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MATHEMATICS FACILITATOR’S GUIDE: PRAC MATHS
Grade 3
A member of the FUTURELEARN group
Mathematics Facilitator’s guide: Prac Maths
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Grade 3
CAPS aligned
B Liebenberg
Facilitator’s Guide G03 ~ Mathematics
CONTENT 1. 2. 3. 4. 5. 6.
7. 8.
Preparation for homeschooling ................................................................................ i Planning ..................................................................................................................... ii Assessment .............................................................................................................. iii The learner’s portfolio ............................................................................................. iii Reward your child .................................................................................................... iv Lesson plans ........................................................................................................... vii Term 1 ........................................................................................................................ 1 Addition and subtraction .............................................................................................. 6 Multiplication, grouping and sharing .......................................................................... 47 Fractions and money ................................................................................................. 72 Patterns and functions ............................................................................................... 89 Space and shape ...................................................................................................... 94 Measurement ............................................................................................................ 98 Data handling .......................................................................................................... 110 Term 2 .................................................................................................................... 113 Addition and subtraction .......................................................................................... 116 Multiplication, grouping and sharing ........................................................................ 149 Fractions and money ............................................................................................... 167 Patterns and functions ............................................................................................. 178 Space and shape .................................................................................................... 183 Measurement .......................................................................................................... 191 Data handling .......................................................................................................... 208 Term 3 .................................................................................................................... 211 Addition and subtraction .......................................................................................... 214 Multiplication, grouping and sharing ........................................................................ 244 Fractions and money ............................................................................................... 262 Patterns and functions ............................................................................................. 273 Space and shape .................................................................................................... 280 Measurement .......................................................................................................... 288 Data handling .......................................................................................................... 307 Term 4 .................................................................................................................... 311 Addition and subtraction .......................................................................................... 314 Multiplication, grouping and sharing ........................................................................ 347 Fractions and money ............................................................................................... 360 Patterns and functions ............................................................................................. 380 Space and shape .................................................................................................... 383 Measurement .......................................................................................................... 391 Data handling .......................................................................................................... 404 Addendum A: Daily timetable............................................................................... 407 Addendum B: Number cards ................................................................................ 411
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Facilitatorâ€™s Guide G03 ~ Mathematics
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Facilitator’s Guide G03 ~ Mathematics
1. Preparation for homeschooling Before homeschooling is started a couple of things should be considered which can influence the quality of the learning programme. Moving from a formal school system to a more informal homeschooling system can be quite a challenge for both learner and parent. The normal school routine should make way for the homeschooling routine, which means that every member of the family will have to adapt and change their schedules and routines. In order to simplify the transition from one routine to another, the family can make use of unschooling. Unschooling is the process through which learners and parents go in order to prepare themselves for the new way of learning which will take place at home. It is important that you as parent and facilitator use this time of unschooling to improve your skills, as the ability of the learner to perform and learn is directly influenced by the parent and facilitator’s conduct. Table 1.1 and 1.2 provides you with a few points which can be considered in order to be a better parent and facilitator to the learner. Each parent should look at themselves critically and decide which aspects could be improved. No parent is perfect, but luckily parenting skills can be improved by attending classes presented at community centres and churches. Many books have been written on this subject and many articles are also available on the Internet. Table 1.1 Focus points for the parent and facilitator • Value the learner’s individuality, but set boundaries where necessary. • Trust in the learner’s abilities. • Respect the learner’s interests, ideas, opinions and personality. • Be loving and accept the learner as he/she is, but with the understanding that it is expected of him/her to behave in a socially acceptable manner at all times. • Punish consistently. • The learner should be aware that it is expected of him/her to be committed and loyal and to perform well, and that he/she will have the necessary support to do so. Table 1.2 The following list was compiled by children … • Treat us with respect. • Be enthusiastic. • Know the work that we have to learn. • Be available when we need extra help. • Make use of multimedia resources. • Be friendly towards us. • Talk to us about your own life. • Use games to help us remember the work better. • Do not discuss too much work with us at one time. • Do not give us too many rules at once. • Give us a chance to also teach a class.
