G
Teacher
Student Book
SERIES
Name _____________________________________
Reading and Understanding
Whole Numbers
Series G – Reading and
Understanding Whole Numbers
Contents
Topic 1 –1 Read
Section
– Answers
and understand
(pp. 1–24) numbers (pp. 1–8)
Date completed
___________________________________
• read
placeand
value
understand
to millionsnumbers_
_________________________ 1 /
/
_ ____________________________________9 /
• types
of numbers_
notation
____________________________________
expanded
/
19 /
• round
order large
and estimate___________________________________
numbers_ ___________________________________
/
• the millionaires’ club – solve______________________________
/
/
• zero the hero – apply____________________________________
/
/
Section 2 – Assessment with answers (pp. 25–32)
• read and understand numbers_ _________________________ 25
Topic 2 – Types of numbers (pp. 9–18)
•
•
•
•
types of numbers_____________________________________ 27
negative numbers_ _____________________________________ /
round and estimate___________________________________ 31
prime and composite numbers____________________________ /
/
/
• mixed practice_________________________________________
/
/
Section 3 – Outcomes
(pp.
33–34)
_______________________________________
numerals
• Roman
/
/
• we need a new system – create_ __________________________
/
/
• Goldbach’s conjecture – investigate________________________
/
/
• round to the nearest power of ten_________________________
/
/
• round and estimate_____________________________________
/
/
• butler, fill my bath! – solve_ ______________________________
/
/
• round and estimate word problems – solve__________________
/
/
Topic 3 – Round and estimate (pp. 19–24)
Series Authors:
Rachel Flenley
Nicola Herringer
Copyright ©
Read and understand numbers – place value to millions
The place of a digit in a number tells us its value.
6 216 085
6 is worth
2 is worth
1 is worth
6 is worth
0 is worth
8 is worth
5 is worth
1
6 000 000 or 6 millions
200 000 or 2 hundred thousands
10 000 or 1 ten thousand
6 000 or 6 thousands
0 or 0 hundreds
80 or 8 tens
5 or 5 units
Fill in the place value chart for each number. The first one has been done for you.
Millions
Hundred
thousands
Ten
thousands
Thousands
Hundreds
Tens
Units
8
1
6
9
5
8
2
5
4
9
5
8
9
1
8
0
6
0
4
8
7
8
7
9
5
8
6
5
6
3
6
2
0
5
5
816 958
1 254 958
1
91 806
3 048 787
3
958 656
1 362 055
2
3
1
Circle the larger number:
a
7 240 547 / 7 241 253
b
8 519 476 / 8 591 476
c
4 353 537 / 4 453 540
d
3 525 461 / 3 525 614
e
2 512 444 / 2 512 333
f
2 432 498 / 2 433 498
Write the next 3 numbers in each sequence:
a + 10 000
b + 1 000 000
c – 1 000
d – 100
33 591
2 459 012
708 518
4 000 524
43 591
3 459 012 707 518
4 000 424 53 591
4 459 012 706 518
4 000 324 63 591
5 459 012
705 518
4 000 224
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 1
SERIES
TOPIC
1
Read and understand numbers – place value to millions
When we work with large numbers, there are lots of zeros to deal with. Sometimes it is easier to
express the number using exponents or powers.
power
Powers tell us how many times to use a number in a multiplication process.
102
102 = 10 × 10 = 100
103 = 10 × 10 × 10 = 1 000
104 = 10 × 10 × 10 × 10 = 10 000
base
Can you see a connection beween the power and the amount of zeros in the number?
4
5
6
Express the numbers below using powers:
a 1 000
=
103
b 10
=
101
c 10 000
=
104
d 100 000
=
105
e 100
=
102
f 10 000 000 =
107
g 1 000 000 =
106
h 100 000 000 =
108
Compare these numbers. Use <, > or = as needed:
a 1 000
>
102
b
100
=
102
c 10 000
=
104
d 100 000
>
103
e
<
1 000 000
f
=
1 000 000
105
Complete the cross number puzzle:
1
1
0
3
4
3
6
1
0
0
4
G 1
SERIES
2
3
7
8
8
8
2
106
TOPIC
4
3
1
4
0
5
9
0
6
0
0
0
2
5
0
4. three million and forty nine thousand five
hundred and six
6
0
0
0
0
Across
1.one million thirty seven thousand eight hundred
and fourteen
0
6. 106
Down
1.one hundred and thirty three thousand eight
hundred and fourteen
2. three hundred and eighty four thousand
3. 105
5. nine thousand six hundred and two
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Read and understand numbers – expanded notation
When we write numbers using expanded notation, we identify and name the value of each digit.
3 154 231 = 3 000 000 + 100 000 + 50 000 + 4 000 + 200 + 30 + 1
1
2
Convert the numbers into expanded notation:
a 4 246 936
4 000 000 + 200 000 + 40 000 + 6 000 + 900 + 30 + 6
b 88 421
80 000 + 8 000 + 400 + 20 + 1
c 2 856 913
2 000 000 + 800 000 + 50 000 + 6 000 + 900 + 10 + 3
d 714 533
700 000 + 10 000 + 4 000 + 500 + 30 + 3
e 7 240 547
7 000 000 + 200 000 + 40 000 + 500 + 40 + 7
f 4 215 632
4 000 000 + 200 000 + 10 000 + 5 000 + 600 + 30 + 2
g 770 421
700 000 + 70 000 + 400 + 20 + 1
h 467 809
400 000 + 60 000 + 7 000 + 800 + 9
Write the number from the expanded notation. Remember to group the digits in 3s.
a 500 000 + 20 000 + 3 000 + 700 + 40 + 1
523 741
_ ________________
b 80 000 + 5 000 + 200 + 70 + 3
85 273
_ ________________
c 400 000 + 5 000 + 200 + 50 + 2
405 252
_ ________________
d 900 000 + 40 000 + 1 000 + 80 + 5
941 085
_ ________________
e 20 000 + 7 000 + 300 + 8
27 308
_ ________________
f 300 000 + 2 000 + 500 + 80 + 4
302 584
_ ________________
g 800 000 + 50 000 + 6 000 + 200 + 30 + 8
856 238
_ ________________
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 1
SERIES
TOPIC
3
Read and understand numbers – expanded notation
How do we write 5 325 in expanded notation using powers?
