Platinum mathematics. 7, Learner’s book

297 Pages·2013·30.049 MB·English

by  Bowie, Lorrainne

CAPS
Mathematics
7
Learner’s Book
L. Bowie • E. Cronje • F. Heany • P. Maritz
G. Olivier • B. Rossouw • S. Willers
Consultants: M. Bali • M. Langa • H. Lewis • H. Roos
It is illegal to photocopy any pages from this book
without the written permission of the copyright holder.
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Contents
Term 1
Topic 1: Whole numbers 4 Topic 4: Constructions 34
Compare, order and round off numbers 4 Measure and classify angles 34
Properties of whole numbers 7 Construct angles 41
Calculations with whole numbers 9 Construct triangles 43
Multiples and factors 12 Construct quadrilaterals 45
Solve problems 14 Construct circles 47
Construct parallel and
Revision 17
perpendicular lines 51
Topic 2: Exponents 18
Revision 55
Compare and represent numbers in
exponential form 18 Topic 5: Geometry of 2D shapes 56
Use laws of operations with exponents 21 Triangles 56
Calculations with exponents 23 Quadrilaterals 59
Solve problems 25 Similarity and congruence 63
Circles 68
Revision 27
Revision 70
Formal Assessment Exemplar: Assignment –
Fun with factors and multiples 28 Formal Assessment Exemplar: Test 72
Topic 3: Geometry of straight lines 30
Straight, perpendicular and
parallel lines 30
Revision 33
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Term 2
Topic 6: Common fractions 76 Formal Assessment Exemplar: Investigation –
Fractions 76 Sense and nonsense about percentages 110
Equivalent fractions 79
Topic 9: Area and perimeter of 2D shapes 112
Compare and order fractions 80
Perimeters of polygons 112
Addition and subtraction of fractions 82
Areas of polygons 117
Multiplication of fractions 85
Solve problems involving area and
Percentages 87
perimeter 122
Revision 89
Revision 125
Topic 7: Decimal fractions 90
Topic 10: Surface area and volume of 3D objects 126
Read and write decimal fractions 90
Solids 126
Rounding off decimal fractions 91
Surface area, volume and capacity 130
Compare and order decimal fractions 92
Solve problems involving surface area
Equivalent forms 94
and volume 135
Addition and subtraction of decimal
Revision 137
fractions 95
Multiplication and division with decimal Formal Assessment Exemplar: Exam Practice 138
fractions 97
Revision 101
Formal Assessment Exemplar: Test 102
Topic 8: Functions and relationships 104
Number sentences and variables 104
Flow diagrams 106
Tables 107
Revision 109
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Term 3
Topic 11: Numeric and geometric patterns 142 Topic 16: Transformation geometry 178
Numeric patterns 142 Investigate translations 178
Geometric patterns 147 Investigate reflections 181
Investigate rotations 183
Revision 149
Enlarge and reduce geometric figures 186
Formal Assessment Exemplar: Assignment – Solve problems involving
Interesting ratios 150 transformations 188
Topic 12: Functions and relationships 152 Revision 190
Use formulae to determine inputs and
Formal Assessment Exemplar: Project – How we
outputs 152
use water
Use flow diagrams to determine inputs
192
and outputs 154

