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Intermediate Phase Grade 6 • 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

• • • • • •

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Study Guide 2/2

2106-E-MAM-SG02

Mathematics Study guide 2/2 Grade 6

2106-E-MAM-SG02

9 781990

946509

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Study Guide 2/2 G06 ~ Mathematics

Contents LESSON ELEMENTS.....................................................................................................................................1 YEAR PLAN....................................................................................................................................................2 FACT SHEET...................................................................................................................................................6 UNIT 3..........................................................................................................................................................19 LESSON 17: MASS..................................................................................................................................... 20 Units of mass....................................................................................................................................................21 Measuring mass...............................................................................................................................................21 ACTIVITY 47.............................................................................................................................................25 Comparing and ordering mass..................................................................................................................27 ACTIVITY 48.............................................................................................................................................28 Converting between measuring units....................................................................................................30 Rounding mass................................................................................................................................................32 ACTIVITY 49.............................................................................................................................................33 LESSON 18: WHOLE NUMBERS............................................................................................................ 35 Counting, ordering, comparing, representing and place value of 9-digit whole numbers..............................................................................................................................................................35 ACTIVITY 50.............................................................................................................................................35 LESSON 19: WHOLE NUMBERS – ADDITION AND SUBTRACTION............................................ 37 Adding and subtracting 6-digit whole numbers...............................................................................37 ACTIVITY 51.............................................................................................................................................39 Calculators.........................................................................................................................................................42 ACTIVITY 52.............................................................................................................................................43 LESSON 20: VIEWS OF OBJECTS........................................................................................................... 45 ACTIVITY 53.............................................................................................................................................47 LESSON 21: PROPERTIES OF 2D SHAPES.......................................................................................... 51 Rectangles and parallelograms.................................................................................................................54 Properties of a circle.....................................................................................................................................55 ACTIVITY 54.............................................................................................................................................59 LESSON 22: TRANSFORMATIONS........................................................................................................ 61 Using transformations to describe patterns.......................................................................................63 Using symmetry to describe patterns....................................................................................................64 ACTIVITY 55.............................................................................................................................................65 LESSON 23: TEMPERATURE.................................................................................................................. 70 Measuring instruments................................................................................................................................71 ACTIVITY 56.............................................................................................................................................73 i

Study Guide 2/2 G06 ~ Mathematics

LESSON 24: PERCENTAGES.................................................................................................................... 76 Equivalent forms of percentages.............................................................................................................78 ACTIVITY 57.............................................................................................................................................81 Arranging percentages, fractions and decimal fractions...............................................................84 ACTIVITY 58.............................................................................................................................................84 Percentage of a number...............................................................................................................................85 ACTIVITY 59.............................................................................................................................................87 LESSON 25: DATA HANDLING............................................................................................................... 90 ACTIVITY 60.............................................................................................................................................91 Analysing and interpreting data...............................................................................................................93 ACTIVITY 61.............................................................................................................................................96

LESSON 26: NUMERIC PATTERNS........................................................................................................ 99 Determining the rule.....................................................................................................................................99 ACTIVITY 62..........................................................................................................................................100 Flow diagrams with two rules...............................................................................................................102 ACTIVITY 63..........................................................................................................................................103 LESSON 27: LENGTH..............................................................................................................................106 Units of length (or distance)...................................................................................................................106 Measuring instruments.............................................................................................................................106 Comparing and ordering length............................................................................................................108 ACTIVITY 64..........................................................................................................................................108 Converting between measuring units.................................................................................................111 Rounding length...........................................................................................................................................115 ACTIVITY 65..........................................................................................................................................115 UNIT 4........................................................................................................................................................118

