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

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Presentation transcript:

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

CEDS – Study Plus in Cornwall 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 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 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

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

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

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

CEDS – Study Plus in Cornwall 2. The Von Koch Snowflake Pattern Number Number of edges Length of each edge Total Perimeter / /985 1/3

CEDS – Study Plus in Cornwall 2. Von Koch Snowflake Pattern Number Number of edgesLength of each edge / /9 10

CEDS – Study Plus in Cornwall 2. Von Koch Snowflake

CEDS – Study Plus in Cornwall Nth terms Number of edges sequence 3,12,48,192,…… 3 x 4 n-1 Length of each edge sequence 9,3,1,1/3,……9 ÷ 3 n-1

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

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

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.