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Geometry and Measurement 6-8 / Week 09 / Monday
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Week 09 · Slides, Flips and Turns

Monday

Three ways to move a tile
// Moving a shape without changing it
⏱ about 20 min

Monday: Three Ways to Move a Tile

Rocket drops a cardboard L on the taped floor grid. "The clubhouse floor pattern. L-shapes everywhere."

He slides it right. He flips it over. He spins it on one corner. "Three moves, one tile."

"Three moves with names," Raven says. "A slide, a flip and a turn. What do you notice about the tile after each one?"

"It is the same tile," Rocket says. "Same size, same corners. Just somewhere else, or facing another way."

Nova hovers over the grid, her light tracing the L and its copy. "Same tile, new address," she says. "Write the new corners."

Rocket reads the grid. "Corner A was at (1, 1). Now it is at (4, 1)." Nova hums. "Every corner moved the same way. Check."

Rocket slides and flips cardboard L-shapes on a taped grid while Raven turns a triangle on a pin, Nova above.

Slide, flip, turn

MoveMath nameWhat happensFloor test
slidetranslationevery point moves the same distance in the same directionpush the tile without turning it
flipreflectionthe shape becomes its mirror image across a linepick the tile up and turn it over
turnrotationthe shape turns about one fixed pointpin one point and spin

The new shape is called the image. Its corners get a mark: corner A lands at A′, read "A prime".

None of the three moves changes the tile itself. Every side stays the same length and every angle stays the same.

A slide on the grid

A triangle at (1, 1), (4, 1), (1, 3) slid 3 right and 2 up to its blue image

The gold triangle has corners (1, 1), (4, 1), (1, 3). The crew slides it 3 right and 2 up.

Every x grows by 3 and every y grows by 2. A (1, 1) lands at A′ (4, 3). B (4, 1) lands at B′ (7, 3).

The blue image is the same triangle. Lay the gold one on it and they match corner for corner.

WHICH MOVE?
  • Read the question.
  • Tap your answer.
The L-tile and its image slid 4 to the right on a gridWhich move takes the gold figure to the blue figure?
A triangle and its mirror image flipped across the x-axisWhich move takes the gold figure to the blue figure?
A triangle and its image after a quarter turn about the originWhich move takes the gold figure to the blue figure?
WHERE DOES THE CORNER LAND?
  • Read the question.
  • Tap your answer.
Corner A at (1, 1) slides 3 right and 2 up. Where does A′ land?
Corner C at (1, 3) slides 3 right and 2 up. Where does C′ land?
Corner B of the L at (3, 1) slides 4 right. Where does B′ land?
StatementTrue or false?
A slide moves every corner the same distance in the same direction.?
A flip makes the tile bigger.?
The image of a tile has the same side lengths as the tile.?
A turn needs one fixed point to turn about.?
WHY THIS EXERCISEKnowing what each move keeps the same is what lets the floor tiles fit without gaps.
Corner A of the L is at (1, 1). After a slide 4 to the right, what is the x-coordinate of A′? Type the number.
WHY THIS EXERCISEA slide changes every corner the same way, so one corner tells you the whole rule.
Try it
Cut an L from grid paper, six squares big. Tape a grid of squares on the table with masking tape.
Slide the L 4 squares right. Write the corner coordinates before and after. Did every corner move the same way?
Safety first
Cut paper with scissors, sitting down, with a grown-up nearby. A grown-up cuts cardboard.
Tape the floor grid flat so no one trips. Shoes on in the garage.
Draw the L at A (1, 1), B (3, 1), C (3, 2), D (2, 2), E (2, 4), F (1, 4). Then draw its image slid 4 right.

Three moves, one tile. Tomorrow each move gets a coordinate rule you can use without a tile.