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Mathematics

Number patterns

Educator section

Memorandum

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

Leaner section

Content

Activity: number patterns (terms) [lo 2.2, lo 2.3.3]

For the next activity you will need a box of matches. Place the matches as shown in the diagram.

4.

  • Complete the table. If necessary, use your matches.
Number of squares 1 2 3 7 10 12
Number of matches

5. did you know?

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

  • Take a look at the heads of sunflowers and the spirals of pine cones to see if you can observe the Fibonacci pattern.

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? __________________________________________________

_____________________________________________________________________

_____________________________________________________________________

_____________________________________________________________________

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.

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 2.2: 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.

Questions & Answers

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Source:  OpenStax, Mathematics grade 7. OpenStax CNX. Sep 16, 2009 Download for free at http://cnx.org/content/col11075/1.1
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