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Facilitator’s Guide G03 ~ Mathematics
2. Planning 2.1 The Impaq curriculum The Impaq curriculum includes all subjects as required by the Department of Education and is compiled in accordance with the Curriculum Assessment Policy Statement (CAPS). Table 2.1.1 The Impaq curriculum for the Foundation Phase (Grade R – 3) consists of the following subjects: SUBJECTS GRADE R GRADE 1 GRADE 2 GRADE 3 Home Language
Home Language
Home Language
Home Language
First Additional First Additional First Additional Language Language Language Mathematics
Mathematics
Mathematics
Mathematics
Life Skills
Life Skills
Life Skills
Life Skills
2.2 Planning Use the following steps and timetable to do your planning for the year. 2.2.1 Planning the year 1. Start by opening the package and unpacking the books that you received from Impaq. Group the books according to the various subjects. In other words, you will have a pile of books for Languages, Additional Languages (not for Grade R), Mathematics and Life Skills. 2. Make use of the Impaq inventory list to double check the books. 3. If you have received all of the books you need, use the year calendar and timetable for the grade (see 7. Daily timetable) to plan your year. 4. To ensure that the planning is complete, do the following: • Compare the facilitator’s guide, study guides, workbooks, reading books and learner support material for each subject. • Make a list of the number of lessons for each term and compare the number of lessons with the daily and weekly timetable for the specific grade. Divide the lessons between the days on the calendar according to your own needs and schedule. • To ensure that the planning for the year is complete, you must also include your own routine, the daily routine of the learner as well as any sports activities and holidays. Tip: To ensure that you cover all the work, the year can be divided into four terms consisting of 10 weeks each, with the necessary holidays in between. 2.2.2 It is important to plan your time Learners in the Foundation Phase like to play; therefore it is important that you keep to the timetable that you have drawn up in your year plan. It is important for the following reasons: • It provides the learner with the necessary fixed routine. • It can disrupt the learner’s routine when learning time is used for play.
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Facilitator’s Guide G03 ~ Mathematics
2.2.3 Written lesson preparation To ensure that you understand the lesson, allow yourself sufficient time to prepare beforehand. Make a list of all the learning support materials that you will need to present the lesson effectively. The use of learning support material in the Foundation Phase is very important. When learners use their eyes, ears, nose, hands and other body parts while learning, they learn better. Therefore it is vital that you incorporate these materials into the lesson. 2.2.4 Creating a pleasant learning area As part of your planning for the year you must also create a learning area for the learner to use. It can be anywhere in the house; a bedroom, a corner of the kitchen or dining room, etc. Use the following ideas to create a pleasant area: 1. Choose an area that will be ideal for studying and learning. It does not have to be in the learner’s bedroom. You can choose any area that will meet the learner’s unique needs. 2. Take down the paintings on the walls and replace it with learning material and educational posters, for example, posters with forms, the alphabet, numbers, etc. 3. The learning area must be fitted with a table that will be big enough to use for writing, using a tablet, doing a project or doing art. There must also be enough space for books and stationary. 4. Ensure that there are comfortable chairs for you and the learner. 5. Create a special area (if the space is available) that can be used for reading, researching projects on a computer, playing educational games or painting. This space will also be valuable if you are homeschooling more than one learner. One learner can be kept busy there while the other learner’s lesson is being presented. 6. Move a bookcase or cupboard into the learning area to keep books, learning materials and stationary in. If there is not enough space for the cupboard in the learning area, another room can be used. A bookcase or cupboard will help your to keep the learning area tidy and will contribute to the quality of the lesson. Organising the bookcase or cupboard: 1. Use part of the space in the cupboard for art supplies, such as paint brushes, paint, coloured paper, small boxes, glue and scissors. 2. Use another part of the space for stationary, such as pens, pencils, erasers, sharpeners and rulers. 3. Use a section of the space for the learning material received from Impaq. It will be a good idea to organise the learning material per subject. 3. Assessment All assessment information can be found in the Graad 3 Portfolio Book. 4. The learner’s portfolio A portfolio is a file in which the facilitator keeps a compilation of the learner’s work in order to organise and file his/her attempts, progress, and achievements for future reference. It is of the utmost importance to keep this portfolio up to date and safe, even after the school year has been completed. Remember that the portfolio is proof of the learner’s school career.
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4.1 Content of the portfolio 1. Buy a file and coloured cardboard. Write the following information on the outside of the file: • Year • Learner’s name and surname • Grade 2. On the inside there should be a contents page containing the following information: Contents 1) Term 1 1.1) Assessment forms 1.2) Proof of work 1.3) Work the learner is proud of 2) Term 2 2.1) Assessment forms 2.2) Proof of work 2.3) Work the learner is proud of 3) Term 3 3.1) Assessment forms 3.2) Proof of work 3.3) Work the learner is proud of 4) Term 4 4.1) Assessment forms 4.2) Proof of work 4.3) Work the learner is proud of 5) Term reports from Impaq. 6) Noncurricular reports, certificates and other achievements. 7) General information: medical history and specialist reports (speech therapists, occupational therapists, hearing specialists). 8) Any other information or documentation that YOU feel should be included in the learner’s portfolio. 5. Reward your child According to research roughly 48% of parents in America reward their children with money for their achievements. It is the opinion of specialists that occasionally rewarding your child with money might motivate the child to do better, but it can also be problematic. If a learner is rewarded with money too many times it can lead to the learner losing his/her inner motivation and he/she will end up working for the money only. Specialists say that if a learner is not naturally motivated to excel, it is better to reward him/her for that which he/she do achieve rather than punishing him/her for a lack of achievement. In other words, still reward the learner for an achievement of 50%, rather than punishing him/her. You can reward the learner for good behaviour, good work or a good report, in one of the following ways. Rewarding the learner often will encourage him/her to work harder and will also build their selfconfidence.
