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Reg. No.: 2011/011959/07
Mathematics
Facilitator’s guide
Grade 1
CAPS aligned
H Erasmus Í7!È-E-MAM-FG01ÉÎ
Introduction for the facilitator
Impaq’s approach to mathematics in Grade 1
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 help them do calculations and solve problems. Number concept is the foundation of maths and enables learners to master the subject.
To teach maths effectively in Grade 1 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 contains 20 learning units spread over 40 weeks. Each unit covers two weeks and comprises 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 an integral part of maths. During these sessions, learners are introduced to basic number concepts and encouraged to reinforce what they have learned by attaching a value to a number without thinking about it. Learners who understand the number concept will do well in mental 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 very important in Grade 1. Learners are introduced to patterns other than shapes. The concept develops logical thinking and is the basis of all operations. Maths is the science of numbers and the patterns they create; encourage learners throughout the year to recognise different 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.
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). Although it may appear to be an easy concept to master, learners’ experience of recognising shapes is the same as recognising numbers – naming
an unknown concept. 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. Use these concepts in daily tasks, e.g., ask them to tell the time or have a scale and measuring tape in class. Use the correct terminology such as millilitre and millimetre even though they are not expected to know them yet.
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 that learners may experience as disorganised. Encourage them to use data handling while playing or tidying up, e.g., sorting toys.
Material and resources
In Grade 1, learners write with lead pencils to make it easy to erase any mistakes. All activities are completed in their workbooks.
How to use the materials and resources
The Grade 1 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. Learner aid
7. Facilitator aid
8. Assessment (portfolio book)
9. Assessment guidelines and memorandum
You must buy:
• Retractable crayons and coloured pencils
• A lead pencil, sharpener and eraser
• Scissors, a ruler and glue (Pritt and wood glue)
• Counting frame, counters (Unifix cubes, seeds, pebbles, etc.) up to 100
• Equipment to measure (measuring tape), to weigh (scale), to measure capacity (empty containers with various capacities)
• Recommended for the classroom: A 100 chart (A2 size) and a long number line (1 to 20). Only put these up once the learners are introduced to it.
Throughout the year and while doing their assessments, learners may use aids such as counters or a 100 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.
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 which 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 concepts that are embedded, 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.
The hand indicates a practical activity.
The optional electronic Cami course which offers excellent revision at the end of each week.
Workbook 1: Term 1
Contains 110 activities and begins with a revision of Grade R work. Once learners have mastered the revision, the focus shifts to number sense.
Workbook 2: Term 2
Contains 113 activities focused on practising addition and subtraction and learning different methods to do calculations.
Workbook 3: Term 3
Contains 99 activities focused mainly on practising addition and subtraction and learning different methods to do calculations.
Workbook 4: Term 4
Contains 93 activities focused mainly on revision and reinforcing work done throughout the year.
SampleThe facilitator aid
Contains wall charts (shapes), dice cards, number cards, number names, signs and symbols, number lines, dice, days of the week, months of the year, 100 chart, bingo cards, flash cards, sum cards, estimation cards, games and money to use in class. It may be worthwhile to laminate this material to prolong use.
The learner aid
Contains number cards, number names, signs and symbols, number lines, dice, 100 chart, games, flash cards, sum cards, money, activity pages for activities 14, 23, 31 and 34 in workbook 1, activity 23 in workbook 2, and activities 11 and 13 in workbook 4.
Per week: 23 hours
Suggested timetable for Grade 1
Home Language (HL): 7/8 hours
First Additional Language (FAL): 2/3 hours
Mathematics: 7 hours
Life Skills (LS): 6 hours
07:50 –
08:05 –
Skills: Personal and Social Well-being and Beginning knowledge
min
Skills: Personal and Social Well-being and Beginning knowledge 30 min 10:50 – 11:20
–
–
12:00 – 12:15
Sample
– 13:15
Learning unit 1
Day 1 Week 1
Session 1: Counting on and back
• Count 10 bricks.
• Count 10 desks.
The learners should already be able to count to 10. Practise counting to 10 again by pointing to different objects. For example, count 10 bricks or 10 desks. The learners will be counting almost every day by using different methods.
