In this lesson, students practice solving fractional inequalities graphically by sketching reciprocal functions and analysing intersections and asymptotes. As they progress, they tackle inequalities involving more complex functions, such as when the numerator and denominator are quadratics.
To support this learning, I’ve created a video tutorial featuring two worked examples.
Members of mr-mathematics.com can download the complete lesson plan on solving fractional inequalities graphically, including the PDF resources used in the video tutorials. These materials are classroom-ready and designed to save teachers time while ensuring a deep and engaging learning experience.
A basic example to establish the core skills of sketching graphs with asymptotes and solving inequalities.
A more advanced question that requires analysing intersections of a rational function with multiple turning points and asymptotes.
Students learn how to sketch reciprocal functions.
Later, as learning progresses, students sketch reciprocal functions where the numerator and denominator can be quadratics.
Solving Fractional Inequalities Graphically - Part 1
Solving Fractional Inequalities Graphically - Part 2
Students learn how to solve fractional inequalities graphically.
Later, as learning progresses students sketch reciprocal functions where the numerator and denominator can be quadratics.
Solving Fractional Inequalities Graphically - Part 1
Solving Fractional Inequalities Graphically - Part 2
A research-backed case exploring why over-reliance on automated math homework platforms and repetitive worksheets lowers student expectations, and how departments can build genuine mathematical thinking.
How to teach converting between fractions, decimals and percentages.
Four problem solving lessons to develop student’s mathematical reasoning and communication skills.
