01 Introduction to Whole Number Sense Learner.ppsx

Introduction to Whole
Number Sense
Level 1
When you have whole number sense, numbers make sense. Whole
numbers are a way of knowing and seeing the world. They allow us
to identify patterns and relationships around us. Whole numbers are
used to measure, count, locate, design, play, and explain.
Draft Version

Recognize how the “base” in a number system determines place value.
Introduction to Whole Number Sense Outcomes
Upon completing Introduction to Whole Number Sense, you will be able to:
1
Identify the place value of whole numbers (0 to 1 million).
Identify, read, represent, and count whole numbers (0 to 1 million).
Move between place values and represent whole numbers in different ways (limited to whole numbers
less than 10 000).
Compare and order whole numbers (0 to 1 million).
Read basic equations addressing the concept of equality (limited to whole numbers and addition).
2
3
4
5
6
7
Explain what whole numbers are, how they are constructed, and how they are used in life.

Click on a title below to go to the section. Complete the sections in order.
Introduction to
whole numbers
1
Introduction to
base systems
2
Place values
(base-10 system)
3
Basic equations
(equality & zero)
4
Moving between
place values
(ones & tens)
5
Number Sense
Moving between
place values
(thousands)
7
Moving between
place values
(hundreds)
6
Comparing &
ordering whole
numbers
8
Writing & saying
whole number
words
9
Level 1

Introduction to
whole numbers
1
Back to Main Menu

What’s in a Number?
Activity A:
Draw the shape of a room in the Learning Centre. Then actually measure the length of each side of
the room and write these measurements on the shape you drew. Use any measuring method you
like. Except: You may not use a ruler or tape measure.
Be sure to include the measuring unit you used when you label each side of your drawing.
You may not use feet, metres, or any other building construction measuring unit.
Activity B:
Measure how tall you are. Use any measuring method that works for you, except a ruler or tape
measure. Record your height, including the measurement unit you used.
Why did you choose the measuring unit you did to measure the room?
Did you change units to measure your height? Why or why not?
Did you write the measurements using a number word or a number symbol (1, 2, 3, etc.)? Why?
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Numbers used for measuring:
When you measure, you are determining how many units there are
in total. A number is used to tell you this information.
A unit is always 1 (a single thing). You use this 1 unit to figure out
how many units there are in total.
What measurement unit is being used?
1 arm span
What is the measurement of each side of the garden box?
long sides: 4 (four) arm spans
short sides: 1 (one) arm span
How are numbers used to show these measurements?
Numbers show how many units there are in total on
each side. (How many units fit along each side.)
For example:
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More Thoughts About Numbers
Numbers can also be used to count things. For example, what numbers do you
think about when you look at the following pictures? Try to think of several
numbers for each picture.
5 (five) flowers
5 (five) stalks
19 (nineteen) leaves
4 (four) seed heads
1 (one) unopened flower
10 (ten) fingers
8 (eight) fingers & 2 (two) thumbs
2 (two) hands
10 (ten) fingernails
2 (two) wrists
4 (four) prints
1 (one) wolf
2 (two) front legs & back legs
20 (twenty) paw pads
16 (sixteen) claws
examples examples examples

Numbers are Connected to Body
Parts
Use fingers and thumbs
to show the number:
0 1 2 3 4 5 6 7 8 9 10
How many ways can you
do this?
1 10 45 120 210 252 210 120 45 10 1
There are many different ways to show the numbers 0 to 10 using your
fingers and thumbs. From the table below, you can see that there are 210
different ways to use your 10 fingers and thumbs to show the number 4.
There are 252 ways to use your 10 fingers and thumbs to show the number 5.
Fingers are “body” calculators.
Try it!
You can also count using
other body parts.

Numbers used for counting:
When you count, you are determining how many units there are in total.
A unit is always 1 (a single thing). One way of counting is to add each
unit as you go (e.g., 1, 2, 3, 4…). The last number you say is the total.
How many sides does the garden box have? 4 (four)
What is the unit you are counting? 1 side
How are numbers used to count the sides?
Numbers show how many units (sides) there are
in total (1 side, 2 sides, 3 sides, 4 sides). The total
is the last number you say.
For example:
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So…what is a number?
• A number is used to show a measurement or a count
(an amount or quantity).
• A number tells you how many units there are in total.
• A number can be a single unit (1 or one).
• A number can also be a collection of units (2 or two, 3 or three,
10 or ten, 16 or sixteen, 21 or twenty-one, etc.).
• Numbers can be described by words you say or write. Different
languages and communities use different words for numbers.
• Numbers can also be written using number symbols such as
1, 2, 3, etc. Most of the world uses the same number symbols.
• Numbers can be shown in “physical” ways (see next slide).
What is a Number?

In Indigenous cultures around the world, there have been many different ways
to show numbers that do not use number symbols or words. For example:
Knotted strings used to
communicate complex
number information in
a community.
Notching used to record
time or to show amounts.
Lines (tally marks)
used to show
amounts.
Carving used to track the phases
of the moon.
Dots and circles used
to show counting.

In many cultures, numbers have special characteristics. In these cultures, numbers
have a relationship with what is being counted. For example, some cultures:
Use the number 4 to communicate life cycles: 4 seasons, 4 stages of life, 4 directions of life,
4 types of life on earth.
Use the number 2 to describe opposite forces and balance in life: good and evil, day and night,
masculine and feminine.
Have no large numbers because there is no need for large numbers in daily life.
Have different words for the same number depending on if the thing being counted is thought
to be alive or not alive.
Have different counting words depending on the shape of the thing being counted (round, flat,
tube-shaped, etc.).
Use the number 1 to describe the whole, the beginning of everything, coming together (harmony).
Only use counting words if there is something to count (no counting just to learn the words).
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Consult with Elders and other people in your community to discover the
following about current and past relationships with numbers:
• What is the relationship between the words used for counting and the things being counted?
(Both now and in the past.)
• What numbers are special or important? Why?
• How are large numbers counted?
• Do any of the counting words refer to body parts?
• In the past, how were counts recorded or shown? What about today?
Community Relationships With Numbers
In what ways has your thinking about numbers changed?
After you finish your research, think about this. click

Arabic Number System
We use the Arabic number system. It is the most common number system in the
world today. In this system, there are only ten symbols that can be used to make
numbers: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9. For example:
The written number 20 is made from 2 and 0. When 2 and 0 are
used in a written number, they are called digits. “Digit” means
“finger”. 20 has two digits so it is called a “double-digit” or
“2-digit” number.
2
0
digit digit
number
A digit can also be a number. For example, the number 2 is made
from the digit 2. All digits are both digits and numbers. A
number made from one digit is called a “single-digit” or “1-digit”
number.
2
digit
number
Remember: 0, 1, 2, 3, 4, 5, 6, 7, 8, and 9 are the only digits
that can be used to make numbers.
single-digit
number
double-digit
number

Digits vs. Numbers
Which picture shows the relationship between digits and numbers?
What story does this picture tell? What story does this picture tell?
What story does this picture tell?
Some numbers are digits and some
digits are numbers.
Numbers and digits are totally
different from each other.
All digits are numbers but only
some numbers are digits.
Answer
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2, 3, 4, 5, 6, 7, 8, 9
How many digits are in these numbers? Use number words for your answers.
An example has been done for you.
Number Digits
34 two
1 one
6566 four
92 809 five
589 three
0 one
Number Digits
2100 four
50 two
10 089 five
467 900 six
300 000 six
2 987 611 seven
Write a 1-digit number (do not
use a number in the tables):
207, 390, 461, 585, 964
(examples only)
1088, 2390, 5498, 9999
(examples only)
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Try These

Write 5 number symbols based on the picture below. One must be a 3-digit
number. You can estimate (guess at) numbers if they are large. Identify how
many digits are in each of your numbers. An example has been done for you.
Number Symbol
and Unit
How many digits?
(use words)
2 large flowers one digit
10 large petals two digits
10 leaves two digits
6 green leaves one digit
39 small flowers two digits
about 125
yellow beads
three digits
example
example
example
example
example

How many numbers in total are shown in the picture below? 48
How many digits in total are shown in the picture below? 67
How many different numbers are shown in the picture below? 18
1 2 3 4 5 6
2 4 6 8 10 12
3 6 9 12 15 18
4 8 12 16 20 24
5 10 15 20 25 30
6 12 18 24 30 36
1
2
1 2 3 4 5 6
3
4
5
6
Digits vs. Numbers
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How many different digits are shown in the picture below? 9 (0 is a digit and
there is no 7)
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This person posted an
Instagram about math.
What math advice would
you give the Instagrammer?
This person does not
understand the difference
between numbers and digits.
The 0 candle is for use as a
placeholder in numbers (ages)
such as 10,50 100, 101, etc.
Advice

Today, most of the world
uses Arabic number
symbols for math.
However, the words for
the Arabic number
symbols vary from
language to language.
Some countries and regions use other number symbol systems instead of or in
addition to the Arabic system. For example:
Roman
Eastern Arabic
Bengali
Thai
Malayalam
Klaltovik Inupiaq
American sign language
Chinese Mandarin
Braille
Arabic
Tally
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Arabic System

Whole numbers:
• Whole numbers are the numbers 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10,
11, 12 and so on.
• They are always positive (no negative numbers allowed).
• They are not parts of a whole (no fractions or decimals
allowed).
What are Whole Numbers?
1 000 987 553
0
-34
6.4
1
3/4
60
2 ½
10
0.008
-1
2767
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In life, whole numbers are
sometimes used for codes or
identification (e.g., passwords,
phone numbers). This is NOT
a math use because there is
no measuring or counting
going on.
Which of the following are whole numbers?
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C The truck was purchased in 2015. (A year measures time.)
N My hunting knife is model number B86755A5.
C I am 6 feet 2 inches tall which is 4 inches taller than my brother.
N Never use the PIN 1234 as it is too easy to guess.
C The jeans cost $40 on sale. (Money math is an amount that can be counted.)
C There are 10 red chairs and 15 blue chairs for a total of 25 chairs.
N U2 is my favourite rock band.
C The speed limit on the ice road is 30 km/h.
N The hockey player wears jersey number 98. (It is just a random number.)
C Class ends at 3 o’clock. (This number measures time.)
Decide if the following are whole numbers used to count, measure, or compare (C);
or whole numbers used in life with no math purpose (N).
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Introduction to
base systems
2
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Today, there is great concern that caribou
populations in the north are in decline.
• Why are caribou important to your community?
• Why are caribou disappearing?
• According to Traditional Knowledge, how can the
damaged relationship between people and caribou be
healed?
• As part of the work to “bring back the caribou”, caribou
are being counted. What are some of the traditional
ways caribou are monitored?
Answer these questions by talking with members of your
family and community:
A Life Example

In one recent caribou project in the NWT, continuous photos of caribou herds
were taken from an airplane. The caribou in the photo were then counted.
• What strategy would you use to count the caribou in this section of a photograph? (Do not
actually count the caribou.)
• Why would you use this strategy?

