iMTB_N4 - BOOK.indb

Transcription

iMTB_N4 - BOOK.indb

iMaths 4 Teacher Book – Important Updates
Important changes to iMaths 4 Teacher Book
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Contents
Earlier edition (2012)
New edition (2013)
iMaths Investigations and Topics
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Investigation notes
New edition (2013)
Investigation 3ÛGd]flqÛg^Ûhac]d]lk
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Investigation 4ÛK`]Ûlae]Ûg^ÛeqÛda^]
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Investigation 7Û8mkka]Û8\n]flmj]
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Investigation 8 Jmh]jÛkhgjlkÛklY\ame
fYe]kÛYf\ÛlgÛ]p[dm\]ÛKgha[ÛMG5
Investigation 9 DYjZd]ÛeYk`
fYe]Û^gjÛMG17
Investigation 10 @l¿kÛgfdqÛfYlmjYd
fYe]Û^gjÛMG5
Investigation 11 =jY[lagfÛ^mf
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Investigation 12 Nice dice
fYe]Û^gjÛMG17
Student Book Answers – Topics
NA2, NA3, NA4, NA13, NA14, NA17,
NA18, NA24, NA25, NA28, NA30, MG5,
MG17
New edition (2013)
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iMaths 4 Teacher Book – Important Updates
Student Book Answers – Challenges
MG5ÛD]Ykmjaf_ÛDYkk
New edition (2013)
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Tracker Book Answers – Topic assessment
NA2, NA3, NA4, NA13, NA24, NA25,
MG5, MG17
New edition (2013)
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iMaths Investigations and Topics
The grid below shows the 12 Investigations and the associated Topics.
Investigation
Page
Topics
1 Ripper rides
20
NA23 Equivalent fractions
NA33 Investigating patterns
MG12 Area
MG13 Area of irregular shapes
MG14 Angles
MG16 Tessellation
2 Keep the keys
28
NA1 Properties of odd and even numbers
NA5 Multiples 3, 4, 5, 6, 7, 8, 9
NA6 Multiplication facts 2, 3, 5, 10
NA9 Division facts 2, 3, 5, 10
NA12 Backtracking
NA19 Division 2-digit ÷ 1-digit
NA35 Equivalent number sentences
3 Plenty of pikelets
36
NA8 Multiplication problem solving
NA17 Multiplication 3-digit x 1-digit
NA31 Simple budgets
NA32 Purchases and giving change
MG1 Graduated scales
MG5 Measuring mass
MG6 Litres and millilitres
4 The time of my life
44
NA2 Place value beyond ten thousands
NA3 Expanded notation
NA13 Addition with larger numbers
NA14 Subtraction with larger numbers
NA15 Subtraction with zeros
NA16 Multiplying by tens and hundreds
NA18 Split and multiply
5 Lengthy leaps
54
NA27 Place value to tenths
NA28 Tenths on a number line
NA29 Place value to hundredths
NA30 Hundredths on a number line
SP4 Organising data
6 iFlicks movie marathon
62
MG9 Read and interpret timetables
MG10 am and pm
MG11 Timelines
SP4 Organising data
SP5 Column graphs
7 Aussie adventure
70
NA4 Multiply and divide by 10, 100, 1000
NA21 Round to 10 and 100
NA22 Estimation strategies
MG3 Kilometres
MG15 Using maps
SP6 Picture graphs
8 Super sports stadium
78
NA11 Division problem solving
NA12 Backtracking
NA20 Division strategies
NA34 Number patterns
9 Marble mash
86
MG7 Volume
MG17 Combining shapes
MG18 Drawing prisms and pyramids
10 It’s only natural
94
NA5 Multiples 3, 4, 5, 6, 7, 8, 9
MG2 Millimetres
MG4 Perimeter
MG5 Measuring mass
MG12 Area
MG16 Tessellation
11 Fraction fun
102
NA24 Fractions on a number line
NA25 Mixed numbers
NA26 Improper fractions
12 Nice dice
110
MG2 Millimetres
SP1 Probability
SP2 Judgments
SP3 Dependent and independent events
SP4 Organising data
The following Topic does not appear in any Investigation: MG8 Converting units of time.
ISBN 978 1 74135 243 6
iMaths 4 Teacher Book
5
Sample yearly program
The grid below shows a suggested yearly plan containing one or two Investigations per term.
An assessment week has been allocated to each Investigation. Topics that are not included in the
Investigations are scheduled for independent teaching and assessment.
Note: The Topics with an * contain problem solving tasks.
TERM 1
Duration
(weeks)
Readiness test (Tracker Book 4)
1
2–3
NA5 Multiples 3, 4, 5, 6, 7, 8, 9*
NA6 Multiplication facts 2, 3, 5, 10*
NA7 Multiplication facts 4, 6, 8, 9*
Problem solving strategies – PS1, PS2, PS4, PS7
Assessment of Topics
2
4–6
Investigation 4 The time of my life
NA17 Multiplication 3-digit x 1-digit*
3
Assessment
1
NA12 Backtracking*
Problem solving strategies – PS3, PS5, PS6
3
1
Semester 1
Investigations and Topics
7
8–10
1–2
3
2
Assessment
1
6–8
Investigation 3 Plenty of pikelets
Revise NA8, NA17*, MG1*
NA31 Simple budgets
NA32 Purchases and giving change*
MG5 Measuring mass
MG6 Litres and millilitres*
3
Assessment
1
ISBN 978 1 74135 243 6
4–5
Investigation 6 iFlicks movie marathon
Revise SP4
MG9 Read and interpret timetables*
MG10 am and pm
MG11 Timelines
SP5 Column graphs
2
Assessment
1
7–9
Investigation 7 Aussie adventure
Revise NA4, NA13
MG3 Kilometres
MG15 Using maps
SP6 Picture graphs
3
10
Assessment
1
TERM 4
Term
weeks
Duration
(weeks)
Investigation 11 Fraction fun
Revise NA6*, NA7*, NA9, NA10
NA23 Equivalent fractions*
NA25 Mixed numbers
3
Assessment
1
5–6
NA11 Division problem solving*
MG8 Converting units of time
MG14 Angles
MG16 Tessellation
2
7–8
Investigation 9 Marble mash
MG7 Volume*
2
Assessment
1
4
4–5
9
3
1–3
NA35 Equivalent number sentences*
MG2 Millimetres
MG4 Perimeter*
Problem solving strategies – PS8, PS9, PS10
Duration
(weeks)
1–3
Duration
(weeks)
Investigation 5 Lengthy leaps
MG1 Graduated scales*
SP4 Organising data
NA33 Investigating patterns*
MG12 Area
SP1 Probability
SP2 Judgments*
6
TERM 2
Term
weeks
Term
weeks
Semester 2
Term
weeks
TERM 3
2
9
13
Introduction to iMaths
Australian Curriculum checklist
The tables on this page and the next list the three content strands and the associated sub-strand descriptions of
the Australian Curriculum, and the Topics from the Student Book that match these descriptions.
Strand
Sub-strand
Number and Number and place value
Algebra
Investigate and use the properties of
odd and even numbers. (ACMNA071)
Student Book Topics
Recognise, represent and order
numbers to at least tens of
thousands. (ACMNA072)
Apply place value to partition,
rearrange and regroup numbers to
at least tens of thousands to assist
calculations and solve problems.
NA4 Multiply and divide by 10, 100, 1000 NA15 Subtraction with zeros
(ACMNA073)
Investigate number sequences
involving multiples of 3, 4, 6, 7, 8,
and 9. (ACMNA074)
NA5 Multiples 3, 4, 5, 6, 7, 8, 9
Recall multiplication facts up to
10 × 10 and related division facts.
Develop efficient mental and
written strategies and use
appropriate digital technologies for
multiplication and for division where
there is no remainder. (ACMNA076)
NA12 Backtracking
Fractions and decimals
Investigate equivalent fractions
used in contexts. (ACMNA077)
(ACMNA075)
Count by quarters, halves and thirds, NA24 Fractions on a number line
including with mixed numerals.
NA25 Mixed numbers
Locate and represent these fractions NA26 Improper fractions
on a number line. (ACMNA078)
Recognise that the place value
system can be extended to tenths
and hundredths. Make connections
between fractions and decimal
notation. (ACMNA079)
Money and financial mathematics
Solve problems involving purchases
and the calculation of change to the
nearest five cents with and without
digital technologies. (ACMNA080)
NA31 Simple budgets
Patterns and algebra
Explore and describe number
patterns resulting from performing
multiplication. (ACMNA081)
Solve word problems by using number NA34 Number patterns
sentences involving multiplication or
division where there is no remainder.
(ACMNA082)
Use equivalent number sentences
involving addition and subtraction to
find unknown quantities. (ACMNA083)
18
ISBN 978 1 74135 243 6
The content strand descriptions © Australian Curriculum, Assessment and Reporting Authority 2012. This material is reproduced with the permission of ACARA.
ACARA neither endorses nor verifies the accuracy of the information provided and accepts no responsibility for incomplete or inaccurate information. You can find the
unaltered and most up to date version of this material at http://www.australiancurriculum.edu.au/Home
Strand
Sub-strand
Measurement Using units of measurement
and Geometry Use scaled instruments to measure and
Student Book Topics
MG2 Millimetres
MG4 Perimeter
MG5 Measuring mass
compare lengths, masses, capacities and
temperatures. (ACMMG084)
Compare objects using familiar metric units MG6 Litres and millilitres
of area and volume. (ACMMG290)
MG7 Volume
MG12 Area
Convert between units of time. (ACMMG085) MG8 Converting units of time
Use am and pm notation and solve simple
time problems. (ACMMG086)
MG10 am and pm
MG11 Timelines
Shape
MG12 Area
Compare the areas of regular and irregular MG13 Area of irregular shapes
shapes by informal means. (ACMMG087)
Compare and describe two dimensional
shapes that result from combining and
splitting common shapes, with and without
the use of digital technologies. (ACMMG088)
Location and transformation
Use simple scales, legends and directions
to interpret information contained in basic
maps. (ACMMG090)
MG3 Kilometres
MG15 Using maps
Create symmetrical patterns, pictures
and shapes with and without digital
technologies. (ACMMG091)
MG16 Tessellation
Geometric reasoning
MG14 Angles
Compare angles and classify them as equal
to, greater than or less than a right angle.
(ACMMG089)
Statistics and Chance
Probability Describe possible everyday events and
SP1 Probability
SP2 Judgments
order their chances of occurring. (ACMSP092)
Identify everyday events where one cannot
happen if the other happens. (ACMSP093)
Identify events where the chance of one will SP3 Dependent and independent events
not be affected by the occurrence of the
other. (ACMSP094)
Data representation and interpretation SP4 Organising data
Select and trial methods for data collection,
including survey questions and recording
sheets. (ACMSP095)
Construct suitable data displays, with and SP5 Column graphs
without the use of digital technologies,
SP6 Picture graphs
from given or collected data. Include tables,
column graphs and picture graphs where
one picture can represent many data
values. (ACMSP096)
Evaluate the effectiveness of different
displays in illustrating data features
including variability. (ACMSP097)
ISBN 978 1 74135 243 6
SP6 Picture graphs
19
Investigation 3
Plenty of pikelets
Traditionally, children have learned many
maths concepts while cooking with a
parent or grandparent. However, today’s
busy lifestyle often prevents children from
having these great learning experiences.
This Investigation allows children to
budget, measure, halve and double
quantities in a real life situation. Producing
an edible result is an added bonus.