LESSON 28: WHOLE NUMBERS..........................................................................................................119 Reading and saying 9-digit whole numbers.....................................................................................119 ACTIVITY 66..........................................................................................................................................119 Place value of 9-digit whole numbers.................................................................................................120 ACTIVITY 67..........................................................................................................................................121 Comparing and ordering 9-digit whole numbers..........................................................................122 ACTIVITY 68..........................................................................................................................................122 LESSON 29: WHOLE NUMBERS – MULTIPLICATION....................................................................125 Properties of multiplication....................................................................................................................125 Quick ways of doing multiplication.....................................................................................................127 Multiples, factors and prime factors....................................................................................................128 ACTIVITY 69..........................................................................................................................................129 Calculation techniques..............................................................................................................................130 ACTIVITY 70..........................................................................................................................................132 © Optimi

Study Guide 2/2 G06 ~ Mathematics

Problem-solving...........................................................................................................................................133 ACTIVITY 71..........................................................................................................................................133

LESSON 30: COMMON FRACTIONS....................................................................................................135 Simplifying and ordering fractions......................................................................................................135 ACTIVITY 72..........................................................................................................................................137 Equivalents of fractions, decimal fractions and percentages...................................................139 ACTIVITY 73..........................................................................................................................................141 Calculations with fractions......................................................................................................................143 ACTIVITY 74..........................................................................................................................................145 LESSON 31: PROPERTIES OF 3D OBJECTS......................................................................................147 Properties of 3D objects...........................................................................................................................149 ACTIVITY 75..........................................................................................................................................151 Nets and models of 3D objects...............................................................................................................155 ACTIVITY 76..........................................................................................................................................157 LESSON 32: PERIMETER, AREA AND VOLUME..............................................................................161 Perimeter and area.....................................................................................................................................161 Measuring perimeter with a ruler and tape measure..................................................................163 Diagonals.........................................................................................................................................................165 Area of a rectangle.......................................................................................................................................166 Relation between the perimeter and area of rectangles and squares..................................167 ACTIVITY 77..........................................................................................................................................169 Volume..............................................................................................................................................................172 ACTIVITY 78..........................................................................................................................................173 ACTIVITY 79..........................................................................................................................................177 Relation between the area and volume of a rectangular prism...............................................179 LESSON 33: THE HISTORY OF MEASUREMENT.............................................................................181 How length, mass and volume were measure in the past..........................................................181 How time was measured in the past...................................................................................................183 ACTIVITY 80..........................................................................................................................................184 LESSON 34: WHOLE NUMBERS – DIVISION....................................................................................185 Rules of divisibility......................................................................................................................................185 Using multiplication to do division – clue board...........................................................................186 Long division.................................................................................................................................................187 ACTIVITY 81..........................................................................................................................................188 Ratio and rate................................................................................................................................................189 ACTIVITY 82..........................................................................................................................................190 LESSON 35: NUMBER SENTENCES....................................................................................................192 ACTIVITY 83..........................................................................................................................................194 iii

Study Guide 2/2 G06 ~ Mathematics

LESSON 36: TRANSFORMATIONS......................................................................................................196 Enlargement and reduction....................................................................................................................197 ACTIVITY 84..........................................................................................................................................199 LESSON 37: POSITION AND DIRECTION.........................................................................................205 Using alpha-numeric grid references to determine location on a grid/map.....................205 Giving directions..........................................................................................................................................207 ACTIVITY 85..........................................................................................................................................208 LESSON 38: PROBABILITY...................................................................................................................212 Identifying possible outcomes...............................................................................................................213 Counting and comparing the regularity of actual outcomes.....................................................213 ACTIVITY 86..........................................................................................................................................215 IMAGE REFERENCES..............................................................................................................................217

Study Guide 2/2 G06 ~ Mathematics

LESSON ELEMENTS The guide containts various lesson elements. Each element is important for the learning process. ICON

LESSON ELEMENT

ICON

Think for yourself

LESSON ELEMENT

Remember or revise

Take note! or

Tips

Important

Research

Self-assessment

Study

Activity

New concept or

Did you know?

