NQF Level: 2 US No: 7480 Learner Guide Primary Agriculture Rational and irrational numbers and number systems My name: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Company: . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Commodity: . . . . . . . . . . . . . . . . . . . . Date: . . . . . . . . . . . . . . . The availability of this product is due to the financial support of the National Department of Agriculture and the AgriSETA. Terms and conditions apply. Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 2 Unit Standard No: 7480 Before we start… Dear Learner - This Learner Guide contains all the information to acquire all the knowledge and skills leading to the unit standard: Title: US No: Demonstrate understanding of rational and irrational numbers and number systems 7480 NQF Level: 2 Credits: 3 The full unit standard will be handed to you by your facilitator. Please read the unit standard at your own time. Whilst reading the unit standard, make a note of your questions and aspects that you do not understand, and discuss it with your facilitator. This unit standard is one of the building blocks in the qualifications listed below. Please mark the qualification you are currently doing: Title ID Number NQF Level Credits National Certificate in Animal Production 48976 2 120 National Certificate in Mixed Farming Systems 48977 2 120 National Certificate in Plant Production 48975 2 120 Are you enrolled in a: Please mark the learning program you are enrolled in: Learnership? Your facilitator should explain the above concepts to you. Short Course? Y Mark N Skills Program? This Learner Guide contains all the information, and more, as well as the activities that you will be expected to do during the course of your study. Please keep the activities that you have completed and include it in your Portfolio of Evidence. Your PoE will be required during your final assessment. This Learner Guide contains all the information, and more, as well as the activities that you will be expected to do during the course of your study. Please keep the activities that you have completed and include it in your Portfolio of Evidence. Your PoE will be required during your final assessment. What is assessment all about? You will be assessed during the course of your study. This is called formative assessment. You will also be assessed on completion of this unit standard. This is called summative assessment. Before your assessment, your assessor will discuss the unit standard with you. Assessment takes place at different intervals of the learning process and includes various activities. Some activities will be done before the commencement of the Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 3 program whilst others will be done during programme delivery and other after completion of the program. The assessment experience should be user friendly, transparent and fair. Should you feel that you have been treated unfairly, you have the right to appeal. Please ask your facilitator about the appeals process and make your own notes. How to use the activity sheets… Your activities must be handed in from time to time on request of the facilitator for the following purposes: The activities that follow are designed to help you gain the skills, knowledge and attitudes that you need in order to become competent in this learning module. It is important that you complete all the activities and worksheets, as directed in the learner guide and at the time indicated by the facilitator. It is important that you ask questions and participate as much as possible in order to play an active roll in reaching competence. When you have completed all the activities and worksheets, hand this workbook in to the assessor who will mark it and guide you in areas where additional learning might be required. You should not move on to the next step in the assessment process until this step is completed, marked and you have received feedback from the assessor. Sources of information to complete these activities should be identified by your facilitator. Please note that all completed activities, tasks and other items on which you were assessed must be kept in good order as it becomes part of your Portfolio of Evidence for final assessment. Enjoy this learning experience! Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 4 How to use this guide … Throughout this guide, you will come across certain re-occurring “boxes”. These boxes each represent a certain aspect of the learning process, containing information, which would help you with the identification and understanding of these aspects. The following is a list of these boxes and what they represent: What does it mean? Each learning field is characterized by unique terms and definitions – it is important to know and use these terms and definitions correctly. These terms and definitions are highlighted throughout the guide in this manner. You will be requested to complete activities, which could be group activities, or individual activities. Please remember to complete the activities, as the facilitator will assess it and these will become part of your portfolio of evidence. Activities, whether group or individual activities, will be described in this box. Examples of certain concepts or principles to help you contextualise them easier, will be shown in this box. The following box indicates a summary of concepts that we have covered, and offers you an opportunity to ask questions to your facilitator if you are still feeling unsure of the concepts listed. My Notes … You can use this box to jot down questions you might have, words that you do not understand, instructions given by the facilitator or explanations given by the facilitator or any other remarks that will help you to understand the work better. