Length and area: Key characters in the curriculum story

Mathematical characters (such as numbers, expressions, or shapes) are the objects of the story, mathematical action is manipulating a character (for example, by adding one to the base of a rectangle and subtracting one from its height), mathematical actors are who performs the action (for example, student, teacher, resource author) mathematical setting is the representation in which the action takes place, such as physical shapes on a table, dynamic geometry software, or shapes drawn on a square grid. With length (and area), the key action is comparison either to a given unit (measurement) or another length. With 2j, the unit can be seen as the semicircle: the blue semicircle is the red length scaled by a factor of 2, but in the red, there are twice as many semi-circular units. 2k is a variation of 2b but without the aligning endpoints. Drawing shapes on a square geoboard using combinations of the units a, b and с, as in Figure 3, offers further opportunities for reasoning, alongside practice of the perimeter/length concepts and the subordinate practice of collecting terms.