# Putting your tools together

#### Prerequisites

- Building equations from the physics
- Telling the story
- The special case tool
- The dimensional analysis tool

Most of the problems we have in this class won't be simple plug-and-chug (that is, find an equation and put in numbers — see "The Equation Hack" below). You'll have to think about what's going on and figure out how to use the variety of tools you've developed to make sense of the problem and build an answer. We call putting together of all these tools to do math-in-science *Building the Equation*. It uses our previous tools together to solve a complex problem: The Telling the story tool and the Building equations from the physics tool, just to mention a few that are almost always involved.

We've chosen an icon that shows lots of folks working together using multiple tools to create something significant. While it's not really a tool, it involves many different rules and strategies, and a lot of thinking. It's fun and intellectually stimulating and we hope you find it so as well!

You can solve lots of different problems with your mathematical toolbelt by putting your tools together.

Although this is NOT an algorithm (a series of steps that you can follow without thinking to get a result) here are some questions you might ask yourself to help you find a path into a complex problem.

- What physical system are we talking about and what happens? (Tell the story.)
- What symbols — variables and parameters — can we use to describe the system? Don't use the same symbol to mean two different things! (Build a model.)
- What physical principles are relevant? Do they lead to any relevant equations? (Think about foothold ideas and anchor equations!)
- What do we have to keep and what can we ignore? (Estimate!)
- What are we given and what are we supposed to find?
- Do we have enough equations to find all of our unknowns?
- If we need something we are not given, can we estimate it?
- Work with symbols to solve. Don't put in numbers until the end! (And check the dimensions of your answer!)
- Does your answer make sense? (Estimate and evaluate!)

This is a rather sophisticated process, and you'll need to be continually making the connections between what you know is happening and true in the physical world and how that information is expressed in equations.

Don't be discouraged if you can't do all the pieces of this right away! Helping you learn to use all of your tools in coordination is a major goal of the class, not something you're expected to know when you come in!

**The Equation Hack**

Too many students try to find simple "I-don't-want-to-think" ways around using their math-in-science tools in a sophisticated way. They often resort to what I call "the equation hack". This is it.

- What symbols am I given?
- Do I remember any equations with those symbols in them?
- Do any of the numbers I’m given fit in my equations? If so, put them in.

When student use the equations hack, they DON'T do this:

- They do NOT check for physical relevance of the principles and models used.
- They do NOT check for units or dimensions.
- They do NOT check for special and limiting cases.
- They do NOT see if their answer makes good physical sense.

Please do NOT do this. The equation hack is more likely to get you into trouble than to save you time.

Joe Redish 7/4/17

Last Modified: May 22, 2019