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . .................................................................................. .................................................................................. .................................................................................. .................................................................................. .................................................................................. Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 5 What are we going to learn? Learner Tips .....................................................………………………………………… 6 What will I be able to do? .....................................................……………………… 6 What do I need to know? .................................................…..……………………… 6 Introduction …………………………………………………………………………………… 7 Session 1 Rational and Irrational numbers....…………………………..…….. 8 Session 2 Representations of Rational and Irrational numbers…….……. 22 Session 3 Scientific notation...........................……………………………….. 39 Am I ready for my test? ........................................................... 49 Checklist for Practical assessment .......................................... 54 Paperwork to be done .............................................................. 55 Bibliography ............................................................................. 56 Acknowledgements .................................................................. 57 SAQA Unit Standard Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 6 Learner Tips There are many activities for this Module. Get organised before you begin, by making sure you have a folder to organise your completed written work into a Portfolio of Evidence. As you read through the module, make your own notes. Keep all your notes in a file. They will be useful in later modules and for your assessment activities. Keep a simple journal about what you are learning. Each week, write comments about the course, about what you are learning and whether or not you are finding it useful. Talk to your facilitator about any difficulties you are having with information or ideas. Your facilitator is a learning resource for you. Throughout this course think about your own experiences as much as possible. Try to relate what you are learning to your own real life experiences. This will make the course more meaningful for you. What will I be able to do? When you have achieved this unit standard, you will be able to: Use and analyse computational tools and strategies, and make estimates and approximations Demonstrate understanding of numbers and relationships among numbers and number systems, and represent numbers in different ways. What do I need to know? It is expected of the learner attempting this unit standard to demonstrate competence against the unit standard: Mathematics and Communications at NQF level 1. Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 7 Introduction In this Learning Guide, you will cover the content and skills you need to master the following learning outcomes: Explain where rational and irrational numbers fit into the number system. Understand the differences and similarities of rational and irrational numbers. Carry our calculations with rational and irrational numbers. Work with percentages, common fractions, decimals fractions, exponential notation. Convert common fractions to decimal fractions Write rational numbers in exponential notation Calculate and justify procedures when calculating Convert very large and very small numbers to scientific notation Apply the mathematical principles involved when applying scientific notation My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 1 Session NQF Level 2 Unit Standard No: 7480 8 Rational and Irrational Numbers After completing this session, you should be able to: SO 1: Use and analyse computational tools and strategies, and make estimates and approximations. In this session we explore the following concepts: Explain where rational and irrational number fit in to the number system Understand the differences and similarities of rational and irrational numbers Carry out calculations with rational and irrational numbers • In this session we will lay the foundation for understanding rational and irrational numbers as well as the principles and methods involved in calculating rational and irrational numbers My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 9 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 10 My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 11 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 12 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 13 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 14 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 15 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 16 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 17 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Please complete Activity 1 at the end of this session. NQF Level 2 My Notes … Unit Standard No: 7480 18 .......................................... .......................................... .......................