IM2
Activity 1.1
3 days
Part 1 - Setup
● Students work as pairs or in groups of 3s
● Give students printed plot map of a parcel of land shaped as a right trapezoid (on a transparency)
● Give students graphing paper
● Ask students - if it’s possible to divide the parcel into two lots, one a rectangle the other one a triangle?
● Students overlay the transparency over the graphing paper
○ Students are free to position the plot map over the graph anyway they want
■ Students are encourage to position the parcel over the graph so each corner of the lot lies
exactly on a grid of the graph
○ Students will transfer the parcel on to the graphing paper
○ Students select a point as an origin and identify it on the graph
○ From the selected origin, students will give the coordinates (x,y) of each corner of the parcel
■ There will be four corners to be identified
○ Students will draw a dashed line dividing the parcel into a rectangle and a triangle
○ Students will identify the coordinates of a fifth corner that will divide the parcel into a triangle &
rectangle
● Ask students to defend how they divided their lot:
○ Did the dash line created a rectangular space and a triangular space?
○ How do they know if it’s a rectangle?
○ How do they know if it’s a triangle?
Part 2 - Proving Rectangles
G-GPE 4,5,6
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Students will label the rectangular portion LOT A and the triangular portion LOT B
Ask students to discuss how they can prove that LOT A is a rectangle
○ Looks like it does not count
○ There are no protractors or rulers to be used
○ Teacher roams around finding a group (or two) that has the most promising proof
○ After some time, teacher invites the group(s) to share their discussion
Teacher extracting properties of rectangles from students
○ Opposites sides parallel
○ Opposite sides congruent
○ Adjacent sides perpendicular (therefore each corner is 90º)
○ Diagonals bisect each other
Teacher look-out for:
○ Use of coordinates to find slope
○ Use of slopes of two adjacent sides to determine if their product is -1 (perpendicular)
○ Use of slopes of two opposite sides to determine if they are parallel
○ Use of distance formula to determine lengths of opposite sides (if congruent)
○ Use of midpoint theorem to determine if diagonals bisect each other
Part 3 - Perimeter & Area
G-GPE 7
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Students discuss how to find the perimeter of LOT A
○ There are no protractors or rulers to be used
○ Teacher roams around finding a group (or two) that has the most promising proof
○ After some time, teacher invites the group(s) to share their discussion
Teacher extracting formulas for perimeter of rectangle
○ P=2L+2W
Students will find the perimeter of LOT A
Teacher look-out for:
○ Use of distance formula to determine lengths of Length & Width
○ Use of Perimeter formula to find perimeter
○ Use of appropriate units (Feet, meters, etc.)
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Students discuss how to find the area of LOT A
○ There are no protractors or rulers to be used
○ Teacher roams around finding a group (or two) that has the most promising proof
○ After some time, teacher invites the group(s) to share their discussion
Teacher extracting formulas for perimeter of rectangle
○ A=LW
Students will find the area of LOT A
Teacher look-out for:
○ Use of distance formula to determine Length & Width
○ Use of Area formula to find Area
○ Use of appropriate units (Ft2, m2, etc.)
Continued as homework
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Prove that LOT B is a right triangle
There are no protractors or rulers to be used
List properties of a right triangle
Find Area & Perimeter
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Teacher look-out for:
○ Use of distance formula to determine side lengths of LOT B
○ Use value of side lengths if they are a Pythagorean triple
○ Use of slopes of two adjacent sides to determine if their product is -1 (perpendicular)
○ Use of Area Formula
○ Use value of perpendicular sides to determine area
○ Use of Perimeter Formula
○ Use value of 3 sides to determine perimeter