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• • • • • • • •
The best way to reward a learner is to show him/her how proud you are. Reward the learner with enthusiasm, “congratulations”, a high five, a kiss and a hug. When possible, display the learner’s achievements in order to show them how proud you are. The learner’s good work or reports can be displayed on the refrigerator for others to see. Bake a cake to make the learner feel special. Write the learner’s name and achievement with icing on the cake. As a reward the learner can be taken on a field trip. Take him/her to their favourite museum, to an amusement park or aquarium. Reward the learner with a trip to the movies, or convert your living room into a movie theatre and rent DVDs which you can watch with them while eating popcorn. Take the learner out for pizza. As a reward, the learner can be allowed extra time to play computer games. Take a trip to the book store and allow the learner to choose a book which you can read together.
For any queries, contact the education specialist at Impaq.
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Facilitatorâ€™s Guide G03 ~ Mathematics
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Facilitator’s Guide G03 ~ Mathematics
6. LESSON PLANS
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Facilitator’s Guide G03 ~ Mathematics
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Facilitator’s Guide G03 ~ Mathematics
6.
Term
1
LESSON PLANS TABLE OF CONTENTS TERM 1
Date
Week
1
2
3
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Concept/Activity
Activity and page number in workbook
Topic: Numbers, operations and relationships Addition and subtraction 1.Number names and symbols Count: p. 3 no. 2.3 Calculations: p. 3 no. 3.1 a – d Wb p. 1 no. 1.1 a – m and p. 2 no. 1.2 2. Number names and symbols Count: p. 4 no. 4.1 Calculations: p. 3 no. 3.1 e – h Wb p. 2 no. 1.3 and p. 1 no. B1.1 n–x 3. Greater than and smaller than Count: p. 5 no. 5 Calculations: p. 3 no. 3.2 a – c Wb p. 2 no. 2.1 and 2.2 4. Place value Count: Wb p. 9 no. C1 a – e Calculations: Wb p. 3 no. 3.2 d – e Wb p. 5 no. 6.1 and 6.2 5. Place value Count: p. 9 no. C1 f – j Calculations: p. 3 no. 3.3 a – d Wb p. 6 no. 6.3 6. Place value Count: p. 10 no. 3 Calculations: Wb p. 4 no. 3.3 e – h Wb p. 6 no. 6.4 7. Adding by breaking Count: p. 10 no. 4 Calculations: p. 4 no. 3.4 a – c down/adding on/building up Wb p. 6 no. 7.1 numbers 8. Adding by breaking down both Calculations: p. 4 no. 3.4 d – f Wb p. 7 no. 7.2 numbers 9. Word sums Calculations: p. 4 no. 3.4 g – h Wb p. 8 no. 1 and 2
Page numbers in facilitator’s guide
7
10
12
14
18
21
23
26 28
10. Calculations
Calculations: p. 9 no. 2.1 a – d Wb p. 10 no. 6.1en p. 11 no. 6.2
30
11. Subtraction with 2digit numbers: Method 1 12. Subtraction with 2digit numbers: Method 2: Breaking down both numbers Expanding method 2 13. Breaking down both numbers to calculate
Calculations: p. 10 no. 2.1 e – h Wb p. 11 no. 8 method 1 Calculations: p. 10 no. 2.2 a – d Wb p. 12 method 2 Wb p. 13 no. 1
33
Calculations: p. 10 no. 2.2 e – h Wb p. 13 no. 2
37
1
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Facilitator’s Guide G03 ~ Mathematics
Term
14. Breaking down both numbers: method 3 Calculations –Test Answers 15 Word sums
4
5
6
7
7
8
9
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Calculations: p. 10 no. 5 and Wb p. 14 Method 3 Wb p. 14 no. 2 Calculations: p. 11 no. 7.1 and 7.2 Wb p. 14 no. 1 and 2 16. Revision – Number concept Count: p. 16 no. 3 Calculations: p. 16 no. 2 part 1 and 2 Wb p. 15 part 1 and 2 17. Calculations Wb p. 16 no. 4 – 8 18. Word sums Wb p. 17 no. 9 Topic: Numbers, operations and relationships Multiplication, grouping and sharing 19. Work with twos Wb p. 18 no. A 1.1 – 1.3 20. Work with fives Wb p. 19 no. 2.1 – 2.3 21. Work with threes Wb p. 20 no. 3.1 – 3.3 22. Work with fours Wb p. 21 no. 4.1 – 4.3 23. Number line: Multiplication p. 22 no. 5.1 – 5.2 