Grade 5 Study Guide 2/2 Mathematics

Intermediate Phase Grade 5 • Study Guide 2/2

Mathematics Comprehensive explanations of concepts in simple language.

Practical, everyday examples with visuals and diagrams to help master concepts.

Learners work at their own pace.

Activities that test learners’ knowledge application and reasoning.

The facilitator’s guide contains step-by-step calculations and answers.

Use in school or at home.

CAPS IEB Mathematics

• • • • • •

home classroom college workplace

9 781990

946448

Study Guide 2/2

2005-E-MAM-SG02

5

Mathematics Study guide 2/2

CAPS aligned

M Vos L Young

2005-E-MAM-SG02

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Grade 5

Study Guide 2/2 G05 ~ Mathematics

Contents LESSON ELEMENTS..................................................................................................................................... 1 UNIT 3............................................................................................................................................................. 2 LESSON 19: COMMON FRACTIONS......................................................................................................... 3 ACTIVITY 42................................................................................................................................................3 LESSON 20: MASS........................................................................................................................................ 7 ACTIVITY 43................................................................................................................................................9

LESSON 21: WHOLE NUMBERS Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers)................................................................................13 ACTIVITY 44.............................................................................................................................................13 LESSON 22: WHOLE NUMBERS (Addition and subtraction).......................................................19 ACTIVITY 45.............................................................................................................................................19 LESSON 23: VIEWS OF OBJECTS............................................................................................................23 ACTIVITY 46.............................................................................................................................................25 LESSON 24: PROPERTIES OF 2D SHAPES...........................................................................................30 ACTIVITY 47.............................................................................................................................................31 LESSON 25: TRANSFORMATIONS.........................................................................................................34 ACTIVITY 48.............................................................................................................................................40 LESSON 26: TEMPERATURE...................................................................................................................45 ACTIVITY 49.............................................................................................................................................46 LESSON 27: DATA HANDLING................................................................................................................51 ACTIVITY 50.............................................................................................................................................52 LESSON 28: NUMBER PATTERNS (Numerical patterns)................................................................58 Input and output values.................................................................................................................................59 The associative property of multiplication............................................................................................61 Types of number sequences.........................................................................................................................64 ACTIVITY 51.............................................................................................................................................65 LESSON 29: WHOLE NUMBERS Multiplication (3-digit whole numbers by 2-digit whole numbers)..................................................................................................................................................................68 ACTIVITY 52.............................................................................................................................................68 UNIT 4...........................................................................................................................................................70 LESSON 30: WHOLE NUMBERS.............................................................................................................71 ACTIVITY 53.............................................................................................................................................71 i

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Study Guide 2/2 G05 ~ Mathematics

LESSON 31: WHOLE NUMBERS Addition and subtraction (5-digit whole numbers).........77 ACTIVITY 54.............................................................................................................................................77 Addition and subtraction of whole numbers........................................................................................77 LESSON 32: PROPERTIES OF 3D OBJECTS.........................................................................................81 ACTIVITY 55.............................................................................................................................................85 LESSON 33: COMMON FRACTIONS.......................................................................................................89 ACTIVITY 56.............................................................................................................................................89 LESSON 34: WHOLE NUMBERS Division (4-digit whole numbers by 2-digit whole numbers).....................................................................................................................................................91 ACTIVITY 57.............................................................................................................................................94

LESSON 35: PERIMETER, SURFACE AREA AND VOLUME..............................................................95 Perimeter..............................................................................................................................................................95 ACTIVITY 58.......................................................................................................................................... 101 Surface area...................................................................................................................................................... 104 ACTIVITY 59.......................................................................................................................................... 105 Volume................................................................................................................................................................ 107 LESSON 36: POSITION AND DISPLACEMENT................................................................................. 110 ACTIVITY 60.......................................................................................................................................... 111 LESSON 37: TRANSFORMATIONS...................................................................................................... 115 ACTIVITY 61.......................................................................................................................................... 115 LESSON 38: GEOMETRIC PATTERNS................................................................................................ 120 ACTIVITY 62.......................................................................................................................................... 120 LESSON 39: NUMBER SENTENCES.................................................................................................... 124 ACTIVITY 63.......................................................................................................................................... 124 LESSON 40: PROBABILITY................................................................................................................... 128 ACTIVITY 64.......................................................................................................................................... 130 References................................................................................................................................................ 135

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Study Guide 2/2 G05 ~ Mathematics

LESSON ELEMENTS The guide contains various lesson elements. Each element is important for the learning process and indicates the skill you must master.

