# Understanding

## Derivative as Instantaneous Rate of Change

(An archive question of the week) Last week we looked at a recent question that touched on the idea of the derivative as a rate of change. Let’s look at a long discussion from a few years ago digging into what that means within calculus. Instantaneous rate, or rate per inch? Here’s the question, from …

## Too Many Variables?

(An archive question of the week) Students often struggle with solving an equation with several variables, for one of those variables. This is also called “solving a formula”, or a “literal equation”; or “making one variable the subject”. Learning to use variables instead of just numbers (as we looked at last week) is the first …

## How Variables and Equations Work

(An archive question of the week) We’re looking at extended discussions of a single topic, which illustrate how we try to guide a student to a deeper understanding. Here, a student asks how to solve an equation, and Doctor Ian takes him through the whole process, clarifying what it means to solve an equation, and …