1.7 Number patterns (fibonacci spiral)

Mathematics

Number patterns

Educator section

Memorandum

6.

a) 1 7 21 35 35 21 7 1

1 8 28 56 70 56 28 8 1

1 9 36 84 126 126 84 36 9 1

b).

i) Answers may differ – it depends on the row chosen

ii) The sum of the 2 numbers on top in the “triangle” is the third number below.

iii) 1; 2; 4; 8; 16; 32; 64; etc.

Answers multiply (x2)

iv) 512

Leaner section

Content

Activity: number patterns (fibonacci spiral) [lo 2.1, lo 2.2]

Fibonacci spiral

6. did you know?

The French mathematician Blaise Pascal lived in the 17th century. The following interesting pattern is named after him and is called the "Pascal triangle".

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a) Are you able to complete the above three rows? ___________________________

b) Work with a friend and choose any diagonal.

(i) What pattern do you observe? _________________________________________

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ii) Explain to your friend how Pascal's triangle works.

iii) Determine the sum of each row. What pattern is formed?

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iv) What will the sum of the 10th row be?

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Assessment

Learning Outcome 2: The learner will be able to recognise, describe and represent patterns and relationships, as well as to solve problems using algebraic language and skills.

Assessment Standard 2.1: We know this when the learner investigates and extends numeric and geometric patterns looking for a relationship or rules, including patterns;

Assessment Standard 2.2: We know this when the learner describes, explains and justifies observed relationships or rules in own words.