Adventures in Algebra*

"A fish starts at a depth of d feet below the surface of a pond.  While searching for food it ascends 4 feet, then descends 12 feet.  Its final depth is 15 feet below the surface.  

What was the fish's initial depth?"

Before we deal with d, let's draw a picture.

Wait, we need a shark.
Never mind that it is a pond and not the ocean.
"Fish are friends, not food."

At this point, I stopped taking pictures, because equations are serious business.  I assure you, the problem did get solved.  The fish's initial depth was -7 feet.

She wrote the algebraic equation after she figured out the answer.  She is an immensely practical person and sees no reason for a variable equation if she can figure out the answer in her head.  But she is learning that if she wants to move on to the next question, she has to show the work in algebra language.  

d + 4 - 12 = -15

*It is really pre-Algebra, but that wouldn't make a pretty alliteration.