Planning the Investigation
Expected duration of Investigation:
3 to 4 weeks
Recommended group size:
3 to 4 students
Students will need:
Tear-out 1 – Pikelet Day
internet access
ingredients required to make pikelets: eggs, sugar,
milk, self-raising flour, salt, butter and toppings
such as honey or jam
utensils required to make pikelets: frying pan,
scales, measuring jug or cup, bowl, spoons, spatula,
whisk and sifter
Topics for this Investigation
Before starting the Investigation, teach the following Topics…
MG5 Measuring mass
NA31 Simple budgets
36
ISBN 978 1 74135 243 6
Investigation 4
The time of my life
Books I have read
Most children are fascinated by amazing facts
about themselves. They will enjoy discovering
such things as: the number of days they have
lived, the number of meals they have eaten
and the number of times their heart beats
every day. This Investigation allows students
to work with large numbers in a way they
will find interesting and informative. They
will also be able to practise collecting and
recording data in a meaningful context. This
Investigation could be linked to a getting to
know you unit early in the year.
3 to 4 weeks
Individuals
Students will need:
Tear-out 2 – The time of my life
internet access
calculator
stopwatch
calendar
44
ISBN 978 1 74135 243 6
3 Gather your base data.
In this part of the Investigation, students should brainstorm ways
to gather information to complete Tear-out 2, The time of my life.
fingertips, not thumb, to feel for the pulse. It may be interesting
to compare a resting pulse to a pulse taken after exercise.
Problem solving
Students should use the problem solving strategy, find smaller
parts of a large problem, in order to calculate required data
about themselves. First, they should perform the small task of
finding out how many school days there are in a year. This base
data will then be used to find the solution to larger problems.
Further into the Investigation, students must perform a series
of smaller tasks when asked to collect data for one day. These
smaller tasks include: finding heart rate per minute, leading to
heart rate per hour, leading to heart rate per school day.
When they have a pulse rate for one minute, students should
brainstorm how this information could help them find how
many heartbeats they have in a school day.
Students will find that there are approximately 200 school days
in a school year. Students can visit imathskids.com.au, click on
Investigation 4 and follow the links to the websites listed to find
information about term durations.
This formula can also be applied to the number of breaths
per day.
To assist with base data, students should determine how many
leap years there have been during their lives. Remind students
that every fourth year is a leap year. Recent leap years have
been 2004 and 2008, followed by 2012. Most students will have
found that they have had two or three leap years in their lives,
depending on the year in which they were born.
With the class, brainstorm ways to count and record blinks,
breaths and heartbeats. Students may need to work in pairs
with one student recording the number of breaths, blinks and
heartbeats of the other in a minute.
You should model ways to find how
many times your heart beats per
minute. Show students how to take
a reasonably accurate pulse on
themselves. The best place to detect
a pulse is on the wrist. Turn the hand
palm up and rest finger tips from
the other hand on the thumb side of
the wrist. Students should use their
The easiest way to calculate the number of beats per school day
is to multiply the number of heartbeats by the number of minutes
in a school day.
There are 360 minutes in a school day. So, as an example:
If Emily’s heart rate is 80 beats per minute,
then 80 x 360 = 28 800 heartbeats per day.
When calculating the number of blinks per day, remind students
that they are not blinking while they sleep, so they should only
calculate blinks for the hours they are awake.
Focus questions
• How many heartbeats did you count in one minute?
• How many minutes are there in one hour?
• How can we find out from these two pieces of information
how many heartbeats are in an hour?
• How many hours are in a school day?
• How can we find out from this information how many
heartbeats are in a school day?
4 Calculate how many days you have lived.
In this step, students must calculate how many days they have
lived. With the class, read through the Step 4 instructions in the
Student Book, ensuring students understand the steps required to
calculate the number of days they have lived (See Fig 4.1).
Step 1: Multiply your age today by 365.
Step 2: Count one day for each of the leap years you have lived.
Step 3: Count the number of days since your last birthday.
Do this month by month.
Step 4: Add the totals to find the number of days you have lived.
Fig 4.1 – Sample answer
I am a 9-year-old student,
born on the 2nd December.
Today, I am 9 whole years old.
9 x 365 days = 3285 days
I have lived through 3 leap years.
3285 + 3 days = 3288 days
My last birthday was the 2nd
of December last year. Today
is the 20th of April.
29 days in Dec + 31 days in Jan
+ 28 days in Feb + 31 days in Mar
+ 20 days in April = 139 days.
3288 days + 139 days = 3427 days
48
ISBN 978 1 74135 243 6
Investigation 4
5 Calculate all the other facts.
School days
There are approximately 200–205 school days per year.
Students should multiply this by the number of years they have
been at school. For a more accurate result, encourage students
to take away the number of days they remember being on long
holidays, away sick, on sports training camps etc.
Leap years
Most students will have had two or three leap years in their
lives, depending on the year they were born.
Fig 4.2 – The time of my life
Heartbeats
Multiply heartbeats in one minute by 60 (for one hour), then
by 6 (for one school day). Students could do this on a calculator.
Blinks
Multiply blinks in one minute by 60 (for one hour), then by the
number of hours students are awake in a day. Students could do
this on a calculator.
Days lived
Refer to the Student Book, Step 4 – How many days have
you lived? – for details about how to calculate this.
Number of summers
Depending on the month of their birth and the time of the year
the Investigation is undertaken, this should be the same as their
age or one different (if they haven’t yet had their birthday this
year, it is their age + 1).
Tear-out 2
Investigation 4: The time of my life
The time of my life
Date of birth:
3
There have been
leap years in my life.
My heart beats at least
28 800
times every school day.
Even when I try not to, I blink about
I have lived for
3427
15 360
times every day.
days to date.
10 summers.
10 281 meals in my life.
I take approximately 28 800 breaths every day.
I have lived through
Note
Wow, I have eaten
No wonder I am tired, I have been at school for
Meals eaten
This should be the number of days they have lived (from Step 4),
multiplied by three.
Breaths
Multiply breaths in one minute by 60 (for one hour), then by 24
(for one day). Students could do this on a calculator.
Jane
2nd December
Name:
A school day is
6 hours long.
875
days.
Tear-out 2
In this step, students should use their base data to calculate
the facts needed to complete Tear-out 2, The time of my life
(see Fig 4.2). It is important that students show all the working
required to complete each calculation. This could be written
onto The time of my life sheet or onto an attached working sheet
(see Fig 4.3).
Place your photo here.
ISBN 978 1 74135 179 8
iMaths 4 Student Book
185
Fig 4.3 – Example working sheet
Leap years
Days lived
Number of meals
Leap years since I was born:
2008, 2004
So, 2 leap years in my life.
I am a 9-year-old student, born on
the 2nd December.
9 x 365 days = 3285 days
I have lived through 3 leap years
3285 + 3 days = 3288 days
My last birthday was the 2nd of December last
year. Today is the 20th of April.
29 days (Dec) + 31 days (Jan) + 28 days (Feb)
+ 31 days (Mar) + 20 days (Apr) = 139 days
3288 days + 139 days = 3427 days
I eat 3 meals per day on average.
I have been alive for 3427 days.
3 x 3427 = 10 281 meals
Heartbeats*
My heart beats 80 beats/minute.
There are 360 minutes in a school day.
80 x 360 = 28 800 beats/school day
Blinks
I blink 16 times/minute.
There are 60 minutes in an hour.
16 x 60 = 960 blinks per hour.
I sleep for 8 hours per day.
24 – 8 = 16
I am awake for 16 hours per day.
960 x 16 = 15 360 blinks/day
Number of summers
I have lived for 10 years, with 1 summer
each year.
So, 10 summers in my life.
Breaths per day*
I breathe 20 times/minute.
There are 1440 minutes in a day.
20 x 1440 = 28 800 breaths/day
Days at school
Average of 205 days/school year
I have had 4 full years of school to
date 4 x 205 = 820 days
The date today is 20th April. There have been 55
school days this year to date.
820 + 55 = 875 days at school
* To consolidate the content in the Topics, direct students to multiply by 60, then 24 rather than 1440. For example: Heartbeats
ISBN 978 1 74135 243 6
80
x 60
4800
4800
x 6
28 800
49
6 Compare yourself with a friend.
In this step, students should use a table to compare and contrast
their data with a friend’s (see Fig 4.4). Revise the layout of tables
with the class. A table should have a title and labelled columns.
List and discuss interesting sentence starters and comparing and
contrasting linking words (see Fig 4.5).
Example sentence starters
• When comparing myself to a friend, I find…
• I was amazed to discover that…
• Unlike my friend, I…
• Compared with my friend, I…
• As incredible as it may sound…
• The difference between…
• As well as…
Students should write five interesting sentences, comparing
themselves to a friend. For example, looking at the data in the
table in Fig 4.4, some comparing/contrasting sentences for
Jane might be:
1 When comparing myself to Emily, I found that she is 274 days
older than I am.
2 I was amazed to discover that Emily and I have lived through
the same number of leap years.
3 Compared with Emily, I breathe 2400 more times per day.
4 I blink 15 360 times per day, unlike Emily who blinks
14 820 times per day.
5 Emily and I are similar in that we have both been to school
for 875 days.
Fig 4.4 – Example data table
The time of our lives
Jane’s Data
Emily’s Data
3
3
Heartbeats per school day
29 260
32 620
Blinks per day
15 360
14 820
3427
3701
10
10
Meals eaten
10 281
11 103
Breaths per day
28 800
26 400
875
875
Number of leap years
Days lived
Number of summers
Number of school days
Fig 4.5 – Contrast and comparison linking words
Contrast linking words (describe differences)
on the other
hand
in contrast to
different from
however
alternatively
but
although
rather than
whereas
while
unlike
yet
even though
less than
more than
whilst
Comparison linking words (describe similarities)
both
same
in both
like
in both cases
similarly
and
as well as
in the same
way
just as...
so...
alike
similar in that
7 Class comparisons.
Students should present their data to the class, including
the comparative sentences. When calculating totals, students
will make many assumptions. These might include:
• that heart rate, breathing and blinking remain constant
• that 3 meals were eaten every single day
• that students had no absences from school.
Some students may make adjustments to negate these
assumptions. For example, students may know exactly how
many absences they have had and subtract this from the total
number of school days.
Student totals will vary for a number of reasons. These could
include: differing birthdates and years, differing heart rates,
illnesses, other reasons for school absence, errors in base
data collection and calculation errors.
Making connections
Discuss the following questions to encourage students to
apply what they have learned in this Investigation to other
everyday situations.
• What other interesting facts could we have investigated
about ourselves?
• Which fact did you find the most fascinating?
• What makes us blink?
• What effects do various activities such as lying still on the
floor, shuttle runs or step ups have on heart rate?
50
Communicating and reflecting
The following questions are designed to help you assess
students’ understanding of what they have learned in
this Investigation.
• How does the data for you and your friend differ?
Why?
• How did you calculate your heartbeats per school day?
• Using your total number of breaths per day, how
would you calculate your total number of breaths
per week or month?
Students should submit:
Tear-out 2, The time of my life, with calculations
table of data for student and friend
5 interesting comparison sentences.
ISBN 978 1 74135 243 6
ISBN 978 1 74135 179 8
ISBN 978 1 74135 179 8
Internet access
Investigation 7
Investigation 17
Investigation
Materials
iMaths 4 Black Line Masters © Carolyn Smales, Wayne Lightbourne and Jane Rheeder 2011 Firefly Education Pty Ltd
#-.T¯
Using maths
2 Research the landmarks and icons.
Go to imathskids.com.au and visit the websites listed
to find the location of each landmark.
