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MATHEMATICS STUDY GUIDE 1/2

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Mathematics Study guide 1/2

1804-E-MAM-SG01

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Study Guide 1/2 G04 ~ Mathematics

CONTENTS LESSON ELEMENTS.......................................................................................................... 5 STUDY HINTS ..................................................................................................................... 6 YEAR PLAN ........................................................................................................................ 7 UNIT 1 ............................................................................................................................... 11 LESSON 1: WHOLE NUMBERS ...................................................................................... 12 Counting with whole numbers......................................................................................... 13 ACTIVITY 1 ................................................................................................................. 14 Ordering whole numbers ................................................................................................ 19 ACTIVITY 2 ................................................................................................................. 21 Place value ..................................................................................................................... 24 ACTIVITY 3 ................................................................................................................. 28 Comparing whole numbers ............................................................................................. 34 ACTIVITY 4 ................................................................................................................. 36 Representing whole numbers ......................................................................................... 39 ACTIVITY 5 ................................................................................................................. 40 LESSON 2: NUMBER SENTENCES ................................................................................ 41 ACTIVITY 6 ................................................................................................................. 42 ACTIVITY 7 ................................................................................................................. 43 ACTIVITY 8 ................................................................................................................. 45 Pairs of equivalent number sentences............................................................................ 49 ACTIVITY 9 ................................................................................................................. 50 Addition and subtraction techniques ............................................................................... 52 Commutative property of addition ................................................................................... 52 Associative property of addition ...................................................................................... 53 ACTIVITY 10 ............................................................................................................... 54 Order of subtraction ........................................................................................................ 56 ACTIVITY 11 ............................................................................................................... 56 LESSON 3: WHOLE NUMBERS ...................................................................................... 58 Addition with whole numbers .......................................................................................... 58 ACTIVITY 12 ............................................................................................................... 58 ACTIVITY 13 ............................................................................................................... 62 Subtraction of whole numbers ........................................................................................ 64 ACTIVITY 14 ............................................................................................................... 66 Estimation ....................................................................................................................... 73 ACTIVITY 15 ............................................................................................................... 76 Rounding ........................................................................................................................ 79 ACTIVITY 16 ............................................................................................................... 82 ACTIVITY 17 ............................................................................................................... 85 Compensation ................................................................................................................ 86 1

Study Guide 1/2 G04 ~ Mathematics

Doubling and halving ...................................................................................................... 87 ACTIVITY 18 ............................................................................................................... 88 ACTIVITY 19 ............................................................................................................... 91 Testing calculations with inverse operations .................................................................. 94 ACTIVITY 20 ............................................................................................................... 96 LESSON 4: NUMBER PATTERNS (Numeric patterns) ................................................. 98 ACTIVITY 21 ............................................................................................................. 100 Input and output values ................................................................................................ 101 ACTIVITY 22 ............................................................................................................. 102 ACTIVITY 23 ............................................................................................................. 104 ACTIVITY 24 ............................................................................................................. 105 The associative property of multiplication ..................................................................... 106 LESSON 5: WHOLE NUMBERS (Multiplication and division) ................................... 109 Multiplication ................................................................................................................. 109 ACTIVITY 25 ............................................................................................................. 118 Division ......................................................................................................................... 120 ACTIVITY 26 ............................................................................................................. 121 ACTIVITY 27 ............................................................................................................. 126 LESSON 6: TIME ............................................................................................................ 128 ACTIVITY 28 ............................................................................................................. 131 ACTIVITY 29 ............................................................................................................. 135 LESSON 7: DATA HANDLING ....................................................................................... 138 Collecting, organising, analysing and interpreting data ................................................ 138 Pictograph .................................................................................................................... 138 Pie chart ....................................................................................................................... 140 Bar chart ....................................................................................................................... 141 ACTIVITY 30 ............................................................................................................. 142 LESSON 8: PROPERTIES OF 2-D SHAPES ................................................................. 146 ACTIVITY 31 ............................................................................................................. 150 LESSON 9: WHOLE NUMBERS (Multiplication of 2-digit numbers and division of 2digit numbers by 1-digit numbers) ............................................................................... 152 ACTIVITY 32 ............................................................................................................. 153 ACTIVITY 33 ............................................................................................................. 155 ACTIVITY 34 ............................................................................................................. 159 UNIT 2 ............................................................................................................................. 162 LESSON 10: WHOLE NUMBERS .................................................................................. 163 Counting with whole numbers....................................................................................... 164 ACTIVITY 35 ............................................................................................................. 166 Â© Impaq

