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4.
4; 8; 12: 28; 40; 48
5. Row is faulty: must be 0; 1; 1; 2; 3; 5; 8; etc.
a) 0 + 1 = 1; 1 + 1 = 2; 2 + 1 = 3; 3 + 2 = 5; 5 + 3 = 8; 8 + 5 = 13; 13 + 8 = 21;
21 + 13 = 34
b) It follows the Fibonacci sequence
c) 55; 89; 144
d) 1 7 - 21 - 35 - 35 - 21 - 7 - 1
1 - 8 - 28 - 56 - 70 - 56 - 28 - 8 - 1
1 - 9 - 36 - 84 - 126v126 - 84 - 36 - 9 - 1
For the next activity you will need a box of matches. Place the matches as shown in the diagram.
4.
Number of squares | 1 | 2 | 3 | 7 | 10 | 12 |
Number of matches |
Leonardo Fibonacci was an Italian mathematician who lived during the 12th century. Because he lived in the town of Pisa, he was also called Leonardo of Pisa. Fibonacci looked at patterns in plants and arrived at the well-known idea of the Fibonacci sequence or series:
0 ; 1 ; 1 ; 2 ; 3 ; 5 ; 8 ; 13 ; 21 ; 34
a) Are you able to explain the pattern? ____________________________________
b) Work in groups of four. Look around in the school garden (or at home) and count the petals of different flowers.
What do you observe? __________________________________________________
_____________________________________________________________________
_____________________________________________________________________
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c) Add three more numbers to the Fibonacci series:
5 ; 8 ; 13 ; 21 ; 34 ; ________________________________________________
d) Ask your educator for graph paper and try and draw the Fibonacci spiral.
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 2.2: We know this when the learner describes, explains and justifies observed relationships or rules in own words;
Assessment Standard 2.3: We know this when the learner represents and uses relationships between variables in order to determine input and/or output values in a variety of ways using;
2.3.3: tables.
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