Why learn how to solve math problems that involve integers?

Beatrice is an oceanographer, and she’s studying the composition of undersea lava flows off the coast of Hawaii. As part of her work, she’s on a scuba diving mission to collect samples of lava rock at various depths. She and her team dive down and then follow the lava flow from the point of eruption along hills and valleys that have formed over time, collecting samples along the way.

Today, Beatrice and her team start their dive by going $110$ feet below sea level. After collecting a few samples, they gradually come back up to sea level. Along the way, they notice a lava formation at $23$ feet below sea level, so they do another dive to collect samples from it.

The team is happy with the undersea samples they’ve collected, and can’t wait to compare their composition to the exposed lava flow on the island. Another team has been collecting samples from above the surface of the water at $518$ feet above sea level, and from the peak of the volcano at $10,679$ feet above sea level.

At the end of the day, Beatrice and her team take their samples back to the lab, and they start thinking about the amazing collective journey they took by following the lava. What’s the total elevation change between samples of rock?

They also 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 find the answers to these questions, you’ll need to know how integers work. Read on to find out what you can do with a good understanding of integers.