You could count the caribou one caribou at a time.
Counting unit: caribou
1 caribou, 2 caribou, 3 caribou, 4 caribou, 5 caribou, etc.
Disadvantages:
• It will take a long time because there are so many caribou.
• If you make a mistake, you must start again.
You could put the caribou in small groups (e.g., groups of three)
and count the small groups. All groups must be the same size!
Counting unit: small groups
1 small group, 2 small groups, 3 small groups, etc.
For example, groups of three
caribou:
1, 2, 3 small groups of 3
Counting Method A (Count each single caribou.)
Counting Method B (Put caribou into small groups and count the groups.)
For example:
1, 2, 3, 4, 5, 6, 7, 8, 9 caribou
Do not double count. Count the small groups and then add any
leftover caribou. There can only be 0, 1 or 2 caribou left over.
Do not count any caribou already in a small group.
Below are some possible methods you could use for counting the caribou:
Click
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For example:
1, 2 large groups
Each large group is made up of 9 caribou (3 small groups of 3 caribou).
Counting Method C (Combine the small groups and count the larger groups.)
If there are too many small groups to count after you complete method B, you could combine the
small groups into larger groups and count the larger groups. There must be the same number of
small groups in each large group (e.g., 3 small groups in each large group).
Counting unit: large groups 1 large group, 2 large groups, 3 large groups, etc.
Do not double count. Count each large group. Then add any small groups left over. Do not count
small groups already in a larger group. There can only be 0, 1 or 2 small groups left over. Then add
any single caribou left over.
Click

Base Systems
Number systems are based on how groups are formed. The number of things
(units) in the smallest group possible provides the name of the base system. So
the caribou counting system was a base-3 system. Other examples:
• A base-16 number system means the smallest group possible is made from 16 things (units).
• The Australian Indigenous base-5 system means the smallest group possible is made from 5 things.
• Computers use a base-2 system meaning smallest groups of 2 (this is the language of coding).
• Inuit counting uses base-20 (because counting was based on 10 fingers and 10 toes).
• The Oksapmin of Papau New Guinea use a base-27 system (they use 27 body parts to count).
• The imperial measurement system uses base-12 (12 inches in a foot).
• The Babylonians used a base-60 system (this is why there are 60 seconds in a minute and 60
minutes in an hour).
The Arabic system uses base-10 which means the smallest group possible is made from 10 things
(units). This system came about because counting was based on 10 fingers.
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The base number also tells you how many different digits there are in the system.
These are the only digits that can be used to make numbers (digits can be repeated).
In a base-3 system, there are only 2 digits plus 0 (3 digits in total).
All written numbers in a base-3 system must be made from 0, 1, 2.
After 2, a new number must be made from 0, 1, 2. See below to see how this works.
There are no more digits
left to count these caribou.
So what happens?
Base-3 means a group is
formed when you reach
“three”.
“1” now means 1 small group of three
caribou. It no longer means 1 single caribou.

What numbers would you write to describe the caribou counts in each photo?
Remember: Do not double count. When you get to three, a new group is formed.
In a base-3 system:
• 0 is 0 in the Arabic system
Click
Click
Click to compare base-3
counting to the system most of
the world uses.
Click

What numbers would you write to describe the caribou counts in each photo?
Remember: Do not double count. When you get to three, a new group is formed.
In a base-3 system:
Click
Click
Click to compare base-3 counting to
the system most of the world uses.
Click

How many caribou are in the photos? Write the answer in the base-3 table.
Do not count any caribou more than once.
What is this number in
the Arabic system?
Groups of
27
Groups of
9
Groups of
3
Single
caribou
1 0 0 2
26
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What is this number in
the Arabic system? 29
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Try this

In a base system, a digit represents different amounts (values), depending on which column it is
located in the number. In the base-3 caribou counting system, a digit can represent:
• 0, 1, or 2 single caribou (not in a group)
• Small groups of 3 caribou
• Larger groups of 9 caribou (3 groups of 3 caribou)
• Larger groups of 27 caribou (3 groups of 3 groups of caribou)
• And so on.
In the base-3 system, whenever you run out of single digits (when you reach “3”), you form 1 group
of 3. This is why it is called base-3. You then “zero out” the column you are working in and add 1
group to the left.
Not allowed in base-3. You only have
the digits 0, 1, 2. Every time you
reach 3, a new group of 3 is formed.
You then count this new group.
Think of this: Sometimes in life,
you think about individuals and
sometimes it is easier to think
about groups (herds, flocks, pods,
forests, communities).
Examples

• In base-10, you have only ten digits to make all the numbers you need for counting and measuring:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9.
In the base-3 caribou count, you had only 3 digits: 0, 1, 2.
• In base-10, you count single things (units) until you run out of digits. 9 is the largest digit you can
use. When you reach 10, the 10 things become 1 group of 10.
In the base-3 caribou count, you ran out of digits after 2. When you reached 3, you thought about
the caribou as 1 group of 3.
• A base-10 system means groups of ten. A new group forms whenever there are 10 things or
10 groups of things.
In the base-3 caribou count, a new group formed when there were 3 caribou or 3 groups of caribou.
A base-10 system has the following characteristics:
What is a Base-10 System?
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In 1994, Kaktovik Inupiaq students at the middle school in Kaktovik, Alaska created a new number
system that is now widely used by the Kaktovik Inupiaq and other Inuit cultures.
The new system solved a problem. Inuit counting used a base-20 system and Arabic counting, a base-
10 system. This meant the Kaktovik Inupiaq did not have enough Arabic numbers to show all twenty of
their Indigenous counting numbers. So the students invented a set of 1-digit numbers that allowed
them to bridge the two systems. This helped revive counting in Inuit languages.
Twenty is
written with a
one and a zero
A New Number System is Created
Notice how a new symbol is added at every fifth place and then “legs” are attached to show the next four
numbers (e.g., 6 uses the symbol for 5 plus one leg, 13 uses the symbol for 10 plus three legs).

Place values
(base-10 system)
3
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In any base system, the value of a digit is determined by the digit’s location in a
number. In a base-10 system, the same digit can be worth ones, tens, hundreds,
thousands, millions, etc. depending on its place (column) in the number.
Place Value (Base-10 Whole Numbers)
This picture shows where
digits can be located in a
number. Each column is called
a place and each place is
worth a different amount
(e.g., ones, tens, millions). The
lowest place value is always
the ones place.
N U M B E R
click

When you write a base-10 whole number in standard
form, the largest digit any place can have is: 9
When you write a base-10 whole number in standard
form, the smallest digit any place can have is: 0
When you write a base-10 whole number in standard form,
the only digits that can be used in any place are:
0, 1, 2, 3, 4, 5, 6, 7, 8, 9
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Example: 5829
The digits 5, 8, 2, and 9 are used to write the number 5829. Each digit is written
in its own place. The place tells you what the value of the digit is.
place place place place
Millions
Hundred
Thousands
Ten
Thousands
Thousands
Hundreds
Tens
Ones
5 8 2 9
whole number places and their values
When you write numbers using digits and no words, it is
called standard form (e.g., 5829, 569, 16, 4). In standard
form, there is room for only one digit in each place.
Answer the questions below: Click

What digit is in the thousands place? 5 Click
What digit is in the ones place? 9
How many hundreds are in the hundreds place? 8
How many ones are in the ones place? 9
In the whole number 5829, does 8 have a larger value than 5?
Explain.
In the whole number 5829, does 9 have a larger value than 2? Explain.
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No. 8 means 8 hundreds and 5 means 5 thousands.
Would you rather have $800 or $5000?
No. 9 means 9 ones (9). This is a smaller value than 2 tens (20).
Answer the following questions using 5829:
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whole number places and their values

To make whole numbers easier to read, spaces are used to collect place values into
groups of three. Hundreds, tens, and ones are grouped together. Thousands are
grouped together. Millions are grouped together.
Never use commas to write whole numbers. Use spaces instead. Using
commas is the “old way” of writing whole numbers in standard form.
Using Spaces to Write Whole Numbers
Count the groups of three starting at the ones place.
1357699 is written 1 357 699
251790 is written 251 790
36295 is written 36 295
5492 is written 5 492 or 5492
871 is written 871
The space is optional with 4 digits.
Examples
Millions
start

Standard form is the way we usually write whole numbers.
Standard form uses digits and spaces. For example:
• Hundreds, tens, and ones are grouped together.
• Thousands are grouped together.
• Millions are grouped together.
Standard form does not use written words or pictures.
Rather, it uses digits. For example:
1
26
478
1 000 000
5391 or 5 391
20 000
In standard form, there can only be one digit in each place.
Standard Form Summary

In which place is the digit 6 in the numbers below? Use the chart to help you.
3675 hundreds
416 518 thousands
7 860 425 ten thousands
8506 ones
460 tens
657 000 hundred thousands
6 219 700 millions
187 362 tens
3 654 211 hundred thousands
46 302 thousands
6 498 052 millions
567 000 ten thousands
In which place is each underlined digit below?
239 ones
30 000 thousands
7 951 631 hundred thousands
1 470 217 millions
827 061 hundred thousands
720 ones
9555 thousands
429 156 hundreds
1 310 890 ones
3 543 291 millions
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Place Value Chart

Answer the following questions based on the whole number 4444.
What digit is in the ones place? What is its value?
What digit is in the tens place? What is its value?
What digit is in the hundreds place? What is its value?
What digit is in the thousands place? What is its value?
digit: 4 value: 4 ones = 4 1+1+1+1 is 4
digit: 4 value: 4 tens = 40 10+10+10+10 is 40
digit: 4 value: 4 hundreds = 400 100+100+100+100 is 400
digit: 4 value: 4 thousands = 4000 1000+1000+1000+1000 is 4000
You can see that
the value of a digit
in a whole number
depends on its
place in the
number.
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Summary

The base-10 system is like a business where you must group your product in
boxes that hold 1, 10, 100, 1000, etc. Think of box size as place value. When
you move left, each box size (place value) is 10x larger than the one before it.
As you move left, box size gets larger but the number of boxes you need gets smaller.
This is because each box holds 10x more than the box before it to the right.
10 of the boxes that
hold one thing can
fit into the 10 box.
10 of the boxes that
hold ten things can
10 of the boxes that hold
one hundred things can
And so on.
holds 1 thing
holds 10 things
holds 100 things
holds 1000 things
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summary

4 ones = 4
4 tens = 40
4 hundreds = 400
4 thousands = 4000
Smaller
Larger
Place values get larger as you move from right (ones place) to
left. For example, tens are larger than ones. Hundreds are
larger than tens. Thousands are larger than hundreds.
Place values get smaller as you move from left to right (ones
place). For example, hundreds are smaller than thousands.
Tens are smaller than hundreds. Ones are smaller than tens.
4 thousands = 4000
4 hundreds = 400
4 tens = 40
4 ones = 4
Place Value
Review
moving left
left
right
moving right

Playing with Place Value
Arrange the digits to make the largest number possible. _________________
Arrange the digits to make the smallest number possible. _________________
What is the smallest whole number you can write? _________
What is the largest whole number you can write? ____________________________________
You have the digits 1, 2, 3, 4, 5.
The largest 3-digit number you can make is __________.
The smallest 2-digit number you can make is __________.
All whole numbers must have a digit in the __________ place.
543
12
0
Whole numbers go forever.
ones
23 789
98 732
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Answer the following:
You have the number 79 328.
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The largest number
is the smallest
number in reverse!!