(5 × 103) + (3 × 102) + (2 × 101) + 5
3
Write the numeral for:
a (6 × 103) + (3 × 102) + (2 × 101) + 5 =
6 325
b (4 × 103) + (2 × 102) + (9 × 101) + 8 =
4 298
c (8 × 104) + (4 × 103) + (5 × 102) + 3 =
84 503
d (2 × 105) + (7 × 104) + (9 × 103) + (9 × 102) + (9 × 101) =
e (9 × 104) + (3 × 103) + (2 × 102) + 1 = 4
279 990
93 201
Match the numerals with their expanded notation form. Colour the boxes that match.
Each pair of boxes (marked with letters) should be shaded in a different colour.
A
23 587 111
D
20 000 + 3 000 +
700 + 10 + 1
F
E
F
4
G 1
SERIES
TOPIC
A
32 590
G
78 934 210
20 000 000 + 6 000 000 +
500 000 + 20 000 + 6 000 + 900
C
70 000 000 + 8 000 000 +
900 000 + 30 000 + 4 000 +
200 + 10
E
4 509 094
G
78 361
B
4 000 000 + 500 000 +
9 000 + 90 + 4
(3 × 104) + (2 × 103) +
(5 × 102) + (9 × 101)
B
D
20 000 000 + 3 000 000 +
500 000 + 80 000 + 7 000 +
100 + 10 + 1
70 000 + 8 000 + 300 + 60 + 1
C
26 526 900
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
23 711
Read and understand numbers – order large numbers
When ordering numbers it is important to look closely at the place of the digits.
1
2
Put the following numbers in order from smallest to largest:
1 548 654
550 654
550 654
995 841
1 547 521
1 256 441
1 485 554
1 485 554
1 547 656
1 547 521
1 256 441
1 547 656
995 841
1 548 654
smallest
largest
Read the following instructions and complete the table:
You are in charge of compiling the ratings for the top 10 television programs for the week. You have ordered
them according to your personal preference but your editor is not amused.
She wants you to reorder them from most popular to least popular according to the number of viewers.
This now seems like a good idea as you like your job and want to keep it.
Use the final column to record the correct order of popularity.
Your order
Program
Viewers
Revised order
1
Guess that Tune
840 000
9
2
Romsey’s Kitchen Nightmares
1 330 000
6
3
Friends and Neighbours
1 432 000
2
4
Big Sister
1 560 000
1
5
Gladiator Fighters
1 290 000
8
6
Sea Patrol 7
1 390 000
3
7
Crime Scene Clues
1 388 000
4
8
Crazy Housewives
1 300 000
7
9
Tomorrow Tonight
740 000
10
10
Better Homes and Backyards
1 360 000
5
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 1
SERIES
TOPIC
5
Read and understand numbers – order large numbers
3
Play this game with 3 friends. The aim is to make the biggest number you can. You’ll each
need to make a copy of this page and cut out your set of digit cards below. Put each player’s
cards together and shuffle. You only need one copy of the 5 points card for the whole group.
copy
0
1
2
3
4
5
6
7
8
9
5 points
Instructions
1 Make sure you have shuffled the cards well before you deal out 7 cards to each player.
2Turn the remaining cards face down in 1 pile.
lay rock paper scissors to see who will go first. When it is their turn, players may swap one of their cards
3 P
for the top card. It’s a lucky dip though; the card may help or hinder!
layer 1 makes the biggest number they can using all their cards. They take the 5 point card as their
4 P
number is the only one out there.
5 Player 2 then tries to make a larger number. If they can do so, then the 5 point card goes to them.
6 Player 3 and 4 follow the same steps.
7 The player with the largest number at the end of the game gets the 5 points. Keep score after each round.
lay again. Or try a different variation such as the smallest number, the largest even number or the
8 P
smallest odd number.
6
G 1
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
The Millionaires’ Club
Getting
ready
What
to do
solve
Congratulations! You and a friend have just inherited a lot
of money and can join the Millionaires’ Club. Your task is
to order the members in the club, and then work out why
there seem to be some cliques within the group.
1 W
rite your names and your respective wealth on the Club Membership Board.
The rule is you must have less than 1 billion or you would be in the billionaires’ club.
2Reorder the board so the richest member of the club is at the top and the
poorest (relatively speaking) is at the bottom. Don’t forget to include yourself and
your friend.
Group
Cliques:
GROUP A
even, divisible
by 4 and 8.
GROUP B
odd, divisible
by 3 and 9.
GROUP C
divisible by 5.
What to
do next
Name
Wealth
Richest to poorest
Student A
$999 999 999
1
Student B
$999 999 998
2
A
John McSnooty
$1 560 016
11
A
Maxy Million
$3 457 342
9
A
Count More
$32 760 212
3
B
Ms Heiress (and dog)
$25 820 433
5
B
Lady Pennypincher
$10 720 899
8
B
Money Hungry
$28 073 061
4
C
Mrs Bigpurse
$2 100 565
10
C
Mr Rich-as
$25 641 265
6
C
Lord Loot
$12 740 090
7
1Within the club there are a few cliques or divisions. Members of the same cliques
have the same letter either A, B or C. You think that is odd. Can you work out
why groups have been formed? Write the groups out again and look carefully at
the numbers. Each group may even have more than one condition of entry. How
many can you find?