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .......................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 1 NQF Level 2 Instructions: Calculate and Estimate 19 My Name: .................. My Workplace: .................. My ID Number: SO 1 1. Unit Standard No: 7480 ................... Calculate rational and irrational numbers with and without the use of technology 1. 34 + 54 2. 432 – 324 3. 748 ÷3 4. 230 x 84 5. {(4890 – 342 ) ÷ 7} 6. 2 – 34 7. 9 – (74 + 63) 8. (9 – 74) + 63 9. 475 x 56 10. 7456 ÷ 4329 11. (9787 ÷ 87) x 2 12. 324 ÷ 43 13. (9800 ÷ 0) x (3 + 329920) 14. 43290 ÷ 10 000 15. (898923 ÷ 3) x (432 ÷ 3) + (24 – 74) Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 2. NQF Level 2 Unit Standard No: 7480 20 Estimate the following answers and round off to the nearest round figure 1. 54 + 78 2. 96 – 23 3. 5,126954 x 4,5 4. 25% of R39,99 5. 33⅓ % of R399,99 6. ⅛ x 54 7. 0,83 of 500 8. 3 x 500 100 9. 15% of 24500 Facilitator comments: Assessment: Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Concept (SO 1) I understand this concept Unit Standard No: 7480 21 Questions that I still would like to ask Computational tools are used efficiently and correctly and solutions obtained are verified in terms of the context or problem. Algorithms are executed appropriately in calculations. Solutions involving irrational numbers are reported or recorded to degrees of accuracy appropriate to the problem. Measurements are reported or recorded in accordance with the degree of accuracy of the instrument used. Estimates and approximations are used appropriately in terms of the situation and distinctions are made between the appropriate use of estimates versus approximations. The roles and limitations of particular algorithms are identified in terms of efficiency and the complexity of the algebraic formulation. The viability of selected algorithms is verified and justified in terms of appropriateness to context and efficiency. My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Session 2 NQF Level 2 Unit Standard No: 7480 22 Representations of Rational and Irrational Numbers After completing this session, you should be able to: SO 2: Demonstrate understanding of numbers and relationships among numbers and number systems. In this session we explore the following concepts: Work with percentages, common fractions, decimal fractions, exponential notation Convert common fractions o decimal fractions Write rational numbers in exponential notation Calculate and justify procedures when calculating In this session, we explain how to work with irrational numbers that are related to different fractions My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 23 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 24 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 25 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 26 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 27 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 28 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 29 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 30 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Please complete Activity 2 & 3 at the end of this session. NQF Level 2 Unit Standard No: 7480 31 My Notes … .......................................... .......................................... .......................................... . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Concept (SO 2) I understand this concept Questions that I still would like to ask Notation for expressing numbers is consistent with mathematical conventions. Methods of calculation and approximation are appropriate to the problem types. Numbers and quantities are represented using rational and irrational numbers as appropriate to the context. My Notes … ................................................................... ................................................................... . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................... ................................................................... ................................................................... ................................................................... ................................................................... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 2 NQF Level 2 Instructions: Calculate and convert 32 My Name: .................. My Workplace: .................. My ID Number: SO 2 1. Unit Standard No: 7480 ................... Simplify the fractions: 1. 9 12 4. 18 81 7. 78 88 10. 1120 1500 13. 35 = 5 77 11 2. 16 32 5. 36 48 8. 91 114 11. 45 65 Version: 01 Version Date: July 2006 3. 21 49 6. 88 112 9. 57 79 12. 17 23 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 2. NQF Level 2 Unit Standard No: 7480 Convert the following into percentage: 1. 