ICON

LESSON ELEMENT

ICON

LESSON ELEMENT

Think for yourself

Take note! Important

Tips

Self-assessment

Research

Activity

Study

Did you know?

New concept or definition

Tip

Remember/Revise

1

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Unit

3

Study Guide 2/2 G05 ~ Mathematics

UNIT 3 This unit covers 19 to 29.

UNIT 3

TOPIC Mental maths: Use Train Your Brain Maths Grade 5 LESSON 19 Common fractions LESSON 20 Mass

LESSON 21 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers) LESSON 22 Whole numbers: Addition and subtraction LESSON 23 Views of objects

LESSON 24 Properties of 2D shapes LESSON 25 Transformations LESSON 26 Temperature

LESSON 27 Data handling

LESSON 28 Number patterns

LESSON 29 Whole numbers: Multiplication (3-digit whole numbers by 2-digit whole numbers) Revision: Use the CAMI programme

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Study Guide 2/2 G05 ~ Mathematics

Unit

3

LESSON 19: COMMON FRACTIONS In lesson 12, you learnt about common fractions and calculating with common fractions. Revise all the methods of working with fractions.

Before you compare or add any fractions, you must always make the denominators the same. When you multiply the denominator by a number, you must also multiply the numerator by the same number.

ACTIVITY 42 1.

DATE:

Complete the equivalent fractions.

1 1.1 ​​__ ​​ = ​​___ ​​ 3 15

________________________________________________________

1 1.2 ​​__ ​​ = ​​___ ​​ 2 10

________________________________________________________

3 21 1.3 ​​__ ​​ = ​​___ ​​ 7 

1.4

________________________________________________________ 2 ​​___ ​​ = ​​__ ​​ 18 3

________________________________________________________

8 32 1.5 ​​__ ​​ = ​​___ ​​ 9

________________________________________________________ 3

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Unit

2.

3

Study Guide 2/2 G05 ~ Mathematics

Use symbols (<; >; =) to show the relationship between the fractions.

4 2 2.1 ​​___ ​​ ______ ​​__ ​​ 10 5 10 2.2 ​​___ ​​ ______ __ ​​52 ​​ 8

2.3 2.4 3.

2 2​​__ ​​ ______ __ ​​73 ​​ 3

1 1​​__ ​​ ______ __ ​​54 ​​ 4

3 2.5 ​​__ ​​ ______ __ ​​12 ​​ 4

Calculate the fractions and write the answer in the simplest form.

3.1

3.2 3.3 3.4

3.5

3.6

3 2 __ ​​58 ​​– 1 ​​__ ​​ =  8

____________________________________________________________________________________________ 5 2 __ ​​14 ​​+ 2 ​​__ ​​ =  8

____________________________________________________________________________________________ 3 7 8 ___ ​​10 ​​– 3 ​​__ ​​ =  5

____________________________________________________________________________________________ 3 1 9 __ ​​78 ​​– (3 ​​__ ​​+ 1 ​​__ ​​) =  4 2

____________________________________________________________________________________________ ____________________________________________________________________________________________ 2 6 ___ ​​43 ​​– (2 __ ​​12 ​​+ 1 ​​__ ​​) =  6

____________________________________________________________________________________________ ____________________________________________________________________________________________ 10 3 (5 __ ​​46 ​​+ 3 ​​___ ​​) – 4 ​​__ ​​ =  4 12

____________________________________________________________________________________________ ____________________________________________________________________________________________

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Study Guide 2/2 G05 ~ Mathematics

3

Unit

5 __ 3 3.7 ​​___ ​​+ ​​5 ​​+ ​​__ ​​ =  12 6 4

4.

____________________________________________________________________________________________

Indicate the type of fraction (proper fraction, improper fraction or mixed number).

4.1

1 __ ​​23 ​​

_________________________________________________

4.3

3 __ ​​15 ​​

_________________________________________________

5 4.2 ​​__ ​​ 2

5.

