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".
| 1 | ||||||||||||
| 1 | 1 | |||||||||||
| 1 | 2 | 1 | ||||||||||
| 1 | 3 | 3 | 1 | |||||||||
| 1 | 4 | 6 | 4 | 1 | ||||||||
| 1 | 5 | 10 | 10 | 5 | 1 | |||||||
| 1 | 6 | 15 | 20 | 15 | 6 | 1 |
_____________________________________________________________________
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? _________________________________________
_____________________________________________________________________
_____________________________________________________________________
ii) Explain to your friend how Pascal's triangle works.
iii) Determine the sum of each row. What pattern is formed?
_____________________________________________________________________
_____________________________________________________________________
iv) What will the sum of the 10th row be?
_____________________________________________________________________
_____________________________________________________________________
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.