Gr 2-Mathematics-Facilitator’s Guide by Impaq

Í2”È-E-MAM-FG01ÆÎ

MATHEMATICS FACILITATOR’S GUIDE Grade 2

A member of the FUTURELEARN group

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

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 © Impaq

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

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. © Impaq

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.

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. © Impaq

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. © Impaq

Activity 31 a) 43 + 32 = 75 b) 36 + 51 = 87 c) 48 + 34 = 82 d) 29 + 38 = 67 e) 26 + 49 = 75

Answers Term 4

Activity 36 75 – 43 = 32 87 – 36 = 51 82 – 48 = 34 67 – 29 = 38 75 – 26 = 49

75 – 32 = 43 87 – 51 = 36 82 – 34 = 48 67 – 38 = 29 75 – 49 = 26

Activity 32 a) 6 g) 6 m) 0 b) 10 h) 12 n) 18 c) 8 i) 16 o) 12 d) 20 j) 14 p) 2 e) 10 k) 18 q) 18 f) 20 l) 16 r) 14

Activity 33 Even numbers are all the numbers in the columns under 102, 104, 106, 108 and 110

a) 9 g) 6 m) 15 b) 6 h) 18 n) 27 c) 12 i) 24 o) 18 d) 6 j) 21 p) 9 e) 15 k) 27 q) 18 f) 30 l) 24 r) 21

Activity 37 Odd numbers are all the numbers in the columns under 101, 103, 105, 107 and 109 Spider sums 24, 28, 32, 36 30, 35, 40, 45

Activity 38 a) 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 30 or 3 x 10 = 30

Spider sums 10, 12, 14, 16 15, 18, 21, 24

b) 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 44 or 11 x 4 = 44

Activity 34

c) 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 36 or 12 x 3 = 36

Column 1 97, 1, 78, 21 Column 2 57, 98, 76 Column 3 44, 71

Activity 35

d) 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 36 or 9 x 4 = 36

Activity 39 a) 68 – 45 = 23 marbles b) 99 – 87 = 12 ℓ c) 87 – 21 = 66 kg d) 78 – 56 = 22 ice lollies

a) 3 + 3 + 3 + 3 + 3 = 15 or 3 x 5 = 15

Activity 40

b) 5 + 5 + 5 + 5 + 5 + 5 = 30 or 5 x 6 = 30

a) 12 g) 12 m) 20 b) 8 h) 24 n) 36 c) 16 i) 32 o) 24 d) 40 j) 28 p) 12 e) 20 k) 36 q) 36 f) 40 l) 32 r) 28

c) 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 + 3 = 42 or 3 x 14 = 42 d) 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 + 4 = 56 or 4 x 14 = 56 307

Workbook Memorandum Grade 2 ~ Mathematics

Activity 41

Activity 44

a) 6 b) 9 c) 12 d) 15 e) 18 f) 21 g) 24 h) 27 i) 30

Row 1 2, 8, 6, 16, 20, 12, 28, 16, 18, 0

2x3 3x3 4x3 5x3 6x3 7x3 8x3 9x3 10 x 3

Row 2 3, 6, 27, 21, 15, 18, 12, 24, 9, 30 Row 3 16, 32, 12, 0, 8, 20, 40, 32, 36, 12

