Rich Learning Tasks

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Questions to facilitate the learning
• Does the triangle have to be taller than the rectangle?
• Does it have to be wider?
• Without doing any calculations, what kind of picture could you draw to show that your results make sense?
[Students might draw an array of 3 rows of 4 copies of the small rectangle to make a large rectangle, cut
the larger rectangle in half and see why the triangle’s area must be 6 times that of the small rectangle.]
Scaffolding the learning
• How do you figure out the area of a rectangle?
• How might that help you figure out the area of this triangle?
Extending the learning
Students who are interested might reverse the situation, where the rectangle’s area is 6 times the
triangle’s area.
What’s the point of this task?
Students have a chance to see how changing the length and/or width of a rectangle affects its area.
The use of the right triangle adds an extra dimension to the problem. Since a right triangle is easily viewed
as a half-rectangle, there is no need for students to know the formula for the area of a triangle yet.
Since the area of the triangle is 6 times greater, students need to discover that the length x width of the
smaller rectangle must be multiplied by 12 to create the larger rectangle of which the triangle is half.
This means that it could be done by tripling length and multiplying width by 4 or doubling length and
multiplying width by 6 or multiplying the length by 12 and not changing the width, etc.
Because no particular values were specified, students can choose any dimensions they wish for the smaller
rectangle and create the associated triangle or vice versa. There are an infinite number of solutions.
Measurement