Quadratics: Put a Ring On It

Tyler Erb, Mathematics, Community House Middle School

Curriculum Unit (pdf)


This curriculum unit will focus on having students get back to basics of using the language of multiplicative inverse and additive inverse while extending students understanding of solving linear and quadratic equations. Students will investigate how to solve both linear and quadratic equations by using modular arithmetic to solve. Using field Z5 and ring Z6, students will have to first start by solving linear equations by finding additive inverses that add the constant to either 5 or 6 respectively. When solving linear equations with a variable other than one, students will discover that the multiplicative inverse for a number is not the reciprocal which is what they are accustom to in their normal solution set of all real numbers. By taking them outside the normal way they solve linear and quadratic equations, they go back to remembering the basics of additive and multiplicative inverse. Students finish the unit by proving that the quadratic formula in Z5 and move on to solving quadratic equations.