24. Grouping p. 22 no. 6.1 – 6.2 25. Multiplication – Revision p. 23 no. 7 and 8 26. Multiples Wb p. 24 no. 9, 9.1, 9.2 27. Doubling Wb p. 24 no. 10 – 13 28. Word sums Wb p. 25 no. 14.1 – 14.6 29. Grouping Wb p. 26 no. B1 – 2 30. Division Wb p. 26 no. 3.1 – 3.3 and 4 – 6 31. Division Wb p. 27 no. 7.1 – 7.4 32. Multiplication and division Wb p. 28 no. 8.1 and 8.2 33. Halve Calculations: p. 28 no. 9a – d Wb p. 28 no. 10 34.Division with a remainder Wb p. 29 no. 11.1 – 11.5 35.Word sums Wb p. 29 no. 12.1 – 12.5 Topic: Fractions and money 36. Fractions Wb p. 31 no. A1 – 3 37. Fractions Wb p. 32 no. 4 – 7 38. Fractions Wb p. 33 no. 8 – 10 39. Fractions Wb p. 34 no. 11 – 12 40. Word sums Wb p. 35 no. 13.1 – 13.3 41. Money Wb p. 35 no. B1 – 4 42. Money Wb p. 36 no. 5 – 7 43. Money Wb p. 37 no. 8 – 10 44. Money Wb p. 38 no. 11 – 14 45. Money Wb p. 39 no. 15 – 16 Topic: Patterns and functions 46. Patterns and number Wb p. 40 no. 1 patterns Wb p. 42 no. 4 47. Patterns and number Wb p. 41 no. 2 patterns Wb p. 42 no. 5
2
39
40
42
43 45
47 49 51 53 55 56 58 59 60 61 62 63 65 66 68 69 70
72 74 76 78 79 80 81 83 85 87
89 90
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Facilitator’s Guide G03 ~ Mathematics
48. Patterns and number patterns
9 10
10
11
11 12
49. 2D shapes 50.Shapes 51. 2D shapes
52. Calendar 53. Time 54. Time 55. Time 56. Time 57. Volume/capacity 58. Volume/capacity
59. Data handling 60. Data handling 61. Data handling
Term
Wb p. 41 no. 3 Wb p. 42 no. 6 and 7 Topic: Space and shape Wb p. 44 – 45 no. 1 Wb p. 46 no. 2.1 – 2.2 and no. 3 Wb p. 47 no. 4.1 – 4.2 Topic: Measurement Wb p. 48 – 49 no. A1 – A2 Wb p. 49 no. B1 – 5 Wb p. 51 no. 6 – 11 Wb p. 52 no. 12 – 16 Wb p. 53 no. 17 – 19 Wb p. 54 no. C1.1 – 1.2, 2.1 – 2.2 Wb p. 55 no. 3.1 – 3.3, 4 Topic: Data handling Wb p. 57 no. 1 – 3 Wb p. 58 no. 4 Wb p. 59 no. 5
1
92
94 95 96
98 100 102 103 105 106 107
110 111 112
Requirements
•
Counters e.g. buttons or beans. Matches (approximately 500), elastic band to tighten it.
•
100 number chart and 200 number chart (added in the back of the book). Enlarged to A3. Can be laminated or placed in a transparent plastic bag so the learner can write on it with the white board pen and erase it again. Blank 100charts (added in the back of the book).
•
Timer e.g. stopwatch.
•
Number names and symbols. Cut it out so the learner can physically work with it. The facilitator can write it on paper/cardboard as needed.
•
White board with marker and eraser. Grey HB pencil, colouring pencils and workbook.
•
White chalk and paving (write on paving with chalk, it can be washed off with water).
•
Place value cards (added in the back of the book), diagram: Monkey park (added in the back of the book).
•
Number line on cardboard, can be laminated so the learner can write on it with a white board marker and erase it. No numbers should be written on the number line.
•
Magazine, pair of scissors, paper, cardboard (A4 and A3), wool, koki pen.
•
South African notes and coins. Actual examples or pictures with which the learner can work.
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1
•
2D shapes (triangle, circle, square, rectangle) and other shapes/objects to make patterns.
•
3D shapes (added in the back of the book) and 3Dnames (added in the back of the book) and pictures.
•
Empty boxes, bottles, jam tin and smaller tin, rock, tennis ball, leaves, measuring cups, pictures of different scales/actual examples of scales, marbles, apple, sand, advertisements and pictures of products with mass/actual examples of products.
•
Calendar, analogue clock (working clock for the room and a clock with arms that the learner can move/laminated clock on which the learner can draw and erase) and digital clock. Paper plate, paper clip that will move the arms.
•
+, –, x, ÷, =, <, > on loose cards (different ones needed – added in the back of the book).
•
Hundreds block, tens blocks, ones blocks (added in the back of the book – a couple of each).