Find the town closest to each landmark and record
them on BLM 7.1, Aussie adventure table.
Find the population of each town and record it on
BLM 7.1. Round each number to the nearest 100.
Survey your class and record how many students have
been to each town. Display this data as a picture graph.
Share interesting information about each landmark.
Go to imathskids.com.au –
the Investigation 7 area contains the
*OWFTUJHBUJPOQMBOXFCTJUFTBOE#-.TUIBU
you need to complete this Investigation.
BLM 7.1 Investigation 7:'%%( &'$
Aussie adventure table
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ISBN 978 1 74135 179 8
4 How far would you travel?
Measure the distance between each town as the
crow flies to work out how far you would travel.
If one centimetre represents 200 km, how many
kilometres would you travel in total? Record this
on your Aussie adventure map.
'$'
ISBN 978 1 74135 179 8
3 Plan your trip.
Use a map of Australia to find each town. Write the
names of these towns next to the appropriate dot on
BLM 7.2, Aussie adventure map. Mark and name your
home town.
Plan your trip and draw your route on the map.
Remember to leave from your home town, follow a
sensible route through all the towns, then return home.
Scale: 1 cm = 200 km
!&%& &$(
Reasoning and reporting
5 Share and discuss.
Display your map. As a class, discuss the different
routes taken. Is one any better than the others? Why?
-PPLBUUIFWBSZJOHQPQVMBUJPOOVNCFSTGPVOEGPS
each town. Are there any variations in your
findings? Why?
Hand in your table, picture graph and map.
Inquiry
Investigate the most appropriate
route and mode of transport for
each stage of your journey. At times
¾ZJOHNJHIUCFUIFCFTUPQUJPOCVU
for some stages it might be better to
drive or take a ferry.
ISBN 978 1 74135 179 8
21
To begin this Investigation, students should use the internet to
research Australian landmarks and icons.
Students can visit imathskids.com.au, click on Investigation 7 and
follow the links to the websites listed to find the relevant information.
Ask students to record each landmark, its nearest town and some
interesting information about each.
Students should record their landmark information on BLM 7.1,
Aussie adventure table, including the closest town, its population
and the population rounded to the nearest 100 (see Fig 7.1). Inform
students that populations may vary for a number of reasons. Fig 7.1
shows the approximate populations at the time of publication.
This is an opportune time to discuss population variation and trends.
In Australia, the high growth area continues to be the south-east
corner of Queensland. Mining town populations swell and diminish
with the demand on the mines. Encourage students to compare
the varying population statistics different people have for the same
town or city. Reasons for such variations could include: age of
information, regional or town figures, authenticity of source, drought
or climate, mining boom or bust, economic or political conditions.
ISBN 978 1 74135 243 6
continued next page
Fig 7.1 – Icons and closest towns
Closest town
Population
Rounded
population
Australian
Stockman's
Hall of Fame
Longreach
4268
4300
The Big Golden
Guitar
Tamworth
47 595
47 600
The Twelve
Apostles
Port Campbell
599
600
Cape Byron
Lighthouse
Byron Bay
4981
5000
Port Arthur
Port Arthur
499
500
Icon
Uluru
Alice Springs
27 481
27 500
Monkey Mia
Denham
1428
1400
Coober Pedy
Coober Pedy
2762
2800
73
The populations of the towns in the table can be found on the
internet by searching: population of (town’s name). For example
the population of Longreach can be found by searching for
population of Longreach.
Fig 7.2 – Example class survey table
Town
Tamworth
Port Campbell
Byron Bay
Engage the class in a discussion about how to conduct a survey.
Ask students to brainstorm ways of gathering information from
their classmates. This can be anything from a simple show of
hands, to a questionnaire each student fills in, to individual
interviews.
Ask students who have visited the towns to share interesting
experiences or information about them with the rest of the class.
Port Arthur
Alice Springs
Denham
Coober Pedy
Fig 7.3 – Example picture graph
Aussie Adventure quest class picture graph
Longreach
Tamworth
Port Campbell
Byron Bay
Town
When creating their picture graphs, the symbols used could
identify each student (initials or a small face). Ensure the graph
clearly shows how many students have visited each town.
Remind students that a picture graph must have a title, correctly
labelled axes and a key for the symbol (see Fig 7.3).
Number of
students visited
Longreach
Next, ask students to conduct a class survey to determine how
many people in the class have actually visited the towns in the
Investigation. Ask them to record their results in a picture graph.
No matter which method students decide to use to collect the
information, they should use a table to collect results before they
graph the data. Revise the use of tally marks for recording this
type of data (see Fig 7.2).
(continued)
Note: Alternatively, students can conduct the survey on which
location they would most like to visit.
Port Arthur
Alice Springs
Denham
Coober Pedy
Number of students
Key:
3 Plan your trip.
= 1 student visit
For this step of the Investigation, students will use BLM 7.2,
Aussie adventure map. Ask students to mark each of the
landmark towns, as well as their own hometown,
on the Aussie adventure map. They should then use the map
to plan their trip around Australia, starting from their
hometown and following a sensible route through all towns,
before returning home.
Students should mark their route with arrows, to show
the direction of travel (see Fig 7.4). For the purpose of this
Investigation, students can move and mark directions as the
crow flies (i.e. a straight line), as it may be too time-consuming
to investigate distances by road. Students could be shown a
physical map of Australia to gain some knowledge about the
kind of terrain they will be crossing. However, for the purposes
of this Investigation, measuring distances in straight lines is
sufficient.
Focus question
• What is a sensible route? (A sensible route would be one
with the least travelling distance and minimal backtracking.)
Fig 7.4 – Example Aussie adventure map
Longreach
Alice Springs
Denham
Coober Pedy
Byron Bay
Tamworth
Perth
(home)
Port Campbell
Port Arthur
74
ISBN 978 1 74135 243 6
Investigation 7
4 How far would you travel?
Using the Aussie adventure map, ask students to measure
the distance between each town to work out how far they
would travel as the crow flies. Tell students that on BLM 7.2,
one centimetre equals 200 km. Ask students to record the
distance from town to town and the total distance travelled on
the Aussie adventure map.
Just for fun, students may like to compare the distances they
calculated as the crow flies against the distances on a road
map or the internet (see Fig 7.6).
Students can visit imathskids.com.au, click on Investigation 7
and follow the links to find websites that show actual distances
by road.
The total distance travelled will vary depending on each
student’s home town (see Fig 7.5).
Fig 7.5 – Example trip distances
Total distance of my trip
Perth – Denham = 700 km
Denham – Alice Springs = 2100 km
Alice Springs – Longreach = 1100 km
Longreach – Byron Bay = 1200 km
Byron Bay – Tamworth = 300 km
Tamworth – Port Arthur = 1400 km
Port Arthur – Port Campbell = 700 km
Port Campbell – Cooper Pedy = 1300 km
Cooper Pedy – Perth = 1900 km
Fig 7.6 – Example road distance comparisons
Journey
Distance as the crow flies
Perth – Denham
Distance by road
3.5 cm
700 km
839 km
10.5 cm
2100 km
3407 km
5.5 cm
1100 km
1816 km
Longreach – Byron Bay
6 cm
1200 km
1318 km
Byron Bay – Tamworth
1.5 cm
300 km
7 cm
1400 km
1978 km (incl ferry)
1007 km (incl ferry)
Denham – Alice Springs
Alice Springs – Longreach
Tamworth – Port Arthur
503 km
Port Arthur – Port Campbell
3.5 cm
700 km
Port Campbell – Cooper Pedy
6.5 cm
1300 km
Cooper Pedy – Perth
9.5 cm
1900 km
1838 km
Totals:
10 700 km
14 016 km
Total = 10 700 km
1310 km
5 Share and discuss.
Ask students to present their Aussie adventure maps and
gathered data to the class, explaining the route they took and
the reasons for their choices. Ask students to highlight the
variations in the findings of classmates and explain how these
variations occur.
Communicating and reflecting
The following questions are designed to help you assess
students’ understanding of what they have learned in this
Investigation.
• Why did you choose this route around Australia?
• How could you have found a more suitable route?
• How did you round the populations of the towns/cities?
• What was the total distance of your journey? How did
you calculate this?
• How did you represent your class survey data on the
picture graph?
ISBN 978 1 74135 243 6
Making connections
Discuss the following questions to encourage students to
apply what they have learned in this Investigation to other
everyday situations.
• Why is it important to plan your route and know
distances before you go on a long journey?
• Why are distances by road usually greater than
distances as the crow flies?
Students should submit:
BLM 7.1 – Aussie adventure table showing towns with
their actual and rounded populations
BLM 7.2 – Aussie adventure map showing the route
of the trip, distance from town to town and total
distance of the trip
picture graph showing the number of students who
have visited each town or city.
75
Reasoning
Proficiency strands
ISBN 978 1 74135 243 6
Understanding, Fluency and Problem Solving
Did not understand that
one picture could represent
a number of items.
Drew the basic shape of a
graph but labels were unclear.
Was unable to complete
the graph.
Had difficulty locating the
towns and reading the
measuring device.
Did not understand how to
use the scale to convert
centimetres to kilometres.
Was unable to complete the task.
Listed the places travelled
but was unable to give
reasons for choosing the
direction of the route.
Was unable to identify the
variations in the information.
Needed teacher guidance to
create a picture graph with
a title and clearly labelled
columns and rows.
Had difficulty creating the key
and transferring the data to
the graph.
Needed teacher guidance
to locate the towns, measure
the distances and use the
scale to convert centimetres to
kilometres.
Had difficulty with the
calculations.
The reasons for choosing
the route were sometimes
confused.
Identified a few obvious
variations in the population
information and the
distances travelled.
Had difficulty offering basic
reasons for these variations.
Needed help to create a
picture graph with a title
and clearly labelled columns
and rows.
Made some errors when
creating the key and
transferring the data to
the graph.
locating the towns and
measuring the distances
between towns.
Needed help to use the
scale to convert centimetres
to kilometres.
Made some errors in
calculations.
Described the route.
Gave a few simple reasons
for route choice.
Identified some obvious
variations in the population
information and the distances
travelled.
Had trouble offering logical
reasons for these variations.
Needed prompting to create
a picture graph with a suitable
title, and clearly labelled
columns and rows.
Made only minor errors
when creating the key and
transferring the data.
Corrected any errors identified
by the teacher when locating
the towns and the distances.
Needed prompting to use the
scale to convert centimetres to
kilometres.
Made only minor errors in
calculations.
Gave clear reasons for
choosing the route.
Identified some variations in
the population information
and the distances travelled.
Offered some basic reasons for
these variations.
Independently created a
picture graph which accurately
represented the data.
Graph was suitably titled.
Columns and rows were clearly
labelled.
Key was accurate and
informative.
Independently located each
town. Accurately measured the
distances between towns.
Independently used the scale
to convert centimetres to
kilometres.
All calculations were error free.
Gave clear and detailed
reasons for choosing the route.
Identified variations in the
population information and
the distances travelled.
Offered logical reasons for
these variations.
Use a picture graph
to record the number
of students in the
class who have
visited these places.
Locate each town.
Choose a sensible
route.
Measure the distance
between the towns
and use the scale
to find the total
distance of the trip
in kilometres.
Discuss the
information on
population and the
routes taken.
Identify any variations
and give possible
reasons for these.
Overall rating
Needed to be given the
population information.
Placed it randomly in the table.
