Apart from any fair dealing for the purpose of research, criticism or review as permitted in terms of the Copyright Act, no part of this publication may be reproduced, distributed, or transmitted in any form or by any means, electronic or mechanical, including photocopying, recording, or any information storage and retrieval system without prior written permission from the publisher.
The publisher has no responsibility for the persistence or accuracy of URLs for external or third-party internet websites referred to in this publication, and does not guarantee that any content on such websites is, or will remain, accurate or appropriate.
There are instances where we have been unable to trace or contact the copyright holder. If notified, the publisher will be pleased to rectify any errors or omissions at the earliest opportunity.
Reg. No.: 2011/011959/07
Mathematics
Facilitator’s guide
Grade 2
SAMPLE
CAPS aligned
W Drijfhout H Erasmus
Introduction for the facilitator
Impaq’s approach to mathematics in Grade 2
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 sense is the foundation of maths and enables learners to master the subject.
To teach maths effectively in Grade 2 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 new concepts such as place value, complex calculations and multiplication tables. Ensure number sense is properly reinforced before introducing more complex calculations. 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.
SAMPLE
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 2. 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 and encourage the 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 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 2, 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 2 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)
SAMPLE
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 200 chart (A2 size) and a long number line (1 to 100). Put numbers 1 to 20 up at the beginning of the year, but only put the other numbers up once the learners are introduced to them.
Throughout the year and while doing their assessments, learners may use aids such as counters or a 200 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 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.
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 65 activities and begins with a revision of Grade 1 work. Once learners have mastered the revision, the focus shifts to building on the knowledge acquired in Grade 1.
Workbook 2: Term 2
Contains 101 activities focused on practising addition, subtraction and multiplication and learning and revising different methods to do calculations.
Workbook 3: Term 3
Contains 93 activities focused mainly on practising addition, subtraction and multiplication and learning and revising different methods to do calculations.
Workbook 4: Term 4
SAMPLE
Contains 83 activities focused mainly on revision and reinforcing work done throughout the year.
The facilitator aid
Contains wall charts (shapes), dice cards, dot cards, number cards, number names, signs and symbols, number lines, dice, days of the week, months of the year, 200 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, dot cards, number lines, dice, days of the week, months of the year, 200 chart, games, flash cards, sum cards, estimation cards, fractions wall and money.
Per week: 23 hours
Suggested timetable for Grade 2
Home Language (HL): 7/8 hours
First Additional Language (FAL): 2/3 hours
Mathematics: 7 hours
Life Skills (LS): 6 hours
–
–
09:30 – 10:00
10:50 – 11:20
SAMPLE
and
and Beginning knowledge
min Life Skills: Personal and Social Well-being and Beginning knowledge
min Life Skills: Personal and Social Well-being and Beginning knowledge 30 min Life Skills: Personal and Social Well-being and Beginning knowledge 30 min
Home Language: Group guided reading 30 min Home Language: Group guided reading 30 min Home Language: Shared reading 30 min
11:20 – 11:45 Home Language: Handwriting 25 min Home Language: Group guided reading 25 min Home Language: Shared reading
Home Language: Group guided reading 30 min Home Language: Writing 30 min
min Home Language: Group guided reading 25 min Home Language: Handwriting 25 min
11:45 – 12:00 FAL: Listening and speaking 15 min FAL: Listening and speaking 15 min FAL: Listening and speaking 15 min FAL: Listening and speaking 15 min FAL: Listening and speaking 15 min
12:00 – 12:15 B R E A K
12:15 – 13:15
Skills: Physical education
FAL: Reading, writing and phonics 20 min
FAL: Reading, writing and phonics 20 min
FAL: Reading, writing and phonics 20 min
Learning unit 1
Day 1 Week 1
Session 1: Count on and back, count in multiples
Counting is a very important skill that needs to 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, jump, spray with water, stamp feet, etc. while counting. It is important that the learners count rhythmically to order the numbers and develop and improve their number concept.
• Count to 100 and bounce a ball with every number that is counted.
• Count back from 100 to 0 and tap rhythmically on the desk.
• Using counters, count in 2s to 100 by making piles of 2.
• Using counters, count in 5s to 100 by making piles of 5.
• Using counters, count in 10s to 100 by making piles of 10.
SAMPLE
The learners should be able to count to 100 and back, which they learned in Grade 1. Practise counting to 100 and back again while the learners rhythmically bounce a ball. Also count to 100 in multiples of 2, 5 and 10. Repeat these exercises daily.
Session 2: Number bonds of 10
Number bonds of 10 is a very important concept. It forms the basis of maths comprehension and calculation. Revise the Grade 1 work on number bonds.
