Pearson Mathematics 7 Student Book

374 Pages·2016·270.276 MB·English

by  Dirk Strasser, Geoff Phillips, Jennifer Nolan

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Challenge 3 169 Chapter 5 Algebra 258
C o n t e n t s
Gamespace: Fractured ravine 170
Recall 5 260
Chapter review 3 172
Exploration Task: Areas of rectangles 260
Numeracy practice 3 175
5.1 Pronumerals and variables 261
Pearson Mathematics writing and development team Maths 4 Real: Prime numbers and encryption 74
111
5.2 Terms, expressions and equations 266
Series features vm 2.4 Introduction to integers 76 Exploration STEM: The secret message 176
Problen1 solving: We all want ice-cream! 270
Using Pearson Mathematics x Puzzle: Ten1perature tangle 82 Exploration STEM: Electric fonts 176
5.3 Using rules 271
Half-time 2 83 Exploration STEM: The best buys 177
Chapter 1 Whole numbers 2
Problen1 solving: Cutting string 277
Exploration Coding: Adding consecutive numbers 177
2.5 Adding and subtracting positive integers 84
Recall 1 4 5.4 Formulas and substitution 278
Problem solving: The slippery snail 88
Chapter 4 Decimals,
Exploration Task: The root of the problem 4 Game: Dicey formulas 283
2.6 Adding and subtracting negative integers 89
percentage and ratio 178
1.1 Mental strategies 5 5.5 Patterns and rules 284
Investigation: Heat beads and ice blocks 94
Game: Greed 10 Recall 4 180 Puzzle: Puzzling tables 290
2.7 Sin1plifying addition and subtraction 96
1.2 Indices 11 Exploration Task: Which deal is best? 180 Half-time 5 291
Puzzle: Pattern sums 100
Problem solving: Teacher's age 18 4.1 Place value and comparing decimals 181 Investigation: Richie's Restaurant 292
Challenge 2 101
Investigation: How many squares on a chessboard? 19 Game: Duelling decimals 190 5.6 Sin1plifying expressions with addition
Chapter review 2 102
Maths 4 Real: Numbers around the wor1d 20 4.2 Rounding decimals 191 and subtraction 294
Numeracy practice 2 105
1.3 More strategies for multiplication 4.3 Decimals and fractions 196 Puzzle: Latin squares 299
and division 22 Mixed review A 106 Puzzle: What are the neighbours having Exploration Spreadsheet: Age matters 300
Problem solving: Wizard maths 28 for dinner? 200 5.7 The Cartesian plane 302
Chapter 3 Fractions 108
Half-time 1 29 4.4 Decimal addition and subtraction 201 Game: Line up 307
Recall 3 110
1.4 Estimating and rounding 30 Game: Closer than you 204 Maths 4 Real: Maths meets art 308
Exploration Task: Sharing again and again ...
Game: Estimation frustration 37 Game: Decimal zilch 204 5.8 Patterns and plotting points 310
makes more? 110
1.5 Order of operations 38 Investigation: Ten dollars and eighty-nine cents 205 Puzzle: Gridlock 313
3.1 Understanding fractions 111
Problem solving: Four 4s = 100? 42 4.5 Decimal multiplication 206 Gamespace: Spy vs spy 314
Puzzle: Fractionally funny fiction 119
1.6 Mixed whole number problems 43 Game: Multiplicity 214 5.9 Interpreting graphs 316
3.2 Working with fractions 120
Problem solving: Nine hundred Half-time 4 215 Puzzle: Solve the grid 322
Puzzle: What fractions are we? 128
and ninety-nine 46
4.6 Decimal division 216 Challenge 5 323
3.3 Estimating and comparing fractions 129
Challenge 1 4 7
Puzzle: Magic square 221 Chapter review 5 324
Game: Flatlining 137
Gamespace: The operation theatre 48
Maths 4 Real: Perplexing prices 222 Numeracy practice 5 328