24 12 12 6 6 6 3 3 3 3

Row 4 5, 30, 15, 45, 25, 10, 35, 40, 0, 20

48 24 24 12 12 12 6 6 6 6

Activity 45

Activity 42 1 x 5 = 5 2 x 5 = 10 3 x 5 = 15 4 x 5 = 20 5 x 5 = 25

6 x 5 = 30 7 x 5 = 35 8 x 5 = 40 9 x 5 = 45 10 x 5 = 50

Activity 43 Sunday Thursday Tuesday Wednesday Friday

Monday Friday Wednesday Thursday Saturday

10 more 6 more

Tuesday Saturday Thursday Friday Sunday

5 less

3 more

8 less

150

160

156

145

153

142

178

188

184

173

181

170

184

194

190

179

187

176

163

173

169

158

166

155

190

200

196

185

193

182

308

a) 42 + 41 = 42 + 42 – 1 or = 83

= 41 + 41 + 1 = 83

b) 34 + 33 = 34 + 34 – 1 or = 67

= 33 + 33 + 1 = 67

c) 45 + 44 = 45 + 45 – 1 or = 89

= 44 + 44 + 1 = 89

d) 22 + 23 = 22 + 22 + 1 or = 45

= 23 + 23 – 1 = 45

e) 33 + 32 = 33 + 33 – 1 or = 65

= 32 + 32 + 1 = 65

f) 41 + 42 = 41 + 41 + 1 or = 83

= 42 + 42 – 1 = 83

g) 23 + 24 = 23 + 23 + 1 or = 47

= 24 + 24 – 1 = 47

h) 31 + 32 = 31 + 31 + 1 or = 63

= 32 + 32 – 1 = 63

i) 11 + 12 = 11 + 11 + 1 or = 23

= 12 + 12 – 1 = 23

Answers Term 4

j) 22 + 21 = 22 + 22 – 1 or = 43

= 21 + 21 + 1 = 43

k) 24 + 23 = 24 + 24 – 1 or = 47

= 32 + 32 + 1 = 47

l) 44 + 45 = 44 + 44 + 1 or = 89

= 45 + 45 – 1 = 89

m) 13 + 14 = 13 + 13 + 1 or = 27

= 14 + 14 – 1 = 27

n) 12 + 13 = 12 + 12 + 1 or = 25

= 13 + 13 – 1 = 25

Activity 48

Activity 46 1 x 10 = 10 2 x 10 = 20 3 x 10 = 30 4 x 10 = 40 5 x 10 = 50

6 x 10 = 60 7 x 10 = 70 8 x 10 = 80 9 x 10 = 90 10 x 10 = 100

June March February October July

and 8 = 4

b) 60 = 30 = 30 + 3 = 33

and 6 = 3

c) 50 = 25 = 25 + 4 = 29

and 8 = 4

d) 70 = 35 = 35 + 4 = 39

and 8 = 4

e) 80 = 40 = 40 + 1 = 41

and 2 = 1

f) 60 = 30 = 30 + 2 = 32

and 4 = 2

Activity 49

Activity 47 May February January September June

a) 80 = 40 = 40 + 4 = 44

July April March November August

5 more

6 less

7 more

3 less

6 more

145

150

139

152

142

151

182

187

176

189

179

188

173

178

167

180

170

179

138

143

132

145

135

144

189

194

183

196

186

195

309

a) 10 x 4 = 40 legs b) 5 x 10 = 50 sweets. Learners draw pictures to demonstrate the answers. c) 8 x 2 = 16 eyes

Activity 51 a) 12 – 3 – 3 – 3 – 3 = 0 b) 20 – 4 – 4 – 4 – 4 – 4 = 0 c) 80 – 5 – 5 – 5 – 5 – 5 – 5 – 5 – 5 – 5 – 5 – 5–5–5–5–5–5=0 d) 72 – 4 – 4 – 4 – 4 – 4 – 4 – 4 – 4 – 4 – 4 – 4–4–4–4–4–4–4–4=0

Activity 52 Addition

26 15 11 9 6 5 5 4 2 3

Workbook Memorandum Grade 2 ~ Mathematics

Activity 56

36 20 16 13 7 9 9 4 3 6

46 23 23 13 10 13 7 6 4 9

Multiplication

48 4 2 2

0 6

2 1

85 38 47 16 22 25 8 8 14 11

0 12 2

0 2

Activity 57

12 4

3 3 3

8 2 1 1

4 2

2 1

a) 200; 190; 180; 170; 160; 150; 140; 130 b) 195; 192; 189; 186; 183; 180; 177; 174 c) 100; 90; 80; 70; 60; 50; 40; 30 d) 155; 150; 145; 140; 135; 130; 125; 120 e) 112; 110; 108; 106; 104; 102; 100; 98 f) 189; 188; 187; 186; 185; 184; 183; 182

62 32 30 14 18 12 6 8 10 2

24 12 2 6 2 1 3 2 1 1

Activity 58

a) 165; 170; 175; 180; 185; 190; 195; 200 b) 182; 184; 186; 188; 190; 192; 194; 196 c) 168; 172; 176; 180; 184; 188; 192; 196 d) 188; 189; 190; 191; 192; 193; 194; 195 e) 173; 176; 179; 182; 185; 188; 191; 194 f) 160; 164; 168; 172; 176; 180; 184; 188

a) 110; 120; 130; 140; 150; 160; 170; 180; 190; 200 b) 184; 183; 182; 181; 180; 179; 178; 177; 176; 175 c) 160; 156; 152; 148; 144; 140; 136; 132; 128; 124 d) 200; 198; 196; 194; 192; 190; 188; 186; 184; 182 e) 198; 194; 190; 186; 182; 178; 174; 170; 166; 162 f) 195; 190; 185; 180; 175; 170; 165; 160; 155; 150 g) 160; 163; 166; 169; 172; 175; 178; 181; 184; 187 h) 200; 195; 190; 185; 180; 175; 170; 165; 160; 155

Activity 54

Activity 59

16 8 4 2

2 2

1 1

Activity 53

Double 15 = 30 35 = 70

22 = 44 32 = 64

45 = 90 28 = 56

Halve 92 = 46 74 = 37

86 = 43 66 = 33

68 = 34 88 = 44

ÂŠ Impaq

Learners draw pictures to demonstrate the answers. If they want to write the number sentences, they may do so as follows: a) 64 = 32 + 32 gloves

310

Answers Term 4

b) Halve 50 = 25 and 5 x 5 = 25. The truck delivers 5 boxes of apples.

d) 20c e) 15c

c) 4 x 9 = 36. It will take her 9 days.