Zeros and Whole Numbers
Zero (0) has two meanings in the world of whole numbers.
Zero as a number
Zero is a digit (0) and a number (0) that means “none” or “nothing”. People are not born
understanding zero as a number. Instead, they must learn what it means. This is because you cannot
see or hear or touch zero like you can other whole numbers. Zero was invented long after all other
numbers. Without zero, there can be no modern math or computing science.
Zero as a placeholder digit
Zero is also used to keep other digits in their correct places. This allows numbers to be written
properly. For example: 502
If there were no zero, 502 would become 52. The
placeholder zero sits in the tens place but it has no
value. It just takes up space to keep 5 as hundreds
and 2 as ones.
And, without zero, 50 would be 5.
The value of 0 is always 0 (none) no matter what place it is in.
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Around 326 BC, the world conqueror, Alexander the Great, met a wise Elder in India. The Elder was
sitting on a rock and staring at the sky. Alexander asked him, “What are you doing?”
“I’m experiencing nothingness. What are you doing?” the Elder replied.
“I am conquering the world,” Alexander said.
They both laughed; each one thought the other was a fool, and was wasting their life.
In early Christianity, religious leaders in Europe argued that since God is in everything that exists,
anything that represents nothing must be satanic. As a result, the use of zero was forbidden.
In some Indigenous cultures, zero is a symbol for the completion of a cycle (the nothingness of
death and completeness of life).
Zeros and Culture
Speak to family, Elders, and community members to see if “zero” has any
special meaning in your culture. How is zero used to explain the world?

Basic equations
(equality and
zero)
4
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What are the different symbols and words your community uses for “equal”?
What does “equal” mean in your culture?
What does the following say to you? 1 + 1 = 2
Thinking About Math Stories

Basic Math Equations
In math, an equation is a way of describing a relationship. The equal sign (=) tells you that the
relationship is balanced. This is why the equal sign is a symbol showing two balanced lines.
What is on one side of the equal sign balances what is on the other side. In a math equation,
both sides have the same value even if they look different.
Since an equation is a balanced relationship, you can read an equation starting from either end.
1 + 1 + 1 + 1 + 1 = 5
1 + 1 + 1 + 1 + 1 = 1 + 1 + 1 + 1 + 1
5 = 5
5 = 1 web of 5
earth = land, sky, water, plants, animals
How could you describe the picture below by using numbers in an equation with
an equal sign? Can you think of more than one description?
Possible
ideas

An equal sign can also be read, “the same as” (a relationship where both sides are the same but they
have different names).
In this resource, equations will be used to describe addition (+). Adding means joining or connecting.
Cassandra has many roles in life. Some of these are: Elder, daughter,
mother, grandmother, auntie, teacher. Same person, different names.
These roles might be represented by this equation:
Write an equation with an equal sign that describes some of the roles
that give you different names (roles that help to define you).
A non-math example:
Cassandra = Elder + daughter + mother + grandmother + auntie + teacher

Equations show the balance between parts and wholes:
• How parts come together to form a whole or a group.
• How a group is made up of parts.
• How parts describe a whole or a whole describes parts.
3 = 1 + 2
2 + 1 = 3 3 = 3
3 = 2 + 1
1 + 2 = 3
An equal sign does NOT mean “and the answer is…” or “do something to find the answer.”
Write several addition equations to describe the picture below:
Possible
answers
A math example:

Zeros and Addition
Try the following number stories that have no words. If it is easier, add words to the
numbers like in the above examples so the numbers make more sense.
2 + 0 = 2 (nothing added to 2 is 2)
1 000 000 + 0 = 1 000 000 (nothing added to 1 000 000 is 1 000 000)
You are adding
nothing to the
number.
When you add 0 to any number, the number stays the same. Zero is the only number
that works this way. For example, calculate the totals based on the stories below:
You caught 5 fish on Monday and none on Tuesday: 5 + 0 = 5
Jackie paid you $4167 last month and $0 this month: $4167 + $0 = $4167
You saw 12 wolves yesterday but zero today: 12 + 0 = 12
There were no tourists in town yesterday and none today: 0 + 0 = 0
Click
Click
Click
Click
Click
Click
Click
Click

You are still
adding nothing
to a number.
You can add 0 to a number using the reverse order and the number will still
stay the same. This is because 0 added to any number does not change
anything. For example:
You can add numbers in any order.
You will get the same total.
32 + 0 = 32
0 + 32 = 32
You caught 0 fish on Monday and 5 on Tuesday: 0 + 5 = 5
Jackie paid you $0 last month and $4167 this month: $0 + $4167 = $4167
You saw 0 wolves yesterday but 12 today: 0 + 12 = 12
There were no tourists in town yesterday and none today: 0 + 0 = 0
Click
Click
Click
Click
1 000 000 + 0 = 1 000 000
Click
Click
Click
Click
(nothing added to 1 000 000 is 1 000 000)
Try adding without the words. Think of your own stories if it helps.

Leading Zeros and Whole Numbers
Leading zeros are located at the front of a whole number. For example:
023
001
000 087 093
0100
Leading zeros have no mathematical purpose. They can be ignored or deleted.
023 = 23 001 = 1 000 087 093 = 87 093 0100 = 100
Leading zeros are NOT
placeholder zeros!
009
017
285
Leading zeros are used in spreadsheets and other calculations to keep place values in numbers lined up.
They are also found in some electronic displays.
What famous spy is
associated with
leading zeros?
click
Where in life might you see a leading zero? click

Moving between
place values
(ones and tens)
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To make movement between place values more “real”, try using objects such as paper clips, cut up
cardboard straws (do not use plastic straws), craft sticks, pencils, crayons, pipe cleaners, etc. to show
amounts. Bundle groups by using elastics, twist ties, cut up pipe cleaners, etc. or link the paper clips if
you are using these.
Make it Real

If a number has only 1 digit, the digit will be in the ones place. The value of a
1-digit number is the value of the digit. The following are examples of numbers
made from 1 digit. (Firewood has been used to illustrate the examples.)
Ones Place Value
3 stands for 3 ones
0 stands for 0 ones
1 stands for 1 one
5 stands for 5 ones
9 stands for 9 ones
7 stands for 7 ones
click
click
0 1 3
5 7 9
click
click
click
click
(cannot be shown with sticks)

Multiplying by 1
When you multiply any number by 1, the number stays the same. For example:
A cookie is 250 calories. You ate 1. How many calories? 1 x 250 = 250 calories
There are 9 metres of duct tape on a roll. You have 1 roll. How many metres? 1 x 9 = 9 m
A truck travels 30 km per hour on an ice road. How many km travelled in an hour? 1 x 30 = 30 km
A parka costs $200. You bought it. How much did you spend? 1 x 200 = $200
You can multiply a number by 1 in the reverse order and the number will
still stay the same. For example:
You can multiply numbers in the
reverse order. You will get the same
answer. For example:
2 x 3 = 6 and 3 x 2 = 6
250 x 1 =250
9 x 1 = 9
30 x 1 = 30
200 x 1 = 200

Ones (1s)
8
To calculate the value of a digit in the ones place, multiply the digit by 1.
Ones (1s)
1
Ones (1s)
5
Remember: When a number is multiplied by 1, the number stays the same.
8 x 1
8 x 1 = 8
1 x 1
1 x 1 = 1
5 x 1
5 x 1 = 5
Multiplying is the same as adding a number to itself (called repeated addition).
8 x 1 = 8
1 +1 +1 +1 +1 +1 +1 +1 = 8
1 x 1 = 1
There is only one 1 so it cannot
be added to itself.
5 x 1 = 5
1 +1 +1 +1 +1 = 5
Calculating the Value of a Digit in the Ones Place
8 ones 1 one 5 ones
Repeated addition click

30, 401, 2229, 656, 98, 211, 14, 2, 879, 5558, 6421
Even and Odd Whole Numbers
The digit in the ones place tells
you if a number is even or odd.
Which of the following numbers are even? click
Whole numbers with a 0, 2, 4, 6, or 8 in the ones place are called even numbers.
If you count by two starting with an even number, all the numbers you say will be even
numbers. For example, the following are all even numbers:
30 0378 80 136 5394
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
30, 401, 2229, 656, 98, 211, 14, 2, 879, 5558, 6421
Try it. click

Whole numbers with a 1, 3, 5, 7, or 9 in the ones place are called odd numbers. For
example, the following are odd numbers:
03
27
0915
8209
When you use whole numbers
to count (0, 1, 2, 3, 4, 5, 6…) an
odd number follows an even
number and vice versa.
Which of the following numbers are odd?
46 561
click
If you count by two starting with an odd number, all the numbers you say will be odd
numbers.
1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21
21, 22, 27, 105, 2, 99, 50, 66, 8883, 5550, 75
21, 22, 27, 105, 2, 99, 50, 66, 8883, 5550, 75
Try it. click

tens ones
tens ones
tens ones
When the amount in the ones place becomes 10, a group of ten is formed. This
is because you are working with a base-10 system. Also, each place can only
have one digit. Now you will count groups of sticks (1 group of ten) instead of
single sticks. In the end, you will have created a new number (10).
Bundle the 10 ones into 1 group of ten.
There will be 0 ones left over.
Write a 0 in the ones column to show there are 0 ones left in the ones place.
1 0
Tens Place Value
For example, you have 9 ones and one
more gets added. In standard form, the
largest digit the ones place can have is 9.
You need the tens place to help out.
Move the 1 group of ten to the tens
place. Write a 1 in the tens column.
Click
Click
Click #3
Click #1
Click #2
Click #4

tens (10s) ones (1s)
2 3
3 ones
2 x 10 3 x 1 = 3
2 tens
click
To learn about multiplying a whole number by 10, click here.
To calculate the value of a digit in the tens place, multiply the digit by 10.

Multiplying a Whole Number by 10
An easy way to think about multiplying a whole number by 10:
When you multiply a whole number by 10, the number stays the same and one zero gets
written at the end of the number. You write one zero because 10 ends with one zero.
For example:
8 x 10 = 80 10 x 8 = 80 36 x 10 = 360 10 x 140 = 1400
2 3
Example
Remember: It does not matter what order you use to multiply numbers.
Click
2 x 10 means 2 tens
10+10 = 20
10 20
OR count by 10s

Multiplying Whole Numbers by 10 (The Real Story)
tens
10s
ones
1s
2 2
When you multiply a whole number by 10, you are actually moving the digits in the number. They all
move one place value to the left, and a zero is added to the now empty ones place.
2 3
2 x 10 = 20
6 0
6 x 10 = 60
Example 1 Example 2
2 tens 6 tens
tens
10s
ones
1s
2
2
tens
10s
ones
1s
2 0
20
tens
10s
ones
1s
6 6
tens
10s
ones
1s
6
6
tens
10s
ones
1s
6 0
60
2 x 10 6 x 10
Click Click

Calculating the Value of a Digit in the Tens Place
2 3
To calculate the value of a digit in the tens place, multiply the digit by 10.
3 x 1 = 3
Earlier you learned how to multiply a digit in the ones
place by 1. In this example, 3 x 1 = 3 OR 1+1+1=3
tens ones
2 0
2 x 10 =
2 tens means there are 2 groups of ten.
Write a 2 in the tens place.
Write a 0 in the empty ones place.
2 x 10 = 20 and 3 x 1 = 3 → 23 = 20 + 3
2 x 10
2 tens 3 ones
2 3
So you can think about 23 this way: click
2 x 10 = 20
You can also use repeated addition: 2 x 10 means 10+10 = 20
Details click

Another example:
6 0
0 ones
6 x 10 0 x 1
6 tens
click
To learn about multiplying by zero, click here.

