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

1902-E-MAM-FG01

Í3”È-E-MAM-FG01ÇÎ

Grade 2

CAPS aligned

W Drijfhout H Erasmus

Facilitator’s Guide Grade 2 ~ Mathematics

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 watch; 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

Facilitator’s Guide Grade 2 ~ Mathematics

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 watch.............................................................................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

Facilitator’s Guide Grade 2 ~ Mathematics

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 watch............................................................................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 watch................................................................................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

Facilitator’s Guide Grade 2 ~ Mathematics

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

Facilitator’s Guide Grade 2 ~ Mathematics

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)

Facilitator’s Guide Grade 2 ~ Mathematics

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

Facilitator’s Guide Grade 2 ~ Mathematics

• • • • • •

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