Task# Same Size, Same Shape?

Illustrative MathematicsVaries

The purpose of the task is to help students transition from the informal notion of congruence as 'same size, same shape' that they learn in elementary school and begin to develop a definition of congruence in terms of rigid transformations. The task can also be used to illustrate the importance of crafting shared mathematical definitions. Note that the term 'congruence' is not used in the task; it should be introduced at the end of the discussion as the word we use to capture a more precise meaning of 'same size, same shape.' The notion of equivalence is a deep one in mathematics, and in first grade, students begin to investigate what it means for two numbers to be equal.