1 4 3. 9 27 5. 1,534 2. 6 25 4. 0,675 3. Convert the following fractions to decimal fractions: 1 3 2 1 5 12 16 4 Version: 01 6 10 13 27 Version Date: July 2006 33 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 34 4. Calculate the following: a 3 /4 + 1/2 b 1 /2 + 1/4 c 7 /8 – 3/5 d 11 /2 – 1/3 e 15 /4 + 32/3 f 1 /4 x 1/2 g 1 /4 x 3/4 h 1 /2 ÷ 7/8 i 10 /15 ÷ 1/3 j 14 /32 ÷ 19 /5 k If a field is divided into 8 equal sections, and 5 sections are planted with cotton, what fraction of the field has cotton growing on it? l What is 5/6 of R120? m How far is 2/3 of 42 km? n 1 o /5 of 965 workers are absent because of taxi strikes. a How many workers are absent? b How many workers are at work? 3 /5 of a sum of money is R 80. a How much is 1/5 of the sum of money? b What is the total sum of money? p A farmer buys a bull weighing 360 kg. A month later the bulls weight has increased by 1/12. How much does the bull weigh now? q At a cattle sale a bull worth R 5400 is sold at 2/3 of its value. What was the sale price of the bull? r A farmer went to town to buy boots for R200. He spent R150 on petrol. After this he found that only 2/5 of the money he had originally was left. How much money did have originally? s While Samuel was on leave he decided to buy a bakkie in Port Elizabeth. An eighth of his leave was spent traveling, half of his leave was spent in Port Elizabeth and the rest of the time was spent at home. If the time spent at home was 4days, how much leave did he take? Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Facilitator comments: Unit Standard No: 7480 Assessment: Version: 01 Version Date: July 2006 35 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 3 NQF Level 2 Unit Standard No: 7480 Instructions: Calculate and simplify My Name: .................. My Workplace: .................. My ID Number: SO 2 1. 36 ................... Work out the answers without using a calculator a (5/8 + 2/3) x (1/3 x 1/2) b 3 c 3 + 7/8 – ( 1/8 x 0,5) d 1 e (72 – 6) ÷ 8 x 2 + 9 – 7 f What 1/3 of 36 added to (36 – 12) and divided by 3 + 15 – 6 /4 + 1/4 x (1/2 of 2) /4 + 1/4 of (9 x 2 ÷ 3 + 3 – 1) Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 2. 3. NQF Level 2 Simplify the following: 1. 33 x 35 x 39 ÷ 34 2. (5352)2 + (34 ÷ 3)4 3. 3-5 4. Which is the larger fraction? a) 0,379 or 3/8 b) 0,856 or 4/7 Simplify the following: 1. 5a + 2b + c + 3a + 5b + 2c 2. 4y -2x - 4x -2y 3. 14m + 7n – 2mn + n 4. (3a + 6b) – (- 3a – 6b) 5. (24b + 14d – 10) ÷ 2 6. 6ab + 6ac + 6ac – 6ab 7. 3(2a -3b + c) 8. 16p – p 9. 24k + 4 10. 4rs – 4r + 5rs + 10r 11. (55abc +22ab) ÷ 11 12. (4m – 4n) – (-5m + 6n) Version: 01 Version Date: July 2006 Unit Standard No: 7480 37 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Facilitator comments: Unit Standard No: 7480 Assessment: Version: 01 Version Date: July 2006 38 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Session 3 NQF Level 2 Unit Standard No: 7480 39 Scientific Notation After completing this session, you should be able to: SO 2: Convert very large and very small numbers to scientific notation Apply the mathematical principles involved when applying scientific notation In this session we explore the following concepts: Scientific notation Writing large numbers in scientific notation Convert small numbers to scientific notation This session will assist you in simplifying your workings with very small and very large numbers. My Notes … ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . ................................................................................... ................................................................................... ................................................................................... ................................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ................................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Version: 01 NQF Level 2 Version Date: July 2006 Unit Standard No: 7480 40 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture Please complete Activity 4 & 5 at the end of this session. NQF Level 2 Unit Standard No: 7480 41 My Notes … . . . . .......................................... ......................................... ......................................... .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ......................................... Concept (SO 2) I understand this concept Questions that I still would like to ask Scientific notation is used appropriately and consistently with conventions. Situations for the use of scientific notation are provided and described in terms of advantages. Conversions between numbers expressed in different ways are accurate. My Notes … ..................................................................... ..................................................................... . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ..................................................................... ..................................................................... ..................................................................... ..................................................................... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . ..................................................................... . