Gr 4-Mathematics-Facilitator's Guide

Í2(È-E-MAM-FG01’Î

1

8

0

4

-

E

-

M

A

M

-

F

G

0

1

MATHEMATICS FACILITATOR’S GUIDE

Grade 4

A member of the FUTURELEARN group

Mathematics Facilitator’s guide

1804-E-MAM-FG01

Í2$È-E-MAM-FG01ÊÎ

Grade 4

CAPS aligned

L Young

Facilitator’s Guide G04 ~ Mathematics

CONTENTS LESSON ELEMENTS.......................................................................................................... 7 INTRODUCTION ................................................................................................................. 8 TIME MANAGEMENT ......................................................................................................... 8 ASSESSMENT REQUIREMENTS .................................................................................... 13 STUDY HINTS ................................................................................................................... 13 YEAR PLAN ...................................................................................................................... 15 UNIT 1 ............................................................................................................................... 19 LESSON 1: WHOLE NUMBERS ................................................................................... 20 Counting with whole numbers......................................................................................... 21 ACTIVITY 1 .............................................................................................................. 23 Ordering whole numbers ................................................................................................ 26 ACTIVITY 2 .............................................................................................................. 27 Place value ..................................................................................................................... 29 ACTIVITY 3 .............................................................................................................. 32 Comparing whole numbers ............................................................................................. 37 ACTIVITY 4 .............................................................................................................. 39 Representing whole numbers ......................................................................................... 41 ACTIVITY 5 .............................................................................................................. 41 LESSON 2: NUMBER SENTENCES ............................................................................. 41 ACTIVITY 6 .............................................................................................................. 43 ACTIVITY 7 .............................................................................................................. 43 ACTIVITY 8 .............................................................................................................. 44 Pairs of equivalent number sentences............................................................................ 47 ACTIVITY 9 .............................................................................................................. 48 Addition and subtraction techniques ............................................................................... 49 Commutative property of addition ................................................................................... 49 Associative property of addition ...................................................................................... 50 ACTIVITY 10 ............................................................................................................ 51 Order of subtraction ........................................................................................................ 52 ACTIVITY 11 ............................................................................................................ 53 LESSON 3: WHOLE NUMBERS ................................................................................... 54 Addition with whole numbers .......................................................................................... 54 ACTIVITY 12 ............................................................................................................ 54 ACTIVITY 13 ............................................................................................................ 56 Subtraction of whole numbers ........................................................................................ 58 ACTIVITY 14 ............................................................................................................ 59 Estimation ....................................................................................................................... 63 ACTIVITY 15 ............................................................................................................ 66 Rounding ........................................................................................................................ 69 ACTIVITY 16 ............................................................................................................ 71 1

© Impaq

Facilitator’s Guide G04 ~ Mathematics

ACTIVITY 17 ............................................................................................................ 73 Compensation ................................................................................................................ 73 Doubling and halving ...................................................................................................... 74 ACTIVITY 18 ............................................................................................................ 75 ACTIVITY 19 ............................................................................................................ 77 Testing calculations with inverse operations .................................................................. 77 ACTIVITY 20 ............................................................................................................ 79 LESSON 4: NUMBER PATTERNS (Numeric patterns) .............................................. 81 ACTIVITY 21 ............................................................................................................ 82 Input and output values .................................................................................................. 83 ACTIVITY 22 ............................................................................................................ 83 ACTIVITY 23 ............................................................................................................ 85 ACTIVITY 24 ............................................................................................................ 86 The associative property of multiplication ....................................................................... 86 LESSON 5: WHOLE NUMBERS (Multiplication and division) .................................. 90 Multiplication ................................................................................................................... 90 ACTIVITY 25 ............................................................................................................ 98 Division ........................................................................................................................... 99 ACTIVITY 26 .......................................................................................................... 100 ACTIVITY 27 .......................................................................................................... 103 LESSON 6: TIME ......................................................................................................... 104 ACTIVITY 28 .......................................................................................................... 107 ACTIVITY 29 .......................................................................................................... 110 LESSON 7: DATA HANDLING .................................................................................... 112 Collecting, organising, analysing and interpreting data ................................................ 112 Pictograph .................................................................................................................... 112 Pie chart ....................................................................................................................... 113 Bar graph ...................................................................................................................... 114 ACTIVITY 30 .......................................................................................................... 115 LESSON 8: PROPERTIES OF 2-D SHAPES .............................................................. 119 ACTIVITY 31 .......................................................................................................... 123 LESSON 9: WHOLE NUMBERS (Multiplication of 2-digit numbers and division of 2-digit numbers by ..................................................................................................... 125 1-digit numbers)............................................................................................................ 125 ACTIVITY 32 .......................................................................................................... 125 ACTIVITY 33 .......................................................................................................... 127 ACTIVITY 34 .......................................................................................................... 131

