Minds On
Ten thousand
Let's imagine you are going to attend a music concert in a big city arena. How many people can attend the concert? Use the place value chart to solve this problem. The number of people who can attend is the biggest number possible that we can make with the chart below. You can work with a partner or independently. What is the biggest number you can create up to ten thousand?
Description
A place value chart representing thousands, hundreds, tens and ones. Each column contains a space to add possible combinations for each place value.
What comes after thousands in place value? Think of other situations where we come across large numbers of up to 10,000 people in real-life.
In this learning activity you will compare and write numbers up to 10,000 in expanded form, round numbers up to the nearest ten (10), hundred (100) or thousand (1,000), and solve problems that will require you to add or subtract whole numbers up to 10,000.
Action
Ten thousand in the real world
There are many places where we can find up to ten thousand people in one place. For example, a parade, street festival, a large stadium or sports arena, or an exhibition event like Toronto's Canadian National Exhibition.
Populations of Canadian townships
Some small towns have between 1,000 to 10,000 people living there. What is the population of the town or city you live in? Is your hometown larger or smaller than 10,000 people? Use a comparison sign, greater than > or less than < to compare your city’s population to 10,000.
Task 1: Place value chart
In this activity, you will work with a list of Canadian towns that have different populations. The largest town has up to 10,000 people. You will practise decomposing and composing these numbers using a place value chart. Decomposing numbers involves taking them apart, and composing involves putting them back together.
Composing: 5,480 is composed of 5 thousands, 4 hundreds, and 8 tens.
Or, 5,000 + 400 + 80.
Decomposing: When we take a number apart.
So, 5,480 = 5,000 + 400 + 80.
When we compose numbers they appear in standard form: 5,480. When we decompose numbers they appear in expanded form: 5,000 + 400 + 80.
The following is a list of some Canadian towns with populations that are less than or equal to 10,000.
Perth6,481
Kirkland Lake7,775
Binbrook8,796
Huron East9,264
Sooke6,145
Dryden8,195
Kincardine6,725
Bracebridge8,238
Carleton Place9,743
Hanceville10,000
South Huron9,982
Sydney Mines7,312
Parry Sound6,469
Bluewater7,044
Iqaluit6,124
Hampstead6,996
Hanover7,255
Selkirk9,653
Yarmouth7,500
Kapuskasing9,240
Goderich8,032
Innisfil7,345
Renfrew8,018
Edson7,975
The Pas6,055
Weyburn9,362
Wasaga Beach7,567
Hinton9,889
Brownsburg-Chatham6,664
Mont-Tremblant8,892
Banff7,502
Saint-Felix-de-Valois6,029
Using a place value chart that includes ten thousand, choose 10 cities from the list and order these city populations from smallest to largest, making sure you include the city with the smallest and largest population (or follow your teacher’s instructions for how many populations to choose).
To help you, use a place value chart and write each population in expanded form.
The following is an example of how to use a place value chart to order the populations of these four Canadian cities from least to greatest:
Wild Rose
8,031
Taber
8,163
Beauceville
6,226
Kirkland Lake
7,775
The populations have each been placed into the place value chart.
The population 8,031 can be expanded in the following way:
8 Thousands looks like this:
8,000
0 Hundreds looks like this:
000
3 Tens looks like this:
30
1 Ones looks like this:
1
+
When we add these all
up, we get
8,031
The expanded form of 8,031 is 8,000 + 000 + 30 + 1. We don’t need to write the 0 value but it’s helpful to remind ourselves that 0 is required as a place value holder for empty values of zero (we still record its value even though its value is zero).
To decide which is the largest number, we look at the LARGEST place value, which is furthest to the left. In this place value chart, the largest place is the thousands.
We have two populations with the digit 8 in the thousands: Wild Rose and Taber.
To decide which city is larger, we look at the NEXT LARGEST place value (one place value over to the right), which is the HUNDREDS place, and compare the digit in 8 0 31 and 8 163.
Since the 1 digit in the HUNDREDS is larger than the 0 in the HUNDREDS, 8,163 is greater than 8,031.
To write a comparison expression using > or <, we write:
Now we order the populations of Wild Rose 8,031, Taber 8,163, Beauceville 6,226, and Kirkland Lake 7,775 from least (smallest) to greatest (largest). We notice Beauceville has a 6 digit in the THOUSANDS, which means 6,000, so Beauceville has the smallest population of these four Canadian cities. Kirkland Lake has a 7 digit in the THOUSANDS, which means a value of 7,000 so it is larger than Beauceville, but not as large as Wild Rose or Taber. Our final answer of populations from least to greatest is: 6,226, 7,775, 8,031, 8,163.
Task 2: Rounding
In this task, you will practice rounding whole numbers to the nearest ten, hundred, or thousand. Rounding numbers makes them easier to work with and understand. People round numbers in many different situations, including real-world situations we'll explore in this task.
In order to round to the nearest place value, follow these steps:
- Look at the digit in the next smaller place value (one place value to the right)
- if that digit is 0-4, then it becomes 0, and the digit stays the SAME. We say to round DOWN.
- if that digit is 5 or above, then it becomes 0, and the digit GOES UP ONE digit higher. We say to round UP.
Access the following episode of Homework Zone to learn about when to ROUND UP and when to ROUND DOWN.
Let’s practice rounding together with the