3.4 Adding and subtracting fractions 138
Chapter review 1 50
4.7 Percentages, fractions and decimals 224
Game: Race to 10 146
Numeracy practice 1 53
4.8 Using percentages 230
Half-time 3 147
Problem solving: The great half-price sale 235
Chapter 2 Integers 54
Maths 4 Real: Musical fractions 148
Maths 4 Real: Our global village 236
Recall 2 56 Investigation: Tangram teaser 150
4.9 Ratio 238
Exploration Task: Is adding always more? 3.5 Multiplying fractions 152
4.10 Rates 245
Is subtracting always less? 56
Game: Fringo! 158
Problem solving: Numberrrrrrrrrs 250
2.1 Multiples, factors and divisibility 57
Problem solving: Fill in the blanks 158
Challenge 4 251
2.2 Primes and composites 65
3.6 Dividing fractions 159
Chapter review 4 252
Puzzle: Gold digger 67
3. 7 Mixed fraction problems 165
Numeracy practice 4 255
Gamespace: Factorpillar 68
Problem solving: Mega-equivalents 168
2.3 Prime factors 70 Mixed review B 256
mathematics 7 Contents
PEARSON 2ND EDITION
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Chapter 6 Measurement 330 Maths 4 Real: Dance party dilemma 414 Chapter 9 Statistics Chapter 10 Transformation
Exploration Spreadsheet: Algebra using and probability 500 and visualisation 576
Recall 6 332
a spreadsheet 416
Exploration Task: What size? 332 Recall 9 502 Recall 10 578
7.5 Solving problems with equations 418
6.1 Units of length 333 Exploration Task: Improving the odds 502 Exploration Task: Shape shifting 578
Problem solving: Algebraic puzzles 422
6.2 Perin1eter 340 9.1 Collecting data 503 10.1 Translations 579
Investigation: The great escape 423
Problen1 solving: Ram's rulers 343 Puzzle: Matchstick puzzles 510 Puzzle: Jigsaw paradox 584
Gamespace: The case of the confusing clues 424
6.3 Area 344 9.2 Measures of centre and spread 511 10.2 Reflections 585
Challenge 7 426
Game: Jungle pathways 351 Problem solving: Running the race 515 Problen1 solving: Mirror, mirror, on the wall,
Chapter review 7 427
Investigation: Paddocks 352 Gamespace: Crack the code 516 does it matter where I stand at all? 591
Numeracy practice 7 429
Half-time 6 354 10.3 Rotations 592
9.3 Graphing univariate data 518
6.4 Area of a parallelogram 355 Chapter 8 Angles and shapes 430 Puzzle: Number puzzles 528 Problem solving: Tan gram magic 600
6.5 Area of triangles and composite shapes 359 9.4 Comparing parts of a whole with graphs 529 Investigation: Diamonds are forever! 601
Recall 8 432
6.6 Volume 367 Problem solving: Missing pieces of the pie 537 10.4 Combined transformations 603
Exploration Task: Are you sure they are parallel? 432
Problem solving: The red cube 371 Half-time 9 538 Game: Conway's soldiers 610
8.1 Measuring, estimating and drawing angles 433
Gamespace: City mission 372 Exploration Spreadsheet: Finding statistics Half-time 10 611
Game: Angle Master 439
Maths 4 Real: Landscape gardening 374 using technology 539 Exploration CAS: Transformations with CAS 612
8.2 Classifying and naming angles 440
Investigation: Blocks of chocolate 376 9.5 Graphing bivariate data 540 Maths 4 Real: Snow logo 616
Problem solving: Count the angles 445
Challenge 6 378 Problem solving: Add it up 547 Gamespace: Ambigrams and symmetry 618
Maths 4 Real: Constructing angles 446
Chapter review 6 379 Maths 4 Real: The 1-watt initiative 548 10.5 Symmetry 620
8.3 Calculating angles 448
( .,;.
