Area: From Counting Squares to Multiplication

Initially your children find area by counting the number of square units required to fill a shape. It is important that they move on from this and see the rows and columns formed by the square units. When they see the rows and columns as groups they are better prepared to use addition or multiplication to calculate the area.

A 4 x 6 grid and 4 x 6 array highlighting the groups of rows.

The three worksheets below provide practice with calculating area.

As your children work on finding and calculating area, they both draw upon and support, their understanding of multiplication. The area method of multiplication is covered here although it is typically taught in 4th grade and this exploration of area is a good introduction to it.

5 x 18 shown on a grid of squares and split into 5 x 10 and 5 x 8

Your children may already be familiar with multiplication’s commutative property (e.g. a x b = b x a). Regardless, comparing the area of a 4 x 6 rectangle with that of a 6 x 4 one and seeing the rotation of a rectangle through 90 degrees supports understanding of this important property.

A 4 x 6 grid of squares shown rotated through 90 degrees to become a 6 x 4 grid

Calculating area can also highlight the distributive property of multiplication as the example below show.

A 3 x 13 rectangle shown split into two 3 x 10 and 3 x 3 rectangles

Have your children try this worksheet worksheet icon in which they are challenged to write multiplication expressions to help calculate area.

Compound Shapes (rectilinear)

With a good understanding of how to find the area of a rectangle, your children will progress to calculating the area of compound shapes as shown below.

A compound shape shown decomposed into two rectangles which calculation for each one and for the total area

The steps to finding the area of compound shapes are:

  1. Decompose into rectangles
  2. Find "missing" lengths
  3. Write expressions for each rectangle and for the whole shape
  4. Resolve the expressions

There are no right and wrong methods for decomposing the compound shape into rectangles as the example below illustrates.

An example of how a compound shape can be decomposed in different ways

Discuss the above examples with your children and encourage them to find the one they like best. Do not assume your children will be able to easily decompose (or break up) the shape. If they struggle then use this worksheet worksheet icon as part of a "hands-on" activity to help them.

More compounding shapes!

With the ability to find decompose shapes and find their area secure, your children can move on to use their knowledge and understanding to calculate the area of more complex compound shapes. This area of compound shapes worksheet worksheet icon will challenge your children to use what they are learning to draw rectangles and compound shapes based on a given area.

Credit: Many of the examples and worksheets on this page were inspired by work published by San Francisco Unified School District (SFUSD) and this is gratefully appreciated and acknowledged.