When you multiply a number by 0, the answer is always 0. Remember that
0 means “no things” or “nothing” or “none”. For example:
When you reverse the order of the multiplication numbers, the answer is
still the same. For example:
Multiplying by Zero
close
There were no herds of 12 elk. 0 x 12 = 0 herds of 12
You have no single moose hide to tan. 0 x 1 = 0 moose hides
You take no steps that are 12 inches. 0 x 12 = 0 twelve-inch steps
You have 12 pans with no muffins in them. 12 x 0 = 0 muffins
You have 12 piles of chopped wood but no pine. 12 x 0 = 0 chopped pine
You make a $1 tip for every customer. You had no customers. $1 x 0 = $0 tips

6 0
0 ones
6 0
6 x 10 =
6 x 10 0 x 1 = 0
6 tens
6 x 10 = 60 and 0 x 1 = 0 
Back to our example:
6 x 10 means 6 groups of ten.
Write a 6 in the tens place.
Write a 0 in the empty ones place.
6 0 60 = 60 + 0 (the 0 adds nothing so
you can omit it: 60 = 60)
Repeated addition: 10 + 10 + 10 + 10 + 10 + 10 = 60
So you can think about 60 this way: click
Remember:
0 x any number = 0
any number x 0 = 0
6 x 10 = 60
Details click

Expanded form is when you break apart a standard form number into
its place values. Expanded form tells you the value of each digit in the
number. It does this by unbundling the packages in each place value
into ones. Add these place values together and you get the number.
45 = 40 ones + 5 ones
45 = 4 tens + 5 ones
45 = 40 + 5
Expanded form tells you how many ones are in each place
when the number is written in standard form.
It is another way of describing a number.
expanded form
Expanded Form of a Whole Number
For example: the whole number 45 standard form
(4 x 10) (5 x 1)
Expanded form
uses plus signs
(addition).
click
click

Write the number 60 in expanded form:
Numbers Already in Expanded Form
60 = 60 + 0
Adding 0 ones does not change the number in
any way. You are adding nothing. This means
you can delete the + 0 from the expanded form.
60 = 60 + 0 60 = 60
In other words, 60 is already in expanded form.
Answer
Click

Write the following in expanded form:
22 = ___________
58 = ___________
13 = ___________
97 = ___________
45 = ___________
71 = ___________
11 = ___________
64 = ___________
Write the standard form that each expanded form is showing:
_______ = 40 + 9
_______ = 10 + 8
_______ = 50 + 5
_______ = 70 + 4
82 = ___________ 33 = ___________
20 + 2
50 + 8
10 + 3
90 + 7
80 + 2
40 + 5
70 + 1
10 + 1
60 + 4
30 + 3
click
click
click
click
click
click
click
click
click
49
18
55
74
click
click
click
click
_______ = 90 +9
_______ = 30 + 7
99
37
click
click

tens ones
tens ones
A 2-digit number can be described in more than one way if you use place
values and words. We will use 12 as an example:
12 = 12 ones (This is too many in the ones place for standard form.)
12 = 1 ten + 2 ones
12 = 10 + 2
1 2
1 x 10 = 10 2 x 1 = 2
1 ten = 10 ones
bundled together
12 = 10 ones + 2 ones
Are there 12 ones or 2 ones in the standard form number 12?
There are 12 ones in total. 10 ones are bundled up in the tens place. 2 ones are in the ones place.
So…there are 12 ones total.
click
Expanded form: click

Different ways to describe the whole number 23 by using words and place values.
tens ones
tens ones
tens ones
23 = 23 ones
23 = 20 ones + 3 ones
There are 23 ones in total. This is too many ones for standard form.
Bundle the ones into tens (there will be 2 tens with 3 ones left over).
Move the 2 tens to the tens place. 3 ones are left in the ones place.
2 3 23 = 20 + 3
2 x 10 = 20
2 tens = 20 ones
3 x 1 = 3
There are 23 ones in total. 20 are bundled as
2 tens in the tens place. 3 ones are in the
ones place. So… there are 3 ones in the ones
place but 23 ones in total.
Are there 23 ones or 3 ones in
the standard form number 23?
click

How do you know that when you write a 2-digit whole number in expanded
form, the tens place value will always end in 0? For example:
56 = 50 + 6 43 = 40 + 3 99 = 90 + 9
When you write a number in expanded form, why will the ones place value not
always be 0? For example:
89 = 80 + 9 36 = 30 + 6 55 = 50 + 5
The digit in the tens place is always multiplied by 10. This means the number will always end in zero.
The digit in the ones place is always multiplied by 1 so it does not change. This means the digit in
the ones place will be 0, 1, 2, 3, 4, 5, 6, 7, 8, or 9.
click
click
Thinking About Expanded Form in More Detail

Fill in the blanks in the examples below. The first one has been done for you.
63 = 63 ones
63 expanded form: 63 = 60 + 3
99 = _______ ones
63 = _______ tens + _______ ones
63 expanded form: ________________
63 = 60 ones + 3 ones
63 = _______ ones + _______ ones
99
9 9
90 9
99 = 90 + 9
47 = _______ ones
63 = _______ tens + _______ ones
63 expanded form: _______________
63 = _______ ones + _______ ones
47
4 7
40 7
40 = 40 + 7
85 = _______ ones
63 = _______ tens + _______ ones
63 expanded form: ______________
63 = _______ ones + _______ ones
85
8 5
80 5
85 = 80 + 5
11 = _______ ones
63 = _______ ten + _______ one
63 expanded form: _______________
63 = _______ ones + _______ one
11
1 1
10 1
11 = 10 + 1
52 = _______ ones
63 = _______ tens + _______ ones
63 expanded form: ________________
63 = _______ ones + _______ ones
52 = 50 + 2
Answers
52
5 2
50 2
52 = 50 + 2
Answers
Answers
Answers
Answers
Example
Example
Example
Example Example

The most 2-digit whole numbers you can make is _______. How do you know this?
What is the largest 2-digit whole number you can make? _____
Write the following as 2-digit standard form numbers:
70 + 7
90 ones + 4 ones
6 tens + 9 ones
1 ten + 7 ones
forty-eight
1 ten + 4 ones
8 tens + 8 ones
ten ones
77
94
69
17
48
14
88
10
90
10 is the first 2-digit number and 99 is the last 2-digit number (100 has 3 digits).
Starting with 10 and ending with 99, there are 90 whole numbers, all with 2 digits.
99
What is the smallest 2-digit whole number you can make? _____
10
More practice:
answer
answer
answer
answer
answer
answer
answer
answer
click
click
click click

Complete the following:
3 x 10 = _______
3 + 0 = _______
3 x 1 = _______
87 + 0 = _______
40 x 1 = _______
8 x 10 = _______
0 + 17 = _______
29 x 1 = _______
7 x 10 = _______
99 + 0 = _______
30
3
3
87
40
80
17
29
70
99
click
click
click
click
click
click
click
click
click
click
42 x 10 = ________
115 x 0 = ________
420
0
click
click 7895 x 10 = ________
78 950
click
800 x 10 = ________
8000
click
10 x 10 = ________
1 x 10 = ________
100
10
click
click
0 x 10 = ________
10 + 0 = ________
0
10
click
click
0 + 10 = ________
10
click
10 x 100 = ________
1000
click
Review
Do as many as you need to make sure you understand the concepts.

29 = ___________
33 = ___________
11 = ___________
53 = ___________
19 = ___________
75 = ___________
86 = ___________
99 = ___________
42 = ___________
67 = ___________
20 + 9
30 + 3
10 + 1
50 + 3
10 + 9
click
click
click
click
click
70 + 5
40 + 2
80 + 6
90 + 9
60 + 7
click
click
click
click
click
More Review

Adding 10 to Whole Numbers
When you add 10 to a number, you are adding 1 ten and 0 ones to that number.
For example: 34 + 10
3 4
1 0
3 tens + 4 ones
tens (10s) ones (1s) tens (10s) ones (1s)
+ =
1 ten + 0 ones 4 tens + 4 ones
34 10 44
4 4
=
+
add tens to tens
add ones to ones
3 + 1 4 + 0
Without pictures:
10 = 1 ten + 0 ones
click

Try this one: 5 + 10
5
1 0
1 5
=
+
add tens to tens
add ones to ones
0 + 1 5 + 0
Adding 10 to a number means the tens place value will increase by 1 ten and the ones place
value will stay the same.
Complete the following (numbers with a 9 in the tens place are not included):
27 + 10 = ______
8 + 10 = ______
10 + 23 = ______
70 + 10 = ______
10 + 53 = ______
160 + 10 = ______
239 + 10 = ______
10 + 5967 = ______
8 + 10 = ______
10 + 21 942 = ______
702 + 10 = ______
9101 + 10 = ______
nothing
here
click
37
18
33
80
63
170
249
5977
18
712
9111
click
click
click
click
click
click
click
click
22 952
click
click click click
Try these: click
Add leading zeros so the numbers have the same amount of digits.
Leading 0

tens (10s) Ones (1s)
Your friend says you can use words and place values to describe 23 in this way:
23 = 1 ten + 13 ones
Is this correct? Use pictures to explain your thinking.
23 = 2 tens (20 ones) + 3 ones
23 = 1 ten + 13 ones
Your friend is correct.
Unbundle 1 ten into 10 ones.
Move the 10 ones to the ones place.
tens (10s) ones
Move 10 ones from
the tens place over to
the ones place. You
still have 23 ones.
standard form (starting point)
Other Ways to Describe 2-Digit Whole Numbers
answer

Describe the number 35 in four ways. Use pictures to help you. One is done for
you as an example.
35 = 2 tens + 15 ones
35 = 1 ten + 25 ones
35 = 35 ones
tens ones
tens ones
tens ones
Click
Click
Click
The first picture. It is the
only picture in which
each place has a single
digit.
tens place: 3
ones place: 5
Which picture represents
the standard form of 35?
How do you know?
Click
Question

$35 = $30 + $5
$35 = 3 tens + 5 ones
$35 = $20 + $15
$35 = 2 tens + 15 ones
$35 = $10 + $25
$35 = 1 ten + 25 ones
$35 = $35
$35 = 35 ones
Another way to think about
place value is in terms of
money.
Example:
$35 can be described in several ways using
ten-dollar bills (tens) and loonies (ones).
Some examples are shown.
Which example represents the standard
form of 35? Click
Click
Click
Click
Standard form has a single digit in
each place.
tens: 3 ones: 5

