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Cube the first 5 square numbers
Square the first 5 cubed numbers What do you notice?
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1 4 9 16 25 1 8 27 64 125 Here are the first five square numbers:
Here are the first five cubed numbers: Students may not need this scaffold 1 8 27 64 125
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The first five square numbers cubed:
π π π π π π ππ π ππ π The first five cubed numbers squared: π π π π ππ π ππ π πππ π What do you notice? Students may not need this scaffold
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We have seen that the following statements are true:
π π = π π π π π π π π ππ π ππ π ππ π ππ π πππ π Without evaluating the powers, convince your partner that the square numbers cubed are equal to the cubed numbers squared.
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How may writing the squared and cubed numbers
We have seen that the following statements are true: ( π π ) π = ( π π ) π ( π π ) π ( π π ) π ( π π ) π ( π π ) π ( π π ) π ( π π ) π ( π π ) π ( π π ) π Students may not need this scaffold How may writing the squared and cubed numbers in this way help?
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( π π ) π = ( π π ) π 1 2 Γ 1 2 Γ 1 2 1 3 Γ 1 3 1 6
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( π π ) π = ( π π ) π 2 2 Γ 2 2 Γ 2 2 2 3 Γ 2 3 2 6
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( π π ) π = ( π π ) π 3 2 Γ 3 2 Γ 3 2 3 3 Γ 3 3 3 6
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( π π ) π = ( π π ) π π₯ 2 Γ π₯ 2 Γ π₯ 2 π₯ 3 Γ π₯ 3 π₯ 6
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Indices and Bases Copy and complete the following sentences: 64 can be written as a square number as can be written as a cubed number as can be written as a power of two as 2 6 ? ? ?
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Index 2 6 Base
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Power 2 6 Base
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Indices and Bases Worked Example Your Turn 27Γ (3 3 ) 2 8Γ (2 2 ) 3
Write the following as a power of 3. 27Γ (3 3 ) 2 Your Turn Write the following as a power of 2. 8Γ (2 2 ) 3 Standard Example
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Indices and Bases Worked Example 2 Your Turn 27Γ 9 2 8Γ 4 3
Write the following as a power of 3. 27Γ 9 2 Your Turn Write the following as a power of 2. 8Γ 4 3 Non Standard Example
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Independent Practise Express as a single power of π
32 81 32Γ 2 4 81Γ 3 2 32Γ16 81Γ9 2 5 Γ 16 2 3 9 Γ 9 2 ( 2 2 ) 5 Γ1 6 2 ( 9 2 ) 5 Γ27 (2 2 ) (3 2 ) Γ81 Create 5 questions that could start with the sentence β Express as a single power of 5β
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Mark and correct your work
Express as a single power of π Express as a single power of π 32= 2 5 81= 3 4 32Γ 2 4 = 2 9 81Γ 3 2 = 3 6 32Γ16= 2 9 81Γ9= 3 6 2 5 Γ 16 2 = 2 13 3 9 Γ 9 2 = 3 13 ( 2 2 ) 5 Γ1 6 2 = 2 18 ( 9 2 ) 5 Γ27= 3 23 (2 2 ) = 2 6 (3 2 ) Γ81= 3 10 Create 5 questions that could start with the sentence β Express as a single power of 5β
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Whiteboards ready⦠5 questions to check your understanding
Mini Whiteboard Plenary
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True or False? 4 6 Γ· 2 3 = 4 3 How do you know? What it is not example
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True or False? 8Γ· 2 3 = 4 β2 How do you know? What it is not example
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The area of this rectangle can be calculated by working out 2 8
True or False? 4 3 The area of this rectangle can be calculated by working out 2 8 How do you know? 2 2 Non Standard synoptic question
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The area of this rectangle can be calculated by working out 4 4
True or False? 4 3 The area of this rectangle can be calculated by working out 4 4 How do you know? 2 2 Non Standard synoptic question
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The area of this rectangle can be calculated by working out 5 6
True or False? 125 The area of this rectangle can be calculated by working out 5 6 How do you know? 25 What it is not example
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