Gr 2-Mathematics-Facilitator's Guide by Impaq

Í4”È-E-MAM-FG01ÈÎ

MATHEMATICS FACILITATOR’S GUIDE Grade 2

Mathematics Facilitator’s guide

2002-E-MAM-FG01

Í4”È-E-MAM-FG01ÈÎ

Grade 2

CAPS aligned

W Drijfhout H Erasmus

Contents Introduction for the facilitator..............................................................................................................9 Impaq’s approach to mathematics in Grade 2....................................................................................9 Numbers, operations and relationships..............................................................................................9 Patterns, functions and algebra..........................................................................................................9 Space and shape...............................................................................................................................9 Measurement...................................................................................................................................10 Data handling...................................................................................................................................10 Material and resources.....................................................................................................................10 How to use the materials and resources..........................................................................................10 Suggested timetable for Grade 2.....................................................................................................12

Term 1 Learning unit 1..................................................................................................................................13 Week 1: Number bonds; multiples....................................................................................................13 Day 1............................................................................................................................................13 Day 2............................................................................................................................................14 Day 3............................................................................................................................................16 Day 4............................................................................................................................................18 Day 5............................................................................................................................................20 Week 2: Calendar; multiples.............................................................................................................21 Day 6............................................................................................................................................21 Day 7............................................................................................................................................23 Day 8............................................................................................................................................25 Day 9............................................................................................................................................26 Day 10..........................................................................................................................................28 Learning unit 2..................................................................................................................................30 Week 3: Place value; calculations: method 1...................................................................................30 Day 1............................................................................................................................................30 Day 2............................................................................................................................................32 Day 3............................................................................................................................................33 Day 4............................................................................................................................................35 Day 5............................................................................................................................................37 Week 4: Doubling and halving..........................................................................................................38 Day 6............................................................................................................................................38 Day 7............................................................................................................................................39 Day 8............................................................................................................................................41 Day 9............................................................................................................................................43 Day 10..........................................................................................................................................44 Learning unit 3..................................................................................................................................46 Week 5: Calculations: method 2; number bonds..............................................................................46 Day 1............................................................................................................................................46 Day 2............................................................................................................................................48 Day 3............................................................................................................................................50 Day 4............................................................................................................................................51 Day 5............................................................................................................................................52

Facilitator’s Guide Grade 2 ~ Mathematics

Week 6: Grouping; number bonds....................................................................................................54 Day 6............................................................................................................................................54 Day 7............................................................................................................................................56 Day 8............................................................................................................................................57 Day 9............................................................................................................................................59 Day 10..........................................................................................................................................60 Learning unit 4..................................................................................................................................62 Week 7: Money; number bonds........................................................................................................62 Day 1............................................................................................................................................62 Day 2............................................................................................................................................64 Day 3............................................................................................................................................65 Day 4............................................................................................................................................67 Day 5............................................................................................................................................68 Week 8: Calendar and analogue clock; number bonds....................................................................70 Day 6............................................................................................................................................70 Day 7............................................................................................................................................72 Day 8............................................................................................................................................73 Day 9............................................................................................................................................74 Day 10..........................................................................................................................................76 Learning unit 5..................................................................................................................................77 Week 9: Formal assessment; measurement....................................................................................77 Day 1............................................................................................................................................77 Day 2............................................................................................................................................79 Day 3............................................................................................................................................79 Day 4............................................................................................................................................80 Day 5............................................................................................................................................81 Week 10: Formal assessment; data handling..................................................................................82 Day 6............................................................................................................................................82 Day 7............................................................................................................................................83 Day 8............................................................................................................................................83 Day 9............................................................................................................................................85 Day 10..........................................................................................................................................85

Term 2 Learning unit 6..................................................................................................................................87 Week 11: Place value.......................................................................................................................87 Day 1............................................................................................................................................87 Day 2............................................................................................................................................88 Day 3............................................................................................................................................90 Day 4............................................................................................................................................92 Day 5............................................................................................................................................93 Week 12: Calculations: method 3.....................................................................................................94 Day 6............................................................................................................................................94 Day 7............................................................................................................................................96 Day 8............................................................................................................................................97 Day 9............................................................................................................................................98 Day 10..........................................................................................................................................99