5 4.4 ​​___ ​​ 6

_________________________________________________ _________________________________________________

Write the fractions as a mixed number in the simplest form.

5 5.1 ​​__ ​​ = _________________ 3 6 5.2 ​​__ ​​ = _________________ 4 7 5.3 ​​__ ​​ = _________________ 5 5 5.4 ​​__ ​​ = _________________ 2

6.

13 5.5 ​​___ ​​ = _________________ 8

Read the scenarios and answer the questions in your exercise book.

2 6.1 Thabang wants to go on holiday. He can take leave for ​​__ ​​of the month. If the month 3 has 30 days, how many days’ leave can he take?

6.2 Thabang has decided on his holiday destination. He will get there by train, which 1 2 will take him 5 ​​__ ​​ hours. If he goes by aeroplane, it will take him only 2 ​​__ ​​ hours.

3 5 How many hours will Thabang save if he takes the plane?

6.3 Thabang decides to take the plane to save time. Unfortunately, the flight is delayed 5 by 1 ​​__ ​​hours. How long did the flight actually take him?

6

1 6.4 Thabang bought 6 gifts for his family and friends. Each gift takes up ___ ​​15 ​​ of his suitcase. If he has 2 suitcases, how much space is left for his own luggage?

6.5 Lerato and her mom are making pancakes. They want to increase the recipe to 3 1 make more pancakes. Her mom’s recipe uses ​​__ ​​ of a cup of water for every ​​__ ​​ of a 4 4 cup of flour. How much water do they need if they want to use 1 cup of flour?

5

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Unit

7.

3

Study Guide 2/2 G05 ~ Mathematics

Which fraction is greater:

6 2 7.1 ​​__ ​​of a kilogram or ​​__ ​​of a kilogram?

8 3

____________________________________________________________________________________________

9 3 7.2 ​​___ ​​of a litre or ​​__ ​​of a litre?

4 12

____________________________________________________________________________________________

4 7.3 ​​___ ​​of an hour or __ ​​13 ​​of an hour?

6

____________________________________________________________________________________________

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

COMMON FRACTIONS Requirements I can indicate common fractions on a diagram.

I can compare and indicate the relationships of common fractions.

I can calculate equivalent fractions.

I can do calculations with fractions (addition of fractions).

I can solve fraction sums with calculations.

I can convert between improper fractions and mixed numbers.

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Can I do it?

Study Guide 2/2 G05 ~ Mathematics

Unit

3

LESSON 20: MASS

Mass measures the quantity of matter (particles) in an object.

For example, a gold bar is the same size as a box of Smarties (53 mm × 118 mm × 8 mm) but has a mass of 1 kg. This means the gold bar has a higher particle density, or more particles, than the box of Smarties.

It is important to remember that mass and weight are not the same, even though mass is used to describe weight. The weight of an object is determined by gravity, while mass is a constant determined by its number of particles. Out in space, where there is no gravity, a brick will have no weight, but its mass will be the same in space and on earth.

Mass is measured in gram (g), kilogram (kg) and ton (t). In Grade 5, we only work with gram and kilogram.

You worked with mass in Grades 3 and 4. Revise what you know about mass.

How do you measure mass?

We use different measuring instruments to determine mass.

Measuring instruments

Bathroom scale

Kitchen scale 7

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Unit

3

Study Guide 2/2 G05 ~ Mathematics

Balancing scale

We measure mass in kilogram and gram.

Kilogram (kg) Gram (g) You use kilogram when measuring objects heavier than 1 000 g. Smaller objects with a mass of less than 1 kg are measured in grams.

When you convert between gram and kilogram, remember that there are 1 000 g in every 1 kg.

Use the diagram below to help with the conversion between gram and kilogram.

kilogram (kg)

× 1 000 ÷ 1 000

gram (g)

Example Convert 8 153 g from gram (g) to kilogram (kg). = 8 153 g ÷ 1 000 = 8,153 kg (Remember: 8,153 kg is 8 kg 153 g – that is 8 full kilograms and 153 grams that are not enough to make up a full kilogram, therefore, the 153 comes after the comma.)

