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Reg. No.: 2011/011959/07
Mathematics
Facilitator’s guide
Grade 3
SAMPLE
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Introduction for the facilitator
Impaq’s approach to mathematics in Grade 3
Mathematics helps to develop mental processes that enhance logical thinking. Using maths effectively equips learners to apply mathematical concepts in real life and the knowledge of basic mathematical concepts helps them do calculations and solve problems. Number sense is the foundation of maths and enables learners to master the subject.
To teach maths effectively in Grade 3 requires learning opportunities, interactions and practical demonstrations focused on developing the learners’ skills to work with numbers and do calculations. The programme for the year has 20 learning units spread over 40 weeks. Each unit covers 10 days or two weeks.
Each day has three maths sessions that cover one or more of these areas:
• Numbers, operations and relationships
• Patterns, functions and algebra
• Space and shape
• Measurement
• Data handling
Numbers, operations and relationships
Numbers, operations and relationships are integral to maths. During these sessions, learners’ number sense is developed when they manipulate concrete objects and divide and combine quantities. Learners reinforce familiar concepts such as place value, complex calculations and times tables through practise. It is very important to embed number sense properly before more difficult operations are introduced. Learners who understand the number concept will do well in maths and calculations.
Make sure learners have enough opportunity to master these fundamental concepts before moving on to something more challenging. As soon as learners are familiar with numbers, mental maths becomes important because it allows them to demonstrate their understanding of maths.
Numbers, operations and relationships include oral, practical and written activities to introduce new concepts and reinforce concepts already taught.
Patterns, functions and algebra
Patterns, functions and algebra are important in Grade 3. Mathematics is the science of numbers and the patterns they create, encourage learners throughout the year to recognise shape and number patterns.
Patterns, functions and algebra teach learners to recognise patterns in real life as well as different shapes and numbers. The patterns are visible in different operations and help learners to understand more difficult concepts. Learners copy patterns to help them understand the logic and reasoning behind this essential aspect of maths.
Space and shape
Learners must develop a good understanding of their position in space (on top, under, left, right) and name spaces not yet filled (top left, below). Learners acquire basic knowledge to give and follow directions. They discover the properties of 3D objects and 2D shapes through sorting, classifying, description and naming. Teaching space and shape as an integral part of other subjects and content areas helps to establish these concepts.
Measurement
Measurement includes time, length, mass and capacity/volume. These are practical, everyday concepts, often taught through hands-on activities and learners should be allowed to experiment. The focus of the concept is on the choice and use of appropriate units, instruments and formulas to quantify events, shapes, objects and the environment.
Measurement is directly connected to learners’ scientific, technological and economic frameworks where they can give meaningful estimates and reasonable measurements and readings. Use these concepts in daily activities, for example, keep a scale, measuring tape and clock in the classroom for activities such as weighing, measuring and telling the time. Use the correct terminology such as millilitre and millimetre and encourage learners to use it too.
Data handling
Data handling focuses on collecting, sorting, representing, interpreting and reporting on data. These concepts teach learners to organise and sort information in their own environment. Maths is abstract and data handling helps create a structure for concepts learners may experience as disorganised. The complete data process is taught, which will teach learners to structure and organise other aspects of their world.
Materials and resources
SAMPLE
In Grade 3, learners write with lead pencils at the beginning of the year to make it easy to erase any mistakes. Later in the year (from about Term 3) they write with pens. If they make a mistake with a pen, they must use a ruler to draw a neat line through the wrong answer and write the correct answer next to or above the wrong answer. All activities are completed in the workbooks.
How to use the materials and resources
The Grade 3 package includes:
1. A facilitator’s guide
2. Workbook 1: Term 1, Weeks 1 – 10
3. Workbook 2: Term 2, Weeks 11 – 20
4. Workbook 3: Term 3, Weeks 21 – 30
5. Workbook 4: Term 4, Weeks 31 – 40
6. Workbook 5: Terms 1 – 4, Weeks 1 – 40
7. Learner aid
8. Facilitator aid
9. Assessment (portfolio book)
10. Assessment guidelines and memorandum
You must buy:
• Retractable crayons and coloured pencils
• A lead pencil, sharpener, eraser and blue/black pen
• Scissors, a ruler and glue (Pritt and wood glue)
• Counting frame, counters (Unifix cubes, seeds, pebbles, etc.) up to 1 000
• Equipment to measure (measuring tape), to weigh (scale), to measure capacity (empty containers with various capacities)
• Recommended for the classroom: A 1 000 chart (A2 size)
Throughout the year and while doing their assessments, learners may use aids such as counters or a 1 000 chart to do calculations. Praise learners who no longer need these aids and encourage them to try doing calculations without help. However, please keep in mind that these aids provide some learners with a sense of security and enable them to do calculations. In Grade 4, the learners must work without aids and it is very important to keep encouraging them to complete their sums without using any aids.
