2.3 How many matches does Kholeka add to each stage to make the following stage?
2.4 If Kholeka has 50 matches in total and uses all her matches to complete her pattern, how many matches will she have left over? Show all your calculations, or explain your reasoning.
Number patterns are often found in geometric patterns. For example, in the second row of the table in Question 2.2 of Exercise 1 above, the following number pattern appears: 4; 7; 10; 13; 16; … .
Some patterns are man-made and some occur in nature. There are many beautiful geometric patterns in nature. Snowflakes, shells, crystals and various parts of plants and flowers are all examples of geometric patterns.
Figure 1 Geometric patterns occurring in nature
The Fibonacci sequence
Leonardo Fibonacci gave his name to a famous sequence of numbers that often appears in nature. The first 16 numbers in the Fibonacci sequence are:
0, 1, 1, 2, 3, 5, 8, 13, 21, 34, 55, 89, 144, 233, 377, 610 and 987.
These numbers are obtained by adding the two previous terms together to get the next term. So, 0 + 1 = 1; 1 + 1 = 2; 1 + 2 = 3; 2 + 3 = 5, and so on. See if you can find the next 10 numbers in the Fibonacci sequence.
Did you know?
Leonardo Fibonacci Leonardo of Pisa (c. 1170 – c. 1250), also known as Leonardo Fibonacci, or, simply Fibonacci, was an Italian mathematician, most famous today for a number sequence called the Fibonacci sequence. Be careful not to confuse Leonardo of Pisa with Leonardo da Vinci! Both were famous Italians, but Leonardo da Vinci was born in 1452, about 200 years after the death of Leonardo Fibonacci.
Unit 1: Investigate and extend patterns
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