© Impaq

2

Facilitator’s Guide G04 ~ Mathematics

UNIT 2 ............................................................................................................................. 134 LESSON 10: WHOLE NUMBERS ............................................................................... 135 Counting with whole numbers....................................................................................... 136 ACTIVITY 35 .......................................................................................................... 137 Ordering whole numbers .............................................................................................. 140 ACTIVITY 36 .......................................................................................................... 141 Place value ................................................................................................................... 143 ACTIVITY 37 .......................................................................................................... 145 Comparing whole numbers ........................................................................................... 148 ACTIVITY 38 .......................................................................................................... 148 Representing whole numbers ....................................................................................... 151 ACTIVITY 39 .......................................................................................................... 151 Rounding ...................................................................................................................... 151 ACTIVITY 40 .......................................................................................................... 154 LESSON 11: WHOLE NUMBERS (Addition and subtraction).................................. 156 Commutative property of addition ................................................................................. 156 Associative property of addition .................................................................................... 157 Order of subtraction ...................................................................................................... 159 ACTIVITY 41 .......................................................................................................... 161 LESSON 12: COMMON FRACTIONS ......................................................................... 164 ACTIVITY 42 .......................................................................................................... 166 ACTIVITY 43 .......................................................................................................... 168 LESSON 13: LENGTH ................................................................................................. 174 ACTIVITY 44 .......................................................................................................... 175 LESSON 14: WHOLE NUMBERS ............................................................................... 178 Distributive property of multiplication ............................................................................ 180 Dividing numbers into factors to multiply them ............................................................. 180 ACTIVITY 45 .......................................................................................................... 181 LESSON 15: PROPERTIES OF 3-D OBJECTS .......................................................... 186 ACTIVITY 46 .......................................................................................................... 189 LESSON 16: GEOMETRIC PATTERNS ...................................................................... 192 ACTIVITY 47 .......................................................................................................... 194 LESSON 17: SYMMETRY ........................................................................................... 196 ACTIVITY 48 .......................................................................................................... 197 LESSON 18: WHOLE NUMBERS (Addition and subtraction).................................. 200 ACTIVITY 49 .......................................................................................................... 200

3

© Impaq

Facilitator’s Guide G04 ~ Mathematics

LESSON 19: WHOLE NUMBERS (Dividing 3-digit numbers by 1-digit numbers) . 204 ACTIVITY 50 .......................................................................................................... 208 UNIT 3 ............................................................................................................................. 213 LESSON 20: CAPACITY/VOLUME ............................................................................. 214 ACTIVITY 51 .......................................................................................................... 218 LESSON 21: COMMON FRACTIONS ......................................................................... 223 ACTIVITY 52 .......................................................................................................... 226 LESSON 22: WHOLE NUMBERS ............................................................................... 231 ACTIVITY 53 .......................................................................................................... 231 LESSON 23: VIEWS OF OBJECTS ............................................................................ 238 ACTIVITY 54 .......................................................................................................... 240 LESSON 24: PROPERTIES OF 2-D SHAPES ............................................................ 244 ACTIVITY 55 .......................................................................................................... 247 LESSON 25: DATA HANDLING .................................................................................. 251 ACTIVITY 56 .......................................................................................................... 253 LESSON 26: NUMBER PATTERNS ............................................................................ 258 Input and output values ................................................................................................ 259 The associative property of multiplication ..................................................................... 260 Types of number sequences ........................................................................................ 263 ACTIVITY 57 .......................................................................................................... 264 LESSON 27: WHOLE NUMBERS (Addition and subtraction [4-digit whole numbers]) .................................................................................................................... 267 Order of subtraction ...................................................................................................... 269 ACTIVITY 58 .......................................................................................................... 271 LESSON 28: WHOLE NUMBERS (Multiply [2-digit whole numbers by 2-digit whole numbers]) .................................................................................................................... 276 Distributive property of multiplication ............................................................................ 276 Dividing numbers into factors to multiply them ............................................................. 277 ACTIVITY 59 .......................................................................................................... 277 LESSON 29: NUMBER SENTENCES ......................................................................... 282 Pairs of equivalent number sentences.......................................................................... 286 ACTIVITY 60 .......................................................................................................... 287 LESSON 30: TRANSFORMATIONS ........................................................................... 289 ACTIVITY 61 .......................................................................................................... 290 © Impaq