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Study Guide 1/2 G04 ~ Mathematics

Ordering whole numbers .............................................................................................. 169 ACTIVITY 36 ............................................................................................................. 171 Place values ................................................................................................................. 173 ACTIVITY 37 ............................................................................................................. 175 Comparing whole numbers ........................................................................................... 179 ACTIVITY 38 ............................................................................................................. 180 Representing whole numbers ....................................................................................... 183 ACTIVITY 39 ............................................................................................................. 184 Rounding ...................................................................................................................... 185 ACTIVITY 40 ............................................................................................................. 188 LESSON 11: WHOLE NUMBERS (Addition and subtraction) ..................................... 190 Commutative property of addition ................................................................................. 190 Associative property of addition .................................................................................... 191 Order of subtraction ...................................................................................................... 193 ACTIVITY 41 ............................................................................................................. 196 LESSON 12: COMMON FRACTIONS ............................................................................ 199 ACTIVITY 42 ............................................................................................................. 200 ACTIVITY 43 ............................................................................................................. 203 LESSON 13: LENGTH .................................................................................................... 209 ACTIVITY 44 ............................................................................................................. 211 LESSON 14: WHOLE NUMBERS (Multiply 2-digit numbers with 2-digit numbers) ........................................................................................................................ 215 Distributive property of multiplication ............................................................................ 217 Dividing numbers into factors to multiply them ............................................................. 217 ACTIVITY 45 ............................................................................................................. 218 LESSON 15: PROPERTIES OF 3-D OBJECTS ............................................................. 223 ACTIVITY 46 ............................................................................................................. 226 LESSON 16: GEOMETRIC PATTERNS ......................................................................... 231 ACTIVITY 47 ............................................................................................................. 233 LESSON 17: SYMMETRY............................................................................................... 237 ACTIVITY 48 ............................................................................................................. 238 LESSON 18: WHOLE NUMBERS (Addition and subtraction) ..................................... 241 ACTIVITY 49 ............................................................................................................. 241 LESSON 19: WHOLE NUMBERS (Dividing 3-digit numbers by 1-digit numbers) .... 247 ACTIVITY 50 ............................................................................................................. 251

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Study Guide 1/2 G04 ~ Mathematics

References: Unit 1 ......................................................................................................... 257 References: Unit 2 ......................................................................................................... 258

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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 it 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

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Study Guide 1/2 G04 ~ Mathematics

STUDY HINTS Many learners struggle with studying. They must learn how to study in an optimal manner so that they can get the best possible results in their examinations. Below are a few study hints to prepare learners for tests and examinations.

1. 2. 3. 4. 5. 6.

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Study Guide 1/2 G04 ~ Mathematics

YEAR PLAN UNIT 1 DATE STARTED

TOPIC

DATE COMPLETED

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

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Study Guide 1/2 G04 ~ Mathematics

UNIT 2 DATE STARTED

TOPIC 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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DATE COMPLETED

Study Guide 1/2 G04 ~ Mathematics

UNIT 3 DATE STARTED

TOPIC

DATE COMPLETED

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

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Study Guide 1/2 G04 ~ Mathematics

UNIT 4 DATE STARTED

TOPIC 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. ÂŠ Impaq

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DATE COMPLETED

Study Guide 1/2 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 Mental maths: Use the Train Your Brain Maths Grade 4 product

TIME AND NOTES 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

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

LESSON 1: WHOLE NUMBERS

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. Examples of whole numbers

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

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.