• Walk 10 steps forward and count from 0 to 10. Walk 10 steps backward and count from 10 to 0.
• Clap your hands 10 times while counting. Stamp your feet 10 times and count from 10 to 0.
• Jump on one leg and count from 0 to 10. Jump on the other leg and count from 10 to 0.
Measure the learners. Let them stand against a wall and use a height chart or make a mark on the wall. Compare the learners’ heights. Who is the tallest? Who is the shortest? Which learners are the same height? etc.
Session 2: Left and right
Sample
The distinction between left and right is one of the most important concepts that have to be embedded. Learners who cannot immediately distinguish between left and right experience problems in all subjects; for example, when the facilitator gives an instruction to write on the top left corner of the page and, while the learner is still trying to figure out where left and right is, gives the next instruction. This skill makes learners comfortable with orientation in relation to the spaces in which they have to move. Ensure that this skill is embedded well.
Give learners the following instructions:
• Show your right hand.
• Show your left hand.
• Touch your forehead with your right hand.
• Touch your tummy with your left hand.
• Touch your knee with your left hand.
• Touch your foot with your right hand.
• Touch the desk with your right hand.
• Touch your shoulder with your left hand.
• Touch your left arm with your right hand.
Complete activity 1 in workbook 1. The learners trace their left and right hands with retractable crayons and colour them.
Session 3: Most and least, more than and less than
Show the learners different quantities of objects, for example, building blocks. Hold 2 building blocks in the one hand and 5 building blocks in the other hand. The learners show which hand is holding the most or least building blocks. The facilitator could also make 3 or 4 stacks with building blocks where it is clearly visible which stack has the most building blocks.
• The learners guess which stacks have the most and least building blocks.
• The learners also look at natural objects and recognise which object has more or less. For example: This tree has more leaves than the other tree.
Day 2
Sample
Session 1: Counting and position in space
Count from 0 to 10 and from 10 to 0 three times.
• Each learner should hold on to an object, for example, a pencil. The facilitator gives the following instructions to the learners:
• Put down the pencil on the desk.
• Put down the pencil below the desk.
• Put down the pencil to the right of the desk.
• Put down the pencil in front of the desk.
• Put down the pencil to the left of the desk.
• Repeat the instruction with another object (for example, a chair) and thereafter also with the learner’s body.
Session 2: Position in space
The learners should be familiar with objects that are on top of and under/above and below. Also revise the concepts 'longer' and 'shorter' by pointing to different objects in the classroom. For example: The ruler is longer than the sharpener.
Complete activities 2 and 3 in workbook 1. The learners colour the correct ball in every picture. They then identify objects that are longer and shorter.
Session 3: Position and capacity
Do the following practical instruction with the learners:
• Put down your eraser on top of your pencil case.
• Put down your eraser to the right of your pencil case.
• Put down your eraser behind your pencil case.
• Put down your eraser below your pencil case.
• Put down your eraser to the left of your pencil case.
Demonstrate capacity practically with a glass filled with liquid and an empty glass. Pour water into the empty glass. Empty the glass. The learners should understand the concept that containers have capacity.
Sample
Complete activities 4 and 5 in workbook 1. The learners draw the correct colour ball in the correct position in relation to the box. Next they follow instructions to complete the worksheet on capacity.
Day 3
Session 1: Creating own patterns
Demonstrate two types of patterns. The first pattern should consist of shapes; for example, circle, triangle, square; circle, triangle, square. The next pattern should consist of different colours; for example, blue, red, yellow; blue, red, yellow.
• Build a geometric pattern with any shapes at the learners’ disposal. It should consist of concrete objects. For example, the learners could use different shapes of leaves and twigs.
• Build a colour pattern with concrete objects. The learners could use any objects.
• Each learner builds his own pattern. (This could include any concept, such as long and short, big and small, etc.)
Session 2: Patterns
Briefly explain again how patterns work.
Complete activity 6 in workbook 1. The learners complete the geometric patterns by drawing the next shape. They then change the geometric patterns into colour patterns by colouring the shapes.