Standard Form Expanded Form
3 tens + 20 ones 50
9 tens + 8 ones 98 98 = 90 + 8
0 tens + 89 ones 89 89 = 80 + 9
2 tens 20
94 ones 94 94 = 90 + 4
8 tens + 0 ones 80
1 ten + 11 ones 21 21 = 20 + 1
5 tens + 10 ones 60
19 ones 19 19 = 10 + 9
Complete the following table. If the number is already in expanded form, leave
the Expanded Form space blank for that number.
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click Click
Click
Click
Click
Click
Click
Review

Moving between
place values
(hundreds)
6
Back to Main Menu

hundreds tens ones
Bundle 10 tens into 1 hundred.
Write a 0 in the tens column to show there are now no tens. Write a 5 in
the ones column to show there are still 5 ones in the ones place.
Hundreds Place Value
For example, you have 9 tens
and 5 ones. A ten gets added.
Now there are too many tens for
the tens place. You need the
hundreds place to help.
Move the 1 hundred to the
hundreds place. Write a 1 in
the hundreds column. Click
Click
hundreds tens ones
hundreds tens ones
1 0 5
When the amount in the tens place becomes 10, a group of 10 tens is formed.
But the tens place can only hold 1 digit. The solution is to use the hundreds place.
Click
Click #1
Click #3
Click #2
Click #4

hundreds tens ones
What whole number is shown below? _____
Use pictures to show what happens when one stick is added.
New number: ________
100
99
click
click
step 1 step 2
step 3
1 hundred + 0 tens + 0 ones
Step 4

Calculating the Value of a Digit in the Hundreds Place
5x1=5
hundreds
(100s)
tens
(10s)
ones
(1s)
3 7 5
7x10=70
3 hundreds
3x100
To calculate the value of a digit in the hundreds place, multiply the digit by 100.
click
To learn about multiplying a whole number by 100, click here.

Multiplying a Whole Number by 100
An easy way to think about multiplying a whole number by 100:
When you multiply a whole number by 100, the number stays the same and two zeros get
written at the end of the number. You write two zeros because 100 ends with two zeros.
For example:
8 x 100 = 800 100 x 8 = 800 36 x 100 = 3600 100 x 140 = 14 000
hundreds
(100s)
tens
(10s)
ones
(1s)
3 7 5
3 x 100
3 x 100 means 3 hundreds
100+100+100 = 300
Example
Remember: It does not matter what order you use to multiply numbers.
100 200 300
Click
OR count by 100s

Multiplying Whole Numbers by 100 (The Real Story)
When you multiply a whole number by 100, you are actually moving the digits in the number. They all
move two place values to the left, and a zero is added to the now empty tens place and ones place.
3 x 100 = 300
Example
3 hundreds
3 300
hundreds
(100s)
tens
(10s)
ones
(1s)
3 7 5
hundreds
(100s)
tens
(10s)
ones
(1s)
3
hundreds
(100s)
tens
(10s)
ones
(1s)
3
3
hundreds
(100s)
tens
(10s)
ones
(1s)
3 0 0
3 x 100
Click

Calculating the Value of a Digit in the Hundreds Place
5x1=5
Earlier you learned how to multiply a digit in the ones
place by 1. You also learned how to multiply a digit in
the tens place by 10.
hundreds
(100s)
tens
(10s)
ones
(1s)
3 7 5
7x10=70
3 hundreds
hundreds tens ones
3 0 0
3 x 100 =
3 hundreds means there is a 3 in the hundreds place. Zeros are added to the tens
and ones places to show they are empty. 3 x 100 = 300
3 x 100 = 300 and 7 x 10 = 70 and 5 x 1 = 5
Expanded form: 375 = 300 + 70 + 5
3x100
hundreds
(100s)
tens
(10s)
ones
(1s)
3 7 5
Expanded form of 375 click
To calculate the value of a digit in the hundreds place, multiply the digit by 100.
Repeated addition: 100+100+100 = 300
Details click

hundreds
(100s)
tens
(10s)
ones
(1s)
4 0 0
Another example.
1x1=1
4 x 100 =
0x10=0
Remember: When a number is multiplied by 0,
the result is 0.
hundreds
(100s)
tens
(10s)
ones
(1s)
4 0 1
4x100
Repeated addition:
100+100+100+100 = 400
4 x 100 = 400 and 0 x 10 = 0 and 1 x 1 = 1
Expanded form: 401 = 400 + 0 + 1  400 = 400 + 1
hundreds
(100s)
tens
(10s)
ones
(1s)
4 0 1
Omit the 0. It
adds nothing
to the number.
Expanded form of 401 click
Remember: When a number is multiplied by 1,
the result is the number itself.
4 hundreds means there is a 4 in the hundreds place. Zeros are added to the tens
and ones places to show they are empty. 4 x 100 = 400
Details click

102 x 100 = ________
12 x 10 = ________
________ x 18 = 1800
100 x 4357 = ________
10 x 989 = ________
2 x ________ = 200
100 x 100 = ________
100 x 10 = ________
________ x 100 = 5600
________ x 10 = 89 600
100 x ________ = 7400
10 x ________ = 250
100 x ________ = 88 000
50 x ________ = 5000
5 x ________ = 500
100 x 1234 = ________
100 x 0 = ________
100 x 1 = ________
Fill in the blanks below by writing a standard form number. Remember to space
large numbers correctly.
10 200
120
100
435 700
9890
100
10 000
1000
0
56
8960
74
25
880
100
100
100
123 400
click
click
click
click
click
click
click
click
click
click
click
click
click
click
click
click
click
click
Practice
Try
more
Try
more

105 = 105 ones 105 = 10 tens + 5 ones
1 hundred = 10 tens
1 hundred = 100 ones
105 = 1 hundred + 5 ones
105 = 10 tens + 5 ones
105 = 100 ones + 5 ones
A 3-digit number can be described in more than one way if you use place values
and words. For example: 105
Which picture represents the standard form of 105?
How do you know?
Each place has a single digit.
hundreds place: 1
tens place: 0
ones place: 5
click
10 tens = 100 ones
105 = 100 ones + 5 ones

Describe the 3-digit number 420 in different ways using place values and words:
hundreds tens ones
420 = _________ ones
420 = _________ + _________
expanded form (how many ones are in each place):
420 = _________ tens + _________ ones
420 = _________ hundreds + _________ ones
2 tens
20 ones
0 ones
4 hundreds
40 tens
400 ones
Group the digits to help you describe a
number in different ways. The place value
to the left of where each grouping ends is
the place you are describing.
420 = _________ ones
420
420 = _________ tens + _________ ones
42
420 = _________ hundreds + _________ ones
4
0
20
420 = _________ hundreds + _________ tens + _________ ones
4 2 0
Another way to think about it if a number is in standard form: click
420
42 0
4 20
4 0
2
400 20
click
click click
click click
click click click
click click

hundreds
(100s)
tens
(10s)
ones
(1s)
5 4 2
4 tens
40 ones
2 ones
5 hundreds
50 tens
500 ones
542 = _________ ones
542 = _________ + _________ + _________
expanded form (how many ones are in each place):
542 = _________ tens + _________ ones
Try one without pictures.
542 = _________ hundreds + _________ ones
5 4 2
542
54 2
5 42
500 40 2
click
click
click
click
click
click
click
click
click click click

hundreds
(100s)
tens
(10s)
ones
(1s)
8 0 9
809 = _________ ones
809 = _________ hundreds + ________ tens + ________ ones
expanded form: 809 = _________ + ________
809 = _________ tens + _________ ones
809 = ________ hundreds + _________ ones
0 tens
0 ones
9 ones
8 hundreds
80 tens
800 ones
8 0
809
80 9
8 9
800 9
9
click
click
click
click
click
click
click
click
click
More practice.
click

103 = 103 ones
63 103 = 1 hundred + 3 ones
expanded form: 103 = 100 + 3
63 103 = 1 hundred + 0 tens + 3 ones
63 103 = 10 tens + 3 ones
999 = _______ ones
= _____ hundreds + _____ tens + _____ ones
expanded form: _____________________
= _____ tens + _____ ones
Answers
Fill in the blanks in the examples below. The first one has been done for you.
= _____ hundreds + _____ ones
999
9 9
99 9
999 = 900 + 90 + 9
9
9 99
Answers
740 = _____ ones
= _____ hundreds + _____ tens + _____ ones
expanded form: _____________________
= _____ tens + _____ ones
521 = _____ ones
= _____ hundreds + _____ tens + _____ one
expanded form: _____________________
= _____ tens + _____ one
521
5 2
52 1
521 = 500 + 20 + 1
1
5 21
Answers
Example
Example
740
7 4
74
740 = 700 + 40
7 40
0
0
Example

Box Size
(How many can the box hold?)
The size of the boxes increases
by x10 as you move left.
Why do you need fewer boxes as you move left from the ones place?
The boxes are getting larger and they hold more.
Why do you need more boxes as you move right towards the ones place?
The boxes are getting smaller and they hold less.
click
click
Questions (Click)
Place Value Review

You are owed $911. You want the money paid back in bills that are as large as possible ($100 bills).
How many $100 will you get? How many other bills? Any coins?
You and your friends baked 183 cookies. You want to package them in groups of 10. How many
packages will you have? How many leftovers will there be?
Can you use the base-10 place value system to solve this problem? Explain.
You want to put 5 chairs around each table for a feast. You have 70 chairs. How many tables will
you use?
Rewrite the problem so you can use place values to solve it.
911 You will get 9 $100 bills plus 1 $10 bill plus 1 loonie.
click
183 There will be 18 packages and 3 cookies left over.
click
The base-10 system uses 10, 100, 1000, etc. as the grouping number. This problem uses 5.
You will put 10 chairs around each table. You have 70 chairs. How many tables will you use?
click
click
Click

Can 420 also be described as 3 hundreds + 12 tens? Provide proof for your answer.
hundreds
100s
tens
10s
ones
1s
hundreds
100s
tens
10s
ones
1s
hundreds
100s
tens
10s
ones
1s
4 hundreds + 2 tens
Unbundle one of the hundreds (10 tens).
Move the 10 tens to the tens place.
420 = 3 hundreds + 12 tens
answer

The most 3-digit whole numbers you can make is _________. Explain how you know.
What is the largest 3-digit whole number you can make? _________
Write the following as 3-digit standard form numbers:
500 + 60 + 4
2 hundreds + 8 tens
6 hundreds + 7 ones
1 hundred + 5 tens + 3 ones
two hundred forty-one
900 + 90 + 9
3 hundreds + 2 tens + 1 one
1x100 and 0x10 and 0x1
564
280
607
153
241
999
321
100
900
100 is the first 3-digit number and 999 is the last 3-digit number (1000 has 4 digits). From 100 to
199 is 100 possible numbers with 3 digits. From 200 to 299 is 100 possible numbers. Continue
until 900 to 999 which is 100 possible numbers. The total is 900.
999
What is the smallest 3-digit whole number you can make? _________
100
click
click
click
click
click
click
click
click
click
click
click
click

Which descriptions of 420 are correct?
420 = 2 hundreds + 22 tens
420 = 1 hundred + 32 tens
420 = 4 hundreds + 1 ten + 1 one (correct answer: + 10 ones)
420 = 42 ones (correct answer: 420 ones)
420 = 4 hundreds + 20 ones
420 = 3 hundreds + 2 tens + 100 ones
hundreds
100s
tens
10s
ones
1s
More ways to describe 420. Use the picture to help you.
420 = 1 hundred + 2 tens + ________ ones
420 = 3 hundreds + ________ tens + 120 ones
420 = ________ hundreds + 220 ones
420 = 2 hundreds + ________ tens + 200 ones
300
0
2
2
click
click
click
click
click
click
click
click
click
click
Use the picture to help you.

