Gr 4-Mathematics-Study Guide 1

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MATHEMATICS STUDY GUIDE Grade 4

A member of the FUTURELEARN group

Mathematics Study guide 1/2

CAPS aligned

L Young

2004-E-MAM-SG01

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Grade 4

Study Guide 1/2 G04 ~ Mathematics

Contents LESSON ELEMENTS..................................................................................................................................... 1 YEAR PLAN.................................................................................................................................................... 2 UNIT 1............................................................................................................................................................. 6 LESSON 1: WHOLE NUMBERS.................................................................................................................. 7

Counting with whole numbers.......................................................................................................................8 ACTIVITY 1..................................................................................................................................................9

Ordering whole numbers...............................................................................................................................12 ACTIVITY 2...............................................................................................................................................14

Place value............................................................................................................................................................16 ACTIVITY 3...............................................................................................................................................19

Comparing whole numbers...........................................................................................................................24 ACTIVITY 4...............................................................................................................................................26

Representing whole numbers......................................................................................................................28 ACTIVITY 5...............................................................................................................................................29 LESSON 2: NUMBER SENTENCES..........................................................................................................30 ACTIVITY 6...............................................................................................................................................31 ACTIVITY 7...............................................................................................................................................32 ACTIVITY 8...............................................................................................................................................34

Pairs of equivalent number sentences.....................................................................................................38 ACTIVITY 9...............................................................................................................................................39

Addition and subtraction techniques.......................................................................................................41

Commutative property of addition............................................................................................................41

Associative property of addition................................................................................................................42 ACTIVITY 10.............................................................................................................................................43

Order of subtraction.........................................................................................................................................44 ACTIVITY 11.............................................................................................................................................45 LESSON 3: WHOLE NUMBERS................................................................................................................46

Addition with whole numbers.....................................................................................................................46 ACTIVITY 12.............................................................................................................................................46 ACTIVITY 13.............................................................................................................................................49

Subtraction of whole numbers....................................................................................................................51 ACTIVITY 14.............................................................................................................................................53 Estimation............................................................................................................................................................59 ACTIVITY 15.............................................................................................................................................62 Rounding...............................................................................................................................................................65 ACTIVITY 16.............................................................................................................................................68 ACTIVITY 17.............................................................................................................................................70 Compensation.....................................................................................................................................................71

Doubling and halving.......................................................................................................................................71 ACTIVITY 18.............................................................................................................................................72 ACTIVITY 19.............................................................................................................................................76

Testing calculations with inverse operations........................................................................................79 ACTIVITY 20.............................................................................................................................................80

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Study Guide 1/2 G04 ~ Mathematics

LESSON 4: NUMBER PATTERNS (Numeric patterns).....................................................................82 ACTIVITY 21.............................................................................................................................................83

Input and output values.................................................................................................................................84 ACTIVITY 22.............................................................................................................................................85 ACTIVITY 23.............................................................................................................................................87 ACTIVITY 24.............................................................................................................................................88

The associative property of multiplication............................................................................................89

LESSON 5: WHOLE NUMBERS (Multiplication and division)......................................................92 Multiplication......................................................................................................................................................92 ACTIVITY 25.......................................................................................................................................... 101 Division............................................................................................................................................................... 103 ACTIVITY 26.......................................................................................................................................... 104 ACTIVITY 27.......................................................................................................................................... 108 LESSON 6: TIME...................................................................................................................................... 109 ACTIVITY 28.......................................................................................................................................... 112 ACTIVITY 29.......................................................................................................................................... 116

LESSON 7: DATA HANDLING................................................................................................................ 118

Collecting, organising, analysing and interpreting data................................................................ 118 Pictograph......................................................................................................................................................... 118

Pie chart.............................................................................................................................................................. 120

Bar graph........................................................................................................................................................... 121 ACTIVITY 30.......................................................................................................................................... 122 LESSON 8: PROPERTIES OF 2D SHAPES.......................................................................................... 126 ACTIVITY 31.......................................................................................................................................... 130 LESSON 9: WHOLE NUMBERS (Multiplication of 2-digit numbers and division of 2-digit numbers by 1-digit number)............................................................................................................. 132 ACTIVITY 32.......................................................................................................................................... 133 ACTIVITY 33.......................................................................................................................................... 135 ACTIVITY 34.......................................................................................................................................... 139