definition

Study Guide 2/2 G06 ~ Mathematics

YEAR PLAN UNIT 1 DATE STARTED

TOPIC

Mental maths: Use Train Your Brain Maths Grade 6

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 (5-digit whole numbers) Lesson 4 Common fractions Lesson 5 Time

Lesson 6 Properties of 2D shapes Lesson 7 Data handling

Lesson 8 Number patterns (numeric patterns) Revision: Use the CAMI program

DATE COMPLETED

Study Guide 2/2 G06 ~ Mathematics

UNIT 2 DATE STARTED

TOPIC

DATE COMPLETED

Mental maths: Use Train Your Brain Maths Grade 6

Lesson 9 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (9-digit whole numbers) Lesson 10 Whole numbers: Multiplication (4-digit whole numbers by 2-digit whole numbers) Lesson 11 Properties of 3D objects Lesson 12 Geometric patterns Lesson 13 Symmetry

Lesson 14 Whole numbers: Division (4-digit whole numbers by 2-digit whole numbers) Lesson 15 Decimal fractions Lesson 16 Capacity/Volume

Revision: Use the CAMI program

Study Guide 2/2 G06 ~ Mathematics

UNIT 3 DATE STARTED

TOPIC Mental maths: Use Train Your Brain Maths Grade 6 Lesson 17 Mass

Lesson 18 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (9-digit whole numbers) Lesson 19 Whole numbers: Addition and subtraction (6-digit whole numbers) Lesson 20 Viewing objects

Lesson 21 Properties of 2D shapes Lesson 22 Transformations Lesson 23 Temperature Lesson 24 Percentages

Lesson 25 Data handling

Lesson 26 Numeric patterns Lesson 27 Length

Revision: Use the CAMI program © Optimi

DATE COMPLETED

Study Guide 2/2 G06 ~ Mathematics

UNIT 4 DATE STARTED

TOPIC

DATE COMPLETED

Mental maths: Use Train Your Brain Maths Grade 6

Lesson 28 Whole numbers: Counting, ordering, comparing and representing, and place value of digits (9-digit whole numbers) Lesson 29 Whole numbers: Multiplication (4-digit whole numbers by 3-digit whole numbers) Lesson 30 Common fractions

Lesson 31 Properties of 3D objects

Lesson 32 Perimeter, area and volume

Lesson 33 The history of measurement

Lesson 34 Whole numbers: Division (4-digit whole numbers by 3-digit whole numbers) Lesson 35 Number sentences Lesson 36 Transformations

Lesson 37 Position and direction Lesson 38 Probability

Revision: Use the CAMI program 5

Study Guide 2/2 G06 ~ Mathematics

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

•

All numbers that are divisible by 2 without a remainder. Even number end with 2, 4, 6, 8 or 0.

•

• •

Alternative words used for operations

Uneven numbers

All numbers that are not divisible by 2 without a remainder. Odd numbers end with 1, 3, 5, 7 or 9.

Addition Add

More than

Add to

Sum of

Plus

Increase by

In total

Subtraction

Decrease by

Left

Less than

Less

Take away

Altogether

Deduct

Left over

Fewer than

Division

Divide

Halve

Difference between/of

Total of

Minus

Percent

Divide equally

How many times

Quotient

Half of

Per

Multiplication

Split into

Double

Times

Goes into

Increase by a factor of Multiply by

And

Out of

Product of 6

Ratio of

Twice

Study Guide 2/2 G06 ~ Mathematics

Useful definitions Term

Definition Example A factor is a number that can be Factor divided into another number without Factors of 24 = 1; 2; 3; 4; 6; 8; 12; 24 a remainder. The first 12 multiples of 6 = 6; 12; 18; Multiple Times tables 24; 30; 36; 42; 48; 54; 60; 66; 72 Prime Numbers with only two factors – The first 10 prime numbers = 2; 3; 5; number 1 and the number itself. 7; 11; 13; 17; 19; 23; 29 Prime factor Factors that are also prime numbers. The prime factors of 24 are 2 and 3.

