Express in surd form; rationalise the denominator Grades 8/9 Surds Express in surd form; rationalise the denominator If you have any questions regarding these resources or come across any errors, please contact helpful-report@pixl.org.uk

Lesson Plan Lesson Overview Progression of Learning Objective(s) Express in surd form; rationalise the denominator Grade 8/9 Prior Knowledge Square roots, Later tasks include Pythagoras, solving quadratics using the formula, expanding binomials, etc. Duration 100 minutes (variable). Resources Slides 18 onwards are printable versions of some of the earlier slides. Equipment Progression of Learning What are the students learning? How are the students learning? (Activities & Differentiation) Introduction; recap of basic rules about surds, square roots. Six expressions, of which two are false. Use this to establish, for example, that two surds can be multiplied and divided but not added or subtracted, and that multiplying two identical square roots together yields the original number inside each root. Following slide has eight calculations that should be tackled with minimal introduction, to follow initial “true or false”input. PRINT SLIDE 18 15 Expressing in surd form After teacher led input, students have differentiated practice, leading to simplification of surds including addition and subtraction after matching surds. PRINT SLIDE 19 20 Reasoning Four differentiated questions about expanding brackets. Those students who successfully obtain results for gold question will have a variant of the “difference of two squares” that can be used in rationalizing the denomnator. PRINT SLIDE 20 10-15 Rationalising the denominator Rationalising the denominator. Again, differentiated practice follows a teacher led input here. The “gold” section uses the difference of two squares to simplify the denominator. PRINT SLIDE 21 20-25 Plenary Four examination style questions; may be best tackled by student working in groups. PRINT SLIDE 22 Surds in exam questions (from specimen papers) PRINT SLIDE 23. This includes 6 exam questions related to objective. Students need to use notes from lesson to answer the questions. Ensure that all steps are shown. Relate to mark scheme to show how the marks are allocated using slides 12 to 17. 10 Next Steps Assessment PLC/Reformed Specification/Target 8/Number/Surds

Key Vocabulary Surd Square root Square number Rationalise Numerator Denominator Difference of two squares

Click on a statement to see whether it is true or false Surds True or false? (for each of the statements that is false, either correct the statement or explain why it is incorrect) TRUE FALSE TRUE FALSE TRUE TRUE Click on a statement to see whether it is true or false

Find the value of each of the following Surds Find the value of each of the following SILVER GOLD 1 2 3 4 5 6 7 8 Click on “Silver” or “Gold” to see answers for that section

Express the following in surd form Surds Express the following in surd form Square number Square number 4 × 5 = 20 9 × 6 = 54

Express the following in surd form Surds Express the following in surd form BRONZE SILVER GOLD 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Reasoning: expand the brackets Surds Reasoning: expand the brackets BRONZE SILVER SILVER GOLD This final result will be very useful in the task that follows… Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Rationalise the denominator Simplify your answer where possible Surds Rationalise the denominator Simplify your answer where possible Same square root on denominator Expand numerator Difference of two squares on denominator Simplify (care with “cancelling”)

Rationalise the denominator Simplify your answer where possible Surds Rationalise the denominator Simplify your answer where possible BRONZE SILVER GOLD 9 10 11 12 1 2 3 4 5 6 7 8 Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Reasoning Simplify your answer where possible Surds Reasoning Simplify your answer where possible BRONZE SILVER Find x, giving your answer in surd form Here is a geometric sequence. Find a and b giving your answers in surd form x 2cm a 2 10 b a = b = 4cm SILVER GOLD Solve the equation, giving your solutions in surd form Find x x 4 Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Exam Questions – Specimen Papers

Find the value of each of the following Surds Find the value of each of the following SILVER GOLD 1 2 3 4 5 6 7 8

Express the following in surd form Surds Express the following in surd form BRONZE SILVER GOLD 1 2 3 4 5 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24

Surds Expand the brackets BRONZE SILVER SILVER GOLD

Rationalise the denominator Simplify your answer where possible Surds Rationalise the denominator Simplify your answer where possible BRONZE SILVER GOLD 9 10 11 12 1 2 3 4 5 6 7 8

Reasoning Simplify your answer where possible Surds Reasoning Simplify your answer where possible BRONZE SILVER Find x, giving your answer in surd form Here is a geometric sequence. Find a and b giving your answers in surd form x 2cm a 2 10 b 4cm SILVER GOLD Solve the equation, giving your solutions in surd form Find x x Click on “Bronze”, “Silver” or “Gold” to see answers for that section

Exam Questions – Specimen Papers