Revise the conversion of volume in lesson 9. To simplify the calculations, you can picture a comma at the end of the number.

When you divide by 1 000, move the imaginary comma three place values to the left (because there are three zeros in 1 000). © Impaq

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Study Guide 2/2 G05 ~ Mathematics

Unit

3

When you multiply by 1 000, move the imaginary comma three place values to the right (because there are three zeros in 1 000).

8 1 5 3 , g ÷ 1 0 0 0 = 8 , 1 5 3 kg

Convert the following mass to gram.

4 kg × 1 000 = 4 000 g

Use the imaginary comma and three zeros after the whole number.

There are three zeros because you are multiplying by 1 000.

It is important to first write a comma and then the zeros.

4 , 0 0 0 kg × 1 0 0 0 = 4 0 0 0 g When we work with or compare units of measurement, they must always be the same units.

ACTIVITY 43 1.

DATE:

Read the mass on each scale and give the answer in g or kg.

1.1

1.2

Cookies

4,5 900

0 g

200

700

300

600

500 1

4

100

800

0 kg

3,5

1,5 3

2 2,5

400 500

___________________________________

___________________________________ 9

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Unit

3

Study Guide 2/2 G05 ~ Mathematics

1.3

1.4 0 kg

1,8

200

1,6

400

1,4

600 1,2

0 kg

1,8

800 1

200

1,6

400

1,4

600 1,2

800 1

2.

___________________________________

Indicate the mass of the objects on the scales.

2.1

___________________________________

2.3 3,625 kg

4,75 kg

4,5

0 kg

9

1

8

4

2.2 175 g

0 g

100 200

800 700

300

600

400 500

3.

Calculate the mass.

3.1

The mass of each © Impaq

2 2,5

5

900

1,5 3

3 6

500 1

3,5

2

7

0 kg

4

= ______ g 10

Study Guide 2/2 G05 ~ Mathematics

Unit

3

3.2

4.

The mass of each

Convert the mass from kilogram to gram, or from gram to kilogram.

4.1

3 kg = _________ g

4.4

954 kg = _________ g

4.2 4.3 4.5 4.6 4.7 4.8 4.9 5.

= ______ kg

5 315 g = _________ kg 87,23 kg = _________ g 5,20 kg = _________ g

3 019 g = _________ kg

3 kg 16 g = _________ g 7,05 kg = _________ g

2 kg 134 g = _________ kg

4.10 1 kg 5 216 g = _________ kg _________ g Do the sums with mass.

5.1

6 kg + 750 g + 250 g = _________ kg

5.4

250 g × 5 = _________ g = _________ kg _________ g

5.2 5.3 5.5 5.6 5.7

15 kg – 750 g = _________ kg 150 g × 5 = _________

3 kg + 200 g + 600 g + 1,6 kg = _________ kg

The difference between 3 kg 35 g and 1 kg 70 g. _________ 475 kg ÷ 25 = _________ kg

2 5.8 ​​__ ​​of 1,5 kg = _________ kg 3

6.

5.9

3 kg 125 g × 9 = _________ kg

Write the masses in descending order.

6.1 6.2

700 g

3 kg

2 600 g

0,8 kg

____________________________________________________________________________________________ 4 500 g

4 kg

4 kg 200 g

4,45 kg

____________________________________________________________________________________________ 11

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Unit

7.

3

Study Guide 2/2 G05 ~ Mathematics

Study the table and answer the questions.

Rolene and her mom buy the following ingredients to bake a cake:

Ingredient 1

Ingredient 2

Ingredient 3

Ingredient 4

Ingredient 5

Ingredient 6

1 orange

150 g butter

1 500 g flour

2 500 g sugar

5 g salt

450 g jam

Ingredient 7 0,1 kg

chocolate

7.1

Which ingredients weigh less than 1 kg? ______________________________________________

7.3

Which two ingredients weigh 250 g altogether? ______________________________________

7.2

7.4

Which ingredients weigh more than 2 kg? ____________________________________________

Arrange the masses of the ingredients in ascending order (do not include the orange).

____________________________________________________________________________________________

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

MASS Requirements

Can I do it?

I can determine the mass of practical objects by estimating and measuring.

I know the different measuring instruments and can take readings from them.