Example: 1 + 9 = 10, 2 + 8 = 10, etc.
• Trace around the learners’ hands on a blank sheet of paper.
• Cut out the hands and paste them on activity 1 in workbook 1.
• Apply glue to only the palm section of the cut-out hands.
• Number the fingers 1 to 10 from left to right.
• The learners practise the number bonds of 10 by folding over the fingers. For example: Subtract 1, how many remain? = 9. Therefore: 1 + 9 = 10.
• Write the number bonds of 10 on a sheet of paper and repeat them daily.
Complete activity 1 in workbook 1. The learners paste the hands and number the fingers, and practise number bonds of 10.
Session 3: Number names and number symbols
Revise the number names and number symbols from 1 to 25.
• Cut the number names, number symbols and dot cards out of the learner aid. Make sure that everything is jumbled before the learners begin to organise the cards.
• Arrange the numbers 1 to 25 and place the correct dot card at each number.
• Read the greater number names carefully. The facilitator may help the learners with the number names above 20.
Day 2
SAMPLE
Session 1: Counting, multiples, and even and odd numbers
It is very important that the learners understand the concepts of ‘even numbers’ and ‘odd numbers’ in order to understand and do future calculations. Explain the concepts. In Grade 1 the learners learned to count in multiples of 2: 2, 4, 6, 8, 10, 12, 14, 16, 18, 20 ... The multiples are even numbers. An even number can be divided into equal parts. An odd number cannot be divided into equal parts. Odd numbers are 1, 3, 5, 7, 9, 11, 13, 15, 17, 19 ... Use counters to refresh the learners’ memories.
• Two counters can be divided into 2 equal groups = 1 counter in each group.
• Three counters can be divided into 2 unequal groups = 1 counter in one group and 2 counters in the other group.
Each learner is to cut out the 100 chart from their learner aid. Laminate them so that the learners can write on the charts and make notes on them with colour pens.
• Count to 100 by pointing to the numbers on the 100 chart.
• Count in 2s to 100 and put your finger on the correct numbers on the 100 chart as you count.
• Count in 5s to 100 and put your finger on the correct numbers on the 100 chart as you count.
• Count in 10s to 100 and put your finger on the correct numbers on the 100 chart as you count.
• Orally revise the number bonds of 10.
• Using counters, count out even numbers to 20.
• Using counters, count out odd numbers to 20.
Session 2: Create simple patterns
Creating patterns is the foundation of sums and mathematical calculations. It is a very important concept and must get a lot of attention. This session serves as a revision of Grade 1 work and an introduction to Grade 2. Use items that are easily accessible in the learners’ daily lives; for example, leaves, blocks, buttons, etc.
• Make a pattern with 3 objects; for example, a pen, a book and a pencil. Repeat the pattern 5 times
• Make a pattern with 4 objects that the learners can pick up outside; for example, a leaf, a stick, a stone and a piece of grass. Repeat the pattern 5 times.
• The learners make their own pattern with different colours (use pencils or colour pens).
Repeat the pattern 5 times.
Complete activity 2 in workbook 1. The learners complete the geometric patterns and number patterns.
SAMPLE
Session 3: Mental maths
As an introduction to the lesson, cut out the scale in the facilitator aid and assemble it with a split pin, or hang a cup on each side of a coat hanger. Use an = in the facilitator aid and paste it on the coat hanger. Ensure that the coat hanger scale balances before addition and subtraction sums are practically demonstrated with the scale.
• Place 2 counters on one side of the scale.
• Place 1 counter on the other side of the scale.
• Ask the learners how many counters need to be added to the one side of the scale in order to balance it.
• Revise the golden rule that learners learned in Grade 1: What is on one side of the = must also be on the other side of the =.
• Do a few sums with the learners.
The learners must answer the following sums orally. If they struggle, let them use counters, their fingers or the scale. Do the sums slowly in the beginning if the learners struggle and repeat them a few times if they find the sums to be easy. =
1 + 9 = 4 + 2 =
5 + 2 = 6 + 0 =
4 + 3 = 8 + 2 =
6 + 1 = 3 + 3 =
1 + 7 = 1 + 5 =
5 + 3 = 7 + 2 =
2 + 3 = 4 + 4 =
4 + 1 = 5 + 1 =
Day 3
Session 1: Count on and back, count in multiples
Ensure the learners can count rhythmically and correctly, and understand the concepts of even numbers and odd numbers. If the learners clap along rhythmically to a musical instrument, make sure that they clap with every number. This improves their number concept. The learners may use the 100 chart when they count in multiples of 2, 5 and 10.