Facilitator’s guidelines The work in this book is not new but the approach is different than most teachers are used to. Die primary goal is to shape a firm foundation of number concepts as well as to develop consciousness about shapes and sizes on which further study of mathematics is based. Learners are able to do calculations and solve mathematical problems by adding, subtracting, multiplying and dividing numbers with skill. When doing calculations learners should not be discouraged to use any method of their choice that they can explain. They should however me lead to use the most effective methods. The learner should do every question in every exercise of this book and master it for the developmental concept training to be advantageous. When there is referred to pages in the facilitator’s guide, it is the pages in the workbook. It is important that learners enjoy every activity in order for them to have a love for mathematics. NB! The facilitator should do every activity before it is taught to the learner. Read through every activity from start to end to know exactly what is expected of the learner and facilitator. Time management: There should be spent 7 hours a week on Mathematics. It is suggested to do Mathematics 1 hour and 30 minutes 4 days a week and one hour on the fifth day. The activities in this guide is compiled with the time management of CAPS in mind. Please take note that the learner cannot concentrate for 1 hour and 30 minutes. Ensure that the learner is given enough breaks. Assessment (2 per term): It is continuous assessment for Grade 3. This means that the facilitator will observe the learner without exposing the learner to tests. Learners should experience mathematics as a game played with numbers. The topics of each term is covered in the order prescribed in the CAPS curriculum.
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Symbols and abbreviations Wb
workbook
e.g.
for example
=
is equal to
i.e.
that is
>
is greater than
a.m.
before noon
<
is smaller than
p.m.
after noon
is approximately equal to
etc.
2Dshape
twodimensional shape
et cetera
3Dshape
threedimentional shape
Requirements The learner should have the following for all activities. Additional requirements are given in each lesson. •
Workbook, grey HBpencil and colouring pencils.
•
100 number chart and 200 number chart, place value cards, laminated number line, counters.
•
Small white board, white board marker and eraser and timer like a stopwatch.
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Facilitator’s Guide G03 ~ Mathematics
Term
Term 1
Numbers, operations and relationships
Section 1
Addition and subtraction
A. In the oral and practical activities section the learner will: 1.
Practise and consolidate objects to 200 by: •
Making groups of tens, twenties and hundreds.
Using blocks, counters or bundles of matches e.g. you should say that the following diagram shows the number one hundred and twentyfour 100
10
10
4
2.
Identify, recognise and read •
Number symbols from 0 to 500 (e.g. 8).
•
Number names from 0 to 250 (e.g. twenty).
B. In the written exercises section the learner will:
1. Write the number names of numbers from 1 to 100 (e.g. twenty). 2. Write the number symbols of numbers from 0 to 500 (e.g. 8). 3. Order and compare whole numbers up to 99. 4. Do mental arithmetic by adding numbers up to 20.
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Facilitator’s Guide G03 ~ Mathematics
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5. Count forwards in ones and multiples of twos, tens, fives up to 200 and hundreds up to 500. 6. Fill in the missing numbers on number lines. 7. Revise the place values of 2digit whole numbers. 8. Revise various methods of adding 2digit whole numbers. 9. Do word sums with answers up to 99. C. 1. Count backwards in ones and multiples of twos, tens, fives from 200 and hundreds from 500 and then write down the numbers. 2. Do mental arithmetic, subtracting numbers from 20. 3. Use addition sums to make subtraction sums and vice versa. 4. Subtract 2digit numbers from one another using various methods. 5. Do word sums involving subtraction with 1digit and 2digit numbers. D. Do mixed exercises.
Activity 1: Number names and symbols Count: p. 3 no. 2.3 Calculations: p. 3 no. 3.1 a – d p. 1 no. B1.1 a – m and p. 2 no. 1.2
Requirements •
100 number chart and 200 number chart (added in the back of the book). Enlarged to A3. Can be laminated or placed in a transparent plastic bag so the learner can write on it with the white board pen and erase it again.
•
Number names and symbols (see lesson), number names from twentyone and number symbols from 1 to 20.
•
White board with marker and eraser, grey HBpencil and workbook.
Count 1. Use 100 counters and pack groups of ten. Count the number of groups (10). Now count in tens while there is pointed to every group (100).
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1
2. Now count in ones from 1 to 50 by using a 200 number chart. The learner must show every number on the number chart while counting. Count and show from 39 to 88. Count and show from 123 to 156.
Written activity: p. 3 no. 2.3
Answers: p. 3 no. 2.3 a) 13, 23, 31, 32, 33
b) 44, 45, 46, 54, 64
c) 44, 55, 66, 77, 88
Mental arithmetic The learner should verbally answer the following calculations as quickly as possible: 5+5=
3+8=
12 + 1 =
6+4=
4+9=
9+3=
2+8=
10 + 2 =
8+5=
Written activity: p. 3 no. 3.1a – d Use a timer to see how long it takes the learner to do the calculations. Write the answer that is correct as well as the time in the workbook. The learner should try to do the calculations of every lesson as quickly as possible.