UNIT 2........................................................................................................................................................ 142 LESSON 10: WHOLE NUMBERS.......................................................................................................... 143

Counting with whole numbers................................................................................................................. 144 ACTIVITY 35.......................................................................................................................................... 145

Ordering whole numbers............................................................................................................................ 148 ACTIVITY 36.......................................................................................................................................... 150

Place value......................................................................................................................................................... 152 ACTIVITY 37.......................................................................................................................................... 154

Comparing whole numbers........................................................................................................................ 158 ACTIVITY 38.......................................................................................................................................... 159

Representing whole numbers................................................................................................................... 161 ACTIVITY 39.......................................................................................................................................... 162 Rounding............................................................................................................................................................ 163 ACTIVITY 40.......................................................................................................................................... 166 © Impaq

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Study Guide 1/2 G04 ~ Mathematics

LESSON 11: WHOLE NUMBERS (Addition and subtraction).................................................... 168

Commutative property of addition......................................................................................................... 168

Associative property of addition............................................................................................................. 169

Order of subtraction...................................................................................................................................... 171 ACTIVITY 41.......................................................................................................................................... 174 LESSON 12: COMMON FRACTIONS.................................................................................................... 177 ACTIVITY 42.......................................................................................................................................... 179 ACTIVITY 43.......................................................................................................................................... 181 LESSON 13: LENGTH.............................................................................................................................. 187 ACTIVITY 44.......................................................................................................................................... 189 LESSON 14: WHOLE NUMBERS (Multiply 2-digit numbers by 2-digit numbers).............. 192

Distributive property of multiplication................................................................................................ 194

Dividing numbers into factors to multiply them.............................................................................. 194 ACTIVITY 45.......................................................................................................................................... 195 LESSON 15: PROPERTIES OF 3D OBJECTS...................................................................................... 200 ACTIVITY 46.......................................................................................................................................... 203 LESSON 16: GEOMETRIC PATTERNS................................................................................................ 206 ACTIVITY 47.......................................................................................................................................... 208 LESSON 17: SYMMETRY....................................................................................................................... 212 ACTIVITY 48.......................................................................................................................................... 213 LESSON 18: WHOLE NUMBERS (Addition and subtraction).................................................... 215 ACTIVITY 49.......................................................................................................................................... 215 LESSON 19: WHOLE NUMBERS (Dividing 3-digit numbers by 1-digit number)................ 220 ACTIVITY 50.......................................................................................................................................... 224 REFERENCES: UNIT 1............................................................................................................................ 229 REFERENCES: UNIT 2............................................................................................................................ 230

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Study Guide 1/2 G04 ~ Mathematics

LESSON ELEMENTS The guide consists of various lesson elements. Every element is important for the learning process and indicates the skill that the learner needs to master.

ICON

LESSON ELEMENT Think for yourself Tips

Research Study New concept or definition Remember/Revise Take note! Important Self-assessment Activity

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Study Guide 1/2 G04 ~ Mathematics

YEAR PLAN UNIT 1 DATE STARTED

TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers) LESSON 2 Number sentences

LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers) LESSON 4 Number patterns: Numeric patterns

LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number) LESSON 6 Time

LESSON 7 Data handling LESSON 8

Properties of 2-D shapes

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) Revision: Use the CAMI programme © Impaq

2

DATE COMPLETED

Study Guide 1/2 G04 ~ Mathematics

UNIT 2 DATE STARTED

TOPIC

DATE COMPLETED

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

LESSON 10 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) LESSON 11 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 12 Common fractions LESSON 13 Length

LESSON 14 Whole numbers: Multiplication (2-digit whole numbers by 2-digit whole numbers) LESSON 15 Properties of 3-D shapes LESSON 16 Geometric patterns LESSON 17 Symmetry

LESSON 18 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 19 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) Revision: Use the CAMI programme

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Study Guide 1/2 G04 ~ Mathematics

UNIT 3 DATE STARTED

TOPIC Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 20 Capacity/Volume

LESSON 21 Common fractions

LESSON 22 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 23 Views of objects

LESSON 24 Properties of 2-D shapes LESSON 25 Data handling

LESSON 26 Numerical patterns

LESSON 27 Whole numbers: Addition and subtraction (4-digit whole numbers)

LESSON 28 Whole numbers: Multiplication (2-digit whole numbers with 2-digit whole numbers) LESSON 29 Number sentences LESSON 30 Transformations

