1.9 Number patterns (gauss calculations)

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.