2 S tuck? There are a couple of the rules hidden in this page. Look carefully at the
text again. Some words may be written a little differently.
3 Which group(s) can you and your friend join according to the rules you find?
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 1
SERIES
TOPIC
7
Zero the Hero
Getting
ready
What
to do
apply
In this activity, you are going to make different numbers by
performing operations (not the medical kind) to remove zeros
from a number. You will work with a partner. You’ll need
a calculator to share.
1 Enter a 6 digit number into a calculator. Make sure it contains 1 zero.
2Pass the calculator to your partner. Their job is to remove the zero
from the calculator using one addition or subtraction problem.
3If they can read the number correctly and explain how they did it in 1 step they
score 10 points.
4 Swap roles. The first person to score 50 points wins the game.
What to
do next
Can you invent a similar game using a calculator? Does it need to be harder or easier
for you to enjoy playing it? How could you change it? What will you ask your partner
do with the numbers? Try it out and refine it until it works well.
Write down your instructions so that another team can play your game. Swap your
instructions with another team and play each other’s game.
Enter the number 46 783 into your calculator.
I want to see a zero in the hundreds place. Can’t
do it? Drop down and give me 20 push-ups.
Having problems reading the numbers? You could put
the numbers under headings to help you identify the
value of the zero.
HT
8
G 1
SERIES
TOPIC
TT
Th
H
T
U
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Types of numbers – negative numbers
Negative numbers are numbers with a value less than zero.
Negative numbers always have a minus sign before them.
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
5
6
7
8
9
10
Negative numbers are used when we measure temperature and in transactions with money.
When we are in debt, we have a negative balance. This means we owe money.
1
What is the temperature showing on each thermometer in °C (degrees Celsius)?
a
b
– 4 °C
c
– 8 °C
d
16 °C
hOn Wednesday morning the
thermometer reads –4 °C.
One hour later it is 3 °C colder.
2
e
– 2 °C
f
5 °C
g
– 10 °C
14 °C
iOn Thursday morning the
thermometer reads –9 °C. One
hour later it is 4 °C warmer.
The new temperature is
– 7 °C
The new temperature is
– 5 °C
Sarah had $10 in her bank account. What would the balance be if she:
a Withdrew $15?
– $5
_ ____________
b Withdrew $9?
$1
_ ____________
c Deposited $5?
$15
_ ____________
d Deposited $2?
$12
_ ____________
e Withdrew $20?
– $10
_ ____________
f Withdrew $12?
– $2
_ ____________
g Deposited $7?
$17
_ ____________
h Withdrew $25?
– $15
_ ____________
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 2
SERIES
TOPIC
9
Types of numbers – negative numbers
3
4
Mark the number line with the amount either added or subtracted. The first one has been done
for you.
a 2 – 7 =
–5
b 1 – 5 =
–4
c –4 + 7 =
3
d –6 + 3 =
–3
e –1 – 7 =
–8
–7 –6 –5 –4
–3
–2 –1
0
1
2
3
4
–10 –9 –8
–7 –6 –5 –4
–3
–2 –1
0
1
2
3
4
–10 –9 –8
–7 –6 –5 –4
–3
–2 –1
0
1
2
3
4
–10 –9 –8
–7 –6 –5 –4
–3
–2 –1
0
1
2
3
4
–10 –9 –8
–7 –6 –5 –4
–3
–2 –1
0
1
2
3
4
Use the number line to complete the number sentence:
a
10
–10 –9 –8
–
6
= –2
b – 10 +
5
= –5
c
–
8
= –7
d – 8 +
9
=
4
1
G 2
SERIES
TOPIC
1
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
0
1
2
3
4
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Types of numbers – prime and composite numbers
A factor is a number that divides equally into another number.
5 × 4 = 20
20 arranged in 5 rows means 4 in each row.
5 and 4 are factors of 20.
1
How many ways can 24 objects be arranged? Use the arrays below to complete the facts:
a
b
3
4
×
6
= 24
2
×
12
= 24
1
×
24
= 24
×
8
= 24
c
d
24 can be arranged in many different ways. The factors of 24 are 1, 2, 3, 4, 6, 8, 12 and 24.
Composite numbers are numbers with more than two factors.
24 is a composite number.
A prime number is only divisible by 1 so has only two factors: 1 and itself. 7 is a prime number.
2
How many ways can 12 objects be arranged?
Draw all the combinations you can think of:
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 2
SERIES
TOPIC
11
Types of numbers – prime and composite numbers
Eratosthenes (276 BC – 194 BC) was a Greek mathematician who developed a clever way to find
prime numbers.
3
Find all the prime numbers in the hundred grid below. (Do not shade the number itself as it is not a multiple.)
a Cross out 1 since it is not prime.
b Shade all the multiples of 2.
c Shade all the multiples of 3.
d Shade all the multiples of 5.
e Shade all the multiples of 7.
fThe remaining numbers are prime numbers, apart from 1 which is a special case. List them:
2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83,
_____________________________________________________________________________________
89, 97
_____________________________________________________________________________________
The Sieve of Eratosthenes
4
12
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99 100
Circle the prime numbers. Use the Sieve of Eratosthenes to help you.
G 2
SERIES
TOPIC
65
89
47
94
25
43
11
27
32
19
21
65
7
53
99
87
26
13
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Types of numbers – mixed practice
1
Work out what the secret numbers are. Assume all numbers are positive, unless stated otherwise.
2
a I am the only even prime number. I am ____________.
bI am one of the two numbers that are neither prime nor composite. I am not zero.