Learning unit 7................................................................................................................................101 Week 13: Calculations: method 3 and method 4............................................................................101 Day 1..........................................................................................................................................101 Day 2..........................................................................................................................................103 Day 3..........................................................................................................................................104 Day 4..........................................................................................................................................105 Day 5..........................................................................................................................................107 Week 14: Recognise almost doubles.............................................................................................108 Day 6..........................................................................................................................................108 Day 7..........................................................................................................................................109 Day 8.......................................................................................................................................... 110 Day 9.......................................................................................................................................... 112 Day 10........................................................................................................................................ 114 Learning unit 8................................................................................................................................ 115 Week 15: Multiplication; calculations: method 5............................................................................. 115 Day 1.......................................................................................................................................... 115 Day 2.......................................................................................................................................... 116 Day 3.......................................................................................................................................... 118 Day 4.......................................................................................................................................... 119 Day 5..........................................................................................................................................120 Week 16: Doubling and halving......................................................................................................122 Day 6..........................................................................................................................................122 Day 7..........................................................................................................................................123 Day 8..........................................................................................................................................125 Day 9..........................................................................................................................................126 Day 10........................................................................................................................................128 Learning unit 9................................................................................................................................129 Week 17: Fractions; money............................................................................................................129 Day 1..........................................................................................................................................129 Day 2..........................................................................................................................................131 Day 3..........................................................................................................................................132 Day 4..........................................................................................................................................134 Day 5..........................................................................................................................................135 Week 18: Space and shape...........................................................................................................136 Day 6..........................................................................................................................................136 Day 7..........................................................................................................................................138 Day 8..........................................................................................................................................139 Day 9..........................................................................................................................................140 Day 10........................................................................................................................................143 Learning unit 10..............................................................................................................................145 Week 19: Formal assessment; analogue clock..............................................................................145 Day 1..........................................................................................................................................145 Day 2..........................................................................................................................................147 Day 3..........................................................................................................................................147 Day 4..........................................................................................................................................149 Day 5..........................................................................................................................................149

Facilitator’s Guide Grade 2 ~ Mathematics

Week 20: Formal assessment; measurement................................................................................150 Day 6..........................................................................................................................................150 Day 7..........................................................................................................................................152 Day 8..........................................................................................................................................152 Day 9..........................................................................................................................................153 Day 10........................................................................................................................................154

Term 3 Learning unit 11..............................................................................................................................155 Week 21: Calculations: method 1 and method 2............................................................................155 Day 1..........................................................................................................................................155 Day 2..........................................................................................................................................156 Day 3..........................................................................................................................................157 Day 4..........................................................................................................................................158 Day 5..........................................................................................................................................160 Week 22: Calculations: method 3 and method 4............................................................................161 Day 6..........................................................................................................................................161 Day 7..........................................................................................................................................162 Day 8..........................................................................................................................................163 Day 9..........................................................................................................................................165 Day 10........................................................................................................................................166 Learning unit 12..............................................................................................................................167 Week 23: Calculations: method 4; vertical addition........................................................................167 Day 1..........................................................................................................................................167 Day 2..........................................................................................................................................168 Day 3..........................................................................................................................................170 Day 4..........................................................................................................................................171 Day 5..........................................................................................................................................172 Week 24: Calculations: method 4; vertical subtraction...................................................................173 Day 6..........................................................................................................................................173 Day 7..........................................................................................................................................174 Day 8..........................................................................................................................................176 Day 9..........................................................................................................................................177 Day 10........................................................................................................................................178 Learning unit 13..............................................................................................................................179 Week 25: Repeated subtraction.....................................................................................................179 Day 1..........................................................................................................................................179 Day 2..........................................................................................................................................180 Day 3..........................................................................................................................................181 Day 4..........................................................................................................................................183 Day 5..........................................................................................................................................184 Week 26: Repeated addition..........................................................................................................185 Day 6..........................................................................................................................................185 Day 7..........................................................................................................................................186 Day 8..........................................................................................................................................187 Day 9..........................................................................................................................................188 Day 10........................................................................................................................................190

