Area Quantity Recognizer

Perceives the amount of two-dimensional space and can make intuitive comparisons. However, when asked to compare, may compare lengths more than areas because lengths are salient and familiar to them (e.g., compare one side of one piece of paper to the side of another) or make estimates based on a “length plus (not times) width” intuition. However, may compare areas correctly if the task suggestions superposition (putting one on top of the other). Asked to partition a space into squares or copy an image of a rectangle partitioned into an array (rows and columns), may simply draw squares (usually!) inside the rectangle or other types of shapes or short paths on or around the rectangle.


You may see this:

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Other Examples:

  • Asked which rectangular "candy" is the "same amount" as a bar 4 cm by 5 cm, one child chooses the 4 by 8 matching the sides of the same length. Another child chooses 2 by 7, intuitively summing the side lengths. 
  • Given square tiles and asked how many fit in a 4 by 5 area, child guesses 15.
  • A child places one sheet of paper over the other and says, "This one is bigger."
  • Measures area with ruler, measuring a length, then moving the ruler and measuring that length again, apparently treating length as a 2D space-filling attribute.

Help your student become a(n) Area Quantity Recognizer

Covering surfaces and talking about area (e.g., on the playground, "this is a really big area for our game" or ""we covered the whole table with no holes") can be helpful. In discussions, differentiate area from quantities (e.g., "Her block building is tallest, but yours covers more of the rug--that's a big area!").

Special Thanks To

Institute of Education Sciences
The research reported here was supported by the Institute of Education Sciences, U.S. Department of Education, through grant numbers R305K050157, R305A120813, R305A110188, and R305A150243. to the University of Denver. The opinions expressed are those of the authors and do not represent views of the Institute or the U.S. Department of Education.