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Geometry and Measurement 6-8 / Week 06 / Friday
5/6
Week 06 · Triangles with Rules, and Slices

Friday

Rules and slices everywhere
// When three straws make a roof, and what a cut face shows
⏱ about 20 min

Friday: Rules and Slices Everywhere

Rocket points at the garage shelf brackets. "Triangles. Three sides each. That is why they do not wobble."

"Three sides, one shape," Raven says. "A square frame can lean. A triangle cannot. What do you notice about the roof?"

"Triangles again," Rocket says. "Every roof is a straw set that closed."

Nova hovers near the clay tray, her light passing through the block like a cut. "And slices?" she says.

"A stack of paper cut straight across is a rectangle," Raven says. "A block of clay cut flat, a rectangle."

"Next week, circles," Rocket says, picking up the empty can. "String around a can."

Nova hums. "A little more than three times across. You will see."

Triangles that hold

Three fixed sides make one triangle, so a triangle frame cannot change shape. That is why braces are triangles.

A four-sided frame with fixed sides can still lean, because its corners are free to change.

Slices to picture

SolidCutFace shape
boxflatrectangle
boxuprightrectangle
pyramidflatsquare
pyramidupright through the toptriangle

A flat cut copies the base. An upright cut through a box copies a side. A cut through a pyramid's top makes a triangle.

Picture the clay before you answer. The string shows the face, and the face is always a flat shape.

A box 4 cm long, 3 cm wide and 2 cm tall
SLICES
  • Read the question.
  • Tap your answer.
A box is sliced with a upright cut. What shape is the cut face?
A pyramid is sliced with a flat cut. What shape is the cut face?
A pyramid is sliced with a upright through the top cut. What shape is the cut face?
A box is sliced with a flat cut. What shape is the cut face?
WEEK REVIEW
  • Read the question.
  • Tap your answer.
Can straws 7, 7 and 7 cm long make a triangle?
Three corners: 60°, 60° and 60°. How many different triangles have these corners?
Three straws: 1, 2 and 3 cm. How many different triangles can they make?
Two straws are 4 and 9 cm. The third straw must be longer than how many cm?
Week reviewTrue or false?
6 + 8 > 10?
4 + 5 > 12?
Three sides that close make exactly one triangle.?
Three corners that add to 180 make exactly one triangle.?
An upright cut through a box shows a rectangle.?
WHY THIS EXERCISEThree sides lock everything in. Three corners leave the size free, so there are many.
OUR WEEK, IN ORDER
  • ?We found the triangle rule with straws 4, 5 and 12.
  • ?We sorted three measures into one triangle, many, or none.
  • ?We ran Build Lab: six straw sets, then clay slices.
  • ?We read the straw page and chose the roof set 5, 9, 9.
WHY THIS EXERCISERule, outcomes, test, then build: the same path every week at the Blueprint Table.
Try it
Find three triangles at home: a bracket, a roof line, a bike frame, a shelf support.
For one of them, guess the three side lengths and check that the rule holds.
Safety first
Look at brackets and frames. Do not climb to reach them or pull on them.
Draw a square frame leaning over, then the same frame with one diagonal brace. Mark the triangles.

A week of straws and string. Tomorrow is Build Day: the family roof frame and a slicing show.

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