Motivate solving quadratic equations
• Generate an intellectual need to solve a quadratic equation.
• Understand the graphical method for solving equations approximately.
In this section students develop an intellectual need for a general method for solving quadratic equations, through an encounter with a problem that is not obviously modeled by a quadratic equation and where the solution isn’t obvious through reasoning or inspection. They solve the problem approximately using graphing technology. Some students may have experience with solving quadratic equations and offer solutions. Solving the equation exactly can be delayed until Section 3, where students can solve it by completing the square.
WHAT: In this activity students are presented with an engaging but difficult problem involving making a frame using paper strips in the most efficient way (MP1). They eventually hone in on the need to find a specific quantity, the width of the frame, which turns out to be the solution to a quadratic equation. They create a quadratic equation (A-CED.A.1$^\star$) and can solve it approximately using graphing technology (A-REI.D.10, MP5). Some students may be able to solve it exactly with algebraic reasoning (A-REI.A.1).
WHY: The purpose of this lesson is to motivate solving quadratic equations (A-REI.B.4b). Students initially experiment with paper and scissors, then encounter the need for a mathematical model to solve the problem (MP4).