Understanding Surds and Fractional Indices in Mathematics
Explore the concepts of surds and fractional indices through worked examples, self-explanation prompts, and interactive problem-solving exercises. Understand the relationship between fractional powers and roots in a clear and concise manner.
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Presentation Transcript
Thats ab-SURD! Explicit teaching
Worked example 1 Fractional indices 2 1 2 2= 91 = 91 9 9 = 91 9 9 1 2 9 = 9 2
Self-explanation prompts 1 Fractional indices 2 1 2 2= 91 = 91 9 9 = 91 9 9 What index law makes this possible? 1 2 9 = 9 How is this shown in the working above? 3
Your turn 1 Fractional indices Justifying your response with working, show how to represent the surd shown using fractional indices. 6 6 = 61 4
Your turn 1 solutions Fractional indices 2 1 2 2= 61 = 61 6 6 = 61 6 6 1 2 6 = 6 5
Worked example 2 Fractional indices 3 1 3 3= 31 33 33 33 33 = 31 = 31 3 1 3 33 = 3 6
Self-explanation prompts 2 Fractional indices 3 1 3 3= 31 33 33 33 33 = 31 = 31 3 1 3 How are the fractional power and the root directly related? 33 = 3 7
Your turn 2 Fractional indices 416 416 416 416 = 21 8
Your turn 2 solutions Fractional indices 4 1 4 4= 161 416 416 416 416 416 = 161 = 161 16 1 4 416 = 16 9
Worked example 3 Fractional indices 1 5 532 2 32 10
Self-explanation prompts 3 Fractional indices 1 5 532 2 32 Can you prove this is the correct answer? 11
Your turn 3 Fractional indices Represent the term below without the use of fractional indices. 1 5 25 12
Your turn 3 solutions Fractional indices 1 5 525 25 This results in an irrational number, so leaving it in surd form is most accurate. 13
Worked example 4 Fractional indices 4 4 3 4 1 3 38 24 16 8 8 1 3 1 3 34096 16 84 4096 14
Self-explanation prompts 4 Fractional indices What index law makes this possible? Why is it possible to solve this in two different ways? 4 4 3 4 1 3 38 24 16 8 8 1 3 1 3 34096 16 84 4096 What index law makes this possible? 15
Your turn 5 Fractional indices Show the steps necessary to remove the fractional index power, writing your answer in its simplest form. You only need to show one way to reach a solution, not multiple. 3 2 4 16
Your turn 5 solutions Fractional indices 3 3 2 3 1 2 23 8 4 4 4 17