Activity 66

Activity 61 a) = b) > c) > d) > e) <

Activity 62

a) 35c b) R1,50 c) 25c

d) 80c e) 20c

a) 90c b) R9,30 c) R1,75 d) R65 e) R99 f) R90,60

g) R1,50 h) R1,50 i) 50c j) R32 k) R43 l) R25

a) < f) > k) = b) > g) > l) > Activity c) = h) > m) < d) = i) < n) < a) R1 e) > j) < o) > b) R5 c) R12 Chain sum 27, 32, 29, 30, 36, 26, 28, 24, 27, 23, 31, 26 a) 60c b) R7,50 c) 45c Activity 63 d) 60c e) 40c f) R2,80

1 whole

3 quarters

1 half

1 quarter

Activity 64 a) 15 b) 19 c) 16

d) 14 e) 6 f) 60

a) 2 c) 5 b) 1 d) 2 and a half or 2 and 2 quarters

Activity 65 Change R2,50, 20c, R5, R2,50, R1 a) R1 b) R4 c) 40c

f) 50c g) 95c h) R35

311

i) R10 j) R90

67 d) R13 e) R45 g) 45c h) 80c i) R85 j) R23 k) R77 l) R1

Activity 68 Column 1 24 8 40 18

Column 2 R3 x 8 = R24 R2 x 4 = R8 R5 x 8 = R40 R3 x 6 = R18

a) R20 b) R40 c) R8

d) R12 e) R16 f) R2

Activity 69 1s = 150; 151; 152; 153; 154; 155 2s = 150; 152; 154; 156; 158; 160 3s = 150; 153; 156; 159; 162; 165 4s = 150; 154; 158; 162; 166; 170 5s = 150; 155; 160; 165; 170; 175 10s = 150; 160; 170; 180; 190; 200

ÂŠ Impaq

Workbook Memorandum Grade 2 ~ Mathematics

Activity 70

Activity 78

a) a (may be marked as correct), d and e b) a (may be marked as correct), b and c

1) D 2) B 3) A

Activity 79

Activity 72

Column 1 18, 8, 9, 12, 2, 6, 20, 24, 12, 10, 8, 21, 9

3s = 160, 163, 166, 169, 172, 175 4s = 160, 164, 168, 172, 176, 180 5s = 160, 165, 170, 175, 180, 185 10s = 150, 160, 170, 180, 190, 200

Column 2 8, 12, 7, 20, 19, 14, 17, 13, 5, 21, 21, 27, 5 Column 3 10, 21, 2, 18, 25, 12, 7, 16, 13, 15, 6, 12, 11

Activity 74 a) minutes b) hours c) 5 o’clock

4) A 5) D 6) C

d) 7 o’clock e) 12 o’clock f) 24 hours

Activity 80 a) heavier c) lighter

Half past 9 to half past 2 = 5 hours 3 o’clock to 9 o’clock = 6 hours

b) weigh the same d) lighter

From light to heavy The ball, the rabbit, the babies, the bell, the car

Activity 75

Activity 81

3s = 170, 173, 176, 179, 182, 185, 188 4s = 160, 164, 168, 172, 176, 180, 184 5s = 170, 175, 180, 185, 190, 195, 200 10s = 140, 150, 160, 170, 180, 190, 200

Column 1 16, 26, 23, 9, 10, 10, 14, 14, 15, 14, 18, 16, 13 Column 2 12, 12, 11, 20, 9, 21, 22, 22, 23, 21, 14, 17, 21

Activity 76 Row 1 10 past 5

25 past 2

5 past 7

Column 3 10, 18, 16, 18, 15, 16, 17, 20, 21, 20, 20, 25, 19

Row 2 quarter past 4

5 to 8

25 to 12

Activity 82 a) 2 ℓ b) 1 ℓ c) 4 bottles

Activity 77 Column 1 18, 26, 23, 9, 10, 10, 14, 14, 15, 14, 18, 16, 13

Word sums a) 5 x 6 = 30 b) 5 ℓ

Column 2 12, 12, 11, 20, 9, 21, 22, 22, 23, 21, 14, 17, 21

Activity 83

Column 3 10, 18, 16, 18, 15, 16, 17, 20, 21, 20, 20, 25, 19

d) 1,5 ℓ or 1 ℓ and 500 mℓ e) 4

a) 2 e) 28 b) 6 f) 2 c) Janice and Zander g) 2 d) 4 312