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Fractals – Lesson 4

Fractals – Lesson 4

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Fractals – Lesson 4

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  1. Fractals – Lesson 4 The perimeter and area of the Von Koch Snowflake

  2. 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. CEDS – Study Plus in Cornwall

  3. 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. CEDS – Study Plus in Cornwall

  4. Lesson 4 - Overview • Patterns in sequences • Position-to-term rules of the Von Koch Snowflake • A curious property! • Thinking about our learning! • Displays and narration CEDS – Study Plus in Cornwall

  5. 1. Patterns in sequences 1, 2, 4, 8, … … … Term to term rule CEDS – Study Plus in Cornwall

  6. 1. Patterns in sequences 10, 13, 16, 19 … … … Term to term rule CEDS – Study Plus in Cornwall

  7. 1. Patterns in sequences … … … … … … Term to term rule multiply by ½ CEDS – Study Plus in Cornwall

  8. 2. The Von Koch Snowflake CEDS – Study Plus in Cornwall

  9. 2. Von Koch Snowflake CEDS – Study Plus in Cornwall

  10. 2. Von Koch Snowflake CEDS – Study Plus in Cornwall

  11. 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 CEDS – Study Plus in Cornwall

  12. × 4/3 × 3/4 Sequence showing the length of the perimeter 27, 36, 48, 64, … CEDS – Study Plus in Cornwall

  13. What is the perimeter of pattern number 6? CEDS – Study Plus in Cornwall

  14. CEDS – Study Plus in Cornwall

  15. 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. CEDS – Study Plus in Cornwall