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Rational Numbers:

Module by: sushie naidoo. E-mail the author

Summary: Lesson Plan Introduction to rational numbers

Lesson Plan

Grade 10

Topic: Rational Numbers

Aspects

  • Identification of rational numbers
  • Writing a recurring number as a rational number

Resources / Aids / References

Chalkboard, worksheets, textbooks

Pre -knowledge

  • Understand the number system and number line

Elaboration / Methodology

Do you know the number system?

Let’s recall

1. The set of natural numbers: N = { 1 ; 2 ; 3 ; 4 ; ......... }

2. The set of whole numbers:No = { 0 ; 1 ; 2 ; 3 ; 4 ; .......}

3. The set of integers Z = { ..... ; -3 ; -2 ; -1 ; 0 ; 1 ; 2 ; 3 ; .....}

4. The set of rational numbers is written as Q

A rational number can be written in the form Q = abab{a} over {b } , a∈Za∈Za in Z , b∈positiveintegerb∈positiveintegerb in positive integer

It is known that nnsqrt{n}cannot be written in the formformula abab{a} over {b } formula

whenever n is not a perfect square

5. Real numbers – all numbers on the number line

6. Non real or unreal number – number that is not on the number line for example −2−2sqrt{-2}

7. Number line

Figure 1
Figure 1 (graphics1.png)

8. How does one convert between recurring and rational numbers?

8.1 How do you change 0,1111111....=190,1111111....=190,1111111.... = {1} over {9}

Method:

Let x = 0,111111 …........ (1)

10x = 1,1111111 …........ (2)

Subtract: (2) – (1)

Now 9x = 1

Therefore x=19x=19x = {1} over {9}

Application and Consolidation

Complete the following table. If it applies then use a tick (P)

R = real numbers R’ = non real numbers

Figure 2
Figure 2 (graphics2.png)

2. Convert 0,222222=290,222222=290,222222 = {2} over {9}

Figure 3
Figure 3 (graphics3.png)

12. Convert 0,222222=290,222222=290,222222 = {2} over {9}

Let x = 0,2222222 ….(1)

10x = 2,2222222 ….(2)

(2) – (1): 9x = 2

x = 2 9 x = 2 9 x = {2} over {9}

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