1
I am ____________.
cI am a 2 digit number. I am less than 40. I am a prime number and my second digit is smaller than
31
my first number. I am ____________.
–1
d I am the negative number closest to positive numbers. I am ____________.
– 99 999
e I am the 5 digit negative number furthest from zero. I am ____________.
98 765
f I am the largest 5 digit number where no number is repeated. I am ____________.
7 532
g I am the largest 4 digit number that uses the 4 smallest prime numbers. I am ____________.
11
h I am a prime number. My digits add to total the smallest prime number. I am ____________.
2
In these next questions, there is more than 1 possible answer.
a Look at the number 1 000 855.
Write 5 numbers that are larger than this with the same number of digits.
Answers will vary.
_____________________________________________________________________________________
Write 5 numbers that are smaller.
Answers will vary.
_____________________________________________________________________________________
b R
ounded to the nearest 100 km, my train trip was 3 000 km long. How long could it have been?
How many answers to this question can you find?
All of the distances between 2 950 km and 3 049 km.
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 2
SERIES
TOPIC
13
Types of numbers – Roman numerals
The numerals we use are part of the Hindu–Arabic numeral system. It is believed to have been
invented in India and transmitted by the Moors (Arabs). Europeans adopted the system in the
12th century.
The Romans had their own system.
Study this Hindu–Arabic to Roman numerals conversion table.
Hindu–Arabic
0
1
2
3
4
5
6
7
8
9
10
Roman
I
II
III
IV
V
VI
VII
VIII
IX
X
Hindu–Arabic
20
30
40
50
60
70
80
90
100
500
1 000
Roman
XX
XXX
XL
L
LX
LXX
LXXX
XC
C
D
M
In the Roman system:
• You can have 4 numerals in a row such as llll but it is customary to write IV.
• If you put a smaller number in front of a larger number, the smaller number is subtracted from
the larger one (XL = 50 – 10 = 40).
• There is no zero.
1
14
Express the following numbers in Roman numerals:
a 5
V
b 6
VI
c 50
L
d 51
LI
e 63
LXIII
f 10
X
g 12
XII
h 55
LV
i 138
CXXXVIII
j 82
LXXXII
G 2
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Types of numbers – Roman numerals
2
Convert the following Roman numerals into Hindu–Arabic numerals:
a VI
6
b XV
15
c VII
7
d XVI
16
e LX
60
f LXI
61
When we are expressing large numbers in Roman numerals, it is useful to work on one place value
at a time.
MCCLXXVII = M + CC + LXX + VII
= 1 000 + 200 + 70 + 7
= 1 277
3
Express the following numbers in Roman numerals:
Thousands
Hundreds
Tens
Units
358
CCC
L
VIII
612
DC
X
II
475
CD
LXX
V
939
CM
XXX
IX
D
LX
III
1 563
4
M
These days, we only use Roman numerals when the credits roll in the
movies – and sometimes on our watches!
These are the 3 top grossing films of all time. When were they made?
a Star Wars Epsiode IV was made in MCMLXXVII
1977
b The Dark Knight was made in MMVIII
2008
c Titanic was made in MCMXCVII
1997
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 2
SERIES
TOPIC
15
We need a new system
Getting
ready
create
In this activity you are going to use what you know
about our Hindu–Arabic number system and Roman
numerals to invent your own number system.
What
to do
Look at the chart below. It shows numbers written in our Hindu–Arabic system and in
Roman numerals. Design your own system. There is a column for you to record it.
What will you use in your system? Will you use symbols? Letters? Shapes? Will you
use different symbols for values such as 1, 2, 3 or will you repeat them as in I, II, III?
Will you use a 0 type symbol to develop a place value system so you can easily write
numbers as 5, 50, 500?
Hindu–Arabic
Roman
0
Hindu–Arabic
Roman
20
XX
1
I
30
XXX
2
II
40
XL
3
III
50
L
4
IV
60
LX
5
V
70
LXX
6
VI
80
LXXX
7
VII
90
XC
8
VIII
100
C
9
IX
500
D
10
X
1000
M
Answers will vary.
What to
do next
Now you have your system, write 5 simple addition or subtraction problems using
your numbers for a friend to solve.
1 __________________________________________________________________
2 __________________________________________________________________
Answers will vary.
3 __________________________________________________________________
4 __________________________________________________________________
5 __________________________________________________________________
Can they work with your number system? It is trickier than it looks to invent
a number system, and you may need to tweak it till you get it working.
16
G 2
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Goldbach’s conjecture
Getting
ready
What
to do
investigate
In the year 1742, a Prussian mathematician called
Christian Goldbach looked at many sums and made
a conjecture. He said that every even number over
4 is the sum of 2 prime numbers. (Actually he said
over 2 but that was when 1 was considered a prime
number. That is now so 1742.)
You have been asked by the Mathematics Institute to test this out.
How high can you go?
What will you need to help you solve this problem? You may want to use the table of
prime numbers on page 18.
You can work by yourself or as part of a small group.
Here are a few to start you off.
Look at 8. It can be made by adding
the prime numbers 3 and 5.
8
5
3
16 can be made by adding 11
and 5, and by adding 3 and 13.
16
11
5
3
13
Use the triangles on page 18 to record your thinking. Or create your own.
You may need more!
What to
do next
Which even number can be made the most ways? Discuss your answer with 2 friends.
Do they agree?
Goldbach’s theory has never been absolutely proven or disproven. The publishing
group Faber and Faber offered a $1 000 000 prize to any one who could do so.
No one was able to claim the prize at the end of the competition time. Who knows,
you could be the one to claim the glory (if not the prize). You could rename the
conjecture. What would you call it?