Answers: p. 3 no. 3.1a – d a) 10, 10, 10, 10, 10, 10, 10, 10
b) 11, 11, 11, 11, 11, 11, 11, 11
c) 12, 12, 12, 12, 12, 12, 12, 12
d) 13, 13, 13, 13, 13, 13, 13, 13
Concept development: Number names and symbols 1. The facilitator packs a few number names and number symbols. It should be different and not match each other. The learner must now unpack the remaining number names and symbols in the correct place so that the number name and number symbol matches. 2. The facilitator gives the learner a big 200 number chart (enlarged to A3). Put the number chart on the floor. The learner sits in front of the number chart and throws a bean or a counter on a number on the chart. Keep the counter on the number. The learner should say what number it is every time. The learner throws the next counter and says what number it is. All the counters should stay on the number chart until completion of this exercise. Try
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1
doing a variety of numbers. The facilitator can also throw the bean/counter and the learner should way what number it is. 3. The facilitator puts down the big 100 number chart in front of the learner. The leaner throws a counter on a number and must then write the same number on the white board. The counters also stay on the numbers so that a number is not repeated. The facilitator can correct spelling mistakes of what the learner has written. The facilitator should however not spend too much time on spelling. It can merely by pointed out to the learner. 4. The facilitator writes a few number names on paper/cardboard and cuts in out. Choose different numbers between 0 and 100. The numbers should not be in sequence. Keep the number names shuffled and show it upsidedown to the learner. The learner chooses one of the number names, reads the name and writes the number symbol on the white board. 5. Properly repeat no. 1 – 3.
Written activity: p. 1 no. 1.1 a – m and p. 2 no. 1.2
Answers: p. 1 no. 1.1 a – m and p. 2 no. 1.2 1.1 a) one
c) four
e) five
g) seven
i) eight
k) fourteen
b) six
d) nine
f) two
h) three
j) eleven
l) seventeen
m) fifteen
1.2 a) 16
f) 45
k) 12
b) 59
g) 18
l) 67
c) 24
h) 22
m) 85
d) 7
i) 15
n) 96
e) 11
j) 39
o) 73
Supplementary exercises The learner can practise the exercise as in no. 1 and 2 above. It is important that the learner can read and write the number names.
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1
Activity 2: Number names and symbols Count: p. 4 no. 4.1 Calculations: p. 3 no. 3.1 e – h p. 2 no. 1.3 and p. 1 no. B 1.1 n – x
Requirements As in activity 1 and circles that the facilitator can make out of paper/plastic that are big enough to cover numbers on the 100 and 200 number charts.
Count 1. Revise counting in twos from 0 to 100. The learner should be able to start and stop and different numbers. 2. The learner marks the numbers on the 200 number chart with the white board marker. Numbers counted in twos from 100 to 200. The learner practises counting these numbers. Ask the learner if he/she can see the pattern that formed. Every second number is marked. The learner should know that when counting in twos, 2 is added every time. 3. Revise counting in tens from 0 to 100. The learner practises to count in these numbers. Ask the learner if he/she can see the pattern that formed. The numbers are all underneath each other. The learner should know that when counting in tens, 10 is added every time.
Written activity: p. 4 no. 4.1
Answers: p. 4 no. 4.1 a) 139, 140, 141, 142, 143
e) 200, 210, 220, 230, 240
b) 178, 179, 180, 181, 182
f) 370, 380, 390, 400, 410
c) 50, 52, 54, 56, 58
g) 80, 85, 90, 95, 100
d) 126, 128, 130, 132, 134
h) 180, 185, 190, 195, 200
Mental arithmetic The learner should verbally answer the following calculations as quickly as possible: 12 + 3 =
4 + 12 =
15 + 3 =
11 + 4 =
13 + 1 =
14 + 5 =
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6 + 11 =
11 + 5 =
12 + 6 =
2 + 14 =
16 + 0 =
9+7=
1
Written activity: p. 3 no. 3.1 e – h Use a stopwatch/timer to see how quickly the learner writes the answers of the columns. Write the time and marks next to the columns.
Answers: p. 3 no. 3.1 e – h e) 14, 14, 14, 14, 14, 14
f) 15, 15, 15, 15, 15, 15
g) 16, 16, 16, 16, 17, 17
h) 18, 18, 18, 19
Concept development: Number names and symbols 1. Revise activity 1. 2. The facilitator puts the plastic/cardboard circles on certain numbers on the 200 number chart. The learner should then say what numbers are underneath the circles. The learner writes the number name and symbol on the white board. 3. The facilitator gives numbers between 100 and 500. The learner should write the number symbol (e.g. 134) on the white board.
Written activity: p. 2 no. 1.3 and p. 1 no. B1.1 n – x
Answers: p. 2 no. 1.3 and p. 1 no. B1.1 n – x 1.3 1.3a) 106
d) 395
b) 273
e) 408
c) 437
f) 106
g) 306
B1.1 n) twelve
o) sixteen
p) thirteen
q) eighteen
r) nineteen
t) thirtyeight
u) fortyone
v) fiftythree
w) sixtyfive
x) eightytwo
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s) twentyseven
Facilitator’s Guide G03 ~ Mathematics
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Supplementary exercises Repeat and practise the different exercises in the activity. The learner should be able to read and write the number names. =
Activity 3: Greater and smaller than Count: p. 5 no. 5 Calculations: Wb p. 3 no. 3.2 a – c Wb p. 2 no. 2.2
Requirements •
Counters e.g. buttons or beans, 200 number chart, white board with marker and eraser, chalk and paving, laminated number line
•
Grey HBpencil, workbook, two items of different sizes, write <, > and = signs on paper and cut it out.
