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Geometry and Measurement 6-8 / Week 02 / Thursday
4/6
Week 02 · Polygons on the Grid

Thursday

Raven's wall plan
// Corners as coordinates, sides as differences
⏱ about 20 min

Thursday: Raven's Wall Plan

Raven opens the Blueprint Book to a page of coordinates. "The whole clubhouse outline. Six corners."

Rocket reads them out. "(0, 0), (6, 0), (6, 3), (4, 3), (4, 6), (0, 6)." He pins string at each.

"And the porch is a triangle," Raven says. "(6, 0), (10, 0), (10, 3)."

"What do you notice about the porch's slanted side?" she asks.

"No shared coordinate," Rocket says. "I cannot subtract for that one. The other two sides I can."

Nova hovers over the plan, her light resting on each corner in turn. "Six walls," she says. "Six subtractions. Then add."

Rocket is already writing. "Six, three, three, three, four, and six. Twenty-five?" Nova hums. "Add again."

The clubhouse outline

The clubhouse outline on a grid, six corners lettered A to F

The outline has vertices (0, 0), (6, 0), (6, 3), (4, 3), (4, 6), (0, 6). Every side is horizontal or vertical, so every side comes from one subtraction.

Rocket added 6 + 3 + 3 + 3 + 4 + 6 and got 25. Check wall CD, from (6, 3) to (4, 3): 6 - 4 = 2, not 3.

The correct perimeter is 6 + 3 + 2 + 3 + 4 + 6 = 24 units. Rocket read one wall as 3 instead of 2.

Raven's wall table

The crew's own wall plan, in grid units, from Raven's Blueprint Book.

WallFromToShared coordinateLength (units)
AB(0, 0)(6, 0)y = 06
BC(6, 0)(6, 3)x = 63
CD(6, 3)(4, 3)y = 32
DE(4, 3)(4, 6)x = 43
EF(4, 6)(0, 6)y = 64
FA(0, 6)(0, 0)x = 06

The outline is a 6 by 3 rectangle with a 4 by 3 rectangle on top. Its area is 18 + 12 = 30 square units.

The porch triangle (6, 0), (10, 0), (10, 3) has a base of 4 and a height of 3. Its area is ½ × 4 × 3 = 6.

READ THE WALL TABLE
  • Read the question.
  • Tap your answer.
Wall CD runs from (6, 3) to (4, 3). How long is it, in units?
Wall DE runs from (4, 3) to (4, 6). How long is it, in units?
The clubhouse outline on a grid, six corners lettered A to FWhat is the perimeter of the whole clubhouse outline, in units?
The clubhouse outline on a grid, six corners lettered A to FWhat is the area of the clubhouse outline, in square units?
THE PORCH
  • Read the question.
  • Tap your answer.
The porch base runs from (6, 0) to (10, 0). How long is it, in units?
The porch's upright side runs from (10, 0) to (10, 3). How long is it, in units?
A right triangle on a grid, corners lettered A, B and CThe porch is the triangle (6, 0), (10, 0), (10, 3). What is its area in square units?
A rectangle has corners (0, 0), (8, 0) and (8, 3). Where is the fourth corner?
How long is wall AB, from (0, 0) to (6, 0)? Type the number of units.
What is the perimeter of the clubhouse outline? Type the number of units.
What is the area of the clubhouse outline? Type the number of square units.
From the wall planTrue or false?
Every wall of the outline shares a coordinate with its neighbor, so each length is a subtraction.?
The porch's slanted side can be found by subtracting one pair of coordinates.?
6 + 3 + 2 + 3 + 4 + 6 = 24?
Rocket's first total, 25, was too big by one.?
WHY THIS EXERCISERocket's slip shows why Raven measures twice: one wrong length changes the whole perimeter.
Try it
Write six coordinates for an outline of your own, all sides horizontal or vertical. Plot and join them.
Find every side, the perimeter and the area. Then string it on the floor grid if you can.
Draw the clubhouse outline and the porch triangle on one grid. Label every vertex and side length.

Six walls, one plan. Tomorrow you find coordinate grids in everyday life and review the week.

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