Wednesday
Wednesday: Shop Lab, What Stays the Same
Comet sets a cardboard flat on the taped floor grid, corner A at (1, 1). "Lab day. Three motions, and we measure everything."
"Measure first," Wren says. "Every side and every corner angle before the flat moves."
Comet measures with the tape and the protractor. "Five sides, five angles. Written down."
She slides the flat 3 right and 5 down, then measures again. "Same five sides. Same five angles."
"Now flip it over the y-axis, then turn it about the origin," Wren says. "What do you notice each time?"
Nova projects a stretched copy of the flat, twice as wide. "Would you like a hint? Measure this one too."
"The stretch broke the lengths," Comet says. "Not rigid. Our designer, run the lab and compare."
Your mission
Move a paper flat three ways on a grid: slide, flip and turn. Before and after each motion, measure every side and angle.
Then draw a stretched copy with the rule (2x, y) and measure it. Write what changed and what stayed the same.
- A paper flat with corners (1, 1), (5, 1), (5, 3), (3, 4), (1, 3), cut from grid paper with scissors.
- Graph paper with both axes drawn, a ruler, a protractor, a pencil and your Shop Book.
- Tracing paper, if you have it, for the turn.
Tape any floor grid flat so nobody trips. A grown-up holds any ladder, and nothing heavy is lifted alone.
Turn the flat on a pencil point held still, or on a paper fastener a grown-up pushed through.
- Place the flat with corners on (1, 1), (5, 1), (5, 3), (3, 4), (1, 3). Measure each side and each angle.
- Slide the flat 3 right and 5 down. Write the new corners. Measure again.
- Put the flat back. Flip it over the y-axis. Write the new corners. Measure again.
- Put the flat back. Turn it 90° counterclockwise about the origin. Write the new corners. Measure again.
- Draw the stretched copy with the rule (2x, y). Measure its sides and angles.
- Compare your table with the crew's table below.
The crew's lab table
These are the crew's own measurements from the floor grid, in grid units, written in Wren's Shop Book.
| Side | Before | After the slide | After the flip | After the turn | After the stretch |
|---|---|---|---|---|---|
| AB | 4 | 4 | 4 | 4 | 8 |
| BC | 2 | 2 | 2 | 2 | 2 |
| CD | 2.24 | 2.24 | 2.24 | 2.24 | 4.12 |
| DE | 2.24 | 2.24 | 2.24 | 2.24 | 4.12 |
| EA | 2 | 2 | 2 | 2 | 2 |
Every side kept its length through the slide, the flip and the turn. Every angle stayed the same too.
The stretch is different: the bottom side doubled and the slanted sides grew. The stretch is not a rigid motion.
- Read the question.
- Tap your answer.
| What the lab shows | True or false? |
|---|---|
| A flip changes the length of the longest side. | ? |
| After the turn, every corner angle of the flat is unchanged. | ? |
| The stretch (2x, y) keeps every side the same length. | ? |
| A slide, a flip and a turn each keep every length and every angle. | ? |
Unfold. Does the traced flat match the reflection you drew with the rule (-x, y)?
Same lengths, same angles, except the stretch. Tomorrow Wren's flat log shows every corner, and the motions line up in sequences.