Rich Learning Tasks

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Quadrilaterals
Questions to facilitate the learning
• Did the side lengths change? Which ones? How much?
• Did the angles change? Which ones? How much?
• Why is your new shape almost the same as the old one?
• Which of your four changes do you think was the biggest change? Why?
Scaffolding the learning
• What makes a [square] a [square]? What could you change so it would not be a square anymore?
• How could you give your shape more sides without changing it much?
• Is it easy to cut your shape in half? How could you change that?
Extending the learning
Ask students what names they might give to ‘almost squares’, ‘almost rectangles’ and ‘almost
parallelograms’. Have them create dictionary definitions for those new shapes.
What’s the point of this task?
This very open-ended task encourages students to consider many different properties of shapes and
communicate about them. Because it leaves a great deal of latitude for what makes shapes different,
the task should appeal to a wide range of learners, whether strong in spatial reasoning or not.
Shapes might be changed using many geometric properties. Two parallel sides might be made not
quite parallel. (Even if parallelism has not been formally studied, students do have an intuitive sense of
it with shapes like rectangles and parallelograms.) Two equal side lengths might be made unequal; the
symmetry of a shape might be slightly altered. (Even if symmetry has not been formally studied, students
have an intuitive sense of it.) A straight side might be slightly bent; a short side might be inserted by
cutting off a corner or a ‘hole’ might be placed in the shape.
Geometry