Exercise 4 Guidelines on how to implement this activity


The concept of irrational numbers may be strange to the learners although they should know that π is an irrational number. Use various calculator displays (8-digit and 10-digit) to bring over the idea that an irrational number has an infinite non- recurring decimal form.


Suggested answers 1


2 3 4 5 6


√ √


√


3 3 3


√ √


√


__ 3 = 1,73205 correct to 5 decimal places


____ 0,5 = 0,71 correct to 2 decimal places


__ 2 = 1,2599 correct to 4 decimal places


___ 10 = 3,162278 correct to 6 decimal places


____ 0,5 = 0,7937 correct to 4 decimal places


Remedial


Some learners may find it difficult to conceptualise the set of irrational numbers, ℚ′. Help them to understand that there are numbers whereby the decimal form does not terminate and does not display a recurring pattern. Some learners may have difficulty in writing rational approximations, correct to a required number of decimal places, of irrational numbers.Work through a few examples with them.


Extension


Challenge learners to investigate the value of π in decimal form: the number of decimal places that experts have calculated using computers. Google “value of Pi”.


Exercise 5 Guidelines on how to implement this activity


The purpose of this unit is to get the learners to form a concept of the Real number system. Before starting the exercise, revise the Real number system using the summary in the Learner’s Book. We can use Exercise 5 as an informal assessment. Learners who manage Exercise 5 have acquired the concept well.


Learner’s Book page 18


Learner’s Book page 17


_____ −10 = −2,154435 correct to 6 decimal places


32 Section 4: Teaching Mathematics


Page 1  |  Page 2  |  Page 3  |  Page 4  |  Page 5  |  Page 6  |  Page 7  |  Page 8  |  Page 9  |  Page 10  |  Page 11  |  Page 12  |  Page 13  |  Page 14  |  Page 15  |  Page 16  |  Page 17  |  Page 18  |  Page 19  |  Page 20  |  Page 21  |  Page 22  |  Page 23  |  Page 24  |  Page 25  |  Page 26  |  Page 27  |  Page 28  |  Page 29  |  Page 30  |  Page 31  |  Page 32  |  Page 33  |  Page 34  |  Page 35  |  Page 36  |  Page 37  |  Page 38  |  Page 39  |  Page 40  |  Page 41  |  Page 42  |  Page 43  |  Page 44  |  Page 45  |  Page 46  |  Page 47  |  Page 48  |  Page 49  |  Page 50  |  Page 51  |  Page 52  |  Page 53  |  Page 54  |  Page 55  |  Page 56  |  Page 57  |  Page 58  |  Page 59  |  Page 60  |  Page 61  |  Page 62  |  Page 63  |  Page 64  |  Page 65  |  Page 66  |  Page 67  |  Page 68  |  Page 69  |  Page 70  |  Page 71