Learning unit 14..............................................................................................................................191 Week 27: Fractions; recognise almost doubles..............................................................................191 Day 1..........................................................................................................................................191 Day 2..........................................................................................................................................192 Day 3..........................................................................................................................................193 Day 4..........................................................................................................................................195 Day 5..........................................................................................................................................196 Week 28: Money; space and shape...............................................................................................197 Day 6..........................................................................................................................................197 Day 7..........................................................................................................................................199 Day 8..........................................................................................................................................200 Day 9..........................................................................................................................................201 Day 10........................................................................................................................................203 Learning unit 15..............................................................................................................................204 Week 29: Formal assessment; analogue clock..............................................................................204 Day 1..........................................................................................................................................204 Day 2..........................................................................................................................................206 Day 3..........................................................................................................................................206 Day 4..........................................................................................................................................208 Day 5..........................................................................................................................................208 Week 30: Formal assessment; measurement................................................................................210 Day 6..........................................................................................................................................210 Day 7.......................................................................................................................................... 211 Day 8.......................................................................................................................................... 211 Day 9..........................................................................................................................................212 Day 10........................................................................................................................................213

Term 4 Learning unit 16..............................................................................................................................214 Week 31: Greater than and smaller than........................................................................................214 Day 1..........................................................................................................................................214 Day 2..........................................................................................................................................215 Day 3..........................................................................................................................................217 Day 4..........................................................................................................................................218 Day 5..........................................................................................................................................219 Week 32: Calculations: method 3 and method 4............................................................................220 Day 6..........................................................................................................................................220 Day 7..........................................................................................................................................222 Day 8..........................................................................................................................................223 Day 9..........................................................................................................................................224 Day 10........................................................................................................................................225 Learning unit 17..............................................................................................................................226 Week 33: Calculations: method 4; place value...............................................................................226 Day 1..........................................................................................................................................226 Day 2..........................................................................................................................................227 Day 3..........................................................................................................................................229 Day 4..........................................................................................................................................230 Day 5..........................................................................................................................................231 7

Facilitator’s Guide Grade 2 ~ Mathematics

Week 34: Multiplication...................................................................................................................232 Day 6..........................................................................................................................................232 Day 7..........................................................................................................................................233 Day 8..........................................................................................................................................234 Day 9..........................................................................................................................................235 Day 10........................................................................................................................................236 Learning unit 18..............................................................................................................................237 Week 35: Multiplication...................................................................................................................237 Day 1..........................................................................................................................................237 Day 2..........................................................................................................................................239 Day 3..........................................................................................................................................240 Day 4..........................................................................................................................................241 Day 5..........................................................................................................................................242 Week 36: Number patterns; problem-solving.................................................................................243 Day 6..........................................................................................................................................243 Day 7..........................................................................................................................................244 Day 8..........................................................................................................................................245 Day 9..........................................................................................................................................246 Day 10........................................................................................................................................247 Learning unit 19..............................................................................................................................248 Week 37: Fractions.........................................................................................................................248 Day 1..........................................................................................................................................248 Day 2..........................................................................................................................................249 Day 3..........................................................................................................................................250 Day 4..........................................................................................................................................251 Day 5..........................................................................................................................................252 Week 38: Space and shape; analogue clock.................................................................................253 Day 6..........................................................................................................................................253 Day 7..........................................................................................................................................254 Day 8..........................................................................................................................................255 Day 9..........................................................................................................................................256 Day 10........................................................................................................................................258 Learning unit 20..............................................................................................................................259 Week 39: Formal assessment; revision..........................................................................................259 Day 1..........................................................................................................................................259 Day 2..........................................................................................................................................260 Day 3..........................................................................................................................................260 Day 4..........................................................................................................................................261 Day 5..........................................................................................................................................262 Week 40: Formal assessment; revision..........................................................................................263 Day 6..........................................................................................................................................263 Day 7..........................................................................................................................................264 Day 8..........................................................................................................................................264 Day 9..........................................................................................................................................265 Day 10........................................................................................................................................265

Answers Workbook 1: Term 1.......................................................................................................................267 Workbook 2: Term 2.......................................................................................................................276 Workbook 3: Term 3.......................................................................................................................288 Workbook 4: Term 4.......................................................................................................................302 © Optimi

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. 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 9

Facilitator’s Guide Grade 2 ~ Mathematics

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. 2. 3. 4. 5. 6. 7. 8. 9.