I know the units of measurement for mass and can use them.

I can solve problems of mass in context.

I can convert between kilogram and gram.

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Study Guide 2/2 G05 ~ Mathematics

Unit

3

LESSON 21: WHOLE NUMBERS

Counting, ordering, comparing and representing, and place value of digits (6-digit whole numbers) This lesson again covers whole numbers. In terms 1 and 2, you studied whole numbers quite comprehensively, but revise lesson 1 if you need to refresh your memory.

Whole numbers do not have fractions or decimals. Whole numbers are always positive and never negative. Remember: 0 is also a whole number.

A set of whole numbers: {0; 1; 2; 3; 4; ...}

You must be able to do the following with whole numbers: • • • • • • • • •

Count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s Do calculations with 6-digit numbers (you have not worked with 6-digit numbers before) Arrange number sets Build and arrange different numbers Break down numbers into place values Give number names Indicate place values Use expanded notation (all three methods) Compare whole numbers

Do you still remember place value? You studied the place values of 4-digit numbers in lesson 1. In this lesson, we will work with 6-digit numbers.

ACTIVITY 44

DATE:

1.

Give the set of whole numbers between 613 546 and 613 553.

2.

Are the numbers whole numbers? Only write 'whole number' or 'not a whole number'.

____________________________________________________________________________________________

2.1

123 123 ___________________________________

2.3

-952 312 ___________________________________

2.2

0 ___________________________________

9 2.4 ​​_________ ​​ ___________________________________ 136 546

2.5 2.6

124 622 ___________________________________

9,133 ___________________________________ 13

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Unit

3.

3 Fill in the missing number to complete the number patterns.

3.1

12 232; 12 234; _______________; 12 238

3.4

7; 14; _______________; 28; 35

3.2 3.3 3.5 3.6 4.

Study Guide 2/2 G05 ~ Mathematics

3.7

100 103; 100 100; _______________ 52; 44; 36; _______________; 20

102; 204; 408; _______________

13 770; _______________; 1 530; 510

45; 225; _______________; 5 625; 28 125

Do the calculations to complete the diagrams.

4.1

100 029

6 12 9

4.2

4.3

100 019 +

7

1

4

8 2 5

42 221 – 20 = _________________________

270 023

8 12 11 3

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11 10 3

4

6

13

270 027 –

10 1 2

5 7 9

14

Study Guide 2/2 G05 ~ Mathematics

Unit

3

4.4

Rule: ______________________________________

4.5

5.

Arrange the numbers as shown in brackets. (‘Descending’ means from great to small and ‘ascending’ means from small to great.)

5.1 5.2 5.3 5.4

340 034; 304 043; 340 340; 430 040; 430 004 (Descending)

____________________________________________________________________________________________ 609 229; 69 929; 609 292; 690 229; 69 292 (Descending)

____________________________________________________________________________________________ 733 533; 735 553; 733 353; 735 535; 735 335 (Ascending)

____________________________________________________________________________________________ 980 001; 99 800; 988 101; 980 010; 980 100 (Ascending)

____________________________________________________________________________________________ 15

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Unit

6.

3 Study the digits 6.1 6.2 6.3 6.4

7.

Study Guide 2/2 G05 ~ Mathematics

5 1 8 9 6 1

Write the largest number you can make with these digits.

____________________________________________________________________________________________ Write the number name of the number you made in 6.1.

____________________________________________________________________________________________ Write the smallest number you can make with these digits.

____________________________________________________________________________________________ Write the number name of the number you made in 6.3.

____________________________________________________________________________________________

Study the number:

712 054

7.1

What is the numerical value of the 2? __________________________

7.3

What is the place value of the 0? ___________________________

7.2 7.4 7.5 7.6

What is the numerical value of the 5? __________________________ What is the place value of the 7? ____________________________ What is the place value of the 4? ____________________________

Write the number in expanded notation (in all three methods).

Method 1

____________________________________________________________________________________________ Method 2

____________________________________________________________________________________________ Method 3

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Study Guide 2/2 G05 ~ Mathematics

7.7

10 000 less than 421 458 is _________________________________.

7.9

100 000 less than 421 458 is _________________________________.

7.8 8.