Could not identify the place
value of some of the numbers.
Was unable to complete the
rounding.
Needed teacher guidance to
find the correct population
information and record it in
the correct place in the table.
Had difficulty rounding
numbers to the nearest 100.
Needed help to identify and
record the population of each
town in the correct place in
the table.
rounding the numbers to
the nearest 100.
Corrected any errors identified
when recording the population
of each town in the correct
place in the table and rounding
the numbers to the nearest 100.
Independently found and
recorded the population of
each town in the correct place
in the table.
Rounded all numbers correctly
to the nearest 100.
Find, record and
round the population
of each town to the
nearest 100.
Teacher comments
E
D
C
Due date:
B
Name:
A
Step Ability to...
Investigation 7
Rubric
77
Investigation 8
Super sports stadium
ManyInvestigation
This
children enjoy
combines
playing chance
sport and
and
data have
may
with the
visited
spatial
a number
concept
of of
sports
3D dice
to create non-traditional,
stadiums.
Using maths skills,
fair such
dice with
as
unique, interesting
estimation,
multiplication
shapes.and
Students
division
are
required
to
designto
a design
junior sports
dice that
stadium
have gives
a fair
chanceaofreal
maths
landing
life, practical
on any face
context.
and also
have a fair representation of letters,
colours or symbols on the faces.
3 to 4 weeks
2 to 4 students
Students will need:
internet access
A4 paper
craft materials
tape measure
NA12 Backtracking
78
ISBN 978 1 74135 243 6
Investigation 9
Marble mash
This Investigation combines
lets students
chance
explore
and
datarelationship
the
with the spatial
between
concept
net size
of 3D dice
to create
and
3D objects,
non-traditional,
developing
fairthe
dice
early
with
unique, interesting
concept
of volume. shapes.
StudentsStudents
will use are
required
trial
and to
error
design
and dice
deduction
that have
to create
a fair
chance
net
designs
of landing
that, when
on any
completed
face andand
also
have a fair representation
constructed,
will hold the maximum
of letters,
colours or
number
of symbols
marbles.on the faces.
3 to 4 weeks
2 to 3 students
Students will need:
internet access
coloured cardboard
A4 paper
craft materials (glue, scissors, tape)
marbles
MG7 Volume
86
ISBN 978 1 74135 243 6
Investigation 10
It’s only natural
The natural
This
Investigation
world combines
is fascinating.
chance and
dataInvestigation
This
with the spatial
demonstrates
concept of 3D
thatdice
to create
maths
exists
non-traditional,
outside the classroom
fair dice with
unique,
in
manyinteresting
plants andshapes.
other natural
Students are
required to design
phenomena,
such as
dice
shells
thatand
have a fair
chanceakes.
snowfl
of landing
Students
on explore
any facethe
and
Topics
also
have
of
Number
a fair representation
and Algebra, Measurement
of letters,
colours
and
Geometry
or symbols
as they
on the
investigate
faces. and
display the pattern they discover in
the natural world around them. This
Investigation is closely linked to science.
3 to 4 weeks
Individuals or pairs
Students will need:
BLM 10.1 – Squared grid paper
internet access
cardboard
digital camera
string and cotton
collection of leaves and flowers, images of plants
library
craft materials
NA5 Multiples 3, 4, 5, 6, 7, 8, 9
MG5 Measuring mass
MG12 Area
MG2 Millimetres
MG4 Perimeter
MG16 Tessellation
94
ISBN 978 1 74135 243 6
Investigation 11 Fraction fun
2 What to eat?
(continued)
Problem solving
To introduce the concept of fractions, use the problem solving
strategy, act out the problem. Playing the following game might
help students see the different ways a group (or in this case,
their class) can be divided into equal parts. You will need clear
floor space for this game.
Write the total number of students in the class on the board.
Call out a number. Students quickly form groups of that number
and sit on the floor. For example, you call out 3 and students sit in
groups of 3. If there are any students leftover, they are out of the
game. Continue the game calling different numbers until only
2 students are left as the winners.
When equal groups are formed with no students left over,
write fraction statements on the board to describe different
grouping arrangements. Discuss the statements with the class.
For example:
• Amy’s group is 14 of the whole class.
• We formed 6 groups of 3. Each group is 16 of the group.
• When we had five equal groups, they were fifths.
3 How many small food items will you need?
For the activities in this step of the Investigation, you will need to
print one copy of BLM 11.1, Small food items, for each student.
When completing their Small food items table, it is important
that students realise that not all party guests will eat every item.
To complete the Small food items table (see Fig 11.2), students
will need to:
• list the small food items
• paste or draw images of the small food items
• estimate and record the number of people who will eat
each item (eg 4 people like cheese cubes)
• record the number of items each of these people will eat
(eg 2 cheese cubes per person)
• calculate the number of items needed (eg 4 people x 2 cheese
cubes each = 8 cheese cubes)
• draw a representation of the food items and write the fraction
to show how they will be shared equally (eg 28 for each person)
• write an equivalent fraction, if possible.
Fig 11.2 – Example Small food items table
Small food items
Item
cheese
cubes
party
pies
Number Number Total Picture or Fraction Equivalent
of
per items diagram
per
fraction
people person
person
eating
4
x2
8
2
8
1
4
2
x2
4
2
4
1
2
4 How many large food items will you need?
For the activities in this step of the Investigation, you will need to
print one copy of BLM 11.2, Large food items, for each student.
It would be helpful if students used paper or card to make a
visual representation of the large food items, so that they can see
whether the size of their pieces would be suitable. Students could
measure containers, such as cake and pizza boxes to make their
visual representations as close to the actual size as possible.
Fig 11.3 – Example Large food items table
Large food items
Item
To complete the Large food items table (see Fig 11.3), students
will need to:
• list the large single-food items to be divided
• paste or draw images of the large single-food items
• estimate and record the number of people who will eat
pieces of this large item (eg 4 people like pizza)
• record the number of pieces each of these people will
eat (eg 2 pieces)
• calculate how many pieces of each item they need to
cut (eg 4 people x 2 pieces each = 8 pieces of pizza)
• draw a representation of the single food item, divided by
the number of pieces needed (eg 8 pieces of pizza)
• write the fraction to show how the items will be shared
equally (eg 28 for each person).
• write an equivalent fraction, if possible.
106
Number Number Total Picture or Fraction Equivalent
of
of pieces diagram
per
fraction
people pieces
person
eating
per
person
4
x2
8
2
8
1
4
3
x2
6
2
6
1
3
pizza
cake
ISBN 978 1 74135 243 6
Investigation 12
Nice dice
This Investigation combines chance
statisticsand
and
data with the
probability
with
spatial
the spatial
concept
concept
of 3D dice
of 3D
to create
dice
to create
non-traditional,
non-traditional,
fair dice
fair with
dice
unique,
with
unique,
interesting
interesting
shapes.
shapes.
Students
Students
are
required
are
required
to design
to design
dicedice
thatthat
havehave
a fair
a
chance
fair
chance
of landing
of landing
on any
on any
faceface
and and
also
havehave
also
a fairarepresentation
fair representation
of letters,
of letters,
colours or symbols on the faces.
3 to 4 weeks
individuals or pairs
Students will need:
internet access
cardboard
craft materials
MG2 Millimetres
SP2 Judgments
SP1 Probability
SP4 Organising data
110
ISBN 978 1 74135 243 6
T
H
t
O
84 509
reads as 84 thousand 509
61 thousand 345
ten thousands
hundreds
b 39 613
c 76 958
34 iMaths 4 Student Book
thousands
a 27 444
( H )
( tT )
( T )
ISBN 978 1 74135 179 8
Thousands may sometimes be written
as K (K is for kilo which is 1000),
especially as an amount of money.
$12K is $12 000
Language reminder
3 The place value of the 2 in 28 900 is ten thousands (tT). Name the value of
the bold digit in each of these numbers, then write its symbol.
2
1 61 345 reads as
Try this
To read a large number, you pause after each group to say the
name of the group before continuing. If you can read a three-digit
number like 444, then you can read these large numbers.
44 444 reads as 44 thousand 444
86 521 reads as 86 thousand 521
tT
hundred
thousands
ten
thousands
HT
thousands
Ones group
hundreds
Thousands group
tens
Millions group
Here are the individual place value names and symbols up
to hundred thousands.
Our system of numeration uses place value. This means
that a digit has a different value depending on its place in
a number. For example, the sevens in 37 947 have different
values — 7000 or 7.
Our numeration system uses a grouping pattern. Knowing
the grouping pattern lets you read and better understand
large numbers.
ones
ISBN 978 1 74135 243 6
119
Belgium
50 000
Croatia
ten thousands
d Ireland
b Slovenia
tens
ones
Ireland
ISBN 978 1 74135 179 8
Challenge
1
2
3
4
35
Topics NA1–NA2
Rearrange the digits to make the greatest number.
Rearrange the digits to make the smallest number.
Use the digits to make a number closest to the area of the Netherlands.
Use the digits to make a number closest to the area of Denmark.
Greatest and smallest: Roll a dice 5 times. Write each number on a line below.
Belgium, Croatia, Denmark, Netherlands, Slovenia
100 000
square kilometres
square kilometres
Area (sq km)
83 858
30 510
56 542
78 866
43 064
103 000
70 230
93 030
41 526
20 273
Hungary
Austria
Country
Austria
Belgium
Croatia
Czech Republic
Denmark
Iceland
Ireland
Hungary
Netherlands
Slovenia
8 Which of the 10 European countries in the table are smaller than Tasmania?
The area of Tasmania is 64 519 square kilometres.
c Denmark thousands
a Belgium
7 What is the place value of the 3 in the area of these countries?
10 000
Slovenia
6 Write the name of a country in each space on the area number line.
41 thousand 526
5 Look at the area of the Netherlands. It reads as:
83 thousand 858
4 Look at the area of Austria. It reads as:
The table shows the area in square kilometres
of 10 countries in Europe.
Topic NA2
120
sa
ou nds
th
7
re
nd ds
hu
2
n
te s
5
on
es
8 x 10 0 00
6 x 1 000
7 x 100
2 x 10
5 x 1
60 000
8 000
200
70
4
b
6 x 10 000
8 x 1000
2 x 100
7 x 10
4x1
n ths
ISBN 978 1 74135 179 8
8 thousands (T)
2 hundreds (H)
7 tens (t)
4 ones (O)
te
a
c 6 ten thousands (tT)
8 ten thousands (tT)
6 thousands (T)
7 hundreds (H)
2 tens (t)
5 ones (O)
1 Show the number 68 274 using three forms of expanded notation.
Try this
80 0 00
6 00 0
70 0
20
5
Here are three ways to show the number in expanded notation.
6
7
8
es
We show:
7 2 5
on
n
te s
a
ou nds
th
sa
ou nds
th
4
8 6
n
te s
We say:
86 725
2
We write:
Numbers can be expanded to show the
value of each digit. A simple example
would be 247 = 200 + 40 + 7. The same
strategy can be used to show the place
value of large numbers like the one below.
3000
3
200
= 70 000 + 40 + 6
= 60 000 + 8000 + 200 + 10 + 3
= 90 000 + 5000 + 800 + 60
= 90 000 + 500 + 9000 + 5 + 50
= 60 + 80 000 + 6000
99 555
86 060
b
c
ISBN 978 1 74135 179 8
Expander for ten thousands: Design an 18-square number expander made from a strip of paper or card.
Label the place values from ones to hundred thousands.