4

Facilitator’s Guide G04 ~ Mathematics

UNIT 4 ............................................................................................................................. 291 LESSON 31: WHOLE NUMBERS ............................................................................... 292 ACTIVITY 62 .......................................................................................................... 292 LESSON 32: MASS ..................................................................................................... 301 ACTIVITY 63 .......................................................................................................... 304 LESSON 33: PROPERTIES OF 3-D OBJECTS .......................................................... 310 ACTIVITY 64 .......................................................................................................... 313 LESSON 34: COMMON FRACTIONS ......................................................................... 317 ACTIVITY 65 .......................................................................................................... 320 LESSON 35: WHOLE NUMBERS (Division [3-digit numbers by 1-digit numbers]) ..................................................................................................................................... 326 ACTIVITY 66 .......................................................................................................... 328 LESSON 36: PERIMETER, SURFACE AREA AND VOLUME ................................... 331 Perimeter ...................................................................................................................... 331 ACTIVITY 67 .......................................................................................................... 337 Surface area ................................................................................................................. 340 ACTIVITY 68 .......................................................................................................... 341 Volume ......................................................................................................................... 342 LESSON 37: POSITION AND MOVEMENT ................................................................ 345 ACTIVITY 69 .......................................................................................................... 348 LESSON 38: TRANSFORMATIONS ........................................................................... 351 ACTIVITY 70 .......................................................................................................... 353 LESSON 39: GEOMETRIC PATTERNS ...................................................................... 355 ACTIVITY 71 .......................................................................................................... 356 LESSON 40: WHOLE NUMBERS ............................................................................... 359 ACTIVITY 72 .......................................................................................................... 359 LESSON 41: PROBABILITY ....................................................................................... 365 ACTIVITY 73 .......................................................................................................... 367 References: Unit 1 ........................................................................................................ 369 References: Unit 2 ........................................................................................................ 370 References: Unit 3 ........................................................................................................ 371 References: Unit 4 ........................................................................................................ 372

5

© Impaq

Facilitator’s Guide G04 ~ Mathematics

Addendum A: colour page ......................................................................................... 373 100 chart ..................................................................................................................... 374

Š Impaq

6

Facilitator’s Guide G04 ~ Mathematics

Unit

1

UNIT 1 This unit covers nine lessons: Lessons 1 to 9.

The table indicates the lesson topics as well as the time the learners will spend on each one.

UNIT 1 TOPIC

TIME AND NOTES

Mental maths: Use the Train Your Brain Maths Grade 4 product

8 hours (divided into 10 minutes every day)

LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers)

2 hours

LESSON 2 Number sentences

3 hours

LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers)

8 hours

LESSON 4 Number patterns: Numeric patterns

4 hours

LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number)

4 hours

LESSON 6 Time

6 hours

LESSON 7 Data handling

10 hours

LESSON 8 Properties of 2-D shapes

5 hours

LESSON 9 Whole numbers:  Multiply (2-digit whole numbers by 1-digit whole number)  Multiply (2-digit whole numbers by 2-digit whole numbers)  Divide (2-digit whole numbers by 1-digit whole number)

5 hours

Revision: Use the CAMI programme

5 hours

TOTAL

60 hours

19

© Impaq

Unit

Facilitator’s Guide G04 ~ Mathematics

1

LESSON 1: WHOLE NUMBERS In this lesson learners will work with different notations of numbers for the first time. It is important to ensure that learners understand notations. It lays the foundation for the language of maths and if learners are already comfortable with this, it can simplify the introduction of new maths concepts. In this lesson, learners will work with whole numbers and do the following:  count  order  compare  represent  indicate place value (which is very important for the calculations that will be done later in the term)

Do you know what a whole number is?

