Building numbers

You have probably put together models of cars and airplanes. You’ve
probably made clay models of animals. But have you ever tried to make a
model of a number?

Remember, to get a square number, you multiply any number by itself. If
you multiply 2×2, you get the square number 4. A square is a flat shape,
so you can make a model of the square number 4 very easily. All you need
are four toothpicks and four tiny balls of clay. The four balls of clay
stand for the four ones that make up the number four.

Make two squares like the one shown. Then, join them together with four
toothpicks.

Now, you have a shape called a cube. Count the balls of clay and you’ll
see there are eight of them. What you’ve made is a model of the cubic
number 8.

To make a cubic number, you multiply any number by itself three times,
such as 2x2x2. Multiplying the first two numbers gives you a square
number—4—and when you multiply by 2 again, you get 8, which is a
cubic number. The number 4 is the square of 2, and the number 8 is the
cube of 2.

When you cube 3, you multiply 3X3X3. You get the cubic number 27. Making
a model of this cubic number is a real challenge. It would look like
this: