LESSON TITLE: The Set of Real Numbers
DESCRIPTION: As we move from arithmetic to study algebra, this lesson allows you to encounter more kinds of numbers. It will expand your imagination of the counting numbers, which you are very familiar of in elementary, to numbers that fill the "gaps" in describing some situations in life that mere counting numbers cannot simply describe like temperatures inside the refrigerator (hehehe if only we have winter!).
LEARNING OUTCOMES
Essential Understanding:
Essential Question: What are the subsets of the real number system? Can you give a situation in daily life where a particular subset is used to describe the situation?
EXPLORATION
When you were a child, the first set of numbers that were exposed to is the set of counting numbers. For this lesson, I'm going to introduce you to another name which is more elegant than counting numbers, the set of natural numbers. So, when we say natural numbers we actually mean the counting numbers. Can you see the child below using the abacus? That's precisely what you did in Grade 1 when you were taught how to count from one to 50 or more!
When you got older, you were introduced to the concept of zero. By now, your set of numbers grew into what we call the set of whole numbers. The set of whole numbers is simply putting the natural numbers together with zero. Putting the set of whole numbers into set notation, we have {0, 1, 2, 3, 4, 5, . . . }.
You grew a little bit older and there seems to be a number which is not yet in your set. Look at the figures below, is there a temperature lower than the freezing point? How do you represent that? Another example, do you know how to represent profit? What about lost?
The set of numbers that combine together natural numbers, zero, and negative numbers is what we call the set of integers.
This time, the next set of numbers is not new to you. Can you name what numbers can describe the following? These numbers, which I can convince myself you know them, are what we call fractions.
When we put together the set of integers and fractions, we come up with a bigger set, the set of rational numbers. The identity of these numbers is that they can be written in fraction form where the denominator cannot be zero. Notice that all integers can be written in fraction with a denominator of one.
There are also numbers, which we are not to discuss them here in Math 1 but maybe in higher math subjects, which also form part of our big set of numbers, the set of irrational numbers. There are two characteristics of these numbers; they are non-repeating and non-terminating. For example, pi is irrational because it does not repeat and does not terminate. Can you name more of these numbers?
Finally, putting or rational numbers and irrational numbers together comprise our big set of numbers, the set of real numbers. That is,
Now, you know that we have a big set of real numbers and under this set are subsets. To arrange these sets in a tree diagram, click here to download the worksheet.
FIRM-UP
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DEEPEN
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