Rich Learning Tasks

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Four Shapes
Questions to facilitate the learning
• Which shape seemed to be the easiest to make? Why?
• Which of your predictions didn’t work out?
• What shape did you use to make a big rectangle? How did you connect those four shapes?
• Were you able to make a triangle? Why not with the rectangles?
• Why didn’t you make a circle?
Scaffolding the learning
• What if you just stacked the rectangles? What would happen?
• Would it help to turn one of the shapes you are using?
• How does the number of sides change if you just push one of the shapes over?
Extending the learning
Students might be challenged to make as many shapes as possible and tell the number of sides possible
starting with either the rectangles, the blue triangles or the green triangles.
What’s the point of this task?
Students will get practice at composing bigger shapes from smaller ones, but, more importantly,
because they are predicting, they will get practice in visualisation and reasoning. For example, students
might reason that they won’t be able to get a triangle out of rectangles, but they might be able to get a
rectangle out of triangles. They might reason that since they can use two rectangles to make a square,
they won’t be able to use four to make a square, that four smaller equilateral triangles can make a bigger
one, etc.
Geometry