fractals – lesson 4
DESCRIPTION
Fractals – Lesson 4. The perimeter and area of the Von Koch Snowflake. Learning objectives. We are learning to: Understand the difference between term-to-term rules and position-to-term rules . Write an expression to describe the n th term of a sequence. Learning outcome. - PowerPoint PPT PresentationTRANSCRIPT
Fractals – Lesson 4
The perimeter and area of the Von Koch Snowflake
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Learning objectives
We are learning to:
• Understand the difference between term-to-term rules and position-to-term rules.
• Write an expression to describe the nth term of a sequence.
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Learning outcome
By the end of the lesson you will:
• Understand the difference between term-to-term and position-to-term rules.
• Have derived the position-to-term rule for the number of edges and the length of each edge of the Von Koch Snowflake.
• Have made a discovery about the curious properties of the Von Koch snowflake.
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Lesson 4 - Overview
1. Patterns in sequences
2. Position-to-term rules of the Von Koch Snowflake
3. A curious property!
4. Thinking about our learning!• Displays and narration
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1. Patterns in sequences
1, 2, 4, 8, … … …
Term to term rule
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1. Patterns in sequences
10, 13, 16, 19 … … …
Term to term rule
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1. Patterns in sequences
… … … … … …
Term to term rule
multiply by ½
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2. The Von Koch Snowflake
Pattern Number
Number of edges
Length of each edge
Total Perimeter
1 3 9 27
2 12 3 36
3 48 1 48
4 192 1/3 64
5 768 1/9 85 1/3
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2. Von Koch Snowflake
Pattern Number
Number of edges Length of each edge
1 3 9
2 12 3
3 48 1
4 192 1/3
5 768 1/9
10
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2. Von Koch Snowflake
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Nth terms
Number of edges sequence
3, 12, 48, 192, … … 3 x 4n-1
Length of each edge sequence
9, 3, 1, 1/3, … … 9 ÷ 3n-1
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Perimeter of the Von Koch Snowflake
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
1 2 3 4
Pattern Number
Len
gth
in
cm
Sequence showing the length of the perimeter
27, 36, 48, 64, …
× 3/4
× 4/3
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What is the perimeter of
pattern number 6?
CEDS – Study Plus in Cornwall
CEDS – Study Plus in Cornwall
Learning outcome
By the end of the lesson you will:
• Understand the difference between term-to-term and position-to-term rules.
• Have derived the position-to-term rule for the number of edges and the length of each edge of the Von Koch Snowflake.
• Have made a discovery about the curious properties of the Von Koch snowflake.