In 3rd grade, students are learning to measure length in fraction units. This skill combined with understanding perimeter and the attributes of 2-dimensional shapes set the stage for early experiences measuring area.
MA.3.GR.2.1 – Explore area as an attribute of a two-dimensional figure by covering the figure with unit squares without gaps or overlaps. Find areas of rectangles by counting unit squares.
MA.3.GR.2.2 – Find the area of a rectangle with whole-number side lengths using a visual model and a multiplication formula.
Measuring Area
Area is the 2-dimensional measurement of the space inside a closed shape. All shapes have a measurable area, but children will only work with squares and rectangles in 3rd and 4th grade. Area is measured in square units because it involves both the length and width of a shape.
For example, 1 square centimeter is a square that is 1 cm long and 1 cm wide. One square inch is a 1 inch by 1 inch square.
Counting & Adding Square Tiles
3rd graders begin learning about area as a measurable attribute of 2-dimensional shapes. Unit squares can be used to find area by tiling a shape and simply counting the squares.
To measure properly, tiles need to be snug with no gaps or overlapping pieces. The total number of unit squares is reported in square units.
Like the photo to the right, the area of squares and rectangles will be an array of equal rows and columns. That means that children can use repeated addition to find the area instead of counting each unit tile.
Measuring Area with Multiplication
Over time, 3rd graders develop the connection between repeated addition and multiplication.
A rectangle with 5 rows of 6 tiles has an area of 30 square inches, and 5 x 6 = 30.
Since multiplication is a major focus of 3rd grade math, the study of area is a great way to reinforce that understanding.
Area is Additive!
Area measurement is additive. That means two adjacent shapes will have a combined area that is the sum of their individual areas. It also means that a rectangle can be decomposed into two smaller rectangles whose areas can be added to find the area of the entire rectangle.
This problem-solving strategy reinforces the understanding of the distributive property, which states that a factor can be decomposed into two addends. Both addends are multiplied by the other factor and the partial products added to find the entire product, or area.
Standards
All three major standard sets cover area in 3rd grade. Florida’s BEST address finding area with multiplication and problem-solving with area and perimeter of single and composite shapes. BEST benchmarks specify that 3rd graders don’t need to use division to find missing side lengths, which is included in the Common Core 3rd grade Measurement standards.
3rd grade multiplication and division skills parallel the skills and concepts of area measurement. Students working at grade level should be ready to use their Algebraic Reasoning to understand missing sides as one of the factors in a multiplication equation when the area measurement is known.
The study of area measurement is a great opportunity to explore more sophisticated multiplication and division concepts in the 3rd grade!
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