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Geometry and Measurement 6-8 / Week 02 / Build Day
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Week 02 · Polygons on the Grid

Build Day

Build Day: The family grid
// Corners as coordinates, sides as differences
⏱ about 20 min

Build Day: The Family Grid

Saturday morning the family kneels on the hallway floor with a roll of masking tape.

"Build Day," Raven says. "Tape a grid, name the corners, and string a polygon from coordinates."

"Each square is one floor tile," Rocket says. "The origin is by the door."

"What do you notice about where the string will turn?" Raven asks.

"At every vertex," Rocket says. "And every wall is a subtraction if the corners share a number."

Nova hovers above the origin, her light marking (0, 0). "Call out each coordinate before the string moves," she says.

Rocket's cousin reads the first corner. "(0, 0) to (4, 0)." The string stretches four tiles. Nova hums. "Four. Measured by numbers."

  1. A point's coordinates are (x, y): across from the origin, then up or down.
  2. A polygon is drawn by plotting its vertices and joining them in order.
  3. Two vertices with the same x make a vertical side; the same y makes a horizontal side. Subtract the other coordinates for the length.
  4. Subtraction works across zero: 4 - (-3) = 7. The four quadrants go counterclockwise from the upper right.
  5. Add the sides for the perimeter. Decompose into rectangles and triangles for the area.
◇ STRING A POLYGON FROM COORDINATES
Tape two axes on a tiled floor, or draw a grid on a big sheet of paper. Mark the origin.
One person writes four to six coordinates for a polygon with horizontal and vertical sides.
Another person strings or draws the polygon, calling out each coordinate before moving.
Everyone predicts each side length by subtracting. Then count the tiles or squares to check.
Find the perimeter and the area together, and record both in the Blueprint Book.
For a grown-up
This week your student learned to draw polygons from coordinates and find side lengths by subtracting.
Ask them how long the side from (2, 1) to (7, 1) is and why. The answer should mention the shared y.
Keep tape flat and string low so nobody trips. Pick up every piece afterwards.
Safety first
Tape the grid flat and keep string low, taut and taped at the corners. Clear the hallway when you finish.
Shoes on. Walk, never run, across the grid.
BUILD DAY CHECK
  • Read the question.
  • Tap your answer.
The first wall runs from (0, 0) to (4, 0). How many tiles long is it?
The second wall runs from (4, 0) to (4, 3). How many tiles long is it?
A rectangle on a grid, four corners lettered A to DThe family's rectangle has corners (0, 0), (4, 0), (4, 3), (0, 3). What is its perimeter in tiles?
A rectangle on a grid, four corners lettered A to DHow many tiles does the family's rectangle enclose?
Build Day checkTrue or false?
Calling out each coordinate before moving the string helps catch a slip.?
A polygon with five vertices has five sides.?
The side from (0, 0) to (4, 0) is vertical.?
WHY THIS EXERCISETaping a real grid shows that coordinates are directions anyone can follow, not only numbers on paper.
Draw the family's polygon on a grid with every vertex labeled, and write the perimeter and area.

Great building, crew. Next week: unfold a box into a net, and find out how much cardboard the walls need.

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