Rounding

Round to the nearest 5

Numbers ending in 3, 4, 5, 6 and 7 are rounded to 5. Numbers ending in 1 and 2 are rounded to the previous 10 (end with a 0). Numbers ending in 8 and 9 are rounded to the next 10 (end with a 0). Round to the nearest 10

Numbers smaller than 5 are rounded to the previous 10 (end with a 0). Numbers ending in 5, 6, 7, 8 and 9 are rounded to the next 10 (end with a 0). Example: Round 6 858 to the nearest 10. Th HTU 6 858

Look at the Tens column.

The ones column must help you decide (8 is greater than 5, therefore the number is rounded to the next ten and ends with a 0 the answer is 6 860.)

Study Guide 2/2 G06 ~ Mathematics

Round to the nearest 100

Numbers smaller than 5 are rounded to the previous 100 (end with a 0). Numbers ending in 5, 6, 7, 8 and 9 are rounded to the next 100 (end with a 0). Example: Round 6 858 to the nearest 100. Th HTU 6 858

Look at the Hundreds column.

The tens column must help you decide (5 and greater are rounded to the next 100 and end with a 0 the answer is 6 900.)

Apply the same method when you round to 1 000. (The Hundreds column must help you decide.) Properties/Laws Commutative law: Numbers may be added or multiplied together in any order. a + b = b + a 10 + 8 = 8 + 10 18 = 18

a×b=b×a 12 × 3 = 3 × 12 36 = 36

Associative law: When you add or multiply numbers together, it does not matter how the numbers are grouped. (a + b) + c = a + (b + c)

13 + 24 + 22 = 13 + 24 + 22 (13 + 24) + 22 = 13 + (24 + 22)

(a × b) × c = a × (b × c)

(37) + 22 = 13 + (46) 59 = 59

3×4×2=3×2×4 (3 × 4) × 2 = 3 × (2 × 4) (12) × 2 = 3 × (8) 24 = 24

Distributive law: The distributive law of multiplication means that you can break down one or all of the numbers in a multiplication sum, multiply them separately and add the products together. © Optimi

Study Guide 2/2 G06 ~ Mathematics

Regular method (5)(8) = 40 (4)(12) = 48 47 × 45 = 2 115

Common fractions

Distributive method 5(6 + 2) = (5 × 6) + (5 × 2) = 30 + 10 = 40

4(7 + 2 + 3) = (4 × 7) + (4 × 2) + (4 × 3) = 28 + 8 + 12 = 48 47 × 45 = 47 × (40 + 5) → Break down the number = 47 × 40 + (47 × 5) → Distributive property = 1 880 + 235 = 2 115

Numerator

1 4

Denominator

The top number (numerator) counts how many of the bottom number (denominator) there are. You can remember the difference by seeing that the denominator is down below. The denominator determines what we name the fraction, for example, quarters, eighths, etc. You may use a fractions wall to compare fractions.

Study Guide 2/2 G06 ~ Mathematics

Important: Before you compare or add fractions, you must always make the denominators the same. It means that you determine the Least Common Denominator (LCD). When you multiply the denominator by a number, you must also multiply the numerator by the same number. How to convert an improper fraction to a mixed number 16 3 1. 2. 3.

Divide the numerator with the denominator. Here it is 16 ÷ 3 = 5 rem. 1. Write down the whole number. Here it is 5. 1 Write the rest on the numerator, next to the whole number: 5__ . 3

How to convert a mixed number to an improper fraction =

Step 3

16 1 + Step 2 = 5 × =15 3 3 1. 2. 3.