The facilitator’s guide
The guide contains 20 learning units. Each unit is spread over two weeks and consists of 10 days. Each day is divided into three sessions that integrate all the focus areas. Refer to the suggested daily programme for the time allocation.
Each session ends with two information boxes: ‘Conceptualisation’ and ‘Resources’. The conceptualisation box provides a short summary of the embedded concepts, while the resources box contains a list of items provided (i) and/or required () for the session.
Each session uses three symbols:
The owl indicates what the facilitator must do.
The pencil indicates what the learners must do.
SAMPLE
The hand indicates a practical activity.
The optional electronic Cami course offers excellent revision at the end of each week.
Workbook 1: Term 1
Contains 97 activities and begins with a revision of Grade 2 work. Once learners have mastered the revision, the focus shifts to building on the knowledge acquired in Grade 2.
Workbook 2: Term 2
Contains 118 activities focused on practising addition, subtraction, multiplication and division and revising different methods to do calculations.
Workbook 3: Term 3
Contains 108 activities focused on practising addition, subtraction, multiplication and division and revising different methods to do calculations.
Workbook 4: Term 4
Contains 111 activities mainly focused on revision and reinforcing work done throughout the year. Some of the activities are more difficult to prepare learners for Grade 4. These activities are indicated in the facilitator’s guide and the learners are not yet required to master them.
Workbook 5: Terms 1 to 4
Contains 58 activities including mental mats, quizzes and problem-solving needed to embed mathematical concepts and logical thinking. Encourage the learners to choose what they want to do, unless you are doing a class speed test or times tables test. Do not give them the answers to the quizzes too quickly and make sure they do not share the answers with one another. At the end of the term, you can give the learners the answers to problems they found particularly difficult.
The facilitator aid
Contains flash cards (number cards and number names, symbols, days of the week, the months of the year, money), number lines, scale and clock to make yourself, expansion cards, 100 chart, 200 chart, 1 000 chart, sum cards and estimation cards to use in class. It may be worthwhile to laminate this material to prolong use.
The learner aid
Contains number cards, number symbols, symbols, number lines, 100 chart, 200 chart, 1 000 chart, calendar, dice, days of the week, the months of the year, clock, expansion cards, place value table, number bond game, sum cards, 3D objects to construct, money and fractions walls.
SAMPLE
Per week: 25 hours
Suggested timetable for Grade 3
Home Language (HL): 7/8 hours
First Additional Language (FAL): 3/4 hours
Mathematics: 7 hours
Life Skills (LS): 7 hours
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09:30 – 10:00
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SAMPLE
Skills: Personal and Social Well-being and Beginning knowledge
10:50 – 11:15 Home Language: Handwriting 25 min Home Language: Group guided reading 25 min Home Language: Shared reading 25 min Home Language: Group guided reading 25 min Home Language: Handwriting 25 min
11:15 – 11:40 Home Language: Group guided reading 25 min Home Language: Group guided reading 25 min Home Language: Shared reading 25 min Home Language: Group guided reading 25 min Home Language: Writing 25 min
11:40 – 12:00 FAL: Listening and speaking 20 min FAL: Reading, phonics and language structure 20 min FAL: Listening and speaking
min FAL: Reading, phonics and language structure 20 min FAL: Listening and speaking 20 min
12:00 – 12:15
12:15 – 13:25
FAL: Reading, phonics and language structure 30 min
Learning unit 1
Day 1 Week 1
Session 1: Count on and back, count in multiples
Counting is a very important skill that must be repeated every day. It improves the learners’ number concept. Maths is a lot of fun when the learners have a good grasp of number concept. Use different techniques to count rhythmically so that counting is fun and concrete. For example; bounce a ball, spray with water, stamp feet, etc. while counting. It is important that learners count rhythmically to order the numbers and develop and improve their number concept.
The learners should be able to count to 200 and back, which they learned in Grade 2. Practise counting to 200 and back again while the learners clap rhythmically. Also count to 200 in multiples of 2, 3, 4, 5 and 10. Repeat these exercises daily.