$420 = $400 + $20
$420 = 4 hundreds + 2 tens
$420 = $300 + $100 + $20
$420 = 3 hundreds + 10 tens + 20 ones
$420 = $200 + $210 + $10
$420 = 2 hundreds + 21 tens + 10 ones
The following are three examples using money. Each example shows a different
way to describe $420 with $10 bills (tens) and loonies (ones).
click
click

Moving Left From the Ones Place
When you move left one place at a time from the ones place, you are bundling
into 10s and adding to the place value to the left.
10 ones = ________ tens bundle
10 tens = ________ hundreds bundle
hundreds
(100s)
tens
(10s)
ones
(1s)
1
1
click
click
100 tens = ________ hundreds bundles
10
click

hundreds tens ones
7 25 38
38 x 1 = 38
25 x 10 = 250
250 = 2 hundreds + 5 tens 38 = 3 tens + 8 ones
7 hundreds 25 tens 38 ones
Answer the following questions:
In the ones column,
does the “3” represent
ones, tens, or hundreds?
Prove your answer.
In the tens column,
Prove your answer.
In the hundreds column,
7 25 38
click click click

hundreds tens ones
7 25 38
38 x 1 = 38
25 x 10 = 250
250 = 2 hundreds + 5 tens 38 = 3 tens + 8 ones
7 hundreds 25 tens 38 ones
Add the 3 to the tens
column because the 3 is
representing tens.
Write the following in standard form (you are moving left).
In the ones column,
Prove your answer.
In the tens column,
Prove your answer.
In the hundreds column,
25 + 3 = 28
8
Add the 2 to the hundreds
column because the 2 is
representing hundreds.
7 + 2 = 9
click
click
Step 1
Step 2
9
7 25 38
Standard Form: 988

3 h 13 t 0 o
Describe the following by showing the place values. One is done for you.
hundreds
100s
tens
10s
ones
1s
8 25 36
8 hundreds 2 hundreds
+ 5 tens
3 tens
+ 6 ones
hundreds
100s
tens
10s
ones
1s
16 18
1 hundred
+ 6 tens
1 ten
+ 8 ones
3 hundreds 1 hundred
+ 3 tens
88 t 40 o
8 hundreds
+ 8 tens
5 h 0 t 74 o
5 hundreds 7 tens
+ 4 ones
9 h 99 t 99 o
9 hundreds
+ 9 tens
4 tens
+ 0 ones
9 hundreds 9 tens
+ 9 ones
click click
click click
click click click
click click
0 ones
click 0 tens
click
click
click

6 h 25 t 36 o
6 h 25 t 36 o
+3
6 h 28 t 6 o
6 h 28 t 6 o
+2
8 h 8 t 6 o
standard form: 886
Start with
the ones
place and
move left.
To make a description of a number into standard form, deal with the places that are “over
sized”.
Rewrite the following in standard form (you are moving left).
• Add 2 bundles of hundreds from
the tens place to the hundreds
place (a move to the left).
• Add 3 bundles of tens from the
ones place to the tens place (a
move to the left).
• Always look for “over sized”
place values by starting with the
ones place. Then move left.
Click
Click

Challenge. Balance the scales by writing the standard form of the amount shown.
100 10 1
2 40 10
100 10 1
4 35 8
100 10 1
4 35 8
4 h 35 t 8 ones
Add 3 hundreds to the
hundreds place. Now there will
be 7 hundreds and 5 tens left
over. The 8 ones in the ones
place will stay the same.
100 10 1
7 5 8
100 10 1
2 40 10
Add 1 ten to the tens place.
Now there are 41 tens and
0 ones. Add 4 hundreds to
the hundreds place. Now
there are 6 hundreds and
1 ten left over.
answer
2 h 40 t 10 ones
100 10 1
6 1 0
41 t
6 h
7 h
answer
possible strategy
click
possible strategy
click

Challenge. Balance the scales by creating the standard form of the amount shown.
100 10 1
2 42 53
100 10 1
3 20 4
100 10 1
3 20 4
3 h 20 t 4 ones
Add 2 hundreds to the
hundreds place. There will now
be 5 hundreds and 0 tens left
over. The 4 ones in the ones
place stay the same.
100 10 1
5 0 4
100 10 1
2 42 53
2 h 42 t 53 ones
Add 5 tens to the tens place.
Now there are 47 tens and 3
ones left over. Add the 4
hundreds to the hundreds place.
Now there are 6 hundreds and 7
tens left over.
answer
answer
5 h
47 t
6 h
100 10 1
6 7 3
possible strategy
click
possible strategy
click

1 h 8 t 15 o 1 h 8 t 15 o 1 h 9 t 5 o = 195
+1
3 h 25 t 7 o 3 h 25 t 7 o 5 h 5 t 7 o = 557
+2
45 t 6 o 0 h 45 t 6 o 4 h 5 t 6 o = 456
+4
2 h 27 t 8 o 2 h 27 t 8 o 4 h 7 t 8 o = 478
+2
6 h 2 t 35 o 6 h 2 t 35 o 6 h 5 t 5 o = 655
+3
Create the standard form of the amount shown. One is done for you.
click
click
click
click

6 h 9 t 23 o 6 h 9 t 23 o 6 h 11 t 3 o 6 h 11 t 3 o = 713
+2
51 t 34 o 0 h 51 t 34 o 0 h 54 t 4 o 0 h 54 t 4 o = 544
+3
15 t 16 o 0 h 15 t 16 o 0 h 16 t 6 o 0 h 16 t 6 o = 166
+1
4h 25 t 20 o 4 h 25 t 20 o 4 h 27 t 0 o 4 h 27 t 0 o = 670
+2
329 o 0 h 0 t 329 o 0 h 32 t 9 o 0 h 32 t 9 o = 329
+32
+1
+5
+3
+1
+2
Create the standard form of the amount shown. One is done for you.
click
click
click
click

Moving Right Toward the Ones Place
When you move right one place at a time heading toward the ones place, you
are unbundling into 10s and adding to the place value to the right.
1 hundreds unbundled = ________ tens
1 tens unbundled = ________ ones
hundreds
(100s)
tens
(10s)
ones
(1s)
10
10
click
click
10 tens unbundled = ________ ones
100
click

hundreds tens ones
3 6 4
2 hundreds
2 hundreds
3 hundreds
2 hundreds + 10 tens 6 tens 4 ones
The number 364 below is in standard form. You can describe 364 a new way by
unbundling one of the hundreds into 10 tens and adding them to the tens place
to the right.
6 tens
6 tens
+ 10 tens
2 hundreds + 10 tens 4 ones
4 ones
16 tens 4 ones
364 = 2 hundreds + 16 tens + 4 ones (not standard form)
364 = 3 hundreds + 6 tens + 4 ones (standard form)
click

3+30 ones
=33
hundreds tens ones
2
2 hundreds
(20 tens)
3
3 tens
(30 ones)
5
5 ones
5
2 0
1 5
2 1
3 + 20 tens
= 23
3 + 10 tens
= 13
5 + 20 ones
= 25
5 + 30 ones
= 35
235 = 23 tens + 5 ones
235 = 2 hundreds + 35 ones
235 = 1 hundred + 13 tens + 5 ones
235 = 2 hundreds + 1 ten + 25 ones
click
click
click
The number 235 is in standard form. Fill in the cells that have question marks by
unbundling place values into 10s and adding the 10s to the place to the right.
Check your answers by clicking on the question marks.
click
?
?
?
?

3+30 ones
=33
hundreds tens ones
3
3 hundreds
(30 tens)
1
1 ten
(10 ones)
0
0 ones
0
2 0
3 0
1 0
1 + 30 tens
= 31
310 = 3 hundreds + 1 ten + 0 ones
310 = 31 tens + 0 ones
The number 310 is in standard form. Fill in the cells that have question marks by
unbundling place values into 10s and adding the 10s to the place to the right.
Check your answers by clicking on the question marks.
1 + 10 tens
= 11
0 + 10 ones
= 10
1 + 20 tens
= 21
click
click
click
click
?
?
?
?

Balance the scales by writing the standard form numbers another way. You will be
moving to the right.
100 10 1
9 8 0
100 10 1
6 7 5
100 10 1
6 7 5
5 h
10 t
7 t 5 o
Unbundle 1 hundred into
10 tens. Add the 10 tens to the
tens place (10+7). Now there
will be 5 hundreds and 17 tens.
The 5 ones in the ones place
will stay the same.
100 10 1
5 17 5
100 10 1
9 8 0
Add 20 ones (2 tens) to the
ones place (20+0). Now there
are 6 tens and 20 ones. The
9 hundreds in the hundreds
place will stay the same.
answer
9 h 6 t
20 o
100 10 1
9 6 20
0 o
answer
17 t
possible strategy
click
20 o
possible strategy
click

Identify the missing numbers. One has been done for you. To check your answers,
move left and you should get the original standard form number.
643 = 5 hundreds ________ tens 3 ones 6 h 4 t 3 o 5 h 14 t 3 o
+10
14
497 = ________ hundreds 19 tens 7 ones 4 h 9 t 7 o 3 h 19 t 7 o
+10
+10
+10
264 = 2 hundreds 5 tens ________ ones 2 h 6 t 4 o 2 h 5 t 14 o
+10
3
10
14
8
click
click
click
click

hundreds tens ones
4
4 hundreds
40 tens
400 ones
7
7 tens
70 ones
2
2 ones
3 h 2 o
17 t
The number 472 is in standard form. Another way to write this number is:
3 hundreds + 7 tens + 102 ones
+10 t
3 h 102 o
17 t +100 o
3 h 102 o
7 t
Why do you add 100 to the ones
place and not 10?
Prove it.
17 tens = 170 ones (17 x 10 = 170)
17 tens = 10 tens + 7 tens
10 tens = 100 ones (10 x 10 = 100)
step 1
step 2
step 3
You add 10 if you are dealing with standard
form numbers (one digit in each place).
1 ten = 10 ones (1 x 10 = 10)
Why?

