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Comparing areas by multiplying

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Comparing areas by multiplying is an exercise under the 3rd grade (U.S.) Math Mission. This exercise practices comparing areas and strengthens the connection of the geometric concept of area with the arithmetic operation of multiplication.

Types of Problems

There are two types of problems in this exercise:

  1. Compare the sizes: This has a visual display in the form of a chart or picture. Users need to figure out the areas of all objects involved, answer a question about which is smallest or largest, and tell the difference between the largest and the smallest.
    Compbymult1

    Compare the sizes

  2. Put in order of size: This problem has several rectangles drawn and the user is to put them in order from smallest area at the top to largest at the bottom.
    Compbymult2

    Put in order of size

Strategies

This exercise is easy to get accuracy badges because calculations are simple. As with most ordering problems, it is medium difficulty to attain speed badges because of dragging times.

  1. The second question on the first type of problem seems to always be the largest minus the smallest.
  2. All shapes involved in all questions are rectangles, so the area formula is always length times width.

Real-life Applications

  1. Area and perimeter are used in many jobs for architecture and interior design.
  2. 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.

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