• Count from 100 to 200 and clap rhythmically as each number is counted.
• Count back from 200 to 100 and tap rhythmically on the desk.
• Count in 2s from 100 to 200.
• Count in 3s from 100 to 200.
• Count in 4s from 100 to 200.
• Count in 5s from 100 to 200.
• Count in 10s from 100 to 200.
Session 2: Addition and subtraction
The learners should comfortably be able to add to and subtract from 100. In Grade 3, the number range is extended to 1 000.
Complete activity 1 in workbook 1. The learners complete the addition and subtraction sums.
Session 3: Number bonds
Practise number bonds to 20 practically with the learners. Flash any number from 0 to 20 in the facilitator aid. The learners must name the correct bond of 20 as quickly as possible.
Complete activity 2 in workbook 1. The learners complete the number bonds of 20.
Day 2
Session 1: Place value: tens and ones
As an introduction, tell the learners the following story: Once upon a time there were two pigs. The one pig was very big and fat and the other pig was very small and thin. The fat pig’s name was Tens. Tens always ate 10 slices of bread at a time with huge bites. The little pig’s name was Ones and he could only take small bites. The most slices of bread he could eat at one time was 9. Each time the pigs ate, a huge number appeared on their bodies showing how much they had eaten. Ones always sat next to Tens so you couldn’t see the big pig’s 0. But with the little pig sitting next to the big pig, it showed how many slices of bread they had eaten altogether.
It is the farmer’s birthday, and to celebrate he brought the pigs a whole loaf of bread with 16 slices.
1 6
• Help the learners to work out how many slices of bread each pig will get.
• Use the place value table in the learner aid to group the numbers.
• Use counters to unpack it.
• Write the correct numbers in the correct columns.
• Repeat the exercise with different numbers of slices of bread or types of food until the learners understand it well.
• Count from 1 to 10.
• Count in multiples of 10 to 200.
• Draw a picture about the story. Draw a small pig and a big pig. Write ‘ones’ above the small pig and ‘tens’ above the big pig. Draw 9 slices of bread in the small pig’s tummy and 20 slices of bread in the big pig’s tummy.
• Cut out the two pigs from the learner aid. The cards should preferably be laminated so that the learners can write different numbers on them.
• The learners must listen carefully to the facilitator and see how many slices of bread can be given to the pigs. Remember, the small pig can only eat ones (1 to 9) and the big pig can only eat tens (multiples of 10 to 90).
• When the learners understand this well, repeat the instruction with different numbers.
• If the learners do not understand this well, repeat the initial instruction.
Session 2: Place value
Make sure that the learners understand the concept of tens and ones. Place value is the foundation of all the mathematical calculations that they will do.
Complete activity 3 and 4 in workbook 1. The learners complete the place values.
Session 3: Place value
SAMPLE
Use the expansion cards with tens and ones in the facilitator aid. Demonstrate to the learners how the tens and ones are built to form numbers. Repeat the exercise with different values by building and breaking down numbers.
Complete activity 5 in workbook 1. The learners break down the numbers to complete the table.
Day 3
Session 1: Number names and number symbols
The learners should be familiar with double numbers such as 52. Just as they learned to count in hundreds, remind them that the words ‘100’, ‘200’, ‘300’, etc. can be said and written in front of the numbers 1 to 99, for example: 152 is a hundred and fifty-two and 223 is two hundred and twentythree. As soon as the learners understand this, they will be able to extend their number concept to 1 000.
• Count from 100 to 150.
• Give the learners the opportunity to write number names between 0 and 200 on the board, for example: ‘twenty-five’ or ‘a hundred and thirty-one’. Each learner must get a turn.
Session 2: Addition with place values
Write the example sum from activity 6 in workbook 1 on the board. Explain to the learners that there is an easy way to add big numbers. Break down each number into tens and ones. First add the tens together, then add the ones together and then add the tens and ones together. The learners do not have to write down the whole calculation, but can do the calculation in their heads. The sums will thus be 60 + 20 and 2 + 7.
62 + 27 = (60 + 2) + (20 + 7) = 80 + 9 = 89
SAMPLE
Complete activity 6 in workbook 1. The learners break down the numbers to complete the addition sums.
Session 3: Number names and number symbols
Flash any of the number names between zero and one hundred in the facilitator aid to the learners. They must give the answer orally as quickly as possible.