Identify the missing numbers (challenging). One has been done for you. To check
your answers, move left and you should get the original standard form number.
199 = 0 hundreds 9 tens ________ ones 1 h 9 t 9 o 0 h 19 t 9 o 0 h 9 t 109 o
+10 +100 (10x10)
109
570 = 4 hundreds 17 tens ________ ones 5 h 7 t 0 o 4 h 17 t 0 o
+10
0
+10 +100
100
+10 +100
100
+20 +200 (20x10)
200
click
click
click
click

Remember:
Bundle and Add
Unbundle and Add

100 10 1
3 21 9
100 10 1
5 0 19
Balance the scales by writing the numbers below (not in standard form) another
way. Move to the left (bundling) and to the right (unbundling).
100 10 1
6 34 3
100 10 1
9 0 43
100 10 1
3 21 9
3 h 21 t 9 o
answer
19 o
+10
+2
5 h 0 t
100 10 1
6 34 3
6 h 34 t 3 o
+3
9 h 0 t
answer
possible strategy
click
+40
43 o
possible strategy
click

146 + 198 = ?
Application
Here is a very cool way to use place values to save you time when you add large
numbers. You will learn more about this when you get to the addition resource.
Add hundreds to hundreds, tens to tens, ones to ones.
146 + 198 =
100s 10s 1s
2 13 14
Write in standard form (moving left starting with the ones).
Step 1 Step 2 Step 3

351 + 79 = ? 351 + 079 = ?
Try it. Add a leading 0 so both numbers have the same number of digits.
Add hundreds to hundreds, tens to tens, ones to ones.
351 + 079 =
100s 10s 1s
3 12 10
Write in standard form (moving left starting with the ones).
click

Adding 100
When you add 100 to a number, you are adding 1 hundred and 0 tens and
0 ones to that number.
For example: 246 + 100
Without pictures:

click
click
click
Add leading zeros so the numbers have the same amount of digits.
Leading 0
Leading 0

999 + 100 =
100s 10s 1s
10 9 9
Write in standard form by moving left. (The 100s place needs adjustment.)
100s 10s 1s
10 9 9
1000s 100s 10s 1s
10 9 9
+1
1000s 100s 10s 1s
1 0 9 9
Try another one: 999 + 100
Adding 100 to a number means the hundreds place value will increase by 1 hundred, and the
tens and ones place values will stay the same. If there is a 9 in the hundreds place, the 1000s
place will be affected.
click
Step 1 Step 2

92 + 10 =
100s 10s 1s
10 2
100s 10s 1s
10 2
+1
100s 10s 1s
1 0 2
999 + 010 =
10s 1s
9 10 9
100s 10s 1s
9 10 9
+1
100s 10s 1s
10 0 9
1000s 100s 10s 1s
10 0 9
+1
1000s 100s 10s 1s
1 0 0 9
Adding 10 to a number means the tens place value will increase by 1 ten, and the ones place
value will stay the same. If there is a 9 in the tens place, the hundreds place will be affected.
Think the same way if you add 10 to a number and there is a 9 in the tens place.
Step 2 Step 3
Another example: 999 + 10
Step 4 Step 5
Click
Leading 0
Step 1

Add $100 to the following amounts of money. Use any method that works for you except a calculator.
$170 + $100 = ________
$100 + $5 = ________
$965 + $100 = ________
$100 + $3462 = ________
$270
$105
$1065
click
$3562
click
click
click
$990 + $100 = ________
$100 + $910 = ________
$760 + $100 = ________
$100 + $1000 = ________
$1090
$1010
$860
click
$1100
click
click
click
Add $10 to the following amounts of money. Use any method that works for you except a calculator.
$95 + $10 = ________
$996 + $10 = ________
$105
$1006
click
click
$10 + $9895 = ________
$10 + $493 = ________
$9905
$503
click
click
$10 + $991 = ________
$290 + $10 = ________
$1001
$300
click
click

Moving between
place values
(thousands)
7
Back to Main Menu

thousands hundreds tens ones
Bundle 10 hundreds into 1 thousand,
and move the 1 thousand to the
thousands place. Write a 1 in the
thousands column.
Write a 0 in the hundreds column to
show there are now no hundreds.
Write a 1 in the tens column and a 2
in the ones column to show there is
still 1 ten and 2 ones.
Thousands Place Value
For example, you have 9 hundreds,
1 ten, and 2 ones. A hundred gets
added to the hundreds place. Now
there are too many hundreds.
Click
Click
1 0
5
When the amount in the hundreds place becomes greater than 9, the hundreds
place needs help from the thousands place. But remember, in standard form, the
thousands place only takes thousands.
Thousands
Hundreds
Tens
Ones
1 0 1 2
Click
Click #1
Click #2
Click #3

Calculating the Value of a Digit in the Thousands Place
3x10=30
Earlier you learned how to multiply a digit in
the ones place by 1. You also learned how to
multiply a digit in the tens place by 10, and a
digit in the hundreds place by 100.
6x100=600
5 thousands
5 x 1000 =
5 thousands means there is a 5 in the thousands place. There are no hundreds, tens, or ones.
Zeros are added to the hundreds, tens, and ones places to show they are empty. 5 x 1000 = 5000
5 x 1000 = 5000
2 x 1 = 2
Expanded form:
5x1000
thousands
(1000s)
hundreds
(100s)
tens
(10s)
ones
(1s)
5 6 3 2
To calculate the value of a digit in the thousands place, multiply the digit by 1000.
thousands
1000s
Hundreds
100s
Tens
10s
Ones
1s
5 6 3 2
2x1=2
5 0 0 0
6 x 100 = 600
3 x 10 = 30 5632 = 5000 + 600 + 30 + 2
Repeated addition:
1000+1000+1000+1000+1000=5000
Details click

3561 = __________________________
4329 = __________________________
5231 = __________________________
2270 = __________________________
7602 = __________________________
7185 = __________________________
8001 = __________________________
1100 = __________________________
2018 = __________________________
9406 = __________________________
3000 + 500 + 60 + 1
4000 + 300 + 20 + 9
5000 + 200 + 30 + 1
2000 + 200 + 70
7000 + 600 + 2
7000 + 100 + 80 + 5
8000 + 1
1000 + 100
2000 + 10 + 8
9000 + 400 + 6
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click

Thousands Place Value
Thousands
1000s
Hundreds
100s
Tens
10s
Ones
1s
Thousands
Hundreds
Tens
Ones
2 3 4 1
Write this number in standard form:
1 ten = __________ ones 1 hundred = __________ tens
1 thousand = __________ hundreds
1 hundred = __________ ones
1 thousand = __________ ones
1 thousand = __________ tens
Fill in the blanks:
Click
10
100
1000
10
100
10
click
click
click
click
click
click

expanded form: 5632 = 5000 + 600 + 30 + 2
5632 = _______ ones
5632 = ___ thousands + ___ hundreds + ___ tens + ___ ones
5632 = ___ hundreds + ___ tens + ___ ones
5632 = ___ thousands + _____ ones
5632 = ___ hundreds + ___ ones
5632 = ______ tens + ___ ones
5632 = ___ thousands + ___ tens + ___ ones
A 4-digit number can be described in more than one way if you use place values
and words. For example: 5632
5 6 3 2
5632
56 3 2
5 63 2
5 632
56 32
563 2
Click
Click
Click
Click
Click
Click
Click
Click

What are the following numbers if you think of them in terms of hundreds?
The first one has been done for you.
3100 _________________________
5800 _________________________
9500 _________________________
2700 _________________________
6900 _________________________
4400 _________________________
7600 _________________________
1100 _________________________
What are the following numbers if you think of them in terms of tens?
4560 _________________________
3910 _________________________
2220 _________________________
8630 _________________________
7180 _________________________
5850 _________________________
31 hundreds
456 tens
58 hundreds
95 hundreds
27 hundreds
69 hundreds
44 hundreds
76 hundreds
11 hundreds
391 tens
click
click
click
click
click
click
click
222 tens
863 tens
718 tens
585 tens
click
click
click
click
click
click

Write the following 4-digit number descriptions in standard form.
3 thousands + 2 hundreds __________
7 thousands + 4 hundreds + 1 ten __________
22 hundreds + 32 ones __________
1200 + 30 + 4 __________
4 thousands + 300 ones __________
6000 + 21 __________
5000 + 203 __________
80 hundreds + 80 tens __________
1 thousand + 1 hundred + 1 ten + 1 one __________
9 thousand + 2 hundreds __________
10 hundreds __________
64 hundreds + 5 ones __________
3200
7410
2232
1234
4300
6021
5203
Click
Click
Click
Click
Click
Click
8080
9200
1111
1000
6405
Click
Click
Click
Click
Click
Click

How many B boxes are needed for 430 objects?
How many C boxes are needed for 5500 objects?
How many B boxes are needed for 5500 objects?
430 43 “tens” boxes
5500 55 “hundreds” boxes
5500 550 “tens” boxes
How many A boxes are needed for 8000 objects? 8800 8800 “ones” boxes
click
click
click
click
How many D boxes are needed for 8000 objects? 8800 8 “thousands” boxes
click

An easy way to multiply by 1000:
Keep the digits the same because you are multiplying by 1 and add three zeros to the end
of the number (ones, tens, and hundreds places). You know to add three zeros because
you are multiplying by 1000 and 1000 has three zeros (ones place, tens place, and
hundreds place).
Multiplying by 1000
When you multiply by 1000, you are actually moving the digits in the number. They all move three
places to the left, and zeros are added to the now empty ones and tens places.
8 8 x 1000 8000
The Real Story: click

Fill in the following blanks:
1000 x 10 = ___________
18 x 1000 = ___________
7 x 1000 = ___________
608 x 1000 = ___________
1000 x 1000 = ___________
96 x 1000 = ___________
1000 x 125 = ___________
11 x 1000 = ___________
2357 x 1000 = ___________
1000 x 1 = ___________
1000 x 100 = ___________
199 x 1000 = ___________
10 000
18 000
7000
608 000
1 000 000
96 000
125 000
11 000
2 357 000
1000
100 000
199 000
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click

If a whole number has four digits, it is a number in the ________________
(thousands, hundreds, tens, or ones).
If a whole number has two digits, it is a number in the ________________
(thousands, hundreds, tens, or ones).
If you multiply a whole number by 10 two times, it is the same as multiplying by __________.
If you multiply a whole number by 10 three times, it is the same as multiplying by __________.
If you multiply a whole number by 10 and then by 0, the answer is __________.
thousands
tens
100
1000
Example: 5 x 10 = 50 50 x 10 = 500 500 = 5 x 100
Example: 5 x 10 = 50 50 x 10 = 500 500 x 10 = 5000 5000 = 5 x 1000
Click
Click
Click
Click
0
Click
Reflection

If you can write a number as thousands, you can also write the number as tens.
If you can write a number as thousands, you can also write the number as hundreds.
If you can write a number as hundreds, you can also write the number as thousands.
If you can write a number as ones, you can also write the number as tens.
If you can write a number as thousands, you can also write the number as ones.
Indicate if the following are true or false. Defend your answers.
Yes. Tens are smaller than thousands. 100 tens make up one thousand.
Yes. Hundreds are smaller than thousands. 10 hundreds make up one thousand.
Not necessarily. The number must be larger than 999 for this statement to be true.
Not necessarily. The number must be larger than 9 for this statement to be true.
Yes. Ones are smaller than thousands. 1000 ones make up one thousand.
Click
Click
Click
Click
Click

7
Use the digits above to make the following 4-digit numbers:
A number with 7016 ones:
A number with 761 ones:
A number with 76 tens:
A number with 76 hundreds:
A number with 170 tens:
7016
0761
7601 or 7610
0761
A number with the expanded form:
7000 + 10 + 6
A number with the expanded form:
6000 + 700 + 1
1706
7016
6701
Click
Click
Click
Click
Click
Click
Click

Comparing and
ordering whole
numbers
8
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Think about the shape of the sign. The wide (open) end is beside the larger
number. The narrow (closed) end is beside the smaller number.
Two ways of
writing the same
information.
23 is greater than 9
greater means larger
less means smaller
23 9
<
Greater Than > and Less Than <
9 is less than 23
9 23
Than (meaning comparison) and then (meaning next) are two different words.

