Week 01 · Points, Lines and the Chalk Grid
Shop Day
Shop Day: the driveway hexagon
// Precise words and string-and-chalk constructions
⏱ about 20 min
Shop Day: The Driveway Hexagon
Saturday the string and chalk go outside. Comet pins one end to a crack in the pavement. "Radius one meter."
Wren walks the chalk around. A circle appears on the driveway. "Now step the string around the rim."
Comet's cousin takes the chalk. One, two, three, four, five, six. "It lands on the start!"
"What do you notice when you join the marks?" Wren asks.
"A hexagon. And every side is the same as the string," the cousin says.
Nova projects a triangle over three of the marks. "Would you like a hint? Try every other mark next."
"Then a square from the diameter," Comet says. "Our designer, your family can build this too."
- Point, line and distance are never defined. Segment, angle, circle, perpendicular and parallel are defined from them.
- A compass copies a distance and a straightedge joins points. Every construction uses only those two moves.
- Equal arcs from both ends of a segment find its perpendicular bisector and midpoint.
- Equal arcs from the two sides of an angle find its bisector.
- A compass set to the radius steps six times around a circle, giving the hexagon and the equilateral triangle.
◇ FAMILY DRIVEWAY HEXAGON
Together, tie chalk to a string one meter long. One person pins the end while another sweeps the circle.
Keep the string at the radius and step chalk marks around the rim. Count them together.
Take turns joining marks with a straightedge or a taut string: all six for a hexagon, every other one for a triangle.
Measure every side with a tape and compare to the radius. Write the results in the Shop Book.
Keep the string at the radius and step chalk marks around the rim. Count them together.
Take turns joining marks with a straightedge or a taut string: all six for a hexagon, every other one for a triangle.
Measure every side with a tape and compare to the radius. Write the results in the Shop Book.
For a grown-up
This week your student learned precise definitions and compass-and-straightedge constructions.
Ask them why the hexagon side equals the radius. The answer should mention the six equal spoke angles.
Pick a flat, dry spot away from cars. You hold the string end while the chalk sweeps.
Ask them why the hexagon side equals the radius. The answer should mention the six equal spoke angles.
Pick a flat, dry spot away from cars. You hold the string end while the chalk sweeps.
Safety first
Chalk only on a flat surface away from any road or driveway in use. Keep string short and never around a neck.
A grown-up holds any ladder, and nothing heavy is lifted alone.
A grown-up holds any ladder, and nothing heavy is lifted alone.
SHOP DAY CHECK
- Read the question.
- Tap your answer.
Your driveway circle has six equally spaced marks. What angle, in degrees, is between neighboring spokes?
The driveway string is 1 meter long. How long should each hexagon side measure, in meters?
Two marks sit at (0, 0) and (6, 0) on a paper grid. Where is the midpoint the bisector should pass through?How many marks does the radius-length string make around the circle? Type the number.
Count the marks before the chalk lands back on the first one.
WHY THIS EXERCISESix is the heart of the hexagon construction, on paper and on the driveway.
Draw your driveway circle with its marks, the hexagon, the triangle and the square, each in a different color.