3

100 more than 421 458 is _________________________________.

Compare the numbers with <,> or =.

8.1

383 565 ______ 383 656

8.3

727 989 ______ 721 999

8.2 8.4 8.5 9.

Unit

945 939 ______ 954 293 465 283 ______ 456 283 103 419 ______ 103 419

Morison is planning his birthday party. He compares the prices of food and snacks at a few shops. His favourite chips are chutney flavoured and he finds the following price options:

Frimax chips Simba chips (48 × 30 g) (1 × 125 g) R139,95 R14,95 9.1

How many packets of Frimax chips are needed to make up 1 packet of Simba chips? ____________________________________________________________________________________________

9.2

____________________________________________________________________________________________

About how much will 1 packet of Frimax chips cost? Tip: First round off the total amount to the nearest whole number. ____________________________________________________________________________________________ ____________________________________________________________________________________________ 17

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Unit

3 9.3

9.4

Study Guide 2/2 G05 ~ Mathematics

Will it be cheaper to buy a few packets of Simba chips or to buy the Frimax chips? ____________________________________________________________________________________________ ____________________________________________________________________________________________

Which option would you choose? Give a reason for your answer.

____________________________________________________________________________________________ ____________________________________________________________________________________________

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

WHOLE NUMBERS Requirements I can count on and back in 2s, 3s, 5s, 10s, 25s, 50s and 100s.

I can work with 6-digit whole numbers.

I can arrange number collections in descending and ascending order.

I can build and arrange different numbers.

I can break down numbers into place values.

I can give number names.

I can indicate place value.

I can do expanded notation (all three methods).

I can use symbols (<, > or =) to compare whole numbers.

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Can I do it?

Study Guide 2/2 G05 ~ Mathematics

Unit

3

LESSON 22: WHOLE NUMBERS (Addition and subtraction) In this lesson you will practise adding and subtracting 5-digit numbers. Revise lesson 3 if you need to refresh your memory.

Make sure you can use these techniques when you do calculations for written work and mental maths: 1.

2.

3.

4.

5.

6.

7.

Breaking down numbers Writing numbers underneath one another Writing numbers next to each other Estimation Rounding Compensating Doubling and halving (remember the new method of breaking down numbers)

Also remember that addition and subtraction are inverse operations of one another and you can use the inverse operations to test your answer.

ACTIVITY 45

DATE:

Addition and subtraction of whole numbers 1.

Break down the numbers to complete the addition and subtraction sums. Do the sums in your exercise book.

2.

1.1 1.2 1.3 1.4 1.5

43 120 + 2 572 8 293 + 12 123 41 542 + 32 121 45 852 + 23 628 50 213 + 17 450

1.6 1.7 1.8 1.9 1.10

1 215 – 1 103 20 940 – 10 730 69 112 – 34 124 91 438 – 51 325 95 195 – 62 184

2.1 2.2 2.3 2.4 2.5

41 215 + 76 004 74 147 – 73 132 75 124 + 12 154 96 421 – 37 348 82 436 – 43 456

2.6 2.7 2.8 2.9 2.10

51 002 + 59 980 60 505 + 52 123 31 483 – 12 859 95 154 – 56 754 70 309 + 69 741

Use any valid method to do the calculations. Test your answers with the inverse operations (and show your test). Do the sums in your exercise book.

19

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Unit

3.

3

Study Guide 2/2 G05 ~ Mathematics

Read the word sums, write down the appropriate number sentence and calculate the answer. Do the sums in your exercise book.

3.1

3.2

3.3

3.4

Tiana and Briana find a scale in the garage. The scale measures in pounds (like in America), not kilograms. Tiana’s dad weighs himself on the scale and gets a reading of 194 pounds. Briana and Tiana get on the scale together and it shows a reading of 273 pounds. How many pounds more do Tiana and Briana weigh than Tiana’s dad?

Ellis sells toffee apples. He makes 12 456 toffee apples to sell in a week. On Monday he sells 1 456. On Tuesday he sells 1 356. On Wednesday and Thursday, he sells an equal number – 2 516 per day – and on Friday he sells 3 002 toffee apples. Does he have enough toffee apples left to sell at least 3 500 on Saturday?

