Perimeter and area from coordinates
- Which lengths come free — 3 tasks
- A perimeter with one radical in it — 3 tasks
- Which number is the height — 6 tasks
- Cutting a figure into measurable pieces — 3 tasks
- The apex moves, the area does not — 3 tasks
- Practice — 22 tasks
- Summary — 2 tasks
- Cool-down — 3 tasks
Classroom activities
Things a class does rather than writes on. Each one is a finished PDF: print it, cut it up if it says so, and hand it round.
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Area on the Coordinate Grid: One Piece, Cut First, or Not Yet? — Cut & Glue Sort 25 minutes, including the cutting · 5 sheets
12 figures on squared paper. Students do not compute: they sort each figure by how its area is found. In one piece (a rectangle, or a triangle with a side along a grid line), after splitting it with lines along the grid, or not on this sheet, because no side is along a grid line and no line along the grid gives a length that can be counted.
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Perimeter and Area from Coordinates: Area, Then Perimeter, of the Same Figures — Answer Maze 10–15 minutes · 4 sheets
8 boxes on one page. Each shows a figure on the coordinate plane with its corners printed and asks for its area or its perimeter, and the route asks both questions of the same figures. Perimeters stay exact; areas come from a base and a height along the grid lines. The wrong answers are the common mistakes: a slant side used as the height, the perimeter given for the area, the half forgotten, a side left out. The row of box numbers at the foot is the check.
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Area on the Grid: Is It Set Up Right? Base, Height and the Slant Side — Mystery Picture 25–35 minutes · 5 sheets
25 squares, each a rectangle or a triangle on squared paper with a setup for its area such as Area = ½ × 6 × 4. Students compute nothing: they count the base and the height on the grid and check the setup. The wrong setups use a slant side as the height, count grid lines instead of spaces, or leave out the ½. Fill it or leave it white, and a picture appears.
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Perimeter and Area from Coordinates: Exact Perimeters, Areas in Square Units — Scavenger Hunt a full class period · 13 sheets
16 cards around the room, each with one figure on the coordinate plane and its corners printed. Area cards and perimeter cards take turns. Perimeters stay exact, a whole number plus a square root; areas come from a base and a height along the grid lines, in square units. Using a slant side as the height, or leaving the slant side out of a perimeter, lands on a card that sends the group back, and a clean run is 8 lines on the record sheet.