## Putting It Together: Integers

At the beginning of this module, we met Beatrice and her team of scientists who were collecting lava at different elevations both above and below sea level. Some of the questions they asked included:

• What’s the total elevation change between samples of rock?
• They notice that the lava samples from $23$ feet below sea level and $518$ feet above sea level are very similar. What’s their vertical distance from each other?

To answer these questions, we can use integers. If we set up a number line like those we saw in the module, we can place the samples of rock at different “elevations” and answer the questions.

We will align sea level with zero on the number line, such that depths below sea level are negative numbers, and heights above sea level are positive numbers. Now we can answer the questions the scientists asked.

What is the total elevation change between the samples of rock? We are being asked the difference between the greatest elevation above and below sea level where samples were taken.  In the module, we learned that difference means subtract, so we can subtract the  elevation below sea level from the elevation above:

$10,679-(-110) = 10,889$

The total elevation change is $10,889$ ft.

The next question asks what is the vertical distance between the sample taken at 23 feet below sea level and the sample taken 518 feet above sea level. We can think of distance from sea level as absolute value, so we can take the sum of the absolute values of the distances.

$|-23|+|518| = 23+518=541$.

The vertical distance between the two samples is $541$ feet.

Integers have helped us orient ourselves in space to answer questions that a scientist would want to know.