Area is the flat space inside or covered by a shape.

Some important ideas about area (in more-or-less the order in which children are ready to understand them)

• Shapes that are exactly the same shape and size have the same area. (first basic idea)
• If you cut a shape into parts (decompose), and then put the parts together to make a new shape (compose), the before and after shapes will have the same area (this concept develops somewhere around 2nd-3rd grade)
  • March 24 class: some examples.
  • Decomposing a parallelogram and composing a rectangle (an additive way (putting together parts) of getting the formula for the area of a parallelogram).
• If a two different shapes are the same fraction of the same larger shape, the shapes have the same area (also somewhere around 2nd-3rd grade).
  • Using two triangles to make a parallelogram
  • More about bases and heights
• You can measure the area of a shape, which means that you are finding the number of unit squares that fit inside or cover the shape. (2nd-3rd grade).
• You can use formulas to find the area of the shape using length measurements from the shape (3rd grade: rectangles only; grades 4-6 for other shapes)
  • You can decompose a shape into pieces you have formulas of and add and subtract to find area. Example h, example i, example j.
• You can use subtraction to find the area of a shape (grade 5-7).
  • Subtracting from a big rectangle to find a small rectangle with the same area as the parallelogram
• You can think of a shape as being made of infinitely many infinitely thin slices (Calculus).
  • Slicing and sliding to understand area of parallelograms and triangles.

Some downloadable Geogebra files that show things about area:

• Parallelograms by cutting
• Parallellograms by slicing
• Parallelograms by subtracting
• Triangle pairs
• Triangles by slicing