## Recapping Linear Inequalities

The start of the lesson recaps solving inequalities between two limits. Then, I remind students to break each inequality into two and sketch their solutions on a number line.

1<\frac{3x-1}{5}
\frac{3x-1}{5}\le4

Students are asked to complete this on mini-whiteboards so I can assess progress and feedback.

When solving quadratic inequalities it is helpful for students to see the equation as a graph. This way, the solutions are where the curve cuts through the x-axis.

Before we sketch the graph manually, I use the Geogebra app below to present some random quadratics. I then ask students to sketch the parabola on their whiteboards and mark the region that satisfies either f(x) < 0 or f(x) > 0.

I can easily feedback by using the checkboxes on the app.

## Problem Solving with Quadratic Inequalities

Towards the end of the lesson, I present the problem-solving question to the left. This takes between 8 to 10 minutes as it challenges students to set up the inequality by writing the surface area in terms of its radius.

Most students were able to set up the quadratic equality as 2πr2 + 36πr < 80π all though some made it equal to 80π. I was pleased that all students correctly factorised out the 2π and went on to solve r2 + 18π – 40 < 0.

## Teach this lesson

My name is Jonathan Robinson, and I am passionate about teaching mathematics. I am currently Head of Maths in the South East of England and have been teaching for over 15 years. I am proud to have helped teachers all over the world to continue to engage and inspire their students with my lessons.

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