Revision: Use the CAMI programme © Impaq

4

DATE COMPLETED

Study Guide 1/2 G04 ~ Mathematics

UNIT 4 DATE STARTED

TOPIC

DATE COMPLETED

Mental maths: Use the Train Your Brain Maths Grade 4 product LESSON 31 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (4-digit whole numbers) Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 32 Mass

LESSON 33 Properties of 3-D objects LESSON 34 Common fractions

LESSON 35 Whole numbers: Division (3-digit whole numbers by 1-digit whole number) LESSON 36 Perimeter, surface area and volume LESSON 37 Position and movement LESSON 38 Transformations

LESSON 39 Geometric patterns

LESSON 40 Whole numbers: Addition and subtraction (4-digit whole numbers) LESSON 41 Probability

Revision: Use the CAMI programme

Find unit 1 and 2 in study guide 1/2 and unit 3 and 4 in study guide 2/2.

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

UNIT 1 This unit covers nine lessons (1 to 9).

UNIT 1

TOPIC Mental maths

LESSON 1 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (3-digit whole numbers) LESSON 2 Number sentences

LESSON 3 Whole numbers: Addition and subtraction (3-digit whole numbers) LESSON 4 Number patterns: Numeric patterns

LESSON 5 Whole numbers: Multiplication and division (1-digit whole number by 1-digit whole number) LESSON 6 Time

LESSON 7 Data handling

LESSON 8 Properties of 2-D shapes

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) Revision: Use the CAMI programme © Impaq © Impaq

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Study Guide 1/2 G04 ~ Mathematics

Unit

1

LESSON 1: WHOLE NUMBERS Do you know what a whole number is?

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

Examples of whole numbers

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

0,5

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.

Study the numbers in the table and circle the whole numbers.

5

10 -2

0,9 24

13 9

101 -24 3

–

15 7

0

-4,1

11

198 4

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

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

Counting with whole numbers In Grade 3 you learnt how to count with whole numbers.

Do you still remember how to count in 2s?

Let’s revise counting in 2s.

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

2

4

+2

6

+2

+2

8

10

+2

12

You can start with any number.

Study the numbers. Do you see that you can start at any number and count in whole numbers? +2

63

65

+2

67

+2

69

+2

71

+2

73

In the above examples, you counted on or forwards.

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

Study the following numbers and complete the missing numbers.

Count back in 3s.

–3

53

–3

50

–3

–3

47

–3

41

–3

38

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

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–3

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Study Guide 1/2 G04 ~ Mathematics

Unit

ACTIVITY 1

1

DATE:

1.

Write the set of whole numbers between 915 and 921.

2.

Indicate whether the numbers are whole numbers. Colour the correct circle.

__________________________________________________________________________________________________ Numbers

Whole number: yes or no?

Example:

35

658

14,3 53 3 1

412

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Unit

3.

1

Study Guide 1/2 G04 ~ Mathematics

Study the number lines. You are not told what number to count with, nor whether you

Example

are counting on or back. Complete the number lines.

3.1 3.2 3.3 3.4 3.5 4.

3;

13;

23;

96;

101;

106;

413;

410;

33;

43 ...

407;

...

8;

108;

308;

...

12;

9;

3;

0

10;

35;

60;

85;

Andrew, Sibongile and Timmy like to play with marbles. They keep their marbles in bags.

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 child has.

Child

Number of bags

Andrew Sibongile

Timmy

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Number of marbles

Study Guide 1/2 G04 ~ Mathematics

5.

Complete the flow charts.

5.1

5.2

+ 50

+ 50

– 25

– 25

– 25

– 25

412

+ 50

+ 50

31

1

Unit

Self-assessment Do you understand the work? Colour the faces that show what you can do.

COUNTING IN WHOLE NUMBERS Requirements

Can I 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.

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

Ordering whole numbers Ordering means to arrange or organise numbers.

order = arrange

We can order or arrange numbers in different ways: from GREAT to small

OR from small to GREAT

Study the number set.

{25; 2; 537; 119; 65} Arrange the numbers from great to small.

Step 1:

Choose the greatest number and write it down first.

Step 2:

Now cross out the greatest number in the number set.

The greatest number in this set is

537.

