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Measuring Up: Prototypes for Mathematics Assessment
given to any response that refers to a square of perimeter 24 cm, or that says there are hexarights of perimeter 24 cm and area arbitrarily close to 36 cm2. Somewhat less is assigned to a response that simply refers to some (finite) sequence of hexarights of perimeter 24 cm and increasing area.
Characteristics of the medium response:
The responses to questions 1-4 show an understanding of what a hexaright is and what the perimeter and area are. There may be a flaw in one of the calculations. The responses to question 5 provides supporting evidence of understanding, if there are any miscalculations.
The figures drawn in questions 5 and 6 are hexarights, although the lengths of the sides may be up to a centimeter wrong in either direction, the angles may not be accurately drawn right angles, and the perimeter may not be exactly 24 cm. (Of course the nature of the errors will depend on the kinds of tools, including type of paper, that the student selects.)
In question 6, the partial understanding that is typical of the medium-level response can be shown in a variety of ways. For example, the student could draw a hexaright with a relatively small area (perhaps 30 cm 2), but report the area accurately (within perhaps 1 cm2 of the correct area). Alternatively, an appropriate hexaright could be drawn very well, but the area misidentified as 23 cm2 rather than 35 cm2.
The response to question 7 is something that is true (for example, that there are lots of hexarights of different areas, for a fixed perimeter) but that does not address any connections between or among hexarights with perimeter 24 cm.