Explain the order of different events. What happens first, second, third and last? Explain it on the basis of the following examples:
Sample
• I write a letter – I mail the letter – the letter goes to the post office – the other person receives the letter.
• The bird builds a nest – the bird lays an egg – the egg cracks – a chick hatches.
• I eat breakfast – I go to school – I go home – I go to bed.
• The waiter takes the order – the chef makes the food – the waiter brings the food – I eat the food.
• I switch on the kettle – I take a mug out of the cupboard – I add coffee and boiling water into the mug – I drink warm coffee.
Session 3: The lazy 8
Demonstrate the lazy 8 on the board. The exercise will help the learners to relax. Give each learner a blank sheet of paper. Ensure that learners place the sheet of paper in line with their waistline on the desk before they start drawing the lazy 8. Start in the middle as indicated on the picture. Let the learners practise the concept over and over again. It is important to complete the exercise in the right direction. It helps to activate different parts of the brain, improve concentration, cross the waistline and represents the start of letter exercises. Let the learners first do the exercise with one hand, then the other hand and finally with both hands together
Complete activity 7 in workbook 1 by tracing over the lazy 8. Start in the middle as indicated by the arrow. Check that the learners turn their workbooks sideways.
The learners draw a lazy 8 on a blank sheet of paper. Let them go over the lazy 8 many times, using both their left and right hands.
Day 4
Session 1: Counting and comparing a collection of objects
Count with the learners from 1 to 10 and 10 to 1. Use animal noises as you count, for example, bark like a dog from 1 to 10, meow like a cat from 10 to 1.
In this session the learners will compare a number of objects in relation to more than and less than. Show the learners a number of objects (5 counters) and let them identify quantities that are more than the number: for example, there are more windows and there are more retractable crayons than counters. They then have to identify objects that are less than the number of counters; for example, there are two dustbins or there is one bookshelf.
Repeat this exercise with different numbers of counters.
Session 2: Position in space, one-to-one correspondence and visual perception
The learners will complete a worksheet on visual perception. This is where learners have to notice the differences and similarities between objects. It is extremely important that this concept is embedded well. Learners who struggle with this also cannot distinguish between letters and numbers; for example, letters such as h, n, u, p, q, b, d, and the numbers 6 and 9, 12 and 21. Ensure that learners’ visual perception skills are embedded well so that they do not struggle later on to learn sounds or double-digit numbers.
Revise position in space by letting learners indicate the following directions with their fingers:
• Where is below?
• Where is above?
• Where is left?
• Where is behind?
• Where is right?
Complete activities 8 and 9 in workbook 1. The facilitator reads the instructions for the learners to follow. They also complete the worksheet on visual perception.
Session 3: Left and right, bigger and smaller
Sample
The learners are familiar with the concepts left and right, as well as bigger and smaller.
Complete activities 10 and 11 in workbook 1. The learners colour the correct pictures.
Day 5
Session 1: Counting and comparing quantities
Show the learners different quantities of objects; for example, building blocks. Hold 2 building blocks in one hand and 5 building blocks in the other hand. The learners show which hand holds the most or least blocks. The facilitator could also make 3 or 4 stacks with building blocks where it is clearly visible which stack contains the most or least building blocks.
• The learners guess which stack has the most and least building blocks.
• The learners build their own stacks with counters or building blocks to show which stacks have the most or the least blocks.
Session 2: Shapes and geometric patterns
Use the circle, triangle and square in the facilitator aid. Flash the shapes. The learners must recognise the shapes immediately.
Complete activities 12 and 13 in workbook 1. The learners colour the shapes as instructed and complete the geometric patterns.
Session 3: Circles
Learners should already be familiar with shapes. In this session, the circle is embedded. ‘Reading’ shapes is the initial stage of reading more abstract letters and numbers later on. If the learners are struggling to recognise shapes, they will also struggle to recognise letters and numbers later on.
Complete activity 14 in workbook 1. The learners cut the circles from the activity page in the learner aid and paste them on the corresponding circles. They decorate the large circle with small pieces of coloured paper.
• 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.
