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Filling rectangles with same-sized squares
Filling-rectangles-with-same-sized-squares 256
Description
Exercise Name: Filling rectangles with same-sized squares
Math Missions: Early math Math Mission, 3rd grade (U.S.) Math Mission
Types of Problems: 1

The Filling rectangles with same-sized squares is under the Early math Math Mission and 3rd grade (U.S.) Math Mission. This exercise fills in a rectangle with smaller squares and introduces the idea of an area model for multiplication.

Types of Problems

There is one type of problem in this exercise:

  1. Determine how many squares it will take to fill: This problem has a rectangle drawn and the length and width are cut into smaller squares. The user is supposed to answer the number of little squares it would take to completely fill in the rectangle.
    Fillsq

    Determine how many squares it will take to fill

Strategies

This exercise is medium to attain both accuracy badges and speed badges especially on the pictures that have above five squares. It takes a bit of care to figure out how many there are along a side and it is easy to miss one if the user goes through it too fast.

  1. Testing indicates that counting vertically first, then horizontally seems to allow fast counting.
  2. The number of squares needed will be the product of the length and width.

Real-life Applications

  1. Area and perimeter are used in many jobs such as 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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