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Students learn how to represent inequalities on a number line and solve an inequation using the balance method.

This unit takes place in Term 6 of Year 10 and follows on from solving equations.

- order positive and negative integers
- apply the four operations, including formal written methods, to integers, both positive and negative;
- solve linear equations in one unknown algebraically (including those with the unknown on both sides of the equation)

- solve linear inequalities in one variable;
- represent the solution set on a number line;
- understand and use the concepts and vocabulary of expressions, equations, formulae, identities and inequalities

- Knowledge of <,>, ≤ & ≥ notation is critical to this topic. Numbers which are less or greater than but not equal to are represented on a number line with a hollow circle. Full circles are used when an inequality can be equal to a number.
- Inequations have a set of solutions whereas equations have distinct solutions.
- Inequations can be solved using the balance method.
- When dividing or multiplying both sides of an inequality by a negative number the sign is reversed.

- Students are often confused with the direction of the inequality sign. Use the number line to show < represents less than and > means greater than.
- Inequalities such as 5 < x ≤ 10 represents x as any value greater than 5 and less than or equal to 10. Encourage students to read such inequalities in two directions i.e., 5 < x and x ≤ 10.

July 6, 2019

Earlier this week, my school took part in a trial OFSTED inspection as part of getting ready for the new inspection framework in September 2019. This involved three Lead Inspectors visiting our school over the course of two days. The first day involved a ‘deep dive’ by each of the Lead Inspectors into Mathematics, English […]

June 30, 2019

The method of how to solve quadratics by factorising is now part of the foundational knowledge students aiming for higher exam grades are expected to have. Here is an example of such a question. Solve x2 + 7x – 18 = 0 In my experience of teaching and marking exam papers students often struggle with […]

June 24, 2019

When learning how to write 3-part ratios students need to understand how ratios can be made equivalent. The start of the lesson reminds students by asking which of six ratios is the odd one out. This is presented to the class as they come into the lesson. Writing Equivalent Ratios A few students immediately go […]