A facilitator’s guide Workbook 1: Term 1, Weeks 1 – 10 Workbook 2: Term 2, Weeks 11 – 20 Workbook 3: Term 3, Weeks 21 – 30 Workbook 4: Term 4, Weeks 31 – 40 Learner aid Facilitator aid Assessment (portfolio book) 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. © Optimi

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 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.

Facilitator’s Guide Grade 2 ~ Mathematics

Suggested timetable for Grade 2 Per week: 23 hours

Home Language (HL): 7/8 hours First Additional Language (FAL): 2/3 hours Mathematics: 7 hours Life Skills (LS): 6 hours TIME

MONDAY

TUESDAY

WEDNESDAY

THURSDAY

FRIDAY

07:50 – 08:05

HL Listening and speaking: Greet, news, oral

08:05 – 09:30 (total Maths period)

MATHEMATICS Mental maths (25 min)

(30 min)

Mathematics

(30 min)

Mathematics

09:30 – 10:00

HL Phonics

10:00 – 10:20

BREAK

10:20 – 10:45

LS Personal and social wellbeing, beginning knowledge

10:45 – 11:10

HL Write and/or handwriting

11:10 – 11:40

HL Reading

11:40 – 11:55

EAT Listening and speaking

LS Creative arts (40 min)

EAT Reading and sounding sight words, writing (20 min)

11:55 – 12:15

12:15 – 13:15

BREAK

LS Physical education

LS Creative arts (40 min)

LS Physical education

EAT Reading and sounding sight words, writing (20 min)

Learning unit 1 Week 1

Learning unit Day 1

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. 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.

• • • • •

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.

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. 13

Facilitator’s Guide Grade 2 ~ Mathematics

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 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. © Optimi

Learning unit 1 Week 1

• • • • • •

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.

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 15

Facilitator’s Guide Grade 2 ~ Mathematics

= 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 = 5 + 2 = 4 + 3 = 6 + 1 = 1 + 7 = 5 + 3 = 2 + 3 = 4 + 1 =

4+2= 6+0= 8+2= 3+3= 1+5= 7+2= 4+4= 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. 16

Learning unit 1 Week 1

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.

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) 17

Facilitator’s Guide Grade 2 ~ Mathematics

• •

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)

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 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.

Learning unit 1 Week 1

• • • • • • •

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. Colours = red, orange, pink, red, orange, pink ... Shapes = circle, triangle, rectangle, circle, triangle, rectangle ... Numbers = 2, 4, 6, 8 (+ 2) 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. 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.

Facilitator’s Guide Grade 2 ~ Mathematics

Session 3: Mental maths with a number line Revise day 3, session 3’s work on number patterns. Use the cut-out and laminated number line. Let the learners repeat the exercise practically if they struggle with the concept. As soon as the learners get it easily, give them more difficult sums to do, writing them on the paving with chalk. Complete activity 4 in workbook 1. The learners use the number lines to complete the addition sums.

Day 5 Session 1: Count on and back, count in multiples, days of the week and months of the year Turn counting into a fun activity; for example, with water games. Let the learners splash water rhythmically while they count on and back. Let them throw the correct number of counters into a bowl filled with water or remove the correct number of counters while they count in multiples.

• • • • • • •

Count to 100 and back to 0. Splash the water rhythmically while you count. Counts 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.

Session 2: Calendar and time The concept of time teaches the learners that there is a sequence of events. It teaches them to plan and to form a routine. © Optimi

Learning unit 1 Week 2

The learners use the blank calendar template in the learner aid to fill in the relevant months and dates. They must do it on their own with another calendar as an example. Explain where the weekdays and weekend days appear on the calendar. The facilitator can also help by writing certain events and routines on it. The calendar must be rewritten monthly and can, over time, be expanded to include birthdays, holidays and historical events.

