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The first instance of Area and the distributive property is under the 3rd grade (U.S.) Math Mission. This exercise discovers the connection between the concept of adding areas and the algebraic distributive property.

Types of Problems

There are two types of problems in this exercise:

  1. Select the expressions that represent the area: This problem has a picture shaded with two different colors. The user is supposed to select all options that represent the total area of the picture.
    Areadist1

    Select the expressions that represent the area

  2. Discovering distribution: This problem has two shapes that share a dimension. Users are supposed to first find the area of both separate parts by writing a multiplicative expression. They then select what they should do to find total area. They finally give the final total area as an answer.
    Areadist2

    Discovering distribution

Strategies

This exercise is easy to get accuracy badges as long as users are careful with counting rectangles. The speed badges feel hard at this time, possibly due to the short time that they are currently set at (hopefully will change eventually).

  1. Users do not need to actually use the different colors in problem type one to answer. Those who can simplify expressions quickly can effectively ignore the colors and just find the answers that evaluate to the total area.
  2. Research indicates that the multiple select seems to require either 3 or 4 selections. This can change, of course, but expect to have to click more than one answer on these.
  3. On the second type of problem always has an answer of "add" to the third part because of the Area Addition Postulate.

Real-life Applications

  1. The ancient Egyptians from over 4000 years ago were very good at shapes and geometry. Every time the Nile burst its banks and flooded the planes, they had to use geometry to measure their gardens and fields all over again.
  2. Area and perimeter are used in many jobs for architecture and interior design.

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