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .. . . . . . . . . . . . . . . . . .................................................................... Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 4 NQF Level 2 Unit Standard No: 7480 Instructions: Rewrite and simplify 42 My Name: .................. My Workplace: .................. My ID Number: SO 2 ................... 1. Rewrite these in scientific notation a 3 687 834 b 234 984 c 996 000 007 d 756 000 000 e 0,009 f 147,235654000 g 0,005648 h 0,000006002 i 456,456 j 831 563 000 000 Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 2. Rewrite these in Ordinary Numbers a 7,413 x 104 b 7,524 x 10-3 c 6,14 x 10-9 d 0,7 x 107 e 3,027 x 102 f 0,324 x 103 g 8,791 x 10-2 h 5,212 x 104 3. Simplify the following without using a calculator a 3,6 x 104 x 3 x 102 b 4,25 x 10-8 x 5 x 107 c 1,98 x 108 x 6 x 109 d 1,05 x 10-2 x 6,4 x 10-4 e 7,34 x 106 x 5,24 x 10-1 Facilitator comments: Assessment: Version: 01 Version Date: July 2006 43 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 5 NQF Level 2 Unit Standard No: 7480 Instruction: Calculations My Name: .................. My Workplace: .................. My ID Number: SO 1-2 1. 2. 44 ................... In January Zondi’s farm makes a profit of R3 600 in the State Lottery. He decides to share his profits with his brothers and sisters. He keeps one third for himself, gives one fifth to each of his two brothers and the remainder to his two sisters, equally shared. a What fraction does each of his sisters receive? b How much does each member of the family receive? Calculate the following: a -27 + 36 – 52 + 18 b -12 – 8 c -45 ÷ -9 d The temperature one morning in Dorpfontein is -5oC. The temperature at midday rises by 10oC and by 7pm that evening it has dropped by a further 12oC. What was the temperature at : ii midday? iii At 7 pm in the evening? Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 3. Unit Standard No: 7480 Paul buys the following at the local Co-op. 2.5 l cattle dip 2l weed killer 4 bags fertiliser 2 m wire mesh One packet of seeds 4. NQF Level 2 @ @ @ @ @ R 150.39 per litre R 59.59 per litre R 25.99 per bag R 61.89 per m R 10.79 a What is the estimated total amount of money he needs? Round off to the nearest R1. b What is the estimated total amount of money he needs? Round off to the nearest R10. c What is the estimated total amount of money he needs? Round off to the nearest R100. Calculate the following: a 73 297 ÷ 4 b 21 592 x 542 c 99,97 ÷ 7 d (1 132 ÷ 3) x (5 ÷ 10) e (-14 973 ÷ -4) x -2 Version: 01 Version Date: July 2006 45 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 5. Calculate the following: a) b) c) d) e) 37% of R 750 One fifth of R 927 0.347 of R 84 975 One quarter of R 648 29,5% of R 212 f) 10 7 g) 6. NQF Level 2 4 x 362 27 x 100 3 37 100 Simplify the following: a 3a + 4a + 3a + 2b + c + 7a b 7x + 3y – 4x – 2y c (13a + 2b + 4c -5a + 6b +4c) ÷ 4 d x – 10 – y Version: 01 Version Date: July 2006 Unit Standard No: 7480 46 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 7. 8. NQF Level 2 Simplify the following exponents a 37423-4 b 144 c 9-2 d (a3 b2 c4)(a4 b6 c2) ½ Calculate the following: 1 2 of 1 1 3 of 1 3 2 79% of 2 3 9. Write the following in scientific notation: a 45 670 000 000 000 b 45,670 c 0,4567 d 0,00004567 Version: 01 Version Date: July 2006 Unit Standard No: 7480 47 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture 10. 11. NQF Level 2 Unit Standard No: 7480 Convert to ordinary numbers a 3 x 104 b 0,5 x 109 c 3,27 x 1011 d 519,24 x 104 e 67,01 x 107 Simplify the following without using a calculator a 5,25 x 104 x 2,25 x 102 b 2,13 x 10-5 x 1,21 x 104 c 171 x 105 x 1,4 x 10-2 d 0,309 x 108 x 32,14 x 10-4 e 1,52 x 10 x 3,4 x 10-2 Facilitator comments: Assessment: Version: 01 Version Date: July 2006 48 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 49 Am I ready for my test? Check your plan carefully to make sure that you prepare in good time. You have to be found competent by a qualified assessor to be declared competent. Inform the assessor if you have any special needs or requirements before the agreed date for the test to be completed. You might, for example, require an interpreter to translate the questions to your mother tongue, or you might need to take this test orally. Use this worksheet to help you prepare for the test. These are examples of possible questions that might appear in the test. All the information you need was taught in the classroom and can be found in the learner guide that you received. 1. 2. I am sure of this and understand it well I am unsure of this and need to ask the Facilitator or Assessor to explain what it means Questions 1. I am sure 1. Calculate the following with the use of a calculator. Give answers correct to two decimal places. a 72 x 4,05 b (0,576 – 0,532) x 67 c {(2190 – 3142 ) ÷ 5} d (9800 ÷ 0) x (3 + 329920) e 705 + 3 x 2 2. Estimate the following to the nearest whole number a 1/4 of 25,55 b 0,57 of 425 c 25% of 786 d 0,2 x 399 e 789 + 1255 3. Express the fractions in their simplest form a 24/36 b 17/35 c 2 60/120 4. Convert the following decimals to a percentage a 15/40 b 7/28 c 120/60 Version: 01 Version Date: July 2006 2. I am unsure Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 5. Calculate the following: a ¼X¾ b ¼ of 596 1 / 2 + 1/ 4 c 34 c /20 - 34/10 d e) 15/35 ÷ 9/5 6. Calculate the following: a 62,5% 0f 8 000 km b 2/5 of R120 c If 2/3 of a sum of money is R90, what was the original sum of money? 