• • • • •

Use the blank calendar in the learner aid. Number the blocks according to the relevant month. Write the days of the week above the correct columns. Start on Sunday and end on Saturday. Write other information in the blocks; for example, weekly events, birthdays, etc. Decorate the calendar and hang it up where the learners can see and update it daily.

Session 3: Mental maths 1 to 10 The learners complete the activity independently. Complete activity 5 in workbook 1. The learners complete the sums and colour the picture using the colour key. Note that the learners must use the colour of the answers that they wrote down and not necessarily the answer of the sum.

Electronic resource

Day 6

Week 2

Session 1: Count, count in multiples The learners must be able to count to 100 and back. Name any number between 0 and 100 and let the learners count from that number to 100 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 100 chart so that they learn to recognise the numbers.

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Count to 100 and back. Tap two pens rhythmically against each other. 21

Facilitator’s Guide Grade 2 ~ Mathematics

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Count on from 50 to 65. Count on from 78 to 100. Count on from 46 to 80. Count back from 34 to 0. Count back from 25 to 0. Count back from 88 to 44. Count on in multiples of 10 to 100 and back while the learners jump up and down.

Complete activity 6 in workbook 1. The learners complete the numbers by counting on and back.

Session 2: Shapes • • • • •

The learners draw the following shapes with chalk on the paving outside: circle, triangle, square, rectangle, star, heart and oval. The learners jump into the shapes and say the name of each shape when they jump into it. Make the shapes two-dimensionally (flat) with clay. Identify all the 3D objects in the classroom, e.g. table = rectangle. Make piles of objects that are the same shape; e.g. book, brick, paper = rectangles. Make ball shapes (spheres) and box shapes (prisms) with clay and identify the shapes in the learners’ environment.

Session 3: Mental maths Revise even and odd numbers. An even number can be divided into two equal parts and an odd number cannot. Use counters to explain this. • •

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.

Name all the even numbers to 50 (count in 2s to 50). The learners show with their fingers which number must be counted on the 100 chart (or they circle the numbers with a colour pencil). • Name all the odd numbers to 50. The learners show with their fingers which number must be counted on the 100 chart (or they circle the numbers with a colour pencil). Complete activity 7 in workbook 1. The learners circle the even numbers with green and the odd numbers with red. The order numbers from great to small and from small to great. © Optimi

Learning unit 1 Week 2

Day 7 Session 1: Count, count in multiples Assist the learners to work with their 100 charts so that they learn to recognise numbers. Count with different rhythmical movements to keep counting interesting.

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Count to 100 and back. The learners knock their feet together rhythmically while they count. Count on from 30 to 40. Count on from 81 to 92. Count on from 53 to 58. Count back from 12 to 0. Count back from 67 to 55. Count back from 89 to 75. Count in 5s to 100 and back while the learners show the numbers being counted on their 100 charts.

Session 2: Greater than and smaller than, order numbers, smallest to greatest, and more than Use objects in the environment (leaves, stones, twigs) and let the learners compare them with each another. For example: Which twig is bigger? Which stone is smaller? Which leaf is bigger? Which tree has more leaves? etc. Greater than and smaller than Show the learners one object that is bigger than another object. Explain to them that numbers work the same way. There are numbers that are greater than others and there are numbers that are smaller than others. Draw a variety of numbers on the paving (1 to 25). Let the learners stand on any number; for example, 5. Then ask them to stand on a number that is greater than 5. The learners stand on 5 again, then ask them to stand on a number that is smaller than 5. Repeat this a few times with different numbers.

Facilitator’s Guide Grade 2 ~ Mathematics

Give two numbers to the learners. They must write the greatest/smallest number on a blank sheet of paper. Repeat this a few times. For example: Which number is the greatest: 5 or 7? Order from small to great The learners must order the number cards from the smallest to the greatest number (1 to 25). Give each learner a blank sheet of paper and write six numbers between 0 and 25 on the board. The learners must arrange the numbers from small to great or from great to small. For example: 3, 6, 2, 10, 22 and 14. More than Let the learners count out 5 red counters. Ask them to count out 2 green counters and add them to the 5 red ones. They must say how many counters there are altogether. They must say the whole sum out loud: 2 more than 5 is equal to 7. Explain that this is the same as addition. Repeat this exercise a few times. The learners who struggle may use a 100 chart.