Step 1

Multiply the whole number with the denominator. In the example it is 5 × 3 = 15. Add the answer of step 1 to the numerator. Here it is 15 + 1 = 16. Write the answer of step 2 on top of the denominator: __ 16 . 3

Decimal fractions

Equivalents They all have the same value 1 whole

1 = __ 1

1,0

100%

one half

1 = __ 2

0,5

50%

a quarter three quarters

1 = __ 4

3 = __ 4

0,25 0,75

= =

25% 75%

Study Guide 2/2 G06 ~ Mathematics

Rules of divisibility • • • • • • • • • • •

No number is divisible by 0. We say it is undefined. Any number is divisible by 1. A number is divisible by 2 if the last digit is an even number (2, 4, 6, 8 or 0). A number is divisible by 3 if the sum of the digits is a multiple of 3. A number is divisible by 4 if the last two digits is a multiple of 4. A number is divisible by 5 if the last digit is a 5 or a 0. A number is divisible by 6 if it is divisible by 2 and 3. A number is divisible by 7 if the three steps work (see below). A number is divisible by 8 if the last three digits are divisible by 8. A number is divisible by 9 if the sum of the digits is divisible by 9. A number is divisible by 10 if the number ends with 0.

Divisibility by 7 Step 1 Double the last digit in the number.

Step 2 Subtract this number from the remaining digits.

Step 3 If the new number is 0 or a number divisible by 7, the original number is also divisible by 7. If the number is still too large to quickly see if it is divisible by 7, repeat step 1 and 2 with the new number.

Time

Analogue time

1 minute = 60 seconds 1 hour = 60 minutes 24 hours = 1 day 7 days = 1 week 4 weeks = 1 month 12 months = 1 year 10 years = 1 decade 100 years = 1 century

NOTE Leap year: Leap year is every 4th year. There are 366 days in a leap year. e.g. 2020; 2024; 2028; ... Digital time

Study Guide 2/2 G06 ~ Mathematics

Length Units: kilometre (km), metre (m), centimetre (cm) and milimetre (mm). 10 mm = 1 cm

100 cm = 1 m

1 000 m = 1 km

× 1 000 × 1 000

kilometre (km)

× 10

× 100

metre (m)

millimetre (mm)

centimetre (cm)

÷ 1 000

÷ 10

÷ 100 ÷ 1 000

Mass Units: ton (t), kilogram (kg) and gram (g)

1 000 g = 1 kg

1 000 kg = 1 ton

× 1 000

ton (t)

× 1 000

kilogram (kg)

÷ 1 000

gram (g)

÷ 1 000

Study Guide 2/2 G06 ~ Mathematics

Volume Units: kilolitre (kℓ), litre (ℓ) and millilitre (mℓ). 1 000 mℓ = 1 ℓ

1 000 ℓ = 1 kℓ

× 1 000

kilolitre (kℓ)

× 1 000

litre (ℓ)

÷ 1 000

millilitre (mℓ)

÷ 1 000

Conversions: Multiply or divide by 10, 100 and 1 000 Example 1 Convert 4 000 g to kilogram. 4 000 g ÷ 1 000 = 4 kg

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).

4 0 0 0 , g ÷ 1 0 0 0 = 4 , 0 0 0 kg

Example 2 Convert 4 kg to gram.

4 kg × 1 000 = 4 000 g

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

4 , 0 0 0 kg × 1 0 0 0 = 4 0 0 0 g 13

Study Guide 2/2 G06 ~ Mathematics

2D shapes Triangle

Square

3 straight sides 3 angles Rectangle

4 straight sides of equal length 4 right angles (90°)

2 long straight sides of equal length 2 shorter sides of equal length 4 right angles (90°) Pentagon

No angles No straight side (a curved surface)

