Unit 2
Area and Multiplication
Unit Goals
- Students learn about area concepts and relate area to multiplication and to addition.
Unit Narrative
In this unit, students encounter the concept of area, relate the area of a rectangle to multiplication, and solve problems involving area.
In grade 2, students explored attributes of shapes, such as number of sides, number of vertices, and lengths of sides. They measured and compared lengths (including side lengths of shapes).
In this unit, students make sense of another attribute of shapes: a measure of how much space a shape covers. They begin informally, by comparing two shapes and deciding which one covers more space. Later, they compare more precisely by tiling shapes with pattern blocks and square tiles. Students learn that the area of a flat figure is the number of square units that cover it without gaps or overlaps.
Students then focus on the area of a rectangle. They notice that a rectangle tiled with squares forms an array, with the rows and the columns as equal-size groups. This observation allows them to connect the area of a rectangle to multiplication—as a product of the number of rows and the number of squares per row.
To transition from counting to multiplying side lengths, students reason about area, using increasingly more abstract representations. They begin with tiled or gridded rectangles, move to partially gridded rectangles or those with marked sides, and end with rectangles labeled with their side lengths.
Students also learn some standard units of area—square inch, square centimeter, square foot, and square meter—and solve real-world problems involving the areas of rectangles.
Later in the unit, students find the area and the unknown side lengths of figures composed of non-overlapping rectangles. This work includes cases with two non-overlapping rectangles that share one side, which lays the groundwork for understanding the distributive property of multiplication in a later unit.