Challenge
fifty-three thousand, nine hundred and sixty-two
5 Write 53 962 in words.
= 40 + 4000 + 7 + 30 000 + 700
34 747
a
2000
30 000
4 The expanded notation is all jumbled up for these numbers. Write the number shown
by each expanded notation.
70 046
68 213
b
c
95 860
a
20
300
100 000
200 000
3 Write the number shown by each expanded notation.
2
30
20 000
2 Colour the cards needed to make the number 33 222. Some cards are not needed.
37
ISBN 978 1 74135 243 6
Topic NA3
ISBN 978 1 74135 243 6
121
f
26 000
e 26 x 1000
d 81 000 ÷ 100
2600
c 26 x 100
81 000 ÷ 1000
b 81 000 ÷ 10
260
a 26 x 10
81
810
8100
ISBN 978 1 74135 179 8
Write 45 000 in the tT, T, H, t and ones place.
Dividing by 10, 100, 1000
45 000 ÷ 10 = 4500 (slide one place to the right)
45 000 ÷ 100 = 450 (slide two places to the right)
45 000 ÷ 1000 = 45 (slide three places to the right)
Write 45 in the tens and ones place.
Multiplying by 10, 100, 1000
45 x 10 =
450 (slide one place to the left)
45 x 100 = 4500 (slide two places to the left)
45 x 1000 = 45 000 (slide three places to the left)
1 Use your number slide to help you calculate these.
Try this
The work on this page will be
easier to understand if you
make the number slide on
Tear-out 4, page 189.
Tip
70 x 10 = 700 (slide 70 one place to the left)
70 ÷ 10 = 7 (slide 70 one place to the right)
Multiplying a number by 10, 100 and 1000 shifts
left.
the number a certain number of places to the left
Dividing a number by 10, 100 or 1000 shifts the
right.
number a certain number of places to the right
On your number slide write 70 in the tens and
ones place. Try these:
tT
T
H
O
5
t
4
T
H
t
O
HT
tT
T
H
t
O
tT
T
H
t
O
ISBN 978 1 74135 179 8
39
Topics NA3–NA4
Make fifty grand: How many ten dollar notes make $50 000? How many hundred dollar notes?
Challenge
HT
Do not remove
the squares!
4 Open the folded strip so that it is flat again.
5 Cut a long strip of stiff paper or card 1 cm wide and at least 30 cm long.
6 Weave the strip along the number slide, starting underneath, then on top
of the white square, then underneath the next region, and so on.
7 Write the number to be multiplied or divided onto the strip and slide it
the correct number of places (see page 38 for details). Carefully erase the
number to re-use the strip.
HT
tT
How to make a number slide
1 Turn to Tear-out 4: Number slide on page 189 and cut out the number slide.
2 Fold exactly in half lengthwise along the fold line.
3 Snip the folded strip 12 times, once at each place indicated.
HT
A number slide is a useful device to show multiplying
and dividing by 10, 100 and 1000. You will find out
how to use a number slide when you read the
explanation on the previous page (page 38).
First you need to make one of your own.
Topic NA4
130
4002
713
+ 31
4746
a 31 + 4002 + 713
1 Write each sum vertically and add.
Try this
You can also use
a calculator to
check your answers.
Remember, when you
want to add numbers with
different numbers of places
(like 52 + 1700 + 4 +
4123), write the largest
number first. That way
you’ll always have enough
places to line up the other
numbers.
Tip
1
13 560
3 324
606
+
4
17 494
1
b 606 + 4 + 3324 + 13 560
4123
1700
52
+
4
5879
4123
1700
52
4
5879
ISBN 978 1 74135 179 8
11
22 555
8 121
85
+ 21
30 782
1
c 8121 + 85 + 21 + 22 555
52 + 1700 + 4 + 4123
When adding large numbers it is important to keep all
the places lined up vertically. This will make sure that
you add the ones, tens, hundreds and thousands in
their correct columns.
BNE – DRW – ASP –
AYQ – ASP – BNE
PER – CNS –
BNE – PER
BNE – CNS – DRW
2 2 2
2847
1288
333
333
+ 1961
6762
1 1 1
3428
1387
+ 3601
8416
11 1
1387
+ 1674
3061
1 2
1
3 4 3
3286
2649
1674
2123
1170
617
464
+ 246
12 229
1
2616
651
+ 3121
6388
1038
+ 3017
4055
Return
HBA – AYQ
MEL – HBA –
SYD – BNE – MEL
MEL – ADL – CBR
Territory
i
f
c
Coral Sea Islands Territory
Territory of Heard and MacDonald Islands
Christmas Island
Macquarie Island
Norfolk Island
Lord Howe Island
Cocos (Keeling) Islands
Ashmore and Cartier Islands
SYD – PER – DRW –
CNS – ADL – HBA –
MEL – CBR – SYD
DRW – ADL –
MEL – DRW
SYD – HBA – PER
780 000
370
135
128
35
15
14
+
2
780 699 sq km
h
e
b
ISBN 978 1 74135 179 8
57
780 000
370
135
128
35
15
14
2
Area (sq km)
via MEL
1 1
via ADL
1
617
1885
+ 333
1 1
2835
+ 2835
5670
Topic NA13
1170
1328
+ 333
1
2831
+ 2831 or
5662
1 1
1 3
617
1038
749
+ 1377
3781
1
1
651
+ 957
1608
Fast flight: Which flight has the shorter distance: Brisbane – Melbourne – Hobart, or Brisbane – Sydney – Hobart?
Challenge
The Australian Antarctic
Territory, which has an
area over six million square
kilometres, is not included in
the table.
3 Australia’s external territories
are those remote from the
mainland and governed by
Australia. What is the total
area of Australia’s external
territories listed in the table?
g
d
a
2 Add the distances shown on Data page 2: Flight distances on
page 182 to calculate how far you travel on the following flights.
ISBN 978 1 74135 243 6
ISBN 978 1 74135 243 6
131
(estimate)
(estimate)
15 171
– 6 290
8 881
9000
33 636
8 128
25 508
20 000
–
e 15 171 – 6290
d 33 636 – 8128
14 10 17
(estimate)
(estimate)
2 16
6000
12 000
2 13
17 581
– 12 191
5 390
4 18
b 17 581 – 12 191
14 000
– 12 000
1 2 0 0 0 (estimate)
12 762
– 1 261
11 501
a 12 762 – 1261
1 Estimate, then subtract.
Try this
1 4 0 6 5 round down
– 1 2 3 4 1 round down
To make sure your answer is reasonable, estimate your answer by rounding
the numbers and subtract. You can usually do this mentally.
14 065 – 12 341
14 065
–12 341
1 724
3 10
When subtracting large numbers, remember to
keep all the places lined up. This will help you
subtract the ones, tens, hundreds, thousands
and ten thousands in their correct columns.
f
44 110
55
44 055
01010
ISBN 978 1 74135 179 8
(estimate)
44 000
–
44 110 – 55
(estimate)
20 000
4 15
20 555
–
273
20 282
c 20 555 – 273
You can also use a
calculator to check
your answer.
8 673
11 004
17 005
12 065
14 487
Destination (city, country)
Mumbai, INDIA
New York, USA
Paris, FRANCE
Rio de Janeiro, BRAZIL
Tokyo, JAPAN
7 17
8 14 11
16 951
– 8 673
8 278
f Paris and
Beijing
14 487
– 10 148
4 339
b Moscow and
Mumbai
13 14 7 17
14 487
– 13 509
978
g Moscow and
Rio de Janeiro
8 14 11
16 951
– 12 065
4 886
c Paris and
Los Angeles
98 599
– 90 343
8 256
e 2001 to 2006
59 902
– 45 187
14 715
8 9 12
b 1986 to 1991
99 670
– 98 599
1 071
5 1610
f 2006 to 2011
62 770
– 59 902
2 868
5 11 17 6 10
c 1991 to 1996
59 902
1991
2011
2006
2001
ISBN 978 1 74135 179 8
59
Topics NA13–NA14
99 670
98 599
90 343
62 770
45 187
1986
1996
35 200
Population
1981
Year
Metro City population
7 16 6 13
11
8 673
– 7 826
847
h Beijing and
Tokyo
9
10 148
– 7 826
2 322
d Mumbai and
Tokyo
Population sort: Sort the five year periods from Question 3 from highest to lowest population growth.
Challenge
90 343
– 62 770
27 573
89 12 14
d 1996 to 2001
45 187
– 35 200
9 987
3 14 11
a 1981 to 1986
3 The population of Metro City is recorded every five years at census time.
Calculate the population growth for each five year period shown.
17 005
– 11 004
6 001
e London and
Cape Town
8 17
15 997
– 13 509
2 488
a New York and
Rio de Janeiro
10 148
15 997
16 951
13 509
7 826
Flight distance (km)
2 Refer to the table above. Work out the difference in flight distances when travelling from Sydney
to the following pairs of cities.
Flight distance (km)
Beijing, CHINA
Cape Town, SOUTH AFRICA
London, UNITED KINGDOM
Los Angeles, USA
Moscow, RUSSIA
International air distances from Sydney
Destination (city, country)
Topic NA14
134
x
1
4
4
2
H
2
O
1
3
6
multiply
7
t
= (300 + 50 + 1) x 3
= (300 x 3) + (50 x 3) + (1 x 3)
= 900 + 150 + 3
= 1053
a 351 x 3
= (700 + 8) x 2
= (700 x 2) + (8 x 2)
= 1400 + 16
= 1416
b 708 x 2
1 Use the split and multiply method to find answers to these.
Try this
ones
(3 x 2 ones)
tens
(3 x 7 tens)
hundreds (3 x 4 hundreds)
2 Place value method
To multiply a 3-digit number by a 1-digit number, multiply
the ones first, then the tens and finally the hundreds.
1 Split and multiply
472 x 3
= (400 + 70 + 2) x 3
= (400 x 3) + (70 x 3) + (2 x 3)
= 1200 + 210 + 6
= 1416
I’ll show you two ways to multiply a 3-digit
number by a 1-digit number.
ISBN 978 1 74135 179 8
= (600 + 10 + 5) x 6
= (600 x 6) + (10 x 6) + (5 x 6)
= 3600 + 60 + 30
= 3690
c 615 x 6
Extras are carried into the next
place when necessary, then added
after the next multiplication.
Tip
398
1116
$115
5
$575
$418
2
$836
$227
x
7
$1589
j 7 nights in
Eureka Station
$423
x
3
$1269
f 3 nights in
Melbourne
x
x
Outback Hotels
Platypus Creek
Dingo Flats
Emu Gully
Eureka Station
$661
x
3
$1983
k 3 nights in
Airlie Beach
$808
x
4
$3232
g 4 nights in
Byron Bay
$241
x
6
$1446
c 6 nights in
Platypus Creek
$808
$418
$938
$661
$241
$115
$121
$227
$938
x
2
$1876
h 2 nights in Noosa
$309
x
4
$1236
d 4 nights in
Canberra
981
109
9
ISBN 978 1 74135 179 8
Bedrooms with a view: Completed in 2005, the Gold Coast’s Q1 became the world’s tallest all-residential
tower. It has 212 one-bedroom apartments, 184 two-bedroom apartments and 81 three-bedroom apartments.
How many bedrooms are in Q1?
Challenge
Weekly walk: Find out how many steps you take from the school gate to the classroom door and back.
How many steps do you take on this journey each week? Hint: you make this journey five times every week.
Use the space provided in iMaths 4 Tracker Book to work out your answer.