Session 3: Number line 1 to 20

10 11 12

13 14 15 16 17 18 19 20

The learners cut out the number line of 1 to 20 from the learner aid. Laminate the learners' number lines so that they can use them repeatedly and write on them with colour pens. The learners complete the activity on their own. If they get the sums right easily, let them create and answer more difficult sums with chalk on the paving outside.

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The learners count from 1 to 20 while rhythmically jumping up and down. Cut out the number line of 1 to 20.

Complete activity 8 in workbook 1. Remember to ‘jump’ from one number to the next to get the answer.

Learning unit 1 Week 2

Day 8 Session 1: Count, count in multiples Assist the learners to work with their 100 charts so that they learn to recognise numbers. Count with different rhythmical movements to keep counting interesting.

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Count to 100 and back. The learners rhythmically tap two pens together while they count. Count on from 43 to 66. Count on from 39 to 47. Count back from 77 to 55. Count back from 66 to 49. Say the days of the week (clap rhythmically). Say the months of the year (stomp feet rhythmically). Say the seasons (turn around and around). Count in 2s back from 100 to 0. Use a 100 chart. Complete activity 9 in workbook 1. The learners complete the missing numbers.

Session 2: Number patterns Revise patterns. If the learners understand the concept, they can do the practical task and activity. If they struggle, create a few patterns with 3D objects (circle, triangle, heart; circle, triangle, heart). Embed the concept by moving to 2D shapes on paper, then create number patterns (3, 2, 4; 3, 2, 4 ...). Create number patterns by adding numbers (the learners can also count out counters). • Each time add 1 to 10 to a number: 1(+2), 3(+2), 5(+2), 7(+2)... • 1, 2, 3, 4 (add 1 between each number) or 3, 6, 9, 12 (add 3 between each number), etc. Explain that the difference between the numbers must be calculated in order to decipher the pattern. Make three number patterns on a blank sheet of paper. For example: 1, 2, 3, 4, 5; 1, 2, 3, 4, 5; ... Complete activity 10 in workbook 1. The learners complete the number patterns and the sums.

Facilitator’s Guide Grade 2 ~ Mathematics

Session 3: Mental maths Count to 20 with the learners. The learners cut out the sum cards in the learner aid and write the answers on the back of each card. They unpack the cards in front of them and say the answers out loud as quickly as possible. They can look on the back of each card to see if they got the answer right.

Day 9 Session 1: Count, count in multiples 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. Assist the learners to work with their 100 charts so that they learn to recognise numbers. Count with different rhythmical movements to keep counting interesting.

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Count to 100 and back while the learners skip. Count in 2s to 100 and back with the help of the 100 chart. Count in 5s to 100 and back with the help of the 100 chart. Count in 10s to 100 and back with the help of the 100 chart. Say the days of the week while the learners rhythmically bounce a ball. Sing the months of the year while the learners rhythmically bounce a ball. Say the names of the seasons.

Learning unit 1 Week 2

Session 2: Number names and number symbols from 26 to 50 Say a number between 1 and 25 and let the learners write the number name on a blank sheet of paper. When the learners have written down a lot of numbers, they can progress to writing the number names between 26 and 50. The learners cut out the number names, number symbols and dot cards of 26 to 50 from the learner aid. When the learners have firmly established these numbers through practice, they can complete the activity. The learners mix up the cards on their desks and then match the ‘friends’; for example: 26 matched with twenty-six and the dot card with 26 dots. Do this with all the cards. Complete activity 11 in workbook 1. The learners write the number name next to each number symbol and draw the correct number of dots in the block. They may use the cards with the number names in the learner aid.

Session 3: Number lines The learners complete the activity on their own. If they get it right easily, let them write more difficult sums on a blank sheet of paper to give to a friend to answer. Count from 1 to 20 while rhythmically jumping up and down. Complete activity 12 in workbook 1. The learners use the number line to complete the addition sums.