Numeracy practice 6 382 9.6 Comparing data sets 550 Problem solving: Symmetry challenge 626
1 Problem solving: Ella's angles 452
Puzzle: Number puzzles 559 10.6 Drawing and visualising 3D shapes 627
8.4 Angles and transversals 453
Mixed review C 383
9.7 Probability and sample space 560 Problem solving: What comes next? 631
Exploration CAS: Investigating angles
Exploration STEM: The grand architect 385 Game: Catch me if you can 567 10.7 Plan views and elevations 632
on parallel lines 458
Exploration STEM: SuNey and discovery 385 Investigation: Billiard ball bounces 462 Investigation: Experimental probability 568 Problem solving: Bird's eye squares 636
Exploration Coding: Creating geometric patterns 385 Half-time 8 464 Challenge 9 570 Challenge 1O 637
8.5 Polygons 465 Chapter review 9 _...... 571 Chapter review 10 638
Chapter 7 Linear equations 386
Problem solving: The hex is gone 468 Numeracy practice 9 J:;;-~ ~ 575 Numeracy practice 10 642
Recall 7 388
8.6 Triangles 469
Mixed review E 644
Exploration Task: Comparing mobile phone plans-
.._,
Puzzle: Eggs, spoons and turtles 477
which is better? 388
Answers 646
Investigation: Angle sum of polygons 478
7.1 Number sentences 389
Glossary and index 727
8.7 Quadrilaterals 480
Game: Star quest 393
Problem solving: Quadrilateral quandaries 485
7.2 Introduction to equations 394
Gamespace: Planet polygon 486
Puzzle: The great number mystery 398
8.8 Compass constructions 488
7.3 Solving equations using backtracking 399
Challenge 8 492
Puzzle: Gold digger returns! 406
Chapter review 8 493
Half-time 7 407
Numeracy practice 8 497
7.4 Solving equations using the
balance method 408
Mixed review D 498
Problem solving: Paper mountain 413
mathematics 7 Contents
PEARSON 2ND EDITION
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PEARSON
Student Book Pearson Lightbook Starter Pearson Places is the gateway to digital learning material
l'f.otJISOltmott. ., 101i:s ,Uoll$Clttmotr..1.olles
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5.8. HP.
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The Second Edition Student Book includes updated Lightbook Starter is an innovative digital resource powered
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questions, activities and design, with full coverage of the by Pearson's award-winning Lightbook technology. It has
li1 Pearson Digital
Australian Curriculum: Mathematics as well as the Victorian been developed to help students learn key mathematical
Curriculum: Mathematics. concepts, evaluate their understanding and track their
Professional Learning,
progress. 'Before you begin' sections assess learner
It incorporates the latest research as well as feedback from
Training and Development
readiness before each chapter topic, while 'Check-in'
teachers and learners across Australia.
questions can be used to evaluate learner understanding
Did you know that Pearson also offers teachers a diverse
Content caters for students of all abilities, with improved
and practice after every chapter section.
Student Book Homework Program range of training and development product-linked learning
differentiation of all exercise questions and more questions
,uJt,o,,, ,,10it.,101101 for students consolidating their skills. Auto-correcting questions are linked to the Progress programs? We are dedicated to supporting your
IC.
Tracker dashboard for easy analysis and viewing of results, implementation of Pearson Mathematics, but it doesn't
Homework Program
which are mapped to progression through the Student stop there.
The Homework Program provides a collection of tear-out Book as well as to Australian Curriculum: Mathematics and Our courses align closely with Pearson Mathematics Second
worksheets for students to practise and revise Victorian Curriculum: Mathematics content descriptions. Edition and offer an in-depth learning experience,
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workshops, courses and conferences at Pearson Academy
[ s]I I support including improved contextual teaching suggestions content specifically developed for Mathematics. It supports
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and strategies, class activities, extra questions, worked you with appropriate online resources and tools for every
Lightbook Starter solutions and answers for every question in the section of the Student Book, including videos, eWorked
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eBook We believe in learning.
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Supporting all learners
Differentiation
Pearson Mathematics Second Edition has been written and designed for the needs of the full ability spectrum
of students in Australian classrooms.
Recall- Each chapter begins with a review of assumed
and necessary knowledge for the chapter. For students
Recall
needing extra revision, Recall Worksheets are available
for each Recall question, with explanations to refresh
understanding and exercises to practise skills.
Exercises-All Exercises include questions according
The Australian Curriculum: Mathematics Pearson Mathematics Second Edition is a compelling
g) to the Australian Curriculum Proficiency Strands:
Expanding brackets
aims to ensure that students: research-based series, written by experienced and
Fluency, Understanding and Reasoning. They have
practising Australian teachers with the support of
• are confident, creative users and been carefully paced to help students build skills,
Australia's leading mathematics education experts.
develop deep conceptual understanding and apply
communicators of mathematics,
It has been specifically designed to scaffold students'
learning. Every Exercise also has 'Open-ended'
able to investigate, represent and
fluency development, conceptual understanding,
questions to encourage students' creative thinking
interpret situations in their personal
reasoning and problem-solving skills. and ability to communicate mathematics effectively.
