What visual model can represent 
many types of numbers?
A number line is probably the 
most versatile model of number.
It is used to show both positive 
and negative integers.
That's right and we can see these
numbers on a thermometer.
Yes, and if we divide the whole into equal
lengths it reveals proper fractions,
improper fractions and mixed numbers
and because these equal parts are tenths,
we can label them using decimal notation.
Aren't all these numbers called 
rational numbers?
Yes, because they can all be expressed as
a common fraction
or as a decimal that either terminates or
forms a repeating pattern.
Can number lines also show irrational numbers?
Well, using Pythagoras' Theorem we know the
hypotenuse of this right triangle
is equal to the square root of two.
So although the square root of two is a decimal
that does not terminate or repeat
this diagram shows it does have a finite link
that can be represented on a number line.
Wow, I think students need to use 
this model more often.