5 straight sides and 5 angles Heptagon

6 straight sides and 6 angles

7 straight sides and 7 angles

8 straight sides and 8 angles

Circle

Hexagon

NOTE: The Castle of Good Hope in Cape Town is a pentagonshaped building

Octagon

Study Guide 2/2 G06 ~ Mathematics

3D objects Objects with only curved surfaces Sphere

Objects with flat and curved surfaces Cone Cylinder

Objects with only flat surfaces Prisms Triangular prism Square prism

Pyramids Triangular pyramid Square pyramid OR tetrahedron

Rectangular prism

Pentagonal prism

Rectangular pyramid

Pentagonal pyramid

Hexagonal prism

Octagonal prism

Hexagonal pyramid

Octagonal pyramid

Study Guide 2/2 G06 ~ Mathematics

Types of angles Name

Right angle

Acute angle

Obtuse angle

Straight angle

Reflex angle

Full rotation (or revolution)

Description

Example

An angle of 90° A quarter of a rotation An angle smaller than a right angle (smaller than 90°) An angle bigger than a right angle (bigger than 90 and smaller than 180°) An angle of 180° Half a rotation

An angle bigger than a straight angle but smaller than a full rotation (bigger than 180° but smaller than 360°) 360° A full (complete) rotation

Transformations Reflection (Mirror image)

figu

Translation (Glide image)

figu

ctio

refle

tran

slat

ion

Study Guide 2/2 G06 ~ Mathematics

Rotation

Enlargement/reduction

figu

rot a

tio

enla

rgem

figu

ent

point of rotation

Data handling Tally table / Frequency table

Write down all the shoe sizes in ascending order.

Shoe size

Make a mark for each data unit. Every fifth mark goes across the group of four marks to make a group of five. It is easier to count data in groups of five.

Tally

Frequency indicates the answer of the count. It shows how many units of data there are.

Frequency

|||| |

|||

|||| |||

||||

8 Total

The median is the data item in the middle of the data set. Here it is shoe size 3.

22 The mode is the data item with the most tallies. The mode of the data set is: Shoe size 3

Pictograph Day

Teddy bears

Day 1 Day 2 Day 3 Every

represents 6 teddy bears. 17

Study Guide 2/2 G06 ~ Mathematics

Bar graph Grade 5 learners' maths test results

30 25 20 15 10 5 0

Double bar graph

Pie chart

Study Guide 2/2 G06 ~ Mathematics

Unit

UNIT 3 This unit covers eleven lessons (lessons 17 to 27).

UNIT 3

TOPIC Mental maths: Use Train Your Brain Maths Grade 6 Lesson 17 Mass

Lesson 21 Properties of 2D shapes Lesson 22 Transformations Lesson 23 Temperature Lesson 24 Percentages

Lesson 25 Data handling

Lesson 26 Numeric patterns Lesson 27 Length

Revision: Use the CAMI program 19

Unit

Study Guide 2/2 G06 ~ Mathematics

LESSON 17: MASS Do you still remember what mass is, from Grade 5? Mass measures the quantity of matter (particles) in an object. Mass is measured in gram (g), kilogram (kg) and ton (t). In Grade 6, we only work with gram and kilogram. We sometimes refer to weight when talking about mass, but they are not the same thing. What is the difference between mass and weight? Mass • • •

Weight •

Mass measures the quantity of matter (particles) in an object. Mass always stays the same, regardless of where it is measured. The standard unit is kilogram (kg).

• •

The weight of an object is determined by gravity. Weight can change, depending on where it is measured. The standard unit is Newton (N).

This picture will help you understand the difference. An astronaut’s mass is 90 kg, but his weight here on earth and on the moon, is different. On earth, the astronaut’s mass is 900 N, while on the moon it is merely 15,24 N!

Calculating weight is complicated, but you do not have to do that yet. You will learn more about mass and weight in Natural Sciences, later on. © Optimi

Study Guide 2/2 G06 ~ Mathematics

Unit

Units of mass The standard unit of mass is kilogram (kg). We can also measure objects in gram (g) and ton (t).