7. Use scientific notation to calculate the following: a 960 000 x 560 000 000 000 b 2,3 x 106 x 4 x 10-3 8. Simplify the following a 3a + 4b + 5c – 6a – 7b + 8c b (2ab – 14bc) – (3ab + 7bc) c (24m + 15n – 21) ÷ 3 d 17m – m e 31p + 5 9. 10. Write as ordinary numbers a 4,567 x 105 b 0,56 x 103 c 482 x 10-4 d 0,007 x 105 e 560023 x 10-2 Give an example of when it is convenient to use scientific notation Explain why you would use scientific notation in the example you have given. Version: 01 Version Date: July 2006 Unit Standard No: 7480 50 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 51 Checklist for practical assessment … Use the checklist below to help you prepare for the part of the practical assessment when you are observed on the attitudes and attributes that you need to have to be found competent for this learning module. Answer Yes or No Observations Motivate your Answer (Give examples, reasons, etc.) Can you identify problems and deficiencies correctly? Are you able to work well in a team? Do you work in an organised and systematic way while performing all tasks and tests? Are you able to collect the correct and appropriate information and / or samples as per the instructions and procedures that you were taught? Are you able to communicate your knowledge orally and in writing, in such a way that you show what knowledge you have gained? Can you base your tasks and answers on scientific knowledge that you have learnt? Are you able to show and perform the tasks required correctly? Are you able to link the knowledge, skills and attitudes that you have learnt in this module of learning to specific duties in your job or in the community where you live? The assessor will complete a checklist that gives details of the points that are checked and assessed by the assessor. The assessor will write commentary and feedback on that checklist. They will discuss all commentary and feedback with you. You will be asked to give your own feedback and to sign this document. It will be placed together with this completed guide in a file as part of you portfolio of evidence. The assessor will give you feedback on the test and guide you if there are areas in which you still need further development. Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 52 Paperwork to be done … Please assist the assessor by filling in this form and then sign as instructed. Learner Information Form Unit Standard 7480 Program Date(s) Assessment Date(s) Surname First Name Learner ID / SETA Registration Number Job / Role Title Home Language Gender: Male: Female: Race: African: Employment: Permanent: Non-permanent: Disabled Yes: No: Coloured: Indian/Asian: Date of Birth ID Number Contact Telephone Numbers Email Address Signature: Postal Address Version: 01 Version Date: July 2006 White: Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Unit Standard No: 7480 53 Bibliography Books: Gray, D.E, 2004. Doing research in the real world. Sage. London Terms & Conditions This material was developed with public funding and for that reason this material is available at no charge from the AgriSETA website (www.agriseta.co.za). Users are free to produce and adapt this material to the maximum benefit of the learner. No user is allowed to sell this material whatsoever. Version: 01 Version Date: July 2006 Demonstrate understanding of rational and irrational numbers and number systems Primary Agriculture NQF Level 2 Acknowledgements Project Management: M H Chalken Consulting IMPETUS Consulting and Skills Development Donors: South Cape College Technical Editing: Ms C Almeida OBE Formatting: Ms B Enslin Design: Didacsa Design SA (Pty) Ltd Layout: Ms A. du Plessis Version: 01 Version Date: July 2006 Unit Standard No: 7480 54 All qualifications and unit standards registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source. SOUTH AFRICAN QUALIFICATIONS AUTHORITY REGISTERED UNIT STANDARD: Demonstrate understanding of rational and irrational numbers and number systems SAQA US ID UNIT STANDARD TITLE 7480 Demonstrate understanding of rational and irrational numbers and number systems SGB NAME NSB SGB for Math Literacy, Math, Math Sciences L 2 -4 NSB 10-Physical, Mathematical, Computer and Life Sciences PROVIDER NAME FIELD SUBFIELD Physical, Mathematical, Computer and Life Sciences Mathematical Sciences ABET BAND UNIT STANDARD TYPE NQF LEVEL CREDITS Undefined Regular-Fundamental Level 2 3 REGISTRATION STATUS REGISTRATION START DATE REGISTRATION END DATE SAQA DECISION NUMBER Reregistered 2004-12-02 SAQA 1657/04 2007-12-02 PURPOSE OF THE UNIT STANDARD This unit standard will be useful to people who aim to achieve recognition at some level in Further Education and Training or to meet the Fundamental requirement of a wide range of qualifications registered on the National Qualifications Framework. People credited with this unit standard are able to: • Use and analyse computational tools and strategies, and make estimates and approximations • Demonstrate understanding of numbers and relationships