Video Transcript

Integers make up a number system that is very useful for certain types of quantities. In this video we will explore what integers are in the context of real-world situations where it makes sense to use integers for counting and measurement.

Let’s start with an example.

There are two mounds of dirt and one hole in the ground at a construction site. What types of numbers can be used to count the mounds and the holes?

We could use whole numbers to count 1-2-3 items, but that doesn’t quite work. These two mounds of dirt are a different thing than this hole in the dirt.

We could say that there are two mounds of dirt and use 2 to count the mounds. But what about the hole? Is it zero? No, in fact, it’s less than zero. This line that indicates the ground is what we could call ground zero.

So how do we count the hole? For this we need a new numbering system, and this gives rise to what we call integers.

Integers include the whole numbers zero and positive numbers 1, 2, 3, etc., but also includes a different class of numbers, negative numbers.

Now we can go back to the mounds and holes and properly count them with integers, Each mound is a +1 and the hole is a -1.

Let’s look at another example.

The fish is five feet below the water line and the sea gull is twenty-five feet above the water line. Use integers to describe their position relative to the water line.

You saw in the previous example that integers can be used to count certain types of objects. In this example, you’ll see that integers can be used to make certain types of measurements, in this case distance.

Here we are looking at positions above and below the water line. The sea gull is 25 feet above the water line and the fish is five feet below the water line. The relative positions of above and below are a hint that integers can be used.

Integers include the positive whole numbers, negative numbers, and zero. Think of the water line as representing zero. We can define that a position above the water line is positive and a position below the water line as negative. This means that the gull is +25 feet above the water line and the fish is -5 feet below the water line.

If we now include a duck swimming on the surface of the water, in other words, on the water line, then its position is at zero.

Let’s look at a final example.

On a winter day in a given city the low and high temperatures for the day are shown in this double bar graph. Describe these temperatures relative to 0°F.

In previous examples, you saw how integers can be used for counting and for measurement. In this example, we look at data written in integer format. This double bar graph shows two different temperatures in integer format. Let’s analyze these data points.

First of all, the horizontal line represents 0°F. So, this bar represents a temperature of 25° above zero, and this temperature represents 8 degrees below zero.

So, in all three examples shown in this video we saw positive integers and negative integers. But just as important, we had to identify a zero point that separated positive values from negative values. Values above the zero mark were positive integers and values below the zero mark were negative.

In the next video you’ll explore how number lines can be used to display integers.