In the same way that we convert between millilitre, litre and kilolitre, we can also convert between gram, kilogram and ton. × 1 000

ton (t)

× 1 000

kilogram (kg)

÷ 1 000

gram (g)

÷ 1 000

To convert mass from gram to kilogram, you multiply by 1 000. To convert mass from kilogram to gram, you divide by 1 000. That means

1 ton = 1 000 kg

1 kg = 1 000 g

1 g = 0,001 kg

We will look at converting between units in more detail later on.

Measuring mass You already know that we use scales to measure mass. In Grades 4 and 5, you learned about the different scales we use to measure mass and most were analogue scales.

Unit

Study Guide 2/2 G06 ~ Mathematics

Analogue scales Each of these scales are used to measure the mass of something specific. Can you guess what it is?

_________________________ _________________________ _________________________ _________________________

_________________________ _________________________ _________________________ _________________________ Reading mass on an analogue scale To determine the amount of liquid in a measuring cup, we look at the cup’s graduation markings. With an analogue scale it works the same way – look at the graduation markings. Let us study an example. Example 1

Looking at the graduation markings on a kitchen scale, we can count 10 markings for each numbered interval. (Count the markings from the long marking at 0 to 1 – there are 10 markings, with the long marking at 1 being the tenth marking.) © Optimi

Study Guide 2/2 G06 ~ Mathematics

Unit

But what does it mean? Every numbered interval is 1 kg. Every kilogram consists of 10 markings, which means that every marking is a tenth of a kilogram, therefore 0,10 kg, or 0,1 kg. If we take the reading on the scale on the previous page at eye level, the red arm indicates the mass of the potatoes as 3,8 kg. (Can you count the markings?) How do we take the reading on a scale? •

•

Remember, zeros that follow on digits after the comma can be left out.

Determine the intervals on the scale.

We determined that every numbered interval (the long markings) = 1 kg.

Stand in front of the scale, at eye level, and read the measurement.

3,8 kg

Determine the value of each interval.

There are 10 markings between each kg. So every unnumbered interval is 1 kg = 1 000 g, therefore, 1 000 g ÷ 10 = 100 g

How much grams will that be? We have already determined that every short marking = 0,1 kg.

How do we convert kg to g? We multiply by 1 000, therefore 0,1 kg × 1 000 = 100 g. Therefore, the mass of the potatoes in the image is 3,8 kg, therefore: 3,8 kg × 1 000 = 3 800 g.

Later on, we will look at conversion between units in more detail.

We can also represent a scale’s round disc on a number line. The numbered markings represent intervals of 1 kg, with 10 spaces between each kilogram. So every numbered interval: 1 kg = 1 000 g, therefore 1 000 g ÷ 10 = 100 g.

Every interval is 100 g. 23

1 kg

Unit

Study Guide 2/2 G06 ~ Mathematics

Example 2 Benji weighs himself on a bathroom scale. He stands still, with his feet even and flat. He looks down at the scale reading, how much does he weigh?

• • •

Determine the intervals on the scale.

Every numbered interval represents 5 kg.

Look down and read the measurement.

The red arm indicates the second marking after 20 kg, therefore, Benji weighs 22 kg.

Determine the value of each interval.

There are 5 markings between each 5 kg, therefore every unnumbered interval is: 5 kg ÷ 5 marks = 1 kg.

Digital scales These days we use digital scales more than analogue scales. It works electronically and has a battery. In Grade 5, you revised reading time on an analogue watch and a digital watch. Analogue scales and digital scales work in the same way. Can you guess what these digital scales are used for?

_________________________

_________________________ _________________________ 24

_________________________ _________________________

Study Guide 2/2 G06 ~ Mathematics

Unit

Instead of determining intervals as we do with an analogue scale, a digital scale gives the reading in numbers, so we must literally just read the measurement. Always make sure of the unit. A kitchen scale can measure in grams or kilograms, for example.

55,5 kg

330 g

ACTIVITY 47 1.

