Wednesday
Wednesday: Build Lab, What Stays the Same
Rocket sets the cardboard L on the taped floor grid, corner A on (1, 1). "Build Lab. Three moves, and we measure everything."
"Measure first," Raven says. "Every side, every corner, before the tile moves."
Rocket measures. "Six sides. Three, two, one, one, two, one squares. Every corner is a square corner."
He slides the tile 3 right and 5 down. He measures again. "Same six sides. Same corners."
"Now flip it, then turn it," Raven says. "What do you notice each time?"
"Nothing changes," Rocket says, "except where it sits." Nova hovers over the tile, her light steady. "Say what else stayed."
"The two long sides were parallel before," Rocket says slowly. "They still are." Nova hums. "That is the whole lab."
Your mission
Move an L-tile three ways on a grid: slide, flip and turn. Before and after each move, measure every side and check every corner.
Write what changes and what stays the same.
- A cardboard L-tile, six grid squares big, cut by a grown-up. A paper copy you cut yourself works too.
- A floor grid taped with masking tape, or a sheet of grid paper with the axes drawn.
- A ruler, a protractor, a marker and your Blueprint Book.
Tape the floor grid down flat so nobody trips. Shoes on in the garage.
Turn the tile on a pencil point held still, or on a paper fastener a grown-up pushed through.
- Set the tile with its corners on (1, 1), (3, 1), (3, 2), (2, 2), (2, 4), (1, 4). Measure each side and check each corner.
- Slide the tile 3 right and 5 down. Write the new corners. Measure again.
- Put the tile back. Flip it across the y-axis. Write the new corners. Measure again.
- Put the tile back. Give it a quarter turn counterclockwise about the origin. Write the new corners. Measure again.
- Check the two long sides: are they still parallel after every move?
The crew's lab table
These are the crew's own measurements from the floor grid, in grid units, written in Raven's Blueprint Book.
| Side | Before | After the slide | After the flip | After the turn |
|---|---|---|---|---|
| AB | 2 | 2 | 2 | 2 |
| BC | 1 | 1 | 1 | 1 |
| CD | 1 | 1 | 1 | 1 |
| DE | 2 | 2 | 2 | 2 |
| EF | 1 | 1 | 1 | 1 |
| FA | 3 | 3 | 3 | 3 |
Every side kept its length through every move. Every corner stayed a square corner, and the parallel sides stayed parallel.
The area stayed too: 4 square units before, and 4 after the flip. The image is congruent to the tile.
- Read the question.
- Tap your answer.
| What the lab shows | True or false? |
|---|---|
| A flip changes the length of the longest side. | ? |
| After a turn, the square corners of the L are still square corners. | ? |
| Parallel sides stay parallel after a slide, a flip or a turn. | ? |
| A slide makes the tile bigger. | ? |
Same lengths, same angles, same parallels. Tomorrow Raven's tile log shows every corner before and after.