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 2
SERIES
TOPIC
17
Goldbach’s conjecture
investigate
Answers will vary.
18
2
3
5
7
11
13
17
19
23
29
31
37
41
43
47
53
59
61
67
71
73
79
83
89
97
101
103
107
109
113
127
131
137
139
149
151
157
163
167
173
179
181
191
193
197
199
211
223
227
229
233
239
241
251
257
263
269
271
277
281
283
293
307
311
313
317
331
337
347
349
353
359
367
373
379
383
389
397
401
409
419
421
431
433
439
443
449
459
461
463
467
479
487
491
499
G 2
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Round and estimate – round to the nearest power of ten
Rounding makes big numbers easier to work with. We round to numbers that we can deal with
easily in our heads.
We most commonly round to the nearest 10 or power of 10.
210
0
100
200
350
300
770 rounds to 800
600
700
800
900
1 000
Round to the nearest thousand:
12 000
a 12 388 _ _________________
b 9 525
40 000
c 39 610 _ _________________
55 000
d 55 239 _ _________________
8 000
_ _________________
90 000
f 89 743 _ _________________
e 8 392
10 000
_ _________________
Round to the nearest ten thousand:
a 14 987
10 000
__________________
b 24 033
20 000
__________________
c 36 095
40 000
__________________
d 77 330
80 000
__________________
250 000
e 245 302 __________________
3
500
Round down when the
number is less than halfway.
400
350 rounds to ______
2
400
Round up when it is halfway
between the 10s or more.
210 rounds to 200
1
770
700 000
f 695 474 __________________
Round to the nearest hundred thousand:
800 000
a 828 549 __________________
700 000
b 653 200 __________________
100 000
c 105 525 __________________
200 000
d 223 669 __________________
900 000
e 856 914 __________________
400 000
f 449 987 __________________
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 3
SERIES
TOPIC
19
Round and estimate – round to the nearest power of ten
4
To find a secret fact about the gorilla, round the numbers in the clues below and insert the matching
letters above the answers.
I
T
C
2 000 50 000
H
N
T
L
D
O
5
6
400
A
N
8 000 20 000
A
H
U
M
8 000
200
70 000
500
A
400
A
N
rounded to the nearest ten thousand
rounded to the nearest thousand
rounded to the nearest hundred
rounded to the nearest thousand
rounded to the nearest thousand
U
C
H
400
200
C
O
L
D
400
7 000
900
10 000
69 623 rounded to the nearest thousand
M
I
C
A
462
2 490
361
7 711
rounded to the nearest hundred
rounded to the nearest thousand
rounded to the nearest hundred
rounded to the nearest thousand
Answer true or false:
a When rounding to the nearest hundred, 18 762 rounds to 19 000.
True / False
b When rounding to the nearest thousand, 17 468 rounds to 17 000.
True / False
c When rounding to the nearest ten, 5 rounds up.
True / False
d We use rounding when we need to be absolutely precise.
True / False
e When rounding to the nearest hundred, 78 050 rounds to 78 100.
True / False
f When rounding to the nearest hundred, numbers round down from 50.
True / False
gYou would be happy for your parents to use rounding for your weekly pocket
money. You receive $14 pocket money.
True / False
A number rounded to the nearest thousand is 4 000. List at least 10 numbers it could be.
Numbers in the range 3 500 to 4 499.
20
T
8 000 50 000
8 000 20 000
249 rounded to the nearest hundred
19 432
49 832
850
10 320
6 625
C
G 3
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Round and estimate – round and estimate
We often round numbers when we are estimating, when being close enough provides us with the
information we need to make a decision or calculation.
1
Work out estimates for the following problems. The first one has been done for you.
b 19 × 22
a 29 × 11
30
×
=
10
300
d 32 × 51
30
×
2
10
×
×
20
=
400
e 62 × 29
=
50
1 500
g 11 × 59
20
c 12 × 41
60
×
=
600
40
×
10
×
40
=
400
40
=
800
70
=
1 400
f 21 × 39
30
=
1 800
h 41 × 39
60
20
×
i 19 × 69
40
=
1 600
20
×
Circle the best estimate:
a 52 + 39 =
20
90
200
b 70 × 29 =
2 100
210
40
c 299 + 415 =
70
500
700
d 812 – 325 =
50
500
600
e 39 × 80 =
50
320
3 200
f 310 + 99 =
4
40
400
g 395 – 198 = 2
20
200
A handy way to quickly multiply large numbers with zeros is to:
1 Cross off the zeros
2 Perform the operation
40 × 20 =
4 × 2 = 8
3 Add EXACTLY the number of zeros you crossed off 8 + 00
40 × 20 = 800
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 3
SERIES
TOPIC
21
Round and estimate – round and estimate
Sometimes it is best to round to a known fact rather than follow the normal rounding rules.
?
For example: 637 ÷ 9 = If we round 637 to 630 instead of 640 we get 630 ÷ 9 =
70
This is easier to work out in our heads because we know the division fact: 63 ÷ 9 = 7
3
4
Estimate the answer to the following division questions. The first one has been done for you.
a 329 ÷ 8 =
320
÷
8
=
40
b 487 ÷ 6 =
480
÷
6
=
80
c 427 ÷ 7 =
420
÷
7
=
60
d 367 ÷ 6 =
360
÷
6
=
60
e 568 ÷ 8 =
560
÷
8
=
70
f 729 ÷ 9 =
720
÷
9
=
80
Hayley and Jack estimated answers to some calculations. Circle the most useful estimate:
Calculation
Hayley
Jack
a12 of you go to a restaurant. The set price is $18 a head. What will
the bill roughly be?
$200
$300
b Y ou want to buy a new MP3 player that costs $157 and 5 songs
from iTunes at $1.69 each. You have $250. Can you do it?
