press Confirm start.
• Only then does the instruction appear. Students perform it and press Check. A correct image drops straight down into the stack; a full row clears.
• A wrong check says what went wrong (“You turned counterclockwise”, “You flipped across the horizontal line”, “You moved it 1 unit, but the instruction says 2”) along with a hint. The first wrong check on a question adds an X; more wrong checks add no more Xs. After the second, the correct move plays slowly on the board and the step starts over, and later a dotted outline of the image appears. Three Xs lose the game, and every completed row removes an X.
• Players take turns on one shared board: one piece each, then the other player’s turn. Each player keeps their own Xs and rows, and their pieces are their own colors.
• The first player to clear the goal number of rows wins (3 on Normal, 4 on Hard). A player whose piece stops above the dotted line loses, and the floor rises one row every few pieces.
• Normal: translations of 1–4 units left or right, rotations of 90° and 180° both ways, and reflections across a line drawn on the board. Hard: rotations up to 360°, translations up and down too, reflection lines that are not drawn (the instruction says where the line is, for example “the vertical line 2 units to the right of the figure”), larger figures, and sequences.
• Practice: one student, no opponent and no Xs, with the skills you pick (translations, rotations, reflections, sequences). Finish from the menu to see results by skill.
• The computer plays by the same rules, gets its own figures and instructions, and never gets a transformation wrong. Students watch it do each one on the same board, a worked example every other turn, but it still has to stack well.
• Everything works from the keyboard, the menus included: arrow keys choose the mode and level and Enter plays; in a game the arrow keys move and flip, and during a rotation the up arrow turns the tracing paper clockwise and the down arrow counterclockwise, and Space or Enter confirms and checks.

Worked examples

Common mistakes the hints target

Ways to use it in class

• Printables. A pre-assessment of the earlier skills, visual notes, an entry ticket, a worksheet with a picture answer key and a two-to-a-page exit ticket match the game.
• Reteach with Practice. Students who struggle with one skill play Practice with only that skill on.
• Real tracing paper first. Do one quarter-turn with real tracing paper and a pencil point, then play: the in-game paper works the same way.
• Partner review. Pairs (or groups of 3 or 4) play Player vs Player on one device, taking turns with the same keys or buttons, and check each other’s transformations out loud.
• Talk while playing. Ask students to say the transformation out loud as they do it: “two quarter-turns, counterclockwise, around the red point.”
• Results by skill. At the end of a game, the results show how many translations, rotations, reflections and sequences each student got right on the first try.

Discussion questions

• Why do 180° clockwise and 180° counterclockwise land in the same place? Why don’t 90° clockwise and 90° counterclockwise?
• Which single rotation does the same thing as 270° clockwise?
• After any transformation in the game, how do you know the image is congruent to the pre-image?

Accessibility

Everything can be played with the keyboard, and a screen reader hears each new figure and where its squares are (by row and column), each instruction with where the red point or line is, every hint, and the Xs and rows. On phones and tablets, on-screen buttons do every move and students play against the computer.