Count The facilitator gives the learner a laminated number line and writes a few numbers on it and the learner should write in the remaining numbers. Get numbers by counting in twos from 120 to 160. Get numbers by counting in fives from 150 to 200. Get numbers by counting in tens from 250 to 450. Get numbers by counting in hundreds between 0 and 500. Erase the number every time and write in the next numbers.
Written activity: Wb p. 5 no. 5
Answers: p. 5 no. 5 A
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C
D
a) 10
20
40
50
b) 10
20
25
35
c)
148
149
151
153
d) 198
200
201
203
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Facilitator’s Guide G03 ~ Mathematics
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e) 164
168
170
174
f)
280
300
310
330
g) 400
410
420
450
h) 0
200
500
600
1
Mental arithmetic The learner should verbally answer the following calculations as quickly as possible: 2+5=
5+6=
6+5=
8+4=
4+4=
7+4=
7+5=
9+5=
2+8=
3+7=
12 + 4 =
12 + 3 =
Written activity: Wb p. 3 no. 3.2 a – c Use a stopwatch/timer to see how quickly the learner writes the answers of the columns. Write the time and marks next to the columns.
Answers: Wb p. 3 no. 3.2 a – c a) 7, 8, 9, 10, 11, 12, 13, 14
b) 8, 9, 10, 11, 12, 13, 14, 15
c) 9, 10, 11, 12, 13, 14, 15, 16
Concept development: Greater and smaller than 1.
Show two items of different sizes to the learner. Now tell the learner that there are also numbers that are bigger than others. Write different numbers between 0 and 100 on the paving with chalk and ask the learner to go stand on a number. Now ask the learner to choose a number that is bigger than the number the learner is standing on and the learner should go stand on the bigger number. Repeat with different numbers until the learner masters it.
2.
Repeat number 1. This time tell the learner that there are also numbers that are smaller than others. Give the learner a number to stand on and ask the learner to go stand on a number smaller than the first number.
3.
Use the numbers on the paving and ask the learner to go stand on a number bigger than ___. Now stand on a number smaller than ___. Give different instructions with greater than and smaller than mixed to see if the learner knows it well.
4.
Show the learner what the greater than sign looks like (>). Draw it on the white board. The learner must draw the sign on paper/cardboard with the words “greater than” next to it. The learner should also write an example, by e.g. 34 > 30. Put the paper up on the wall. Repeat with the smaller than sign (<). The learner also writes the words “smaller than” with an
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Facilitator’s Guide G03 ~ Mathematics
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example and put it up on the wall. Explain the easy way of remembering which sign is which to the learner: the greater than sign (>) looks like the beginning of the “g” of greater than (> = g). This can also be written on the cardboard on the wall. 5.
Show the = sign to the learner, written on the white board and ask the learner what it is. The learner will know that it is the “equals” sign. Ask the leaner if he/she knows what the sign means. (One side is exactly the same as the other side). The learner draws the = and the words “is equal to” with an example on the paper on the wall. E.g. 33 = 33 and 12 + 3 = 15.
6.
Now give two numbers to the learner and the learner should write it on the white board. The learner should put the <, > or = cut out of paper between the two numbers. Check to see if the learner used the correct symbol.
#
Should the learner experience problems, the 100 number chart can be used to see what number is bigger and what number is smaller. Show the learner to which side we move when the numbers become bigger and when the numbers become smaller.
Written activity: Wb p. 2 no. 2.2
Answers: p. 2 no. 2.2 a) >
b) <
c) <
d) <
e) <
f) >
Supplementary exercises Write two numbers on the white board and the learner should use the different signs to complete the sum. The learner can use the 200 number chart to see what number is bigger/smaller.
Activity 4: Place value Count: Wb p. 9 no. C1a – e Calculations: Wb p. 3 no. 3.2 d – e Wb p. 5 no. 6.1 and 6.2
Requirements •
Counters, 200 number chart, white board with pen an eraser, grey HB pencil, workbook.
•
Monkey diagram, bundles of matches (9 x 10 per bundle tied with an elastic band and 9 loose matches). The learner should make the bundles of 10 him/herself. Unifix blocks or legos can also be used. Place value cards (added in the back of the book).
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Count 1. The learner uses the 200 number chart and count backwards in twos. Focus on numbers between 100 and 200. The learner can mark the numbers on the white board with the white board marker. 2. Count backwards in tens from 200 to 100. Can do like no. 1. 3. Count backwards in fives from 200 to 100. Can do like no. 1.
