Week 01 · Points, Lines and the Chalk Grid
Friday
Constructions everywhere
// Precise words and string-and-chalk constructions
⏱ about 20 min
Friday: Constructions Everywhere
Comet folds a sheet of paper so one edge lands on itself. "Look. A fold is a perpendicular bisector."
"Fold a corner so the two edges meet, and the crease bisects the angle," Wren says. "Paper is a compass too."
"The carpenter's square is a perpendicular. The shelf brackets are parallels," Comet says. "What else?"
Nova projects a bicycle wheel over the turntable sketch. "Would you like a hint? Count the spokes you can picture."
"Equal spokes, equal angles, like our hexagon marks," Wren says.
"Review day," Comet says. "Our designer, every definition and every construction, then next week the flats start moving."
Constructions in a day
- Folding a paper edge onto itself makes a crease perpendicular to the edge.
- Folding one edge of a corner onto the other makes a crease that bisects the corner angle.
- A carpenter's square checks a perpendicular. Two shelf brackets at equal heights make parallel shelves.
- Equal spokes around a hub are equally spaced marks around a circle, like the turntable.
The week in five lines
- Point, line and distance are never defined. Everything else is defined from them.
- A circle is all points at one distance from a center. Perpendicular lines meet at 90°. Parallel lines never meet.
- A compass copies a distance. A straightedge joins two points. Together they make every construction.
- Equal arcs from two points cross at points equally far from both. That is why bisectors work.
- A compass set to the radius steps six times around a circle: hexagon, triangle and square all follow.
EVERYDAY CONSTRUCTIONS
- Read the question.
- Tap your answer.
Comet folds a paper edge onto itself. Which construction does the crease match?
Wren folds a corner so its two edges meet. What does the crease do to the corner angle?
A crease bisects a right angle, then a second fold makes a 35° angle on one side. What is the rest of the right angle?
WEEK REVIEW
- Read the question.
- Tap your answer.
Chalk line 1 passes through (0, 0) and (4, 2). Line 2 passes through (1, 5) and (5, 7). Parallel, perpendicular or neither?
Chalk line 1 passes through (0, 0) and (4, 2). Line 3 passes through (2, 0) and (1, 2). Parallel, perpendicular or neither?
Chalk line 1 passes through (0, 0) and (4, 2). Line 4 passes through (0, 3) and (4, 4). Parallel, perpendicular or neither?
The hexagon on the turntable has six corner angles. What do they add to, in degrees?
Check each point with the distance formula: on the circle means exactly 5 from the center.
| Week review | True or false? |
|---|---|
| A good definition may use the word it is defining. | ? |
| Every point on the perpendicular bisector of AB is the same distance from A and from B. | ? |
| A compass copies a distance, and a straightedge joins two points. | ? |
| Parallel lines meet at exactly one point. | ? |
| The point (-4, 3) is on the chalk circle with center (0, 0) and radius 5. | ? |
| The point (2, 3) is on the chalk circle with center (0, 0) and radius 5. | ? |
WHY THIS EXERCISEThese are the facts next week builds on, when the flats slide, flip and turn.
OUR WEEK, IN ORDER
Monday was the definitions. Wednesday was the lab. Thursday was the table.
- ?We named the three ideas we never define, then defined segment, angle, circle, perpendicular and parallel.
- ?We learned the seven constructions and why each one works.
- ?We built a hexagon and a triangle inside a circle in Shop Lab.
- ?We read the crew's turntable data and checked every chord and spoke angle.
WHY THIS EXERCISEEach day used the same two tools and one more reason why they work.
Try it
Fold a paper edge onto itself and check the crease with the corner of a book. Is it a right angle?
Fold a corner so the edges meet. Measure both halves of the angle with a protractor.
Fold a corner so the edges meet. Measure both halves of the angle with a protractor.
Draw a paper rectangle, the crease that bisects one corner, and the crease perpendicular to one edge. Label both.
Terrific week. You can define, construct and check. Tomorrow is Shop Day.