• Count to 100 and back. Use a musical instrument to count rhythmically.
• Count in 2s to 100. Use 20 counters and make groups of 2.
• Count in 5s to 100. Use 100 counters and make groups of 5.
• Count in 10s to 100. Use 100 counters and make groups of 10.
• Write multiples of 2, 5 and 10 with chalk on the paving outside.
Session 2: Write and recognise number names to 25
The writing of number names (one, two, three, etc.) is important. Revise this informally. Name a number between 1 and 25 – the learners are to write the number name on a blank sheet of paper. Give a number between 1 and 25 and instruct the learners to place counters on the correct numbers on their 100 charts. When the learners have written down quite a few number names, they can complete activity 3 in workbook 1. Assist the learners who struggle, as they will not yet be familiar with the numbers 21 to 25.
• Place the number symbols, number names and dot cards that were cut out on day 1, session 3, all jumbled up on the floor.
• Learners are to find all the cards that match, for example: the number name ‘one’, the number symbol 1 and the dot card with 1 dot on it. They are to do this with all the other cards.
• Learners must listen carefully to the facilitator and place a counter on their 100 charts on the number that is given.
Complete activity 3 in workbook 1. The learners match the number name with the correct number symbol and dot card.
SAMPLE
Session 3: Mental maths with a number line
A number line can be horizontal or vertical. A number line can start on any number and end at any successive number. When we work on the horizontal line, we count from left to right; and when we work on the vertical line, we count from the bottom to the top.
Revise horizontal number lines. Use the numbers in the facilitator aid to put up a number line to 20 in the classroom.
Draw a number line on the paving outside. The learners must write the numbers in. For example: We begin at 0 and end at 10. Let the learners stand on a number and give them instructions such as ‘Stand on 3 and jump 2 steps forward.’ Then write the sum on the paving: e.g. 3 + 2 = 5.
Do the following sums step-by-step with the learners:
• Stand on 2 and move 5 places forward. What number are you standing on now? (7)
• Stand on 5 and move 3 places forward. What number are you standing on now? (8)
• Stand on 3 and move 6 places forward. What number are you standing on now? (9)
• Stand on 4 and move 4 places forward. What number are you standing on now? (8)
• Stand on 7 and move 2 places forward. What number are you standing on now? (9)
0 1 2 3 4 5 6 7 8 9 10
Let the learners draw curves with chalk when they jump to the next numbers. In this way they can see how many places were jumped when they count to get the answer.
Now ask three-digit sums: Stand on 3, jump 2 places forward, then jump 2 more places forward. Ask the learners to say the number they are standing on out loud: 3 + 2 + 2 = 7. Write the number sentence on the paving.
Now do the following sums:
• Stand on 1. Move 2 places forward. Move another 2 places forward. What number are you standing on now? (5)
• Stand on 5. Move 2 places forward. Move another 1 place forward. What number are you standing on now? (8)
• Stand on 3. Move 4 places forward. Move another 2 places forward. What number are you standing on now? (9)
• Stand on 4. Move 3 places forward. Move another 3 places forward. What number are you standing on now? (10)
• Stand on 2. Move 2 places forward. Move another 3 places forward. What number are you standing on now? (7)
Day 4
SAMPLE
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. When the days of the week are being revised, the learners can, for example, clap, jump, sing or skip.
• Count to 100 and back to 0. Throw a ball rhythmically against the wall while you count.
• Count in 2s to 100.
• Count in 5s to 100.
• Count in 10s to 100.
• Jump rhythmically on one leg while you say the days of the week.
• Sing the months of the year.
• Say the names of the seasons (use examples from nature, e.g. write the seasons on leaves).
Session 2: Patterns
Revise the concept of patterns. Creating patterns is a very important concept in Maths. It requires problem-solving strategies that are important for mathematical understanding and calculations. Patterns are shapes, colours or numbers that repeat.
Arrange different patterns with pencils, shapes or blocks and counters. Use the number symbols in the facilitator aid when you are working with number patterns.
• Make patterns with colour pencils or crayons. Repeat the pattern 5 times.
SAMPLE
• Make patterns with different shapes (cut them out of the learner aid). Stick the cut-out shapes on a blank sheet of paper to make a geometric pattern. Repeat the pattern 5 times. Colour the pattern according to a colour pattern.
• Make number patterns with counters. Each time, add 1 to 10 to a number: 1(+2), 3(+2), 5(+2), 7(+2)...
• Learners are to repeat number patterns until they understand them well.
• 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.