In what unit will these items be measured? Use the abbreviations g, kg and t. 1.1

1.2

1.3

1.4

Unit

Study Guide 2/2 G06 ~ Mathematics

1.5

1.6

Read the mass on the scales. Give the reading in the unit on the scale, and then convert it to gram or kilogram.

2.1

2.4

2.2

2.5

2.3

2.6

Study Guide 2/2 G06 ~ Mathematics

Unit

2.7

2.8 95.85 g

How much do the objects weigh? Give your answers in gram. Look carefully at the unit on the scale. 3.1

3.2

3.3

Do you know how much you weigh? Use a bathroom scale if you do not know. Write your weight in kilogram and convert it to gram. I weigh _______ kg. It is _________ g.

Comparing and ordering mass Before we look at converting units of mass in more detail, you must practise comparing and ordering mass. 1 kilogram = 1 kg or 1 000 g

1 half a kilogram = __ 2 kg or 0,5 kg or 500 g

1 kg or 0,25 kg or 250 g quarter of a kilogram = __ 4

3 three-quarters of a kilogram = __ 4 kg or 0,75 kg or 750 g 27

Unit

Study Guide 2/2 G06 ~ Mathematics

What is the mass of 1 ℓ water?

What is the mass of 1 mℓ water?

1 mℓ water weighs 1 g

1 ℓ water weighs 1 kg

Here, we converted the amount of water to weight. BUT as a rule it is not possible to convert between different units; water is an exception..

ACTIVITY 48 1. 2.

Explain the difference between mass and weight in your own words. You and your mom buy these items in a shop: A bag of 3 apples 2 ℓ cold drink A 750 mℓ bottle of tomato sauce

Arrange the items from heaviest to lightest. Estimate the mass of the objects.

3.1

3.3

3.2

3.4

A bread 2 kg bag of flour

Study Guide 2/2 G06 ~ Mathematics

Unit

Bonus: Arrange the objects in question 3 in descending order, based on your answers. 4.

Use the correct symbol (>, < or =) to indicate the relationship between the masses.

4.5

__ 24 kg _______ 400 g 15 ___ 20 kg _______ 850 g 75 _____ 100 kg _______ 760 g ___ 35 25 kg _______ 1 200 g ___ 15 50 kg _______ 400 g

5.1 5.2 5.3 5.4 5.5

30 mℓ 2 300 mℓ 1 550 mℓ 18 458 mℓ 5 mℓ

4.1 4.2 4.3 4.4

6. 7.

Each of these amounts of water is stored in its own container. How much does each container of water weigh? Give your answers in kg.

What is the difference between an analogue scale and a digital scale?

Test your knowledge of conversion between units, before we discuss it in more detail. 7.1 7.2 7.3 7.4 7.5

How many grams are in a kilogram? How many kilograms are in a gram? How many grams are in 3,7 kg? How many grams are in 100 kg? How many kilograms are in 49 350 g?

Unit

Study Guide 2/2 G06 ~ Mathematics

Converting between units of measurement Earlier in the unit, we looked at converting between different mass units.

Converting something means changing it from one thing to another.

× 1 000

ton (t)

× 1 000

kilogram (kg)

÷ 1 000

gram (g)

÷ 1 000

But wait, there is an easier way to convert between units without using a calculator. Can you still remember how, from Grade 5? When we convert from kilogram to gram, we multiply by 1 000. The comma moves three place values to the right (because there are three zeros in 1 000).

•

× 1 000

When we convert from gram to kilogram, we divide by 1 000. The comma moves three place values to the left (because there are three zeros in 1 000).

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÷ 1 000

1 kg = 1 000 g Let us look at some examples. Example 1 Convert 2,75 kg to gram. • • •

From which unit to which unit am I converting? Must I multiply or divide?

I am converting from kg to g.

I must convert from a larger unit to a smaller unit, so I must multiply.

Where does the comma move The comma moves to the right. to?