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- Year 10•
- Higher
Rationalising a two term denominator
I can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.
- Year 10•
- Higher
Rationalising a two term denominator
I can use the technique of rationalising the denominator to transform a fraction to an equivalent fraction.
Lesson details
Key learning points
- Fractions should be given in their simplest term.
- The denominator should be written as simply as possible.
- Combining your knowledge of equivalent fractions and the distributive law will help.
Keywords
Surd - A surd is an irrational number expressed as the root of a rational number.
Common misconception
Pupils may struggle to see why using the difference of two squares is important.
The grid method for multiplication can be used to explore why two of the terms cancel each other.
To help you plan your year 10 maths lesson on: Rationalising a two term denominator, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: Rationalising a two term denominator, download all teaching resources for free and adapt to suit your pupils' needs.
The starter quiz will activate and check your pupils' prior knowledge, with versions available both with and without answers in PDF format.
We use learning cycles to break down learning into key concepts or ideas linked to the learning outcome. Each learning cycle features explanations with checks for understanding and practice tasks with feedback. All of this is found in our slide decks, ready for you to download and edit. The practice tasks are also available as printable worksheets and some lessons have additional materials with extra material you might need for teaching the lesson.
The assessment exit quiz will test your pupils' understanding of the key learning points.
Our video is a tool for planning, showing how other teachers might teach the lesson, offering helpful tips, modelled explanations and inspiration for your own delivery in the classroom. Plus, you can set it as homework or revision for pupils and keep their learning on track by sharing an online pupil version of this lesson.
Explore more key stage 4 maths lessons from the Surds unit, dive into the full secondary maths curriculum, or learn more about lesson planning.
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Prior knowledge starter quiz
6 Questions
Q1.Expand the following expression: $$(3\sqrt {2} + \sqrt {3})(3\sqrt {2} - \sqrt {3})$$
Q2.Expand the following expression: $$(\sqrt {6} + 1)(\sqrt {6} - 1)$$
Q3.Expand the following expression: $$(2\sqrt {5} - 3\sqrt {3})(2\sqrt {5} + 3\sqrt {3})$$
Q4.Expand the following expression: $$(5\sqrt {7} - 4\sqrt {2})(5\sqrt {7} + 4\sqrt {2})$$
Q5.Expand the following expression: $$(\sqrt {8} + \sqrt {2})(\sqrt {2} - \sqrt {8})$$
Q6.Expand the following expression: $$(\sqrt {10} + 2\sqrt {5})(2\sqrt {5} - \sqrt {10})$$
Assessment exit quiz
6 Questions
Q1.Match the brackets and their expanded form.
12 -
$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$
$$28+8\sqrt {10}$$ -
$$(\sqrt {8}+2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$
-12 -
$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}+\sqrt {8})$$
$$-28+8\sqrt {10}$$ -
$$(\sqrt {8}-2\sqrt {5})(2\sqrt {5}-\sqrt {8})$$
Q2.You can use the to make an integer from a surd expression.
Q3.What would you multiply $$(13 + \sqrt {17})$$ by to make an integer?
Q4.Simplify $${{8} \over {4 - \sqrt {5}}}$$
Q5.Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$a$$?
Q6.Express $${6} \over {2\sqrt {3} - 4}$$ in the form $$a(d+\sqrt {3})$$. What is the value of $$d$$?