What is “x”? Or how do we represent variables and functions on spreadsheets?
This Lab introduces a method for solving or estimating the solution to an equation digitally that can be applied to many types of equations. This Functional Thinking approach reduces the need to remember a variety of rules and procedures. It is 1 of 3 Labs on this topic.
This problem is typical of the earliest algebra problems that likely came out of India. It is interesting historically, and it is the kind of problem students are still taught to solve today. We can do it very differently using spreadsheets.
Solving systems of equations sometimes called simultaneous equations with graphs is simply a matter of finding out where they intersect. One of the most valuable things students can learn is to be able to visualize linear equations and systems of equations so that they can tell the quadrant where the intersection and therefore the solution is. This develops the valuable ability to estimate solutions. We suggest students practice picturing and then graphing systems with a variety of slopes and intercepts. Significant relationships like perpendicular lines should be another focus.
Typical algebra courses start with equations and solving equations and then move to graphing and functions. We start with functions and use them to solve equations. We treat an equation as the equality of two functions, graph each one and then look at their intersection. This is a powerful way to think about solving equations due to Judah Schwartz and one that we believe will help many student to understand this algebra.