Use tables to determine inputs and
outputs 156 Topic 17: Geometry of 3D objects 194
Classify 3D objects 194
Revision 157
Prisms and pyramids 196
Topic 13: Algebraic expressions 158 Building 3D models 202
Use mathematical language 158
Revision 205
Use variables in algebra 160
Write terms of an expression 161 Formal Assessment Exemplar: Test 206
Revision 163
Topic 14: Algebraic equations 164
Solve number sentences by inspection 164
Use number sentences to solve
problems 166
Revision 167
Topic 15: Graphs 168
Interpreting graphs 168
Drawing graphs 174
Revision 176
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Term 4
Topic 18 Integers 210 Formal Assessment Exemplar: Investigation –
Count, order and compare integers 210 Make an architectural model 242
Calculate with integers 212
Topic 23: Collect, organise and summarise data 244
Properties of integers 215
Collect data 244
Solve problems with integers 216
Organise data 247
Revision 217 Summarise data 250
Topic 19: Numeric and geometric patterns 218 Revision 253
Describing patterns 218
Topic 24: Represent data 254
Using rules to complete tables 220
Draw bar graphs and double
Revision 223 bar graphs 254
Draw histograms 256
Topic 20: Functions and relationships 224
Draw pie charts 258
Number sentences 224
Number variables 225 Revision 259
Use flow diagrams and tables 226
Topic 25: Interpret, analyse and report data 260
Revision 227 Interpret data 260
Analyse data 262
Formal Assessment Exemplar: Assignment –
Report data 266
How rates affect a business 228
Revision 267
Topic 21: Algebraic expressions 230
Algebraic expressions used in Topic 26: Probability 268
number patterns 230 Elementary probability 268
Use flow diagrams to illustrate
Revision 273
expressions 231
Use tables to illustrate expressions 234 Formal Assessment Exemplar: Exam Practice 274
Revision 235
Glossary 278
Topic 22: Algebraic equations 236 Index 286
Solve number sentences with Useful resources 290
integers 236
Use number sentences to solve
problems 239
Revision 241
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1 Term 1
The full moon in the night sky A ripe orange hanging from a tree
The face of a sunflower A circular cross-section of a watermelon
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Topics 1–5
Starting off
When we look at Earth and the different objects
around us, we discover one basic shape that is
repeated over and over.
The pictures show a variety of objects that we find
in nature. Although these objects are very different,
they all share a common property.
Look at the objects in the pictures.
1. Name the property they have in common.
2. Name two more objects found in nature that
have this property.
3. ‘Nature favours circles and spheres over squares
and cubes.’ Do you agree with this statement?
Saturn with its rings
Explain your answer.
4. Discuss the relationship between these three
words: circle, sphere, cycle.
Contents covered in Term 1
Topic 1: Whole numbers; Topic 2: Exponents; Formal Assessment Exemplar:
Assignment; Topic 3: Geometry of straight lines; Topic 4: Constructions;
Ripples in water Topic 5: Geometry of 2D shapes; Formal Assessment Exemplar: Test
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Topic
Whole numbers
1
Compare, order and round off numbers
Maths ideas
• Compare, order All the positive numbers 1; 2; 3; 4; … are called the set of natural numbers.
and round off If we include 0 in the set of natural numbers, we get the set of counting
numbers. numbers or whole numbers. We use numbers to add, subtract, multiply
• Use properties of and divide. We can also write numbers in a particular order. For example,
whole numbers. the numbers 124; 2 514; 479 180; 9 823 010 are written in order of size from
smallest to largest.
• Recognise
properties of 0
and 1. When we need to estimate,
we can round off numbers
• Estimate and
to the nearest 5, 10, 100
calculate using all
four operations. or 1 000.
• Use multiples and
For example: if 36 783 fans
factors of whole
filled a soccer stadium, we
numbers.
can round the number off to
• Find LCM and HCF
the nearest 5, which would
of numbers.
be 36 785; or we could
• Solve problems.
round the number off to the
nearest 1 000 which would
Key words be 37 000 fans.
• whole numbers – Rounding off is often used We approximate the number of people in
or counting
to make calculations easier. large crowds when we do not need the
numbers are the
To round off a number to exact number.
numbers 0; 1; 2;
the nearest 5, you should
3; 4; … and are
look at the last digit of the number (the units digit) and round the number
represented by the
symbol N off to the closest number that 5 divides into. Look at the number line below.
0
7 rounds down to 5 and 8 rounds up to 10; 22 is rounded down to 20 and
• natural numbers –
23 is rounded up to 25.
are whole numbers
greater than or
equal to 1: (1; 2;
3; 4; …) and are
0 5 10 15 20 25
represented by the
symbol N
In general, to round off a number, decide which digit is to be rounded.
The digit to be rounded will either remain unchanged or increase by one.
When rounding off to the nearest 10, look at the units digit.
When rounding off to the nearest 100, look at the tens digit.
When rounding off to the nearest 1 000, look at the hundreds digit.
4 Term 1
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If the digit you are looking at is a 5 or larger, increase the required digit by
Key words
one and make the last digit(s) zero. This is called rounding up. If it is a 4 or
less, leave the required digit as it is and make the last digit(s) zero. This is • rounding up –
means
called rounding down.
approximating to
a number larger
For example, 465 784 rounded off to the nearest 10 is 465 780.
than the original
number
465 784 rounded to the nearest 100 is 465 800.
• rounding
465 784 rounded to the nearest 1 000, is 466 000. down – means
approximating to
Often the exact number is not really important but an approximation is a number smaller
good enough. than the original
number
Example
1. Three stadiums hold a soccer tournament. Stadium A can hold
42 000 people, Stadium B can hold 68 000 people and Stadium C can
hold 55 000 people.
Write the names of stadiums in order of capacity from smallest to largest.

2. Round off 987 516 to:
a ) the nearest 5 b ) the nearest 10
c ) the nearest 100 d ) the nearest 1 000
e ) the nearest 10 000 f ) the nearest 100 000.
Answers
1. Stadium A, Stadium C, Stadium B
2. a ) 987 515 b ) 987 520 c ) 987 500
d ) 988 000 e ) 990 000 f ) 1 000 000
Topic 1: Whole numbers 5
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