Comparing Whole Numbers
To compare whole numbers with the same amount of digits, stack the
numbers. Then compare the different place values from left to right. When
you come to a number that is larger than its counterpart, STOP. You have
found the larger number.
Which is larger? 2943 vs. 3120
Since 3 is greater than 2, STOP right there.
3120 > 2943
Click to see answer
1000s 100s 10s 1s
2 9 4 3
3 1 2 0
Which is larger? 3561 vs. 3571
Since 3=3, move right.
Since 7 > 6, STOP right there.
3571 > 3561
1000s 100s 10s 1s
3 5 6 1
3 5 7 1
Click to see answer

Comparing Whole Numbers
Which is larger? 821 vs. 1000 1000s 100s 10s 1s
8 2 1
1 0 0 0
Which is smaller? 4103 vs. 4102
Since 2 < 3, you know 4102 < 4103
1000s 100s 10s 1s
4 1 0 3
4 1 0 2
1000 > 821
With whole numbers, the number with
the most digits is always larger.
Remember: When comparing whole numbers, the number with the fewest digits is the smallest.
The number with the largest amount of digits is the largest. Leading zeros do not count.

2 _______ 4 165 _______ 166 39 696 _______ 41 698
288 _______ 288 5 328 _______ 6 319 72 _______ 84
934 000 _______ 934 015 885 _______ 893 6 064 _______ 6 064
18 555 _______ 16 673 999 98 _______ 999 98 2 145 _______ 2 137
67 _______ 65 1 026 _______ 1 018 56 370 _______ 56 348
1 000 000 _______ 2 000 000 29 672 _______ 29 672 14 890 _______ 12 890
212 300 _______ 212 300 999 999 _______ 1 000 000 66 677 _______ 66 777
Should a <, >, or = sign go in each blank below?
<
=
=
=
=
=
>
> >
>
>
>
<
<
<
<
<
<
<
<
<
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Click
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Click
Click
Click

Ascending Order
If you are asked to list
whole numbers in
ascending order, it
means from smallest
(least) to largest
(greatest).
e.g., $3 < $6 < $9
Descending Order
If you are asked to list
whole numbers in
descending order, it
means from largest
(greatest) to smallest
(least). Think “d” =
“decreasing”.
e.g., $9 > $6 > $3
Reminder: Ascending vs. Descending Order

A
B
C
D
E
F
0 km
G
100 km 40 km
20 km 80 km
90 km
10 km
30 km
50 km
60 km
70 km
You are planning a trip. You have made a rough estimate of distances and all
the stops you plan to make. Indicate how far (estimate) each stopping point is
from where you start. Choose from the km options below:
20 km
50 km
40 km
60 km
90 km
When you write numbers on a route or
“line”, how must the numbers be
spaced?
Click
They must be spaced evenly according to their
values. For example, the distance between 40 and
60 would be twice as much as between 40 and 50.
You need two numbers on the line before you can
set up the spacing (e.g., 0 and 100).
Click

x = unknown
List the 5 most populated communities
in descending order.
List the 5 least populated places in
ascending order.
How many centres have fewer than 300
people? In what region are the majority
of these centres located?
Answer the following questions
based on the population table.
Yellowknife
Hay River
Inuvik
Fort Smith
Behchokò
Jean Marie
Sambaa K’e
Nahanni Butte
Enterprise
Sachs Harbour
10, Dehcho Region (has 4)
click
NWT Population Table
click
click

Reading and Using Words to Write Whole Numbers
Note the spelling of forty and ninety.
(20) twenty
(30) thirty
(40) forty
(50) fifty
(60) sixty
(70) seventy
(80) eighty
(90) ninety
Below are some reminders about how to write numbers using English words.
Usually when you write words to describe
2-digit numbers greater than 20, you place a
hyphen between the tens digit and the ones
digit. For example:
(25) twenty-five (99) ninety-nine
(41) forty-one (32) thirty-two
(71) seventy-one (53) fifty-three
(11) eleven
(12) twelve
(13) thirteen
(14) fourteen
(16) sixteen
(17) seventeen
(18) eighteen
(19) nineteen
(15) fifteen

• What are the written number words for 1 to 20 in your Indigenous language?
• What are some similarities and differences between number writing (using words) in your
Indigenous language and in English?
• Are there any patterns in the counting words in your Indigenous language that make the words
easy to learn?
• Can there be more than one word for a number in your Indigenous language? If so, when does
this happen?
Think about writing number words in your Indigenous language. Then answer
the following:
Writing Numbers…Reflection
Counting can be very different in different languages. Counting words matter!

Write the English word names for the following whole numbers. Then try
the names in your Indigenous language.
9 __________________
70 __________________
18 __________________
56 __________________
99 __________________
11 __________________
48 __________________
60 __________________
19 __________________
Write the standard form for the following number word names (English):
forty-three _______
eighty _______
sixty-eight _______
twenty-two _______
thirty _______
ninety-five _______
thirteen _______
fifty-one _______
two _______
nine
seventy
eighteen
fifty-six
ninety-nine
eleven
forty-eight
sixty
nineteen
43
80
68
22
30
95
13
51
2
click
click
click
click
click
click
click
click
click
Click
Click
Click
Click
Click
Click
Click
Click
Click
Try these: click

Writing and
saying whole
number words
9
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3-digit numbers (hundreds with no digits in the tens or ones places)
To write hundreds with digits in the tens and ones places:
The word AND is not used when you read
whole numbers. For example, do not say “two
hundred and fifteen”.
Say “two hundred fifteen”.
(200) two hundred
(300) is three hundred
(100) one hundred (400) four hundred
(500) five hundred
(600) six hundred
(700) seven hundred
(800) eight hundred
(900) nine hundred
Do not use a hyphen.
Do NOT place a hyphen between the
hundreds and other place values.
(101) one hundred one
(109) one hundred nine
(146) one hundred forty-six
(199) one hundred ninety-nine

Write the English word names for the following whole numbers. Then try the
names in your Indigenous language.
387 ______________________________
601 ______________________________
240 ______________________________
999 ____________________________
745 ____________________________
147 ____________________________
502 ________________________
810 ________________________
419 ________________________
Write the standard form for the following number word names:
three hundred twenty-five _______
seven hundred ninety-nine _______
eight hundred forty-three _______
nine hundred sixty-six _______
six hundred thirty-one _______
two hundred fifty _______
one hundred two _______
four hundred four _______
five hundred nine _______
three hundred eighty-seven
six hundred one
325
799
843
966
two hundred forty
nine hundred ninety-nine
seven hundred forty-five
one hundred forty-seven
five hundred two
eight hundred ten
four hundred nineteen
631
250
102
404
509
click
click
click
click
click
click
click
click
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click
click
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Try these: click

Use grouping when reading and using words to describe large numbers. Each
group has a 3-digit number. For example: 154 876 923.
Starting from the left, read each group as if it were its own 3-digit number.
Then say the name of the group. The last group has no name to say.
154 million 876 thousand 923
One hundred fifty-four million eight hundred seventy-six thousand nine hundred twenty-three
Reading and Using Words to Describe Large Whole Numbers
• The last 3 numbers have no group name. This group
has the ones, tens, and hundreds place values.
154 876 923
thousand
group
no name
group
million
group
• The next 3 numbers to the left are the thousand group.
• The next 3 numbers to the left are the million group.
• After the million group, there is the billion group,
trillion group, quadrillion group, etc.
How to read 154 876 923: click

1 40 603
thousand
group
no name
group 40 thousand 603
forty thousand six hundred three
Whole number: 40 603
More examples:
1 293 001
thousand
group
no name
group 293 thousand 1
two hundred ninety-three thousand one
Whole number: 293 001
1 000 000
thousand
group
no name
group
nine million
Whole number: 9 000 000
million
group
9
9 million Never say or
write the word
“zero”.
1 58 000 006
thousand
group
no name
group 58 million 6
fifty-eight million six
Whole number: 58 000 006
million
group
Never say or
write the word
“zero”.
Click
Click
Click
Click

3300 3030 3003 3333
three thousands +
333 ones
3333
three thousand three
3003
3 thousands + 3 tens
3030
three thousand thirty
3030
three hundred thirty
tens
3300
three thousand three
hundred thirty-three
3333
3 thousands + 3
hundreds
3300
30 hundreds + 3 ones
3003
thirty-three hundreds
thirty-three
3333
300 tens + 3 ones
3003
30 hundreds + 3 tens
3030
thirty-three hundreds
3300
Match each number below to its description. Each number will match with
three descriptions.
click click click click

fifty-three million four hundred one thousand seven hundred forty-two ____________________
In life, no one writes out large numbers in words. However, writing out
the words teaches you how to read and say the numbers.
Turn the following into standard form numbers:
seventy-nine thousand one hundred eighty-nine ____________________
four million two hundred five thousand five hundred fifty-three ____________________
five hundred thirty-six thousand ____________________
two thousand eleven ____________________
seven hundred forty-one thousand eight ____________________
twenty-one thousand one hundred ____________________
53 401 742
79 189
4 205 553
eight million twelve ____________________
536 000
2 011 or 2011
741 008
21 100
8 000 012
31 000 005
thirty-one million five ____________________
click
click
click
click
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click

Write the following standard form numbers using words and numbers. The first
one is done for you as an example.
16 760 ______________________________________
48 165 016 __________________________________
9 990 ________________________________________
32 000 000 __________________________________
724 006 ______________________________________
1 000 013 ___________________________________
2007 _________________________________________
85 936 _______________________________________
16 thousand 760
48 million 165 thousand 16
9 thousand 990
32 million
724 thousand 6
1 million 13
2 thousand 7
85 thousand 936
click
click
click
click
click
click
599 100 _____________________________________ 60 320 _______________________________________
599 thousand 100 60 thousand 320
click
click
click

Congratulations! You have now
completed Introduction to Whole
Number Sense.
Number Sense
Click on the Back to Main Menu button if you wish to review a topic. Otherwise,
press the Esc key to exit the PowerPoint.
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Level 1

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