Complete activity 7 in workbook 1. The learners connect the number names and the number symbols.
Day 4
Session 1: Counting and time
Revise the concepts of time (days of the week, months of the year and seasons). In maths it is very important that the learners experience the concepts as part of gross motor play (with their bodies) to understand them and make them concrete.
• Count from 100 to 180.
• Count in 2s to 100.
• Count in 5s to 100.
• Count in 10s to 100.
• Say the days of the week.
• Sing the months of the year.
• Say the names of the seasons.
SAMPLE
Session 2: Subtraction with place values
Write the example sum from activity 8 in workbook 1 on the board. Explain to the learners there is an easy way to subtract big numbers. Break down each number into tens and ones. First subtract the tens from each other and then subtract the ones from each other, then add the tens and ones together. The learners do not have to write down the whole calculation, but can do the
calculations in their heads. The sums will thus be 60 – 10 and 4 – 2.
64 – 12 =
64 – 12 = (60 + 4) – (10 + 2) = 50 + 2 = 52
Complete activity 8 in workbook 1. The learners break down the numbers to complete the subtraction sums.
Session 3: Number names and number symbols
The learners must be able to read number names without getting confused by the number symbols. Write the number name ‘a hundred and twenty-six’ on the board. Write the numbers 126 and 162 next to it. Let the learners choose the correct number symbol by voting. Explain the concept again to the learners who chose the incorrect number symbol.
Complete activity 9 in workbook 1. The learners colour the correct block to match the number name and the number symbol.
Day 5
Session 1: Greater than and smaller than
The learners already learned this concept in Grade 2. Refresh their memories by writing the numbers 5 and 9 on the board. Which number will the hungry crocodile want to eat? (9)
Tell the story: One day there was a very hungry crocodile that lived in a dam. He was always hungry and ate everything! He always snapped up the biggest, fattest buck that came to drink water from the dam. One day two numbers came to drink water – a 9 and a 5. The crocodile quickly swam closer because he was ravenous. Which number do you think he ate? (The 9 because it is greater than 5.)
Repeat the story with different numbers between 0 and 100.
Draw a picture on the board like the one below and revise the symbols:
> =
Explain that the ‘open mouth’ of the symbols for greater than and smaller than must always point to the greatest number. Also explain that an = is used between the numbers when they are the same. For example:
23 > 3
23 < 30
23 = 23
SAMPLE
• Count from 100 to 200.
• Write a lot of numbers on the paving (1 to 25). Let the learners stand on any number, for example, 5. Ask them to stand on a number that is greater than 5. Let them stand on 5 again. Then ask them to stand on a number that is smaller than 5. Repeat this a few times.
Session 2: Greater than and smaller than
Complete activity 10 in workbook 1. The learners fill in the symbols <, > or =.
Session 3: Mental maths
This weekly session is used for mental maths or logical thinking. Workbook 5 contains mental maths, quizzes and problem-solving needed to embed mathematical concepts. Encourage the learners to choose what they want to do, unless you are doing a class speed test or times tables test. Do not give them the answers to the quizzes too quickly and make sure they do not share the answers with one another. At the end of the term you can give the learners the answers to problems they found really difficult. The learners may use any aids to help them with quizzes or problemsolving, such as blocks, matches, their 200 chart, etc.
Day 6
Session 1: Count, count in multiples and division
SAMPLE
Week 2
The learners must be able to count to 200 and back. Name any number between 0 and 200 and let the learners count from that number to 200 or back to 0. The learners must also try to count back in multiples. Start with multiples of 10. Help the learners to work with the 200 chart so that they learn to recognise the numbers
Write the division sign (÷) on the board. Ask the learners if they know the sign and what it means. The division sign means to divide something equally. They learned that times or multiply (x) makes groups more. Divide by splits big numbers into groups. Sometimes it happens that there is a remainder (like 5 ÷ 2 = 2 and a half). The remainder can be written as such: 5 ÷ 2 = 2 remainder 1. The learners will later be taught to write the remainder as a fraction.
Write the following sum on the board: 6 ÷ 3 = ___.
Explain that the first number indicates the items (bananas) and the second number indicates the groups (children)
• Easy to teach daily lessons for the whole year.
• Three sessions a day combining the different learning areas.
• Fun oral, practical, and written activities to introduce new concepts.
• Complete full-colour facilitator aid, learner aid, and a workbook for each term.
• Comprehensive explanations of concepts in plain language.
