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- Year 10•
- Higher
The distributive law with two or more binomials
I can apply the distributive law to two or more binomials.
- Year 10•
- Higher
The distributive law with two or more binomials
I can apply the distributive law to two or more binomials.
Lesson details
Key learning points
- The distributive law can be used with expressions containing surds.
- This can be extended to finding the product of two or more binomials.
- Any binomial could contain surd terms.
Keywords
Distributive law - The distributive law says that multiplying a sum is the same as multiplying each addend and summing the result.
Common misconception
Pupils may suggest using FOIL (or similar) to expand both brackets and make errors whilst doing so.
The grid method is derived from the area model and therefore the area model supports expanding both one binomial and two binomials.
To help you plan your year 10 maths lesson on: The distributive law with two or more binomials, download all teaching resources for free and adapt to suit your pupils' needs...
To help you plan your year 10 maths lesson on: The distributive law with two or more binomials, 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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Lesson video
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Prior knowledge starter quiz
6 Questions
Q1.Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$x$$?
Q2.Write $$7(2\sqrt {5} + 3\sqrt {3})$$ in the form $$x\sqrt {5} + y\sqrt {3}$$. What is the value of $$y$$?
Q3.Write $$5\sqrt {3}(2\sqrt {8} + 3\sqrt {2})-\sqrt {3}(\sqrt {8} + 2\sqrt {2})$$ in the form $$a\sqrt {b}$$. What is the value of $$b$$?
Q4.Write $$5\sqrt {3}(2\sqrt {8} + 3\sqrt {2})-\sqrt {3}(\sqrt {8} + 2\sqrt {2})$$ in the form $$a\sqrt {b}$$. What is the value of $$a$$?
Q5.Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$b$$?
Q6.Write $$\sqrt {5}(3\sqrt {5} + 2)-(3\sqrt {5} + 2)$$ in the form $$a-\sqrt {b}$$. What is the value of $$a$$?
Assessment exit quiz
6 Questions
Q1.Expand $$(2\sqrt {3} + \sqrt {3})(\sqrt {3} - 1)$$
Q2.Expand $$(\sqrt {2} + 1)(\sqrt {2} - 1)$$
Q3.Expand $$(\sqrt {5} + \sqrt {2})(\sqrt {5} - \sqrt {2})$$
Q4.Expand $$(3\sqrt {7} - 2\sqrt {3})(\sqrt {7} + \sqrt {3})$$
Q5.Expand $$(\sqrt {10} + 2\sqrt {6})(\sqrt {10} - 2\sqrt {6})$$
Q6.Expand $$(4\sqrt {2} - \sqrt {5})(4\sqrt {2} + \sqrt {5})$$. What is the result?