{25; 2; 537; 119; 65}

You can no longer choose the number 537. Š Impaq

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Study Guide 1/2 G04 ~ Mathematics

Step 3:

Step 4:

Unit

1

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

537; 119

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

When you are done, the set of numbers must look as follows:

{537; 119; 65; 25; 2} You have now arranged the number set from greatest to smallest.

Can you arrange the following number set from small to great?

{913; 902; 35; 11; 1}

Tip: Start by choosing the smallest number, not the greatest one.

Write your answer in the box below.

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

ACTIVITY 2 1.

Arrange the numbers from small to great.

Question and answer

1.1 1.2 1.3 1.4 1.5 2.

DATE:

321 56 724 65 527

645 72

256 201

568 34 471

782 114

147 12

127

98

274

47

298

355

71 638

138

Arrange the numbers from great to small.

Question and answer

2.1 2.2 2.3 2.4 2.5 Š Impaq

620 36 116 58 457

541 48 98 39 325

635 21

514

65

53 44

57

76 28

147

623

110 13

471 14

352

Study Guide 1/2 G04 ~ Mathematics

3.

Build and arrange the numbers.

Answer

Example

Question

Write down the numbers that you

3.1

can build with 1, 4 and 5 and arrange

3.2 3.3 3.4 3.5

1

Unit

can build with 6, 3 and 2 and arrange them from small to great.

Write down the numbers that you

236; 263; 326; 362; 623; 632

them from great to small.

Write down the numbers that you

can build with 7, 2 and 9 and arrange them from small to great.

Write down the numbers that you

can build with 8, 1 and 6 and arrange them from great to small.

Write down the numbers that you

can build with 9, 1 and 2 and arrange them from small to great.

Write down the numbers that you

can build with 9, 1 and 1 and arrange them from great to small.

Self-assessment Do you understand the work? Colour the faces that show what you can do.

ORDERING WHOLE NUMBERS Requirements

Can I do it?

I can arrange number sets from great to small.

I can arrange number sets from small to great.

I can build and arrange different numbers.

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

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

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

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 a number.

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

Hundreds

Tens

Units

In each box you can find the digits 0 to 9. As soon as the number becomes greater than 9, it jumps over the wall into the next box. Š Impaq

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Study Guide 1/2 G04 ~ Mathematics

Unit

Hundreds

Tens

1

Units

7

The 7 in the Units box means that there are 7 Units. We can also write it as 7 x 1.

Can you see that there are no numbers in the Tens and Hundreds boxes?

This means that there are 0 x Tens and 0 x Hundreds in this number.

Let’s see what happens with a number greater than 9.

Hundreds

Tens

Units

13

There may only be one number in each box, but now there is a 1 and a 3 in the Units box.

What does the 13 mean? It consists of 10 + 3.

The 3 is in the Units box and it means 3 x 1, which is shown as 3.

The 10 jumps over the wall into the Tens box.

You CANNOT carry the full 10 across, because it then indicates 10 x Tens, which means 10 x 10, which equals 100. Therefore, only the 1 jumps across.

Hundreds

Tens

10

Units

3

1 × Tens means 1 × 10 = 10 If you want to indicate the place value of 13, it will look like this:

Hundreds

Tens

1 17

Units

3

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

The same happens when there is a number greater than 9 in the Tens box.

Hundreds

Tens

84

Units

2

Since the 8 in the Tens box indicates 800, it must jump over the wall into the Hundreds box.

It means 8 x 100 = 800.

Hundreds

8

Tens

4

Units

2

It is not always as easy or practical to draw boxes to determine place value and it can take a lot of time. There are three other methods to do the same without drawing boxes.

Use the number

534.

Write down where each digit would go, without drawing the blocks.

METHOD 1

5 Hundreds + 3 Tens + 4 Units METHOD 2 5 × 100 + 3 × 10 + 4 × 1 METHOD 3 500 + 30 + 4 These three methods are called expanded notation. When we write a number in expanded notation, we break down a number to show the place value of each digit.

Expanded notation ‘shows’ place value.

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Study Guide 1/2 G04 ~ Mathematics

Unit

ACTIVITY 3 1.

Question

Answer

Example

213

Two hundred and thirteen

1.1

495

1.3

463

1.4 1.5 2.

DATE:

Write the number names.

1.2

122 751 99

Write the numbers in the correct column in the place value table.