and work lives and as active citizens
Navigator
Navigator-Three optional graded pathways
• develop an increasingly sophisticated
,. 2, 3, "· s.. a. 1. 10, 12. 13. 1a. 2ca, ~ "· s. a. 1, a.. 9, 10. 12, 13, 2 • · b), "(a).sea>. a (a). 1 <e>, a, through every Exercise, with every question rated
19, 22 14. 18.. 19, 20. 21, 22 9, 10, 11, 14, IS. 18.. 17, 18, 19,
understanding of mathematical concepts 20, 21, 22, 23
as Foundation, Standard or Advanced level.
and tluency with processes, and are able
to pose and solve problems and reason
Challenge-Every chapter includes a full page Challenge
in number and algebra, measurement and
section for early finishers and advanced students.
geometry, and statistics and probability
• recognise connections between the areas
of mathematics and other disciplines and
• • •
appreciate mathematics as an accessible
Regular revision and reinforcement
and enjoyable discipline to study.
Pearson Mathematics Second Edition has a broad range of cumulative and chapter-based revision.
(0 Australian Curriculum,
Assessment and Reporting Authority
Half-time-A mid-chapter review of chapter
I
content so far.
/A
Australian
'(ij1 CURRICULUM
Chapter review Chapter review-An end-of-chapter thorough review
of chapter content.
Pearson Mathematics shares these aims.
Mixed review Mixed review-Cumulative revision that mixes content
from previous chapters.
Using Pearson Mathematics
PEARSON mothemotics 7 2ND EDITION
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Encouraging inquiry Real-life contexts
and problem solving and engagement
Investigation Exploration Spreadsheet Exploration Task and STEM Home Page
dCAS
These are scaffolded to be accessible to all learners Practical contexts provide useful learning Anticipate the 'Why learn this?' question and
and structured following a Se+ format. opportunities and natural pathways into interesting, provide a motivating entry into every new
Pearson Mathematics Second Edition relevant mathematics. chapter topic, including discussion-provoking
understands the importance places of students
Forum questions.
Exploration tasks are rich tasks that encourage
Investigation
developing technological literacy. Explorations
student engagement, questioning and creative
with CAS technology and spreadsheet
thinking. STEM activities allow students to explore
software allow students to learn and practise
topics related to Science, Technology, Engineering
their technical proficiency, while also helping
and Design with a Mathematics perspective. Integers
to develop students' deeper understanding ---11 .. -
- ··-'°'-'"--"--
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of the mathematical concepts covered.
Exploration Task
Exploration Spreadsheet
----
Exploration STEM
·-----
Exploration CAS ·=--=-=--~-
=---=
Pearson Mathematics Second Edition has been designed to capture students' interest,
Exploration Coding
with the incorporation of Maths 4 Real, Gamespace and more.
Algorithmic thinking is an increasingly relevant
component of mathematics education for the Maths 4 Real Gamespace
These are located throughout every chapter
21 st century. Algorithmic thinking and coding tasks
and give students fun opportunities to develop
encourage learners to understand and develop
Scenarios that help students make Skill consolidation and reinforcement wrapped up
their problem-solving skills and logical reasoning. reasoning skills with computational procedures,
connections with mathematics in the real world. in fun and quirky scenarios, including multi-player
algorithms and logical problem-solving, exploring a
maths board games and solve-the-riddle,
coding environment within a mathematical context.
find-the-clue tasks and games.
Problem solving Exploration Coding --
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mothemotics 7
PEARSON 2ND EDITION
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e r s
It's a Santa stampede! Another Guinness
World Record, this time for 'the largest
gathering of Santa Claus'. ( 18 112 of them!)
For decades, Guinness World Records has resources we use. Every day, people need to
been recording extreme and bizarre feats, find totals, work out dlfferences, divide
Including 'the most cockroaches eaten In one quantities, and make estimates. To live In lhfs
minute' (36), and 'the most consecutive world, you need to be able to work with
skateboard fronts!de ollies off a half-pipe numbers!
ramp' (348). The book itself holds the record
for being the best-selling copyrighted series of
all time. People are fascinated to know the Forum
most, the biggest, the fastest and the tallest.
Is It Important to keep 'world records'?
To keep records, you need a system of If so, then what kinds of of achievements
numbers to count, order, measure and should records be kept for?
calculate with. People also need numbers for
What other kinds of records are good
our personal lives: how much money we
to keep?
spend, save and earn; how far and how often
we travel; and how much of the Earth's
Why learn this?
You are buying two $18 T-shirts and a $65 pair of jeans. Will $100 be enough? If you swim
12 laps of a 50 metre pool 4 times a week, how many metres per week Is that? Working with
numbers means more than just being able to add, subtract, multiply and divide. It means
being able to choose which skill to use, to estimate and round numbers, and to have a range
of mental skills so that you can work things out efficiently and accurately.