Whole numbers are numbers without fractions or decimals. Whole numbers are also always positive and never negative. Remember: 0 is also a whole number.

Learners have been introduced to whole numbers in Grade 3, even if they did not necessarily call them whole numbers. Ensure that learners know that a whole number is not a fraction. Different games can be used to reinforce this concept.

Example Write down different numbers, including fractions and whole numbers. Learners close their eyes and randomly point to a place on the page. They identify the number they chose as a whole number or not.

Examples of whole numbers

{0; 1; 2; 3; 4; 5; 6; ...}

© Impaq

20

Facilitator’s Guide G04 ~ Mathematics

Unit

1

If numbers such as the above are placed in curly brackets { }, we call it a set of numbers.

This means that {0; 1; 2; 3; 4; 5; 6; ...} is a set of whole numbers.

Look at the numbers in the table and circle the whole numbers.

15 7

11

5

0,9

101

10

24

-24

0

198

-2

13 9

3

-4,1

4

-

In this lesson, you will do the following with whole numbers:  count  order  compare  represent  indicate place value

Counting with whole numbers

It is very important that the learners count every day – both on (forwards) and back (backwards). In the beginning, learners may count with a 100 number chart, but when they have completed the lesson, they must be able to count without any help. (See the 100 number chart at the back of this facilitator’s guide.)

Counting must not only be seen as oral counting – learners must understand the calculations that are happening to count on or back.

Learners may use the following to count:  countable objects (marbles, balls, beans, beads, etc.)  an abacus (available at any educational or plastics shop)  number charts or tables  rows or diagrams, for example:

In Grade 3 you learnt how to count with whole numbers. Can you still remember how to count in 2s?

21

© Impaq

Unit

Facilitator’s Guide G04 ~ Mathematics

1

Revise counting in 2s.

When you count in 2s, always add 2 to the previous number to get the next number.

You can start with any number.

Look at the numbers. Do you see that you can start at any number and count in whole numbers?

In the above examples, you counted on or forwards.

Using whole numbers, you can also count back or backwards.

Look at the following numbers and complete the blank blocks.

Count back in 3s.

44

35

Now that your memory has been refreshed, you can apply what you have learnt.

Š Impaq

22

Facilitator’s Guide G04 ~ Mathematics

Unit

1

ACTIVITY 1 1.

Write the set of whole numbers between 915 and 921. {916; 917; 918; 919; 920}

2.

Indicate whether the numbers are whole numbers or not. Colour the correct circle.

Numbers

Whole number: yes or no?

658

14,3 53 3 1

412

3.

Study the number lines. You are not told what number to count with, nor whether you are counting on or back. Complete the number lines.

3.1

96;

101;

106;

111

...

3.2

416

413;

410;

407;

...

3.3

8;

108;

208

308;

...

3.4

12;

9;

6

3;

0

3.5

10;

35;

60;

85;

110

23

Š Impaq

Unit

4.

Facilitator’s Guide G04 ~ Mathematics

1

There are three Grade 4 learners in the class that like to play with marbles. Each learner keeps their marbles in a different size bag.

Andrew’s bag can hold 10 marbles. Sibongile’s bag can hold 25 marbles. Timmy’s bag can only hold 3 marbles.

Look at the following example and count in 10s, 25s and 3s to determine how many marbles each learner has.

Learner

5.

Number of bags

Andrew

30

Sibongile

25

Timmy

27

Complete the flow charts.

5.1

5.2

© Impaq

Number of marbles

24

Facilitator’s Guide G04 ~ Mathematics

Unit

1

After each lesson learners must fill in a self-assessment of the completed lesson. You may use the self-assessment to determine if learners need additional help in the specific lesson, and to address the gap immediately. You may also use the self-assessment to plan enrichment activities. When learners have mastered each lesson additional enrichment will still be hugely beneficial.

Self-assessment After learners have completed this topic, they should be able to do the following.

Look at the requirements and let the learner colour the face that best describes their skill or ability.

COUNTING WITH WHOLE NUMBERS Requirements Can the learner do it?