Question

Example

1

265

2.1

123

2.2

395

2.3

645

2.4

21

2.5

4

Answer

H

T

U

2

6

5

H

T

U

H

T

U

H

T

U

H

T

U

H

T

U

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Unit

3.

1

Study Guide 1/2 G04 ~ Mathematics

Write the numbers in expanded notation. Use all three methods.

Question

Answer

METHOD 1: 9H + 0T + 2U (You never have to write out Hundreds, Tens or Units.)

Example

902

METHOD 2: 9 × 100 + 2 × 1 (If there is a place value of 0, this does not have to be indicated.)

METHOD 3: 900 + 2 METHOD 1: 3.1

265

METHOD 2: METHOD 3: METHOD 1:

3.2

123

METHOD 2: METHOD 3: METHOD 1:

3.3

395

METHOD 2: METHOD 3: METHOD 1:

3.4

27

METHOD 2: METHOD 3: METHOD 1:

3.5

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METHOD 2: METHOD 3:

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Study Guide 1/2 G04 ~ Mathematics

4.

Give the value of the underlined numbers.

Question

Answer

Example

286

80

4.1

196

4.3

92

4.2 4.4 4.5

Unit

1

542 842 154

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Unit

5.

1

Study Guide 1/2 G04 ~ Mathematics

Board game: Roll the dice and move the correct number of squares along on the board.

Say the number of the block on which you land out loud. If you cannot say the number, move one block back. The first person to reach the finish block wins.

Start Finish

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Study Guide 1/2 G04 ~ Mathematics

1

Unit

Self-assessment Do you understand the work? Colour the faces that show what you can do.

PLACE VALUE Requirements

Can I do it?

I can break down numbers into Hundreds, Tens and Units.

I can give number names.

I can indicate place value.

I can do expanded notation (all three methods).

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

Comparing whole numbers When we compare numbers, we study the numbers to determine what is asked.

When you compare numbers, you must look at the value of the digits.

Compare the following numbers and circle the greatest number:

932

923

933

You already know how to compare numbers because you can order numbers. You also compare numbers when you complete sequences on number charts or number lines.

Example: Which whole numbers do the letters A and B represent?

25

A

29

31

B

Answer: A = 27 | B = 33 Example: Fill in the missing numbers on the number chart.

Answer:

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Study Guide 1/2 G04 ~ Mathematics

Unit

1

You can now compare numbers, say which number is the greatest and which is the smallest, and arrange them. But how do you indicate which number is the greatest or smallest without circling or underlining it?

We use symbols to indicate greater than, less than, and equal to.

The symbols are:

<;>;=

To remember which way around the < and > signs go, just remember:

BIG > small small < BIG

The ‘small’ end always points to the smaller number. The ‘big’ end always points to the greater number.

3

<

932

OR

457

When two values are equal, we use the = to show that they are the same.

874 = 874

25

>

125

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Unit

1

Study Guide 1/2 G04 ~ Mathematics

ACTIVITY 4 1.

DATE:

Compare and arrange the numbers. The symbols (< and >) show whether the numbers must be arranged from small to great or from great to small.

Question

89

1.1

453

1.2

16

1.3

782

1.4

35

1.5 2.

>

118

<

654

>

57

<

953

>

74

>

29

<

295

>

81

<

76

>

23

>

218

<

192

>

68

<

298

>

92

<

385

>

45

<

26

>

80

Provide the correct symbol (>, < or =) to indicate whether the following numbers are greater than, smaller than or equal to.

Question and answer

2.1

362 _____ 583

2.3

200 _____ 178

2.2 2.4 2.5 Š Impaq

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181

183 _____ 362 738 _____ 482 679 _____ 697 26

Study Guide 1/2 G04 ~ Mathematics

3.

1

Unit

Which whole numbers do the letters (A to G) represent?

Question

A 3.1

13

3.2

310

Answer

B

14

17

18

19

C 370 D

3.3

499

3.4

79

3.5

546

E 999

F 82

91

G 566

586

606

Self-assessment Do you understand the work? Colour the faces that show what you can do.

COMPARING WHOLE NUMBERS Requirements

Can I do it?

I can arrange number sets from great to small.

I can arrange number sets from small to great.

I can complete missing numbers (in sequence and on number charts and number lines).

I can use the correct symbols to indicate which numbers are greater than, smaller than or equal to other numbers (< , > or =).

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