After completing this chapter you will be able to:
• choose and use a range of mental strategies for calculations
• understand how the properties of numbers can be used to calculate efficiently
• Interpret and work with numbers In Index form
• estimate answers to problems using estimating and rounding strategies
• apply the order of operations
• solve problems Involving whole numbers.
1 Whole numbers
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Recall M e n t a l s t r a t e g i e s
Prepare for this chapter by attempting the following questions. lf you have difficulty with a
This section looks at some strategies that are useful for doing calculations in your
question, you can download a Recall Worksheet from the eBook or the Pearson Places website.
head. Try writing them out first, before you do them only in your head. You might find
1 What is the place value of the red digit shown?
some methods easier than others, or you might have different strategies of your own.
(a) 45 783 That's okay-people are different in the way they like to approach things.
A eight B tens C eighty-three D hundreds Strategy 1-Make easy numbers
(b) 1264184
This strategy uses these two properties of numbers:
A two B hundreds C ten-thousands D hundred-thousands
1 The order in which you add or multiply any two numbers does not change the result.
2 (a) Rearrange the following numbers in ascending order (from smallest to largest).
For example: 2 x 3 = 6 and 3 x 2 = 6 ------------------,
o,
567, 4500, 74, 11100, 6008, 12,602 I \
4 + 5 = 9 and 5 + 4 = 9 1 The word 'commutative' comes 1
: from the Latin word commuts/8, :
(b) Rearrange the following numbers in descending order (from largest to smallest).
This is known as the commutative law.
: which means to :
1200, 204, 987, 2196, 240, 95, 2400, 1010 2 The order in which three or more numbers are added, or the order in 1 s_w_itc h or change! 1
\ .... ,-- I
3 Find: which they are multiplied, also does not change the result. ...... I
.......... .'
(a) 50 000 + 6000 + 800 + 90 + 5 (b) 7 000 000 + 20 000 + 5000 + 70 + 3 In the following examples, brackets are used to show which pair of
numbers is added or multiplied first.
4 (a) Round 1245 to the nearest:
Multiplication:
(i) 10 (ii) 100 (iii) 1000
(2 X 3) X 5 and 2 X (3 X 5)
(b) Round 8983 to the nearest:
=6x5 =2X 15
(i) 10 (ii) 100 (iii) 1000 =30 =30
5 Find: Addition:
(a) 3 X 2 X 3 (b) 5 X 3 X3 X 2 (C) 2 X 2 X 2 (d) lOxlOxlOxlO (6+ 7) +8 and 6 + (7 + 8)
=13+8 =6+ 15
6 Set out these calculations in your preferred way and work out the answers.
=21 =21
(a) 456 + 56 (b) 16 + 2047 (c) 90 + 1267 + 341
Th is is known as the associative law.
7 Set out these calculations in your preferred way and work out the answers.
It is important to understand that the commutative and associative laws do not apply to
(a) 298 - 123 (b) 854 - 227 (c) 1406 - 249
subtraction and division, which both need to be worked from left to right.
8 Set out these calculations in your preferred way and work out the answers.
For example: (9 - 5) - 4 but 9 - (5 - 4)
(a) 45 x 7 (b) 134 x 5 (c) 34 x 95 =4-4 =9-1
=0 =8
l_ _ 9 Set out these calculations in your preferred way and work out the answers.
(40+10)+2 but 40 + (10 + 2)
(a) 844 + 4 (b) 3708 + 9 (c) 897 + 7
=4+2 =40+5
=2 =8
The order in which you add numbers and the order in which you multiply numbers does
Exploration Task
not change the result. The order only changes the result for subtraction or division.
..
You can use the commutative and associative laws to'shuffle' or rearrange the calculation to
create multiples of 10, which are easier to add and multiply.
You can download this activity from the eBook or the Pearson Places website.
For example:
The root of the problem 7 + 9 + 3 is the same as: 3 + 7 + 9 5 x 37 x 2 is the same as: 5 x 2 x 37
=10 + 9 = 10 37
X
You can also split one number into two parts, then use the associative law to add one part to
ln this activity, you will explore the relationship between square roots and the
the other number to create a multiple of 10.
geometric properties of squares.
4 PEARSON mathematics 7 2ND EDITION 1 Whole numbers