I can count on and back in 2s.

I can count on and back in 3s.

I can count on and back in 5s.

I can count on and back in 10s.

I can count on and back in 25s.

I can count on and back in 50s.

I can count on and back in 100s.

I can do all of the above up to the number 1 000.

25

Š Impaq

Unit

Facilitator’s Guide G04 ~ Mathematics

1

Ordering whole numbers Ordering means to arrange or organise numbers.

ordering = arrange We can order or arrange numbers in different ways:

from LARGE to small

OR from small to LARGE

Study the set of numbers.

Arrange the numbers from large to small.

Step 1:

Choose the largest number and write it down first.

The largest number in this set is

Step 2:

Now cross out the largest number in the number set.

You can no longer choose the number 537.

Š Impaq

26

Facilitator’s Guide G04 ~ Mathematics

Unit

Step 3:

From the remaining numbers, choose the largest number and write it next to 537.

Step 4:

Now repeat steps 2 and 3 until you have crossed out all of the numbers.

1

When you are done, your number set should look as follows:

You have now arranged the set of numbers from largest to smallest.

Can you arrange the following set of numbers from small to large?

Hint: Start by choosing the smallest number, not the largest one.

Write your answer in the box below.

1; 11; 35; 902; 913

ACTIVITY 2 1.

Arrange the numbers from small to large.

1.1 1.2 1.3 1.4 1.5 2.

Question 321 645 256 782 127 56 72 201 114 98 724 568 147 274 355 65 34 12 47 71 527 471 298 638 138

Answer 127; 256; 321; 645; 782 56; 72; 98; 114; 201 147; 274; 355; 568; 724 12; 34; 47; 65; 71 138; 298; 471; 527; 638

Arrange the numbers from large to small.

2.1 2.2 2.3 2.4 2.5

Question 620 541 635 514 623 36 48 21 65 57 116 98 53 76 110 58 39 44 28 13 457 325 147 471 352

Answer 635; 623; 620; 541; 514 65; 57; 48; 36; 21 116; 110; 98; 76; 53 58; 44; 39; 28; 13 471; 457; 352; 325; 147

27

Š Impaq

Unit

3.

Facilitator’s Guide G04 ~ Mathematics

1 Build and arrange.

3.1

3.2

3.3

3.4

3.5

Question Write down the numbers that you can build from 1, 4 and 5 and arrange them from large to small.

Write down the numbers that you can build from 7, 2 and 9 and arrange them from small to large.

Write down the numbers that you can build from 8, 1 and 6 and arrange them from large to small.

Write down the numbers that you can build from 9, 1 and 2 and arrange them from small to large.

Write down the numbers that you can build from 9, 1 and 1 and arrange them from large to small.

Answer 541; 514; 451; 415; 154; 145

279; 297; 729; 792; 927; 972

861; 816; 681; 618; 186; 168

129; 192; 219; 291; 912; 921

911; 191; 119

Self-assessment After learners have completed this topic, they should be able to do the following.

Look at the requirements and let the learner colour the face that best describes their skill or ability.

ORDERING WHOLE NUMBERS Requirements I can arrange number sets from large to small.

I can arrange number sets from small to large.

I can build and arrange different numbers.

Š Impaq

28

Can the learner do it?

Facilitator’s Guide G04 ~ Mathematics

Unit

1

Place value

Place values are extremely important for developing number concept. If learners’ number concept is not firmly established, they will find calculations difficult. Later on in the term, calculations will already require a firm grasp of place value, which is why learners must spend enough time on this topic.

Ensure that learners understand this concept really well.

Use additional resources to ensure the proper comprehension of place value, such as:  100 number chart  Flash cards  Dienes cubes Various methods are covered in this topic. Learners must be aware of all the different methods, but they are only required to use one method during assessment. The facilitator and learners together decide which method will work best.

Visit goo.gl/nBhGsR to find additional activities.

Place value helps us to determine the value of a digit.

Our number system (the numbers that we work with) contains digits only from 0 to 9.

What do we do when we must work with numbers greater than 9?

We use place value to indicate when we are working with numbers greater than 9.

It means that the value of a digit is determined by its place or position in the entire number.

When we work with place value, we can think of each value as a box with high walls

29

© Impaq