Problem solving task
$121
x
9
$1089
i 9 nights in
Emu Gully
x
e 5 nights in
Dingo Flats
$532
x
3
$1596
Beach Resorts
Byron Bay
Gold Coast
Noosa
Airlie Beach
b 2 nights in Perth
City Apartments
Perth
$418
$532
Sydney
$309
Canberra
$423
Melbourne
a 3 nights in Sydney
3156
e
Accommodation Package Deals (prices per night)
3 How much will accommodation cost for each stay?
2570
2 Use the place value method to find the answers to these.
a
b
c
d
514
199
372
526
x
5
x
2
x
3
x
6
65
ISBN 978 1 74135 243 6
Topic NA17
ISBN 978 1 74135 243 6
135
+
37
x 25
41
x 32
b
a
=
=
740
3 7
x 2 0
1230
4 1
x 3 0
+
+
82
4 1
2
185
3 7
x
5
x
1 Use the split and multiply strategy to answer these.
Try this
34
x 20
680
34
x 23
=
34
x 20
34
x 23
Split and multiply
34 x 23
Split 23 into 20 + 3 then multiply each part.
Add the two answers.
34
3
=
=
+
+
34
x 3
102
x
Multiplying a 2-digit number by a 2-digit number
combines two ideas you have already learned:
(1) 2-digit x 1-digit multiplication and
(2) multiplication by tens.
Use the split and multiply strategy shown below.
925
740
185
1312
1230
82
1734
1530
=
204
34
x 3
ISBN 978 1 74135 179 8
680
+ 102
782
34
x 20
13
1
31
x 24
124
+ 620
744 hours
4 How many hours in January?
43
x 24
172
+ 860
1032 cans
b 43 cartons
66
x 17
462
+ 660
1122 cents $11.22
ISBN 978 1 74135 179 8
4
b Wednesday
Summer daze: How many hours in summer?
Challenge
75
x 17
525
+ 750
1275 cents $12.75
3
a Monday
$15.81
93
bund
le s
66
bund
le s
75
bund
le s
67
Topics NA17–NA18
2
93
x 17
651
+ 930
1581 cents
c Sunday
13
64
x 48
512
+ 2560
3072 pages
5 How many pages in 48 books with
64 pages in each?
18
x 24
72
+ 360
432 cans
13
c 18 cartons
6 Jack is paid 17 cents for each bundle of catalogues he delivers to the houses in his
suburb. The table shows how many bundles he delivered last week.
How much did he earn each day?
59
x 12
118
+ 590
708 eggs
1
3 How many eggs in 59 dozen?
28
x 24
112
+ 560
672 cans
a 28 cartons
2 A carton of soft drink holds 24 cans.
Work out the number of cans on
each stack.
Topic NA18
ISBN 978 1 74135 243 6
141
1
2
1 112 2 2 12
1
3
2
3
( )
3
3
1
1
4
2
4
b
0
a
3
4
1
( 44 )
c
d
1 14
1
2
4
e
1 34
f
2
(1 44 )
2 14
2 24
g
2
1 13
1 Count by quarters from 0 and write the number shown by each arrow.
Try this
0
3
4
h
3
(2 44 )
i
1 23
3 14
The number line below shows thirds placed between 0 and 1, then 1 and 2.
Count aloud by thirds from 0 to 1, then 1 to 2. Continue counting aloud till you reach 3.
0
3
3
4
4
(3 44 )
ISBN 978 1 74135 179 8
j
3 24
2
(1 33 )
A fraction placed on
a number line shows
its value compared to
other numbers. The
position of fractions on
a number line also helps
us to sort, order and
compare fractions.
2 14
5 12
1
3
b
c
b
7
1
( 33 )
b
2 34
( 62 )
2
c
c
1 13
3 14
d
f
e
9
2
(1 33 )
e
d
( 8 22 )
8 12
1 23
(
3 44
4
)
f
e
2 23
10
(9 22)
d
g
3 13
4 24
f
i
h
12
i
4 34
4
4
j
5 14
h
j
i
8
79
( 54 )
4
6
15
(14 22)
5
(4 33 )
5 24
13 12
4 13
Topics NA23–NA24
j
( 33 )
3
g
h
( 11 22 )
11 12
( 23 )
3
3
g
Blank number line: Mark where the number 6 12 should go on the number line below.
Show any working and explain how you chose where to place your mark.
Challenge
2
(1 44 )
a
5
(4 22)
a
0
a
ISBN 978 1 74135 179 8
4
3
2
Write the missing fractions
on these number lines.
Topic NA24
142
1 34
1
4
2
4
3
4
1
( 44 )
1 14
1 24
156
b
3 38
1
5
2
a
b
2
3
2
2 Write the mixed number shown by these fraction models.
a
1 Colour the fraction models to show these mixed numbers.
Try this
0
1 34
2
(1 44 )
c
c
5
2 13
2 14
2
1
2 24
This number line shows quarters placed between 0 and 1, then 1 and 2.
Count aloud by quarters from 0 to 1, then 1 to 3. Continue counting aloud until you reach 4.
We write:
We say: One and three quarters
We show:
When a number is written as a mixture of
a whole number and a fraction, it is called
number A mixed number is part
a mixed number.
whole number, part fraction.
NA25 Mixed numbers
3
(2 44 )
ISBN 978 1 74135 179 8
2 34
g
b
1 12 2 45 2 14
2 12 8 34 1 25
9 34 2 47 3 56
c
9
quarters
f
b
1
33
( 33 )
3
4
2
43
g
c
e
1
53
f
2
53
5 halves
14 fifths
h
e
g
h
1
63
h
2
63
7 fifths
j
i
ISBN 978 1 74135 179 8
7
81
( 63 )
3
d 35 quarters
Tweenies: Which of the fractions in Question 3 above are greater than 2 but less than 4? There are five to find.
c
3 23 b
Challenge
3
(2 33 )
a
d
18 sevenths
3 halves
5 Write the number shown by each arrow.
e 23 sixths
a
4 How many pieces are shaded in each fraction model in Question 3?
The first one is done for you as an example.
f
d
a
3 Match each fraction model with a mixed number.
Draw a line between each pair. Circle the odd one out.
ISBN 978 1 74135 243 6
Topic NA25
5
10
6
10
7
10
8
10
9
10
1
2
3
4
5
6
7
8
9
110
110
110
110
110
110
110
110
110
3.2
2
3 10
b
3.5
5
3 10
4
c
4.1
1
4 10
3.1
3
a
b
3.6
c
4
3.9
2 Draw an arrow to show the position of the numbers in the boxes.
3
a
2
d
d
4.4
4
4 10
4.5
e
5
5
5.0
4.9
9
4 10
ISBN 978 1 74135 179 8
e
1 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2
(1.0)
(2.0)
1
1 Write the missing number in the empty boxes. Write fractions and decimals for each.
Try this
4
10
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9
3
10
0
2
10
1
10
0
This number line shows tenths between 0 and 1, then 1 and 2.
Count aloud by tenths from 0 till you reach 3.
A decimal placed on a number line shows
its value compared to other numbers.
Decimal numbers can also be written as
fractions. 0.1 and 101 are both ways of
tenth They occupy the
showing one tenth.
same position on the number line.
8.3
7.9
12.5
5
1210
5,
8.7,
5.1,
1.4 ,
21.2,
60.8,
9
3310
3
310
,
1.1 ,
20.9 ,
60.5 ,
33.9 ,
9
5.4 ,
33.9
3.3
8.5
7.7
7.3
8.7
1
,
20.8 ,
60.4 ,
34 ,
9.1 ,
f
34.1 ,
9.2 ,
5.6 ,
8
7310
7
110
0.9 ,
20.7 ,
60.3 ,
c
9.6
9.9
9.7
5.5 ,
8.6
7.4
ISBN 978 1 74135 179 8
10
0.8
20.6
60.2
34.2
9.3
5.7
73.8
1.7
8.9
9.4
9.3
11
9.1
87
Topics NA27–NA28
Blank number line: Mark where the number 10.1 should go on the number line below.
Show any working and explain how you chose where to place your mark.
1.2 ,
21 ,
21.1 ,
1.3 ,
60.6 ,
33.8 ,
8.9 ,
5.3 ,
e
b
8.4
7.8
60.7,
33.7 ,
8.8 ,
5.2,
Challenge
c 1.5,
b 21.3,
a 60.9,
6 Count back by tenths.
c 33.5, 33.6 ,
b 8.6,
a
5 Count on by tenths.
d
9.4
4
a 910
4 Rewrite the mixed numbers as decimals.
8.2
8.1
3 Write the missing numbers on
this measuring tape.
7.5
9.
8
9.
2
ISBN 978 1 74135 243 6
145
Topic NA28
ISBN 978 1 74135 243 6
147
0.05
0.1
0.2
0.25
0.3
0.30
0.4
0.47
0.5
0.52
f
8.04
8.1
8.2
g
b
8.22
8.3
8.3
40
e 23100
58
d 42100
42.58
24
b 9100
8.4
1.73
73
a 1100
2 Rewrite the mixed numbers as decimals.
8
a 8.09
23.4
9.24
h
8.59
8.5
c 8.52
1 Write the number shown by the arrow in a to e.
Draw an arrow from the box to the number line in f to j.
Try this
0
0.09
8.6
0.6
This number line shows hundredths between 0 and 1.
Look carefully at where the examples are placed on the number line.
If you look closely at the number lines below
you can see marks between all the tenths.
They are the hundredths marks.
10 hundredths make 1 tenth
10 tenths make 1 (one)
Let’s try counting on from 0.1 in hundredths:
0.1, 0.11, 0.12, 0.13, 0.14, 0.15, 0.16,
0.17, 0.18, 0.19, 0.2, 0.21, 0.22, 0.23.
What are the next three?
8.7
8.8
0.8
9
f 78100
78.09
37
c 2100
2.37
i
8.7
d 8.74
0.76
0.7
0.71
0
}
1
8.92
8.98
0.94
0.98
9
1
ISBN 978 1 74135 179 8
j
8.9
e
0.9
3.05
f
a
f
3.1
0.02
0.1
0.08
3.07
3 m
a
g
0.2
b
g
3.2
1
85
7100
c
47
100
0.3
5
10
d
5.5
5.51
0.8
3.8
10
e
3
210
2.04
21
2100
0.88
11
1m
0.93
3.95
4 m
4
j
0.9
e
j
3.9
e
91
Topics NA29–NA30
Blank number line: Mark where the number 10.25 should go on the number line below.
Show any working and explain how you chose where to place the number.
Challenge
7.09
8
710
27
1100
b
1.32
1.4
ISBN 978 1 74135 179 8
a
3
5 10
, 1.01 , 1.02 , 1.03
6 Compare each set of three numbers. Colour the bubble of the largest.
0.99 ,
6.38 , 6.39 , 6.4 , 6.41 , 6.42
0.8
6.35, 6.36, 6.37,
i
0.7
0.96, 0.97, 0.98,
0.6
3.8
d 0.74
i
3.7
3.7
c
0.61
0.5
0.48
3.48
3.6
d
b
h
c
h
3.5
3.5
17.4, 17.41, 17.42, 17.43 , 17.44 , 17.45 , 17.46 , 17.47
0.4
3.4
c
a
0.22
0.3
0.25
3.31
3.3
b 3.28
5 Count on by hundredths.
4
3
Write the missing numbers and draw
arrows to show the correct position
on these measuring tapes.