Facilitator’s Guide Grade 2 ~ Mathematics

Day 10 Session 1: Revise counting For the last two weeks, the learners have revised what they already mastered in Grade 1. They also learned and practised how to count back in multiples of 2, 5 and 10. This is the foundation of multiplication and will be repeated often. Ensure that the learners can easily count to 100 and back. At the end of Grade 2 they will need to count to 200. The daily focus on counting activities will help to embed number concept.

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The learners count to 100 and back while hitting a drum. Count in 2s to 100 and back with the help of a 100 chart. Count in 5s to 100 and back with the help of a 100 chart. Count in 10s to 100 and back with the help of a 100 chart. Say the days of the week while the learners rhythmically bounce a ball. Sing the months of the year while the learners rhythmically bounce a ball. Say the names of the seasons.

Complete activity 13 in workbook 1. The learners count in multiples to complete the number patterns.

Session 2: Problem-solving – addition Word sums form a very important part of Maths. They teach learners how to solve problems. This skill can be applied in real life, which makes Maths more practical. The learners make a poster with a mind map about word sums. Ensure that the concepts below appear on the poster. Vocabulary: Explain that the words ‘together’, ‘altogether’, ‘in total’ and ‘have/has’ mean the same as ‘plus’. A word sum must be answered step-by-step to get the right answer. Use counters, 100 charts and abacuses to answer the sums or to better understand the questions. 1. First draw pictures to better understand the word sum. 2. Always write a sum next to the word sum, for example: 4 + 6 =. © Optimi

Learning unit 1 Week 2

3. A word sum must always have an answer, for example: 10. 4. A word sum always has an extended sentence or word after it, for example: 10 flowers.

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Create a poster about the vocabulary and facts about word sums. Do the following word sums with the facilitator. Use your poster as a resource when doing the word sums.

Word sums 1. There are 5 girls and 5 boys. How many girls and boys are there altogether? 2. Sandy picks 6 flowers on Monday and 8 flowers on Tuesday. She puts them together in one big vase. How many flowers did she put together? 3. There are 6 cars that need to be fixed. Then another 4 arrive. How many cars must be fixed in total? 4. Johnny has 4 sweets. His granny gives him another 3 sweets. How many sweets does he have now?

Session 3: Mental maths Complete activity 14 in workbook 1. The learners listen to the word sums and write down the number sentence and the answer. They complete the rest of the activity using learned concepts.

Electronic resource

Facilitator’s Guide Grade 2 ~ Mathematics

Learning unit Day 1

2 Week 3

Session 1: Estimate and count Start the lesson on estimation by covering between 10 and 50 counters (leaves, buttons, blocks, marbles, etc.) with a cloth. Lift the cloth to quickly show the counters to the learners, then cover them again. The learners must estimate how many counters are under the cloth. Start with a small number and gradually add more counters. Let the learners count the counters independently when they have given their estimations. Encourage the learners to group the counters to make it easier to count them. They can count twice to make sure they counted the counters correctly the first time. Repeat this exercise at least five times. Complete activity 15 in workbook 1. The learners first estimate how many objects there are and then count them.

Session 2: 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. The little pig always sat next to the big pig 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, so he brought the pigs a whole loaf of bread with 16 slices for the pigs.

16 © Optimi

Learning unit 2 Week 3

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Help the learners to work out how many slices of bread each pig is going to 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.

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Count from 1 to 10 and count in multiples of 10 to 100. 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 pigs 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.

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Session 3: Place value and mental maths As an introduction to this activity, learners should cut out the flash cards from the learner aid. Give a number for the learners to build with the correct tens card and the correct ones card. For example: 25 = 2 tens + 5 ones. The learners build the following numbers by placing the ones card over the 0 on the tens card: 51, 84, 26, 39, 8, 65, 13, 92, 77, 46. The learners answer the following sums orally. Learners who struggle may use their 100 chart. 6 + 9 = 5+6= 5 + 2 = 6+0= 11 + 3 = 9+2= 6 + 1 = 12 + 3 = 5 + 4 = 3+7=

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Cut out the flash cards from the learner aid. Listen carefully to the facilitator and build the numbers you are given with the cards. Do the sums orally.