Wednesday
Wednesday: Shop Lab, the Tape-Measure Check
Comet ties the chalk to a string and holds the other end on the taped center. "Lab day. Chalk circle, radius 5 squares."
She walks the chalk around. The circle wobbles a little near the ramp. "Close enough?"
"Measure, do not guess," Wren says, kneeling with the tape. "What does the evidence say? Pick a grid point on the line."
"(8, 2). Over 5, up 0." Comet reads the tape. "Exactly 5 from the center."
"Now (6, 5). It looks like it is on the line." Wren measures. "Over 3, up 3. That is not 5."
Nova projects the table she will fill as they go: point, change in x, change in y, squares. "Would you like a hint?"
"The squares have to add to 25," Comet says. "Our designer, run the check on your own circle."
What you need
- A floor or driveway grid taped with masking tape, or a large sheet of graph paper on a table.
- A piece of string about as long as 5 grid squares, a piece of chalk or a pencil, and tape.
- A tape measure or a ruler and your Shop Book.
Chalk stays on the floor or the paper, and hands get washed after. Nothing heavy is moved alone.
If you work outside, a grown-up picks the spot away from any road.
Run the lab
- Tape or draw a grid. Mark the center at (3, 2) with a cross.
- Tie the string to the chalk. Hold the free end on the center and pull it tight to 5 squares.
- Walk the chalk around the center to draw the circle.
- Pick eight grid points that look like they sit on the chalk line. Write each one down.
- For each point, subtract the center, square both differences and add. Write the sum.
- A sum of 25 means the point is on the circle. Measure with the tape to confirm.
The crew's lab table
These are the crew's own readings from the taped stage grid, with center (3, 2) and radius 5.
| Point | Change in x | Change in y | Sum of squares | Distance | On the circle? |
|---|---|---|---|---|---|
| (8, 2) | 5 | 0 | 25 | 5 | yes |
| (6, 6) | 3 | 4 | 25 | 5 | yes |
| (0, 6) | -3 | 4 | 25 | 5 | yes |
| (-1, -1) | -4 | -3 | 25 | 5 | yes |
| (7, 5) | 4 | 3 | 25 | 5 | yes |
| (6, 5) | 3 | 3 | 18 | 4.24 | no |
| (3, 8) | 0 | 6 | 36 | 6 | no |
| (-2, 3) | -5 | 1 | 26 | 5.1 | no |
Six of the eight points passed. (6, 5) and (-2, 3) looked right but the squares did not add to 25.
The chalk line is only as good as the string. The equation is exact, and the tape measure agrees with it.
- Read the question.
- Tap your answer.
The crew checked (7, 5). How far is it from the center (3, 2)?The crew checked (-2, 3). How far is it from (3, 2)? Round to 2 decimal places.How far is (3, 8) from the center (3, 2)?| Statement | True or false? |
|---|---|
| The point (7, 5) is on the circle with center (3, 2) and radius 5. | ? |
| The point (6, 5) is on the circle with center (3, 2) and radius 5. | ? |
| The point (-2, 3) is on the circle with center (3, 2) and radius 5. | ? |
| A point is on the circle when its squared distance from the center equals r². | ? |
| A point with a sum of squares of 18 is outside the circle of radius 5. | ? |
Careful measuring, designer. Tomorrow the lamp reflector turns a focus and a line into a curve.