Topic NA30
ISBN 978 1 74135 243 6
157
kilogram
1
2
or
kg)
A 250 g
jar of jam
250 g
100 grams
1 kg
30 kilograms
or
1 kilogram
or
2 kilograms
or
d 2000 grams
kg)
1
10
kilogram
1000 grams
An orange
100 g
1
(10
e
kilogram
or
ISBN 978 1 74135 179 8
1
10
100 grams
30 kilograms
30 000 grams
2000 grams
500 grams
1 kilogram
kilogram
1
2
b 30 000 grams c 1000 grams
2 kilograms
a 500 grams
kg)
An iMaths
book
500 g
( 14
Grams may be abbreviated as g and kilograms may be abbreviated
as kg (no full stop, no capital letter and no ‘s’ for plural).
Language reminder
A 1 kg packet
of sugar
1 kg
kg
A 2 kg packet
of flour
1 kg
2 kg
1 Match each object with two correct masses.
Try this
A full 10 litre
bucket of water
10 kg
( 12
To get an idea of how to estimate and measure using grams and
kilograms, it helps to know the mass of some everyday objects.
The kilogram is the basic unit for measuring mass.
It is part of the metric system of measurement.
Sometimes we need a smaller unit for measuring mass, so
we use the gram
gram.
One thousand grams equal one kilogram. (1000 g = 1 kg)
1
One gram is one thousandth of a kilogram. (1 g = 1000
kg)
MG5 Measuring mass
7
2
8
3
9
4
2
3
4
Charli
5
Jade
Alex
10
5
ISBN 978 1 74135 179 8
Topics MG4–MG5
111
Kate
Max
Personal referent: It helps to know the measurements of some everyday objects. You can refer to them and
compare when estimating. Such measurements are called your personal referents. Find a personal referent for one
kilogram. Use a one kilogram weight to help you find an object with a similar weight. (How many iMaths books have
a mass equal to one kilogram?) Also find a personal referent for 500g.
Challenge
c Calculate the difference in mass between each pencil case in order.
1
b Use kitchen scales to find the mass of each pencil case.
Record the measurements in order below.
3 a Pencil cases come in all shapes and sizes. Who do you think has
the heaviest pencil case in your group? Sort five pencil cases from
heaviest to lightest as you estimate their mass.
c Calculate the difference between the heaviest and
lightest items of sports equipment.
6
1
b Use bathroom scales to find the mass of each object.
Record the measurements in order below.
2 a Collect up to 10 items of sports equipment to weigh.
Sort the items from heaviest to lightest by estimating their mass.
Topic MG5
5
ISBN 978 1 74135 243 6
169
Rectangular
prism
Square
pyramid
6
0
1
0
rectangles
circles
0
4
b
rectangular
prism
triangles
a
square
pyramid
c
0
0
4
triangular
pyramid
d
2
1
0
cylinder
e
0
6
0
cube
0
3
2
ISBN 978 1 74135 179 8
f
triangular
prism
1 Write a number in each box to complete the table. How many triangles, rectangles and circles are needed to
make each 3D object? (Remember that squares are also rectangles.)
Try this
Triangular
pyramid
Cylinder
A net is made by combining a number of 2D shapes.
A flat pattern can be cut out, folded and assembled
to make a 3D model. Look carefully at the nets of
these 3D objects.
b 4 triangles and 1 square
rectangular prism d 6 squares
cylinder
b Square
pyramid
c Cylinder
cube
ISBN 978 1 74135 179 8
Topics MG16–MG17
Package nets: The world of packaging uses millions of nets every day! Carefully open and lay out
a cereal box or similar to reveal the net used to create it. Trace the net onto a new piece of card.
Design and colour your own original product package before folding and gluing.
Challenge
5 Use Tear-out 5: Combining shapes on page 191. Cut around the outlines of the
square pyramid and the triangular prism. Fold the nets and glue the tabs to create
the two 3D objects.
135
square pyramid
4 Remove Tear-out 5: Combining shapes on page 191. Cut and separate the Four Triangles puzzle
pieces. Arrange the four pieces to make these shapes. Draw your solutions inside the shapes.
a Triangular
pyramid
3 Which of these nets will make the 3D object? Colour two bubbles in each box.
c 6 rectangles
a 1 rectangle and 2 circles
2 Name the 3D object with a net made from the shapes given.
Topic MG17
NA31 Simple budgets
Making a profit: The profit from the car wash above can be calculated by subtracting the expenses from the income.
What was the profit from the car wash?
Answer: $330 – $56 = $274 profit
Tendering correct amounts: For each of the orders from the problem solving task, which notes and coins would you tender
if you were to pay with the exact amount?
Answer: Answers can vary. a $2.65: $2, 50c, 10c, 5c b $0.60: 50c, 10c c $8.40: $5, $2, $1, 20c, 20c
What’s the 15th term? Without writing the 11th, 12th, 13th and 14th terms, can you predict the
15th term for each of the growing patterns above?
Answer: 43 shapes, 48 matchsticks, 29 squares
Double Trouble: Start at one and keep doubling. What is the 10th number in this pattern? Can you get to the 15th?
Answer: 512, 16 384
Challenges
Kelly versus Mick: In the surfing final, Kelly’s next wave scored a 9.9 to combine with his 8.8.
What score will Mick now need to add to his 9.8?
Answer: 9
Fruit fees: The basket of five oranges cost $5.00 and the basket of two bananas cost $1.60.
How much should the last basket of fruit cost?
Answer: $4.20
MG2 Millimetres
Book boxes: iMaths 4 Student Books are packaged in boxes of 20. What are the dimensions (length by width by height)
inside the boxes?
Answer: 1 Book = 275 mm x 200 mm x 10 mm, 20 books 275 mm x 200 mm x 200 mm
MG3 Kilometres
Road roundup: What is the total distance in kilometres of all roads on the map in Question 2?
Answer: 19.5 km
MG4 Perimeter
Net perimeter: What is the perimeter of the net of a 5 cm cube? Try drawing the net to help.
Answer: 5 cm x 14 sides = 70 cm
MG5 Measuring mass
Personal referent: It helps to know the measurements of some everyday objects. You can refer to them and
compare when estimating. Such measurements are called your personal referents. Find a
personal referent for one kilogram. Use a one kilogram weight to help you find an object with a similar weight.
(How many iMaths books have a mass equal to one kilogram?) Also find a personal referent for 500g.
A 375 mL can, can you? Drinks are sold in a range of cans, cartons, glass and plastic bottles.
List as many types of drinks as you can, together with the volume of liquid each
container holds in litres or millilitres.
ISBN 978 1 74135 243 6
185
a
47 + 10 = 67
13 + 13 = 26
22 + 18 = 40
b
32 – 2 = 30
77 – 5 = 72
80 – 9 = 71
c
8x1=8
6 x 10 = 60
12 x 3 = 36
d
777 – 333 = 444
232 – 101 = 131
900 – 111 = 789
e
56 + 3 = 59
55 + 5 = 60
52 + 8 = 60
f
24
+ odd
+ even
− odd
− even
NA5 Multiples 3, 4, 5, 6, 7, 8, 9
a 10, 15, 25 b 21, 42, 49 c 9, 21, 24
d 8, 14, 20 e 32, 48, 64
f mostly multiples of 7 g mostly multiples of 2
h mostly multiples of 9 i mostly multiples of 5
j mostly multiples of 2
NA6 Multiplication 2, 3, 5, 10
= 40
g
180
NA4 Multiply and divide 10, 100, 1000
a 3700 b 480 c 22.5 d 19 e 63 000
f 13 x 1000 g 9900 ÷ 100 h 540 x 10
i 2700 ÷ 10 j 80 x 100
= 56
a 4x2= 8
2 x 8 = 16
b 3 x 7 = 21
3 x 3 = 9 3 x 8 = 24
c 5 x 5 = 25
5 x 8 = 40
d 10 x 9 = 90
e 2 x 5 = 10
h
9
x odd
x even
= 72
2 3 5
2 4 6 10
4 8 12 20
10 20 30 50
X
f
i
136
− odd
− even
= 99
6
h
j
x odd
x even
= 289
a 2
b 1
c 7
d thousands e ten thousands
f
g
h
i
j
City
Gladstone, Qld
Shepparton, Vic
Tamworth, NSW
Dubbo, NSW
Geraldton, WA
Population
52 949
50 909
48 262
38 383
37 842
a 71 849 b 34 567 c 52 873
d fifty-four thousand three hundred and twenty-one
e Forty thousand and four
f $40 700 g $96 000 h $55 555
i $84 500 j $50 200
194
5 x 4 = 20
6 x 10 = 60
5 x 3 = 15
14
g
7 x 10 = 70
5 x 10 = 50
10
7 5
4 2 x2 4 8
9 6
18
i
18 6 x3 5 15
3
17
9
2 3
2 x 6 = 12
1 7
21
12
9 7 4
5 45 35 20
3 27 21 12
2 18 14 8
X
j
3 x 7 = 21
2x2=4
10 x 9 = 90
5 x 2 = 10
6 x 2 = 12
5 x 8 = 40
3x3=6
5 x 3 = 15
5 x 5 = 25
2 x 8 = 18
3 x 4 = 12
10 x 1 = 10
10 x 10 = 20
a 2x4= 8
b 5 x 5 = 25
c
2 x 6 = 12
4 x 4 = 16
9 x 5 = 45