among numbers and number systems, and represent numbers in different ways. LEARNING ASSUMED TO BE IN PLACE AND RECOGNITION OF PRIOR LEARNING The credit value is based on the assumption that people starting to learn towards this unit standard are competent in Mathematics and Communications at NQF level 1. UNIT STANDARD RANGE This unit standard covers: • Approximation in relation to the use of computing technologies, the distinction between exact and approximate answers in a variety of problem settings and measurement error in relation to the accuracy of instruments More detailed range statements are provided for specific outcomes and assessment criteria as needed. Specific Outcomes and Assessment Criteria: SPECIFIC OUTCOME 1 Use and analyse computational tools and strategies, and make estimates and approximations. OUTCOME RANGE This outcome includes the need to: • use technology such as calculators • demonstrate understanding of mathematical relationships and principles involved in computations • find rational approximations to irrational numbers. ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 1. Computational tools are used efficiently and correctly and solutions obtained are verified in terms of the context or problem. ASSESSMENT CRITERION 2 2. Algorithms are executed appropriately in calculations. ASSESSMENT CRITERION 3 3. Solutions involving irrational numbers are reported or recorded to degrees of accuracy appropriate to the problem. ASSESSMENT CRITERION 4 4. Measurements are reported or recorded in accordance with the degree of accuracy of the instrument used. ASSESSMENT CRITERION 5 5. Estimates and approximations are used appropriately in terms of the situation and distinctions are made between the appropriate use of estimates versus approximations. ASSESSMENT CRITERION RANGE Technological and non-technological settings. ASSESSMENT CRITERION 6 6. The roles and limitations of particular algorithms are identified in terms of efficiency and the complexity of the algebraic formulation. ASSESSMENT CRITERION 7 7. The viability of selected algorithms is verified and justified in terms of appropriateness to context and efficiency. SPECIFIC OUTCOME 2 Demonstrate understanding of numbers and relationships among numbers and number systems. OUTCOME NOTES Demonstrate understanding of numbers and relationships among numbers and number systems, and represent numbers in different ways. OUTCOME RANGE This outcome includes the need to: • work with rational and irrational numbers • explore repeating decimals and convert them to common fraction form • use scientific notation for small and large numbers. ASSESSMENT CRITERIA ASSESSMENT CRITERION 1 1. Notation for expressing numbers is consistent with mathematical conventions. ASSESSMENT CRITERION 2 2. Methods of calculation and approximation are appropriate to the problem types. ASSESSMENT CRITERION 3 3. Numbers and quantities are represented using rational and irrational numbers as appropriate to the context. ASSESSMENT CRITERION 4 4. Scientific notation is used appropriately and consistently with conventions. Situations for the use of scientific notation are provided and described in terms of advantages. ASSESSMENT CRITERION 5 5. Conversions between numbers expressed in different ways are accurate. ASSESSMENT CRITERION RANGE Between decimal and scientific notation and between repeating decimals and common fractions. UNIT STANDARD ACCREDITATION AND MODERATION OPTIONS Accreditation Option: Providers of learning towards this unit standard will need to meet the accreditation requirements of the GENFETQA. Moderation Option: The moderation requirements of the GENFETQA must be met in order to award credit to learners for this unit standard. UNIT STANDARD ESSENTIAL EMBEDDED KNOWLEDGE The following essential embedded knowledge will be assessed through assessment of the specific outcomes in terms of the stipulated assessment criteria. Candidates are unlikely to achieve all the specific outcomes, to the standards described in the assessment criteria, without knowledge of the listed embedded knowledge. This means that the possession or lack of the knowledge can be inferred directly from the quality of the candidate`s performance against the standards. • Number systems and rational and irrational numbers • Estimation and approximation. Critical Cross-field Outcomes (CCFO): UNIT STANDARD CCFO IDENTIFYING • Collect, analyse, organise and critically evaluate information: Gather, organise, evaluate and interpret numerical information • Use mathematics: Use mathematics to analyse, describe and represent realistic and abstract situations and to solve problems. UNIT STANDARD CCFO COMMUNICATING • Communicate effectively: Use everyday language and mathematical language to describe relationships, processes and problem solving methods. UNIT STANDARD NOTES N/A All qualifications and unit standards registered on the National Qualifications Framework are public property. Thus the only payment that can be made for them is for service and reproduction. It is illegal to sell this material for profit. If the material is reproduced or quoted, the South African Qualifications Authority (SAQA) should be acknowledged as the source.

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