Yes – $250
Yes – $170
c Y ou travel 365 km on one day, 478 km the next, and 541 the next.
Roughly how far have you travelled altogether?
1 400 km
1 000 km
3
10
e 47 + 32 + 67 =
150
800
f Y ou have $32. A packet of lollies costs $2.95. Roughly how many
packets can you buy with your money?
10
7
50 000
60 000
d94 divided by 9 equals
g 1 020 × 58 =
22
G 3
SERIES
TOPIC
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Butler, fill my bath!
Getting
ready
What
to do
solve
Your very demanding employer has decided he wants to
bathe in lemonade as he believes the bubbles and sugar will
make him young and attractive again. You think it will take
more than lemonade, but you do his bidding anyway.
Using only a pencil and paper, work out the approximate number of 375 mL cans you
will need to fill the 265 litre bathtub. His Lordship hates wastage, so you need to be
as close as you can with your estimate.
Think of a strategy. Try it out. Are you on the right track?
This activity requires
you to estimate, not to
work out exact figures.
Compare your answer with that of a friend. Are your answers similar? If not, discuss
how each of you solved it, and work together to see if you can come up with an
answer you both agree on.
Perhaps a table or list
may help.
What about converting
the quantities so that
they are the same?
Answers will vary.
What to
do next
Can you get closer with your estimate? The more accurate you are, the fewer cans
are used.
Accept answers in the range 650–750.
The precise answer is 706.6.
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
G 3
SERIES
TOPIC
23
Round and estimate word problems
What
to do
solve
Solve these problems
a D
ixie earned $10 433 in her first year as a singer. The next
year her career took off and she earned $107 420. In the
following year she raked in a cool $822 000. What were her
earnings over the 3 years to the nearest ten thousand dollars?
$10 000 + $110 000 + $820 000 = $940 000
__________________________________________________________________
b S adly for Dixie, success is fickle, and her career took a nosedive. In the fourth
year, she made only $10 000 and had spent all but $100 000 of her previous
earnings. The tax office then decided she owed $150 000 in back taxes. Will she
have to go into debt to pay them back? If so, by how much?
Yes, she will be in $40 000 of debt.
__________________________________________________________________
c A
ngus and his brothers are saving for a speed boat. Angus has $2 878, Richard has
$1 790, and Jack has $4 213. The boat costs $15 000. Approximately how much
more money do they need?
$15 000– ($3 000 + $2 000 + $4 000) = $6 000
__________________________________________________________________
dJack has changed his mind about buying the speed boat. Instead he decides to
join a get rich quick scheme that requires just $4 000 from him as a joining fee.
Angus and Richard ask their cousin Fred to take Jack’s place. Fred puts in $2 000
to the boat fund.
How much more money do they now need to buy the speed boat?
$8 000
__________________________________________________________________
Which information provided in the story is irrelevant to solving the problem?
That the get rich quick scheme requires $4 000 from Jack as
__________________________________________________________________
a joining fee.
__________________________________________________________________
How long before Jack regrets his decision?
Not long!
__________________________________________________________________
eBelle wants to buy 11 mini-chocolate bars. They each cost 80 cents.
She estimates this will cost her $10. Is this a reasonable estimate?
Yes.
______________________________________________________
f D
ion goes for a run 5 days a week. Each run is 5 km long. He tells his mates he
runs about 50 km a week. Is this a reasonable estimation or is he just bragging?
Explain your thinking:
24
G 3
SERIES
TOPIC
He is just bragging. 5 days × 5 km = 25 km a week
__________________________________________________________________
Reading and Understanding Whole Numbers
Copyright © 3P Learning Pty Ltd
Read and understand numbers
1
Name_ ____________________
Write the following numbers using expanded notation:
a 240 583
b 1 126 423
c 8 200 782
2
In the number 5 783 082, which digit:
a is in the thousands place?
b is in the tens place? c will change if a million is added?
3
Arrange the numbers in Line A in descending order:
A
4 763 221
4
5
6
7
4
8
12 703 170 1
2
4 967 211
9
3
844 008
804 048
3 703 170
What is the largest number you can make using these digits?
__________________________________________________
Express the following numbers as powers of 10.
a 10 000 = 10
b 100 = 10
c 1 000 000= 10
d 1 000 = 10
e 10 = 10
f 100 000 = 10
Write the numeral for:
a (7 × 103) + (2 × 102) + (2 × 101) + 8 =
b (8 × 104) + (3 × 103) + (4 × 102) + 1 =
c (4 × 105) + (8 × 104) + (3 × 103) + (9 × 102) + (2 × 101) =
Skills
Not yet
Kind of
Got it
• Expresses numbers in expanded notation to 7 digits
• States the place value of any digit in numbers to 7 digits
• Orders numbers to 7 digits
• Expresses numerals as powers of 10
Series G Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
25
Read and understand numbers
1
2
3
Write the following numbers using expanded notation:
a 240 583
200 000 + 40 000 + 500 + 80 + 3
b 1 126 423
1 000 000 + 100 000 + 20 000 + 6 000 + 400 + 20 + 3
c 8 200 782
8 000 000 + 200 000 + 700 + 80 + 2
In the number 5 783 082, which digit:
a is in the thousands place?
3
c will change if a million is added?
5
4
6
b is in the tens place? 8
Arrange the numbers in Line A in descending order:
A
5
Name_ ____________________
7
12 703 170 12 703 170 4 967 211 4 763 221
4
8
1
2
4 967 211
4 763 221 9
3
844 008
3 703 170 804 048
3 703 170
844 008
804 048
What is the largest number you can make using these digits?