6 x 8 = 48
4 x 7 = 28
5 x 7 = 35
4 x 6 = 24
d 8 x 8 = 64
8 x 4 = 32
8 x 6 = 48
e 4 x 5 = 20
8 x 5 = 40
6 x 6 = 36
f 12
g 24
h $45
i 28
j
5 x 9 = 45
8 x 9 = 72
8 x 8 = 64
4 x 7 = 28
3
x
8
=
24
9 x 9 = 18
6x1=6
6 x 3 = 18
5 x 6 = 30
7 x 8 = 56
2 x 8 = 19
7 x 9 = 63
7 x 8 = 54
a $15 b $39 c $48 d $60 e $66
f $20 g $42 h $52 i $80 j $69
ISBN 978 1 74135 243 6
a
8÷2= 4
14 ÷ 2 = 7
18 ÷ 2 = 9
b
9÷3= 3
21 ÷ 3 = 7
15 ÷ 3 = 5
c
20 ÷ 5 = 4
45 ÷ 5 = 9
25 ÷ 5 = 5
d 70 ÷ 10 = 7
30 ÷ 10 = 3
90 ÷ 10 = 9
e
50 ÷ 10 = 5
27 ÷ 3 = 9
f $10 ÷ 2 = $5
g 30 ÷ 5 = 6
h 12 ÷ 4 = 3
i 12 ÷ 2 = 6
j
80 ÷ 10 = 8
35 ÷ 5 = 7
20 ÷ 5 = 3
4÷2=2
12
÷
3
=4
6
÷
3
=
3
10 ÷ 2 = 5
21 ÷ 3 = 7
12 ÷ 2 = 6
10 ÷ 5 = 5
30 ÷ 10 = 3
6÷2=3
14 ÷ 2 = 7
a $40 ÷ 8 = $5
b 42 ÷ 7 = 6
d 16 000 (estimate)
10 808
5 100
+
92
16 000
f
1700
+ 2705
4405 km
g
4015
+ 2705
6720 km
i
1700
955
+ 875
3530 km
j
1490
1535
+ 725
3750 km
c 30 ÷ 6 = 5
d 27 m ÷ 3 = 9 m e $36 ÷ 4 = 9
f
g
h
i
j
4 7
28
5 6
30
6 8
48
4 8
32
7 9
63
4 x 7 = 28
7 x 4 = 28
5 x 6 = 30
6 x 5 = 30
6 x 8 = 48
8 x 6 = 48
4 x 8 = 32
8 x 4 = 32
7 x 9 = 63
9 x 7 = 63
b 15 000 (estimate) c 6000 (estimate)
5757
14 316
434
529
7
+
8
+
6
14 853
6204
e 78 000 (estimate)
70 007
7 070
+
700
77 777
a
b
8521
– 2013
6508
f
e 53 728
– 958
52 770
h
c 60 180
– 493
59 687
5777
– 1817
3960
1879
– 1452
427 years
1451
1819
i
– 412
– 1452
39 years
367 years
f–j
a
SALES
Paintings at $6
Clay pots at $7
Sculptures at $9
Mosaics at $7
Screen prints at $6
$42
$56
$72
$ 21
$48
30 ÷ 5 = 6
b
3 x 7 = 21
21 ÷ 7 = 3
c 32 ÷ 4 = 8
8 x 4 = 32
d 81 ÷ 9 = 9
9 x 9 = 81
e
6 x 3 = 18
18 ÷ 3 = 6
f
381
÷ 3 = 127
127 x 3 = 381
g
212
x 4 = 848
848 ÷ 4 = 212
g
1926
– 1819
107 years
j
1926
– 1879
47 years
c $5000
– 1293
$3707
2002
– 189
1813
e $30.00
– 18.15
$11.85
a
34
x 2
68
h 1029 – 955 = 74
74 + 955 = 1029
i
869 – 323 = 546
ISBN 978 1 74135 243 6
d 98 455
–18 711
79 744
f–j
a 6 x 5 = 30
j 12 306 ÷ 6 = 2051
b
6000
– 1523
4477
d $70.00
– 48.35
$21.65
NA12 Backtracking
546 + 323 = 869
875
725
+ 2690
4290 km
28 ÷ 4 = 7
28 ÷ 7 = 4
30 ÷ 5 = 6
30 ÷ 6 = 5
48 ÷ 6 = 8
48 ÷ 8 = 6
32 ÷ 4 = 8
32 ÷ 8 = 4
63 ÷ 7 = 9
63 ÷ 9 = 7
a 6 rides b 4 rides c 9 rides d 9 rides e 8 rides
7
8
8
3
8
h
Tracker Book
16 ÷ 2 = 8
a 3000 (estimate)
2099
+ 909
3008
2051 x 6 = 12 306
c
33
x 3
99
e
22
x 4
88
f
20
x 70
1400
b
34
34
x 20 x 200
680
6800
21
21
x 40 x 400
84
d
33
33
x 30 x 300
990
21
x 4
9900
840
41
x 2
8400
41
41
x 20 x 200
82
820
8200
70
x 6
420
j
22
22
x 40 x 400
880
g
8800
80
x 30
2400
h
90
x 900
81000
i
50
x 5
250
195
a 1500 (estimate) b 3600 (estimate) c 800 (estimate)
523
x 3
1569
601
x 6
3606
d 1800 (estimate) e 3500 (estimate)
885
x 2
1770
f
$713
x
6
$4278
71
x 23
213
+ 1420
1633
g
$205
x
3
$615
h
i
$130
x
9
$1170
j
$676
x
3
$2028
$742
x
7
$5194
b
8000
– 3000
5000
c
f
$6.00
+ 3.00
$9.00
g
$6.00
x
3
$18.00
h
g
48
x 42
96
+ 1920
2016
h
i
36
x 16
216
+ 360
576
95
x 25
475
+ 1900
2375
a 154 b 162 c 123
4 616
5 810
7 861
d
157
3 471
e
j
g
2
4
j
78
x 21
78
+ 1560
1638
8
16
1
3
i $3.00
x
5
$15.00
$4.00
+ 6.00
$10.00
1
3
d
2
3
300
3 927
j $12.00
8.00
12.00
+ 6.00
$38.00
4
6
=
e
2
10
=
1
5
6
8
i
50
100
4
8
9
10
f
1
2
g
2
3
h
2 34
b 12 12
c 15 12
3
6
5
10
7
14
20
40
4
40
15
30
113
6 678
0
1
2
i
3
j
1 14
d
f
g
h
f Gold Coast
74
70
100
g Mackay
978
980
1000
h Townsville
1355
1360
1400
i Cairns
1703
1700
1700
j Mount Isa
1910
1910
1900
i
j
e 17 22
d 18
1
0
1
2
1
2
3
2
4
6
0
2
NA25 Mixed numbers
a
b
Road distances from Brisbane
Distance
Distance
Distance
(km)
(nearest 10 km) (nearest 100 km)
2 35
e
0
1
4
0
1
4
1
2
2
4
1 15
2 12
c
1 13
2
4
3
4
1
3
0
2
3
3
4
1 14
1
1 24
1 34
1 13
1
2
1 23
2
1 1 14 1 24 1 34 2 2 14 2 24 2 34 3 3 14 3 24 3 34 4
1 25
1 35
1 45
2
3 12
3
2 15
2 25
4 12
4
2 35
5
2 45
5 12
3
6
a–c
0
d 2 12 or
4
6
h
10
20
a 9 12
a 61 b 738 c 480 d 329 e 819
196
2
6
e
70
x 30
2100
$121 g $185 h $131 i $118 j $123
4 $605
3 $555
6 $786 4 $472
7 $861
Destination
2
4
d
400
x 40
16 000
a 28 = 14
b 13 = 39
c 26 =
f
a 32 b 21 c 34 d 11 e 30
f 55 ÷ 5 = 11 rows
g 69 ÷ 3 = $23
h 48 km ÷ 4 = 12 km i 36 eggs ÷ 3 = 12 eggs
j 44 ÷ 4 = 11 apples
f
200
600
+ 100
900
513
x 7
3591
a 2000 (estimate) b 1800 (estimate) c 2700 (estimate)
53
61
86
x 43
x 27
x 25
159
427
430
+ 2120
+ 1220
+ 1720
2279
1647
2150
d 3000 (estimate) e 2700 (estimate)
59
93
x 52
x 31
118
93
+ 2950
+ 2790
3068
2883
f
a
173
x 4
692
1
5
2
e 3 23 or 11
3
6
4
7
4
f 1 34
g
2 2 14
5
3
h
10
3
3
i
9
4
j
5
2
ISBN 978 1 74135 243 6
f 15 kg
g 30 kg
h 1 kg
i $45 + $94 = $120 + 19 Need $19 more
j Add $45 and $94 then subtract $120.
MG11 Timelines
1930
a 640 mL b 105°c
c 50 km/h d 38 g
e 600 rpm
f 8.9 mL g 900 mL h 700 mL i 1600 mL j 1 L
1940
1950
Switzerland 1954
MG2 Millimetres
a 80 mm b 60 mm c 100 mm d 240 mm e 24 cm
f 273 mm g 27.3 cm h 45 mm i 225 mm j 22.5 cm
1970
MG3 Kilometres
a 3 km
b 6 km
f 10 km g 9 km
c 6 km
h 10 km
d 9 km
i 12 km
e 8 km
j 11 km
1980
Mexico
MG4 Perimeter
a 20 cm b 39 mm
f 6m
g 9 cm
c 24 m
h 100 m
d 50 cm
i $800
d 4 times
a 2000
b 12 a litre c 1500
f 300 mL g 900 mL h 1200 mL or 1.2 L
i 800 mL j 3200 mL or 3.2 L or 3L 200 mL
MG7 Volume
a 10 cm3 b 16 cm3 c 15 cm3 d 28 cm3
f 2 cubes g 8 cubes h 9 cubes i 2 cubes
MG8 Converting units of time
a 2 minutes
b 180 minutes c 21 days
e 600 seconds f 240 seconds g 4 weeks
i 1.5 hours or 1 12 hours
j Sunday
b
e
x
d 2 days
h 150 minutes
d
x
a
x
e
x
c
x
12:00 pm 1:00 pm 2:00 pm 3:00 pm 4:00 pm 5:00 pm 6:00 pm 7:00 pm 8:00 pm 9:00 pm 10:00 pm 11:00 pm 12:00 am
g 4 hours h 12:00 pm i 7 hours
198
1966
Spain
1982
Italy
1990
France
1998
200
2000
USA
1994
Brazil
2014
2010
South Africa 2010
2020
f–j
12:00 am 1:00 am 2:00 am 3:00 am 4:00 am 5:00 am 6:00 am 7:00 am 8:00 am 9:00 am 10:00 am 11:00 am 12:00 pm
pm
England
a 6 cm²
b 12 cm²
c 18 cm²
d 10 cm²
e 6 cm²
e 16 cm3
j 8 cubes
MG10 am and pm
a 4:00 pm b 12:00 am c 6:00 pm d 7:00 am e 12:00 pm
x
1962
MG12 Area
a 8 squares b 18 squares c 10 squares
d 9 squares e 15 squares f 9 squares
g 30 squares h 20 squares i 10 squares
j 60 squares
e 250
a 4:00 pm b 30 min c 7:00 pm d 4:30 pm e Mon, Fri
f 1 hour g Tues, Wed, Thurs
h Six-mile Creek
i Six-mile Creek and Emu Park
j 30 min, 30 min, 2 hours, 1 hour
am
Chile
1986
1990
e 4m
j $2200
MG5 Measuring mass
a 1000 kg b 10 kg c 2 kilograms d 30 kg e 100 grams
f Patch 8 kg, Fido 5 kg
g Fido 5 kg, Patch 8 kg, Buzz 12 kg, Bluey 16 kg, Lola 27 kg
h 19 i 24 j 7 kg
f
1960
j 10 hours
MG14 Angles
a acute angle b right angle
c obtuse angle
d–f R
R
O
A
g 3 h 3 i 2 j Clock hands at 9 o’clock
MG15 Using maps
a north b west
c east
f W, N, E, S
g N, E, S, N
i E, W, N
j S, W, E, S, N
d Uluru e Cairns
h N, W, S, E
ISBN 978 1 74135 243 6
MG16 Tessellation
b
a
c
SP1 Probability
a likely b never
c even chance d unlikely e certain
f 1 unlikely
g 1 even chance
h 1
never
2
2 even chance
2
never
certain
3
3 even chance
3
likely
never
d
i
2
3
e
f kitchen floor tiles
g a brick wall
h a chess board
i honeycomb
1
4
b
1
c
2
4
d
f–j
lose lose
lose win
SP2 Judgments
a fair b unfair
c unfair d fair e fair
f Fair – all faces are same size and shape
g Unfair – different shapes and sizes of faces
h Fair – all faces are identical
i–j
j
a
j
unlikely
unlikely
likely
1
2
4
e
6
a dependent b independent c independent d independent
e independent f independent g independent h independent
i dependent j independent
SP4 Organising data
a–j
SP5 Column graphs
World’s ten fastest fish
110
10 0
90
80
Speed (km/h)
b
a
70
60
50
e
f
Tarpon
Flying fish
Tunny
Wahoo
Tracker Book
0
Marlin
10
Sailfish
20
Swordfish
30
Bonefish
d
Bluefin tuna
c
Great Blue shark
40
Fish
a great blue shark b true c sailfish, marlin, wahoo
d 30 km/h e sailfish
SP6 Picture graphs
g
This month’s weather
h
fine
cloudy
i
j
rainy
stormy
a 2 days b Fine weather c 12 days
d No e fine, rainy, cloudy, stormy
ISBN 978 1 74135 243 6
199

iMTB_N4 - BOOK.indb

Transcription

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