Kiara and her friends pick up litter on the playground. Kiara picks up 54 pieces of rubbish. Phia picks up 63 pieces, and Riana and Kabelo pick up 59 pieces. Simon also picks up litter. If they collect 297 pieces of rubbish altogether, how many pieces did Simon pick up?

Thabiso and his brother Samuel are training for cross-country season and follow a specific training programme. The programme recommends that athletes who are not fit yet must do the following: in week 1, run 7 km per day; in week 2, they 1 must run 1 ​​__ ​​ times the distance per day; in week 3 they must run double as far; 2 and in week 4, double the distance of week 2. How many kilometres did Thabiso and Samuel run in a month if the month had 4 weeks and they trained for 6 days a week?

Estimation 4.

Estimate whether you have enough fuel in your car to travel the given distances. Do the sums in your exercise book.

4.1 4.2 4.3

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From Piketberg to Springbok. You have enough fuel for 420 km.

From Vanrhynsdorp to Malmesbury. You have enough fuel for 240 km.

From Keetmanshoop in Namibia to Vanrhynsdorp. You have enough fuel for 650 km.

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Study Guide 2/2 G05 ~ Mathematics

5.

3

Unit

Use estimation to solve the word sums. Do the sums in your exercise book.

5.1 5.2

5.3

Every day PostNet receives 12 452 parcels to courier. 451 parcels are insured.

Determine how many parcels are not insured.

CJ’s family enjoys camping and visits the Almega campsite in Dinokeng over the weekend. Almega is 71,2 km away. The campsite manager tells them that Mystic Monkeys is not far, so they decide to drive there on Saturday. CJ’s dad resets the car’s odometer and measures the distance from Almega to Mystic Monkeys as 23,7 km. Estimate how far CJ and his family drove from their house and back again over the weekend.

Andrea wants to buy her friend a gift, but she must buy the essentials on her shopping list: • Shampoo: R67,00 • Perfume: R675,25 • Jacket: R230,95 • Colour pens: R199,95

She wants to buy her friend a watch:

If Andrea gets R1 200 pocket money, will she have enough money to buy her friend a gift? Use estimation.

Doubling and halving 6.

Double the numbers. You may use any method. Do the sums in your exercise book.

7.

6.1 6.2 6.3

520 6.4 5 625 6.5 12 856

54 899 63 125

7.1 72 7.3

15 966 7.4 10 568 7.5 12 322

98 560 85 626

Halve the numbers. You may use any method. Do the sums in your exercise book.

21

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Unit

3

Study Guide 2/2 G05 ~ Mathematics

Rounding 8.

Round the numbers to the nearest 5, 10, 100 and 1 000.

Number

8.1

405

8.3

27

8.2

732

8.6

2 125

429

8.7

15 956

8.9

19 999

8.8 8.10

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Rounded to the nearest 10

458

8.4 8.5

Rounded to the nearest 5

21 156 10 211

22

Rounded to the nearest 100

Rounded to the nearest 1 000

Study Guide 2/2 G05 ~ Mathematics

3

Unit

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

WHOLE NUMBERS Requirements

Can I do it?

I can add and subtract with whole numbers.

I can break down numbers as a method of addition and subtraction of whole numbers.

I can write an appropriate number sentence.

I can estimate whole numbers.

I can work with money, distance and time (estimation, rounding, addition and subtraction).

I can round numbers to the nearest 5, 10, 100 and 1 000.

I can double whole numbers.

I can halve whole numbers.

I can do inverse operations to test answers.

LESSON 23: VIEWS OF OBJECTS You studied views of objects in geography this year. Can you recognise and draw the different views of objects? Revise views of objects.

An object’s view is the direction from which you look at it.

We will work with these views: • Top view: Also called the plan view. What you see when you look at an object from directly above or from the TOP. • Side view: What an object looks like when you look at it from the SIDE. • Front view: What an object looks like when you look at it from the FRONT. 23

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Unit

3

Study Guide 2/2 G05 ~ Mathematics

Your facilitator will show you a video that explains the different views.

Examples The different views of a bottle of flavoured water.

Front view

The different views of a figurine.

Front view

The different views of a tub of clay.

Front view

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Side view

Top view

Side view

Top view

Side view

Top view

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