0,9

101

10

24

-24

0

198

3

-4,1

4

-2

13 9

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

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Study Guide 1/2 G04 ~ Mathematics

Unit

1

Counting with whole numbers In Grade 3 you learnt how to count with whole numbers. Can you still remember how to count in 2s? Letâ&#x20AC;&#x2122;s 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.

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

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Unit

Study Guide 1/2 G04 ~ Mathematics

1 ACTIVITY 1

1.

Write the set of whole numbers between 915 and 921. _________________________________________________________________ _________________________________________________________________

2.

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

Whole number: yes or no?

Example:

35 658 14,3 53 3 1 412

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Study Guide 1/2 G04 ~ Mathematics

1

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.

Example

3.

Unit

3;

13;

23;

3.1

96;

101;

106;

413;

410;

3.2

33;

43 ...

407;

...

3.3

8;

108;

308;

...

3.4

12;

9;

3;

0

3.5

10;

35;

60;

15

85;

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

4.

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

Number of bags

Andrew

Sibongile

Timmy

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Number of marbles

Study Guide 1/2 G04 ~ Mathematics

5.

Unit

1

Complete the flow charts.

5.1

5.2

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Unit

Study Guide 1/2 G04 ~ Mathematics

1 Self-assessment

After you have completed this topic, you should be able to do the following. Look at the requirements (the things you must be able to do) and colour the face that best describes your skill or ability. COUNTING IN WHOLE NUMBERS Requirements 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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Can I do it?

Study Guide 1/2 G04 ~ Mathematics

Unit

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.

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

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

You have now arranged the number set from largest to smallest. Can you arrange the following set of numbers from small

to large?

Tip: Start by choosing the smallest number, not the largest one. Write your answer in the box below.

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Study Guide 1/2 G04 ~ Mathematics

Unit

1

ACTIVITY 2

1.

Arrange the numbers from small to large. Question

2.

1.1

321 645 256 782 127

1.2

56 72 201 114 98

1.3

724 568 147 274 355

1.4

65 34 12 47 71

1.5

527 471 298 638 138

Arrange the numbers from large to small. Question 2.1

620 541 635 514 623

2.2

36 48 21 65 57

2.3

116 98 53 76 110

2.4

58 39 44 28 13

2.5

457 325 147 471 352

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

3.

Build and arrange.

Example

Question

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Write down the numbers that you can build from 6, 3 and 2. Arrange them from small to large.

3.1

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

3.2

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

3.3

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

3.4

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

3.5

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

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236; 263; 326; 362; 623; 632

Study Guide 1/2 G04 ~ Mathematics

Unit

1

Self-assessment After you have completed this topic, you should be able to do the following. Look at the requirements (the things you must be able to do) and colour the face that best describes your skill or ability. ORDERING WHOLE NUMBERS Requirements

Can I do it?

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.

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

Place value

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 values 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.

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 and into the next box.

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Study Guide 1/2 G04 ~ Mathematics

Hundreds

Unit

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. Letâ&#x20AC;&#x2122;s see what happens when the number becomes 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 now jumps over the wall into the Tens box.

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Unit

Study Guide 1/2 G04 ~ Mathematics

1

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

Hundreds

Tens

Units

10

3

1 × ten means 1 × 10 = 10

If you want to indicate the place value of 13, it will look like this:

Hundreds

Tens

Units

1

3

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

Hundreds

Tens

Units

84

2

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Study Guide 1/2 G04 ~ Mathematics

Unit

1

Since the 8 in the Tens box indicates 800, it must jump over to the Hundreds box. Now it means 8 x 100 = 800.

Hundreds

Tens

Units

8

4

2

It is not always as easy or possible to draw boxes to determine place value and it can take a lot of time. There are a number of 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

METHOD 3

5 × 100 + 3 × 10 + 4 × 1 500 + 30 + 4

These three methods are called expanded notation. When we write a number in expanded notation, we break apart each digit of a number to show the place value of each digit.

Expanded notation ‘shows’ place value.

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