Written activity: Wb p. 9 no. C1a – e
Answers: p. 9 no. C1a – e a) 140, 139, 138, 137, 136 b) 123, 122, 121, 120, 119 c) 108, 106, 104, 102, 100 d) 164, 162, 160, 158, 156 e) 150, 140, 130, 120, 110
Mental arithmetic The learner should verbally answer the following calculations as quickly as possible: 12 + 6 =
12 + 5 =
10 + 4 =
4 + 15 =
3 + 11 =
9+8=
8+3=
10 + 8 =
6+7=
Written activity: Wb p. 3 no. 3.2 d – e Use a stopwatch/timer to see how quickly the learner writes the answers of the columns. Write the time and marks next to the columns.
Answers: Wb p. 3 no. 3.2 d – e d) 10, 11, 12, 13, 14, 15, 16, 17
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Concept development: Place value Requirements: Attached diagram. Bundles of matches (9 x 10 per bundle tied with an elastic band and 9 loose matches). The facilitator tells the following story to the learner: One day there was a boy (adjust according to the learner, e.g. Peter) that went on an outing with his mother. Mother said they were going to the monkey park. They climb in the car and drive very far. On their way there they enjoy snacks and play counting games. Peter is very excited to arrive at the monkey park because he’s been sitting still for so long. The tour guide takes them through the monkey park and tells them everything they need to know about the park. He also tells them that the cages work in a special way. The different cages have different rules. The first row has nine cages and there can only be one monkey per cage because the cages are small. This row is called the ONES. The second row has space for 10 monkeys in every cage and there may not be less than 10 in these cages because it is very hard work to clean these cages. This row is called the TENS row. A truck with 29 monkeys has just stopped at the park. Will you quickly help the guide to put the monkeys in cages? Now the learner must use the matches to represent the monkeys. Ask the learner if he/she knows how to put the monkeys into the cages. Note: Start at the bottom of the diagram and work your way to the top. Help the learner to add two bundles of 10 matches to the tens column and one match per block in the ones column. Emphasise that the ones row can get one monkey per cage and the tens row 10 monkeys per cage. Phew, we worked very hard. I think we can drink a cold drink. While you drink cold drink, another truck arrives. In which cage will we put this monkey? Give the learner the opportunity to get to the answer him/herself. Remember that one monkey cannot go into the TENS row. Those cages are only opened for ten monkeys. The ONES is full with one monkey per cage. Solution: we take one monkey from the ONES cages and put it together with the monkey that just arrived. Now there are 10 monkeys that can go into the TENS row. Now three of the TENS cages are full and all the ONES cages are open. Not long thereafter another four monkeys arrive. Where will they fit? Place matches in the correct column (one in every cage and pack from the bottom up). Now three of the TENS cages are full and four of the ONES cages are full. The story can be expanded until you are sure that the learner understands the concept. Use matches to represent the monkeys every time.
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Facilitatorâ€™s Guide G03 ~ Mathematics
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3.
4.
1
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The learner packs the following numbers in bundles of matches and 9 loose matches in the diagram. Start packing from the bottom. After every number is packed, ask questions: How many tens are there and how many ones are there? Like the bold letters below. The learner packs the number of matches and first says e.g. 26 = 2 bundles of 10 and 6 loose matches. Then the learner writes on the white board e.g. 26 = 20 + 6 26
=
2 bundles of 10 and 6 loose matches
26 = 20 + 6
2 tens and 6 ones
15
=
1 bundle of 10 and 5 loose matches
15 = 10 + 5
1 ten and 5 ones
18
=
1 bundle of 10 and 8 loose matches
18 = 10+8
1 ten and 8 ones
39
=
3 bundles of 10 and 9 loose matches
39 = 30 + 9
3 tens and 9 ones
27
=
2 bundles of 10 and 7 loose matches
27 = 20 + 7
2 tens and 7 ones
The learner must know how many ones there are in 10. The learner packs 10 matches. Show the learner packs 10 matches. Show the learner that 10 matches makes a ten. (Tighten the bundle with an elastic band). How many ones are there in 100? (100). How many tens are there in 100? The learner takes 100 matches and makes groups of 10 and tightens it with an elastic band. The learner should see that there are 10 bundles and it means that 10 tens make 100. The learner should know which side of the number is tens and which side is ones. The number 36: the 3 is the tens and the 6 is the ones.
Written activity: Wb p. 5 no. 6.1 and 6.2
Answers: p. 5 no. 6.1 and 6.2 a) 10
b) 100
c) 10
d i) 6
ii) 8
ii) 3
iii) 2
iv) 4
v) 7
vi) 9
iii) 3
iv) 4
v) 9
vi) 7
e i) 1
Supplementary exercises If the learner cannot master the written activity, keep exercising with the matches. Ask the learner to pack e.g. 12 matched and then repeat 12 = 10 + 2 = 1 ten (1 bundle of matches) and 2 ones (loose matches). Repeat until the learner has mastered it. Unifix blocks or legos can also be used. Make rows of 10 and 9 loose blocks. Repetition if the value of numbers is important. The learner should master it well with matches/blocks before doing the written activity. Use place value cards to further practise the concepts of ones and tens Learners who master it quickly, can use bigger numbers. E.g. 67 = 60+7 = 6 tens and 7 ones
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