9 874 321
__________________________________________________
Express the following numbers as powers of 10.
a 10 000 = 10
4
b 100 = 10
2
c 1 000 000= 10
6
d 1 000 = 10
3
e 10 = 10
1
f 100 000 = 10
5
Write the numeral for:
a (7 × 103) + (2 × 102) + (2 × 101) + 8 =
7 228
c (4 × 105) + (8 × 104) + (3 × 103) + (9 × 102) + (2 × 101) =
Skills
b (8 × 104) + (3 × 103) + (4 × 102) + 1 =
83 401
483 920
Not yet
Kind of
Got it
• Expresses numbers in expanded notation to 7 digits
• States the place value of any digit in numbers to 7 digits
• Orders numbers to 7 digits
• Expresses numerals as powers of 10
26
Series G Topic 1 Assessment
Copyright © 3P Learning Pty Ltd
Types of numbers
1
Name_ ____________________
Use the number line to help answer the following questions:
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
2
0
1
2
a 4 – 7 =
b 2 – 8 =
c –3 + 4 =
d –9 + 5 =
3
4
At 11 pm, the temperature was 2 °C. By 2 am, it had dropped 7 °C. What was the temperature at 2 am?
_______________________________________________________________________________________
3
The temperature in Broome was 27 °C. On the same day it was –6 °C on the top of Mt Hotham. How much
colder was it on Mt Hotham than in Broome?
_______________________________________________________________________________________
4
A composite number has more than two factors. Circle the composite numbers:
19
5
13
51
12
46
57
14
15
A prime number has only two factors, itself and one. Circle the prime numbers:
23
6
72
22
11
18
27
95
37
2
27
17
Express the following numbers in Roman numerals or as Hindu–Arabic (our system) numerals:
a 10
b 8
c 50
d 75
e LX
f LXI
Skills
Not yet
Kind of
Got it
• Recognises the location of negative numbers on a number line
• Adds and subtracts negative numbers
• Identifies prime and composite numbers to 100
• Expresses and reads numbers as Roman numerals
Series G Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
27
Types of numbers
7
Complete the Roman numerals chart:
1
I
6
VI
20
XX
LXX
80
LXXX
XC
7
3
8
VIII
40
XL
90
4
9
IX
50
L
100
V
30
70
2
5
8
Name_ ____________________
10
60
1 000
M
500
Express the following numbers in Roman numerals:
a 55
b 40
c 110
d 12
e 49
f 62
9
If your father was born in MCMLXIV, how old would he be in 2008?
10
If your teacher was born in MCMLXXIX, how old would he or she be in 2008?
11
Express your birth year in Roman numerals.
12
What is the time?
Skills
Not yet
Kind of
Got it
• Expresses numbers in Roman numerals
• Converts numbers to Roman numerals
• Reads dates and times in Roman numerals
28
Series G Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
Types of numbers
1
Name_ ____________________
Use the number line to help answer the following questions:
–10 –9 –8 –7 –6 –5 –4 –3 –2 –1
2
0
1
2
3
4
a 4 – 7 =
–3
b 2 – 8 =
–6
c –3 + 4 =
1
d –9 + 5 =
–4
At 11 pm, the temperature was 2 °C. By 2 am, it had dropped 7 °C. What was the temperature at 2 am?
– 5 ºC
_______________________________________________________________________________________
3
The temperature in Broome was 27 ˚C. On the same day it was –6 ˚C on the top of Mt Hotham. How much
colder was it on Mt Hotham than in Broome?
33 ºC colder
_______________________________________________________________________________________
4
A composite number has more than two factors. Circle the composite numbers:
19
5
13
51
12
46
57
14
15
A prime number has only two factors, itself and one. Circle the prime numbers:
23
6
72
22
11
18
27
95
37
2
27
17
Express the following numbers in Roman numerals or as Hindu–Arabic (our system) numerals:
a 10
X
b 8
VIII
c 50
L
d 75
LXXV
e LX
60
f LXI
61
Skills
Not yet
Kind of
Got it
• Recognises the location of negative numbers on a number line
• Adds and subtracts negative numbers
• Identifies prime and composite numbers to 100
• Expresses and reads numbers as Roman numerals
Series G Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
29
Types of numbers
7
8
Name_ ____________________
Complete the Roman numerals chart:
1
I
6
VI
20
XX
70
LXX
2
II
7
VII
30
XXX
80
LXXX
3
III
8
VIII
40
XL
90
XC
4
IV
9
IX
50
L
100
C
5
V
10
X
60
LX
500
D
1 000
M
Express the following numbers in Roman numerals:
a 55
LV
b 40
XL
c 110
CX
d 12
XII
e 49
XLIX
f 62
LXII
9
If your father was born in MCMLXIV, how old would he be in 2008?
44
10
If your teacher was born in MCMLXXIX, how old would he or she be in 2008?
29
11
Express your birth year in Roman numerals.
12
What is the time?
Teacher check.
4:30
Skills
11:15
Not yet
Kind of
Got it
• Expresses numbers in Roman numerals
• Converts numbers to Roman numerals
• Reads dates and times in Roman numerals
30
Series G Topic 2 Assessment
Copyright © 3P Learning Pty Ltd
Round and estimate
1
Name_ ____________________
Round these numbers to the nearest 10:
a 6 357
2
b 99 236
Round these numbers to the nearest 100:
a 132 778
3
b 547 942 Round these numbers to the nearest 1 000:
a 5 673
4
5
Circle the best estimate:
a 59 × 32
=
180
1 800
1 500
b 43 × 102
=
4 000
40 000
400
c 329 ÷ 8
=
50
23
40
d 536 ÷ 9
=
60
70
6
Look at the populations of the towns in the District of Springfield in the table below:
Springfield
134 777
Margetown
56 000
Burnsville
48 999
Flanders
10 003
Krustyton
9 887
St Barts
6
b 679 432
Round each population to the nearest 10 000.
