Begin by helping your child cut out different shapes from paper. Use an inch or centimeter
ruler to draw and mark off the sides of squares, rectangles, triangles, and other shapes in
whole units (such as 5 centimeters or 3 inches). After cutting out a square or rectangle,
ask your child to find the area it covers in square units (square inches or square centimeters).
If your child knows the formulas, he should use them. Then ask him to explain why these
formulas work. If he doesn’t know the formulas, encourage him to draw square units
with a ruler on the shape (by marking off units on the edges and then drawing lines straight
across). Then he can count the squares. Ask him to find the areas of other rectangles and
squares and try to come up with a quicker way of doing it (without drawing and counting).
In this way, he can find the formulas on his own.
For example, if your child is exploring a rectangle that is 5 inches long and 3 inches
wide, he can use a ruler to draw square units on the shape. He can then count up all the squares
to get an area of 15 square units. He will remember that 3 times 5 equals 15. He will also
see from his shape that he has 3 rows of 5 squares, which is a way to model 3 times 5. After
doing this a number of times, he will begin to understand that the way to find the area of
a rectangle (or a square) is to multiply length times width.
Once your child has determined a quick way to find the areas of squares and rectangles,
try triangles next. Again, help him see how formulas relate to drawing and counting squares
and produce the same results. Help him understand why the formulas work.
Don’t worry if you don’t know or remember all the formulas. After working with
your child on this activity, you will.
Next, you and your child can work on finding the area of other, more complicated shapes
such as those in this picture. Encourage your child to find connections between these new
shapes and basic shapes (such as squares, rectangles, and triangles) and the ways of finding
their areas.
