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Copyright © 3P Learning – These resources have been created in partnership with Dr. Marian Small.
For more information visit
www.mathletics.comQuestions to facilitate the learning
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Do the trapezoids need to have the same area? Could they?
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Is it possible for all three shapes to have the same area? Explain.
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How do you know that there are many possible solutions?
Scaffolding the learning
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What can trapezoids look like?
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How do you figure out the area of a triangle?
Extending the learning
Students might create a shape made up of three or four of their own shape choices with a given total area.
What’s the point of this task?
This problem provides an opportunity to use formulas for areas of triangles, parallelograms and rectangles
and perhaps trapezoids. Because they have the total area, instead of the area of each shape, students
have much more latitude to create a solution.
Some students might start with a rectangle with an area of 50 cm
2
, separate it into two trapezoids and a
triangle and indicate the dimensions of the pieces. They still need to describe the dimensions and areas of
each piece.
Others will start with the trapezoids and triangle and use what they know about area formulas to ensure
that the total area is correct. Students also have an opportunity to reinforce their understanding of what
different trapezoids can look like.
Providing a grid in the background allows students to count squares if they need to.
Combined Shape
Measurement