What is the population of the district to the
nearest 10 000?
39 011
Is this estimate reasonable?
1
Stavros is saving
of his pocket money for a new game. He receives $12 per week and
2
estimates that by the end of 10 weeks, he will have saved between $100 and $150. Is he right? _________
Skills
Not yet
Kind of
Got it
• Rounds to the nearest 10, 100, 1 000
• Mentally solves algorithms using rounding and estimation
• Uses rounding to make reasonable estimates
Series G Topic 3 Assessment
Copyright © 3P Learning Pty Ltd
31
Round and estimate
1
Round these numbers to the nearest 10:
a 6 357
2
5
132 800
b 547 942 547 900
6 000
b 679 432
679 000
Circle the best estimate:
a 59 × 32
=
180
1 800
1 500
b 43 × 102
=
4 000
40 000
400
c 329 ÷ 8
=
50
23
40
d 536 ÷ 9
=
60
70
6
Look at the populations of the towns in the District of Springfield in the table below:
Springfield
134 777
130 000
Margetown
56 000
60 000
Burnsville
48 999
50 000
Flanders
10 003
10 000
Krustyton
9 887
10 000
39 011
40 000
St Barts
6
99 240
Round these numbers to the nearest 1 000:
a 5 673
4
b 99 236
6 360
Round these numbers to the nearest 100:
a 132 778
3
Name_ ____________________
Round each population to the nearest 10 000.
What is the population of the district to the
nearest 10 000?
300 000
Is this estimate reasonable?
1
Stavros is saving
of his pocket money for a new game. He receives $12 per week and
2
No
estimates that by the end of 10 weeks, he will have saved between $100 and $150. Is he right? _________
Skills
Not yet
Kind of
Got it
• Rounds to the nearest 10, 100, 1 000
• Mentally solves algorithms using rounding and estimation
• Uses rounding to make reasonable estimates
32
Series G Topic 3 Assessment
Copyright © 3P Learning Pty Ltd
Series G – Reading and Understanding Whole Numbers
Region
Topic 1
Read and understand
numbers
Topic 2
Types of numbers
Topic 3
Round and estimate
NS3.1 – orders, reads and writes numbers of any size
NSW
• order numbers in ascending
and descending order
• apply an understanding of
place value and the role
of zero to read, write and
understand numbers
• record large numbers using
expanded notation
• recognise the location of
negative numbers in relation
to zero
• link negative numbers with
subtraction (WM)
• recognise, read and convert
Roman numerals
• identify differences
between the Roman and
Hindu–Arabic systems of
recording numbers
• round numbers when
estimating
• apply strategies to estimate
large quantities (WM)
• identify prime and
composite numbers
• model integers (positive and
negative whole numbers
and zero)
• create factor sets
• use the mathematical
structure of problems
to choose strategies for
solutions (WM)
• use estimates for
computations and apply
criteria to determine if
estimates are reasonable
or not
• recognise and investigate
the use of mathematics
in real and historical
situations (WM)
• describe and analyse
operations with rational
numbers and relationships
between them
• analyse, use and appreciate
number concepts from
diverse cultural origins
• use a variety of estimating
and calculating strategies
with whole numbers
• estimate quantities using
a variety of strategies,
including rounding and
setting upper and lower
boundaries
VELS Number – Level 4
VIC
• comprehend the size and
order of large numbers
• recognise and calculate
simple powers of whole
numbers
• model integers (positive and
negative whole numbers
and zero)
• engage in investigations
involving mathematical
modeling (WM)
3.6, 3.8
SA
• represent and analyse
relationships amongst
number concepts and use
these to make sense of, and
represent the world
• deconstruct numbers into
smaller parts and recombine
them in different ways using
patterns, rounding to groups
of 10 and 100, and place
value relationships
Series G Outcomes
Copyright © 3P Learning Pty Ltd
33
Series G – Reading and Understanding Whole Numbers
Region
Topic 1
Read and understand
numbers
Topic 2
Types of numbers
Topic 3
Round and estimate
Number – numbers, key percentages, common and decimal fractions and a range of strategies are
used to generate and solve problems
QLD
WA/NT
• count, read, write, say and
order whole numbers to
hundred thousands
• know that numbers can be
made up of digits and words
• compare 4 digit whole
numbers
• whole numbers, including
positive and negative
numbers can be ordered
and compared using a
number line
• whole numbers have factors,
prime numbers have only
2 distinct factors
• estimation strategies
including rounding, and
estimates based on powers
of 10, assist in checking
for reasonableness of
calculations involving
whole numbers
N6a.4 – understand whole numbers and decimals
read, write, say, count with and compare whole numbers into the millions
16 – understand and apply number
16.LC.2
understand the concept of
place value for comparing and
ordering whole numbers and
how place value changes
ACT
16.LC.10
the history of whole numbers,
counting, and symbol systems
in more than one cultures
16.LC.5
factors of whole numbers and
prime numbers
16.EA.17
choose and use a range of
strategies to solve problems,
including sensible choices
about mental, written
and electronic methods
for calculation
16.EA.2
positive and negative numbers
to at least seven digits
16.EA.18
make estimates for
calculations using knowledge
of number systems and
relationships, mental
calculation, rounding and
magnitude based on powers
of 10
• place different
representations of numbers
appropriately on number
lines including negative
integers
• compare and order integers
in context e.g. temperature
• use a variety of methods to
form estimates and make
approximations in context
Standard 4 – Stages 9–10
TAS
34
• understand the relationship
between adjacent place
values within whole
numbers
• explore order of operations
in a range of contexts
Series G Outcomes
Copyright © 3P Learning Pty Ltd