Mathematics
Number patterns
Educator section
Memorandum
8.
c) (i) 465
(ii) 1 508
b).
Leaner section
Content
Activity: number patterns (gauss calculations) [lo 2.2]
8. did you know?
Karl Friedrich Gauss (1777 - 1855) was 9 years old when his educator asked him to add all the numbers from 1 to 100. He did this in record time and the method he used is now known as the "Gauss method".
a) How would YOU solve this problem? ___________________________________
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b) Let us look at how Gauss calculated the sum!
- The sum total of each pair, e.g. 1 + 100 or 3 + 98, is 101. There are 50 pairs in total. The sum is therefore 50 × 101 = 5 050. Easy, isn't it?
c) Use Gauss' method to calculate:
i) the sum of the numbers from 1 to 30
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ii) the sum of the numbers from 5 to 55
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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 2.2: We know this when the learner describes, explains and justifies observed relationships or rules in own words.