3.MD.C.5

Recognize area as an attribute of plane figures and understand concepts of area measurement.
   
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A square with side length 1 unit, called “a unit square,” is said to have “one square unit” of area, and can be used to measure area.
  - A plane figure which can be covered without gaps or overlaps by n unit squares is said to have an area of n square units.

 

Summary:

This standard explores the concept of area. The main idea of this standard is that students should understand that a square with side length of 1 unit is defined to have one square unit of area, and the area of a figure that can be tiled with unit squares (such as a rectangle) is the number of unit squares needed to cover that figure without gaps or overlaps. While perimeter is understood as the distance around the boundary of an object, area is distinguished as being the amount of space that exists within an object.

Understanding the Standard:

  • Hands-on exploration opportunities will allow students to place “unit square” cubes (the cubes that come with base-ten blocks) within the boundaries of a variety of polygons. This activity will reinforce that “square units” may not overlap one another or extend beyond the boundary of the polygon. Additionally, the inside of a polygon must be completely covered. Students should count the number of unit sqares (or cubes) and understand that the number of unit squares is the area of the figure.
  • Students should have the opportunity to find the areas of two shapes that have the same areas but different perimeters, such as differently shaped rectangles. This exercise shows that while two shapes may have the same area, they may be different in shape and have different perimeters as well.
  • Having students trace and create their own shapes to find the area is an excellent way to enhance discovery of this concept.
  • The main focus of this standard is finding areas of rectangles. Other right-angled figures (that can be decomposed into rectangles) are fine, but students are not expected to find areas of other polygons in grade 3.

Questions to Focus Instruction:

  • Can students articulate the concept of area as the measurement of the amount of space within a particular object?
  • Are students able to lay “square unit” tiles within a polygon and count them to determine the area?

Skills

Prior to: Altough students have knowledge of basic shapes, they have not yet been introduced to the concept of area.

At Grade Level:
Students at this level are able to understand area as the number of unit sqaures that will fit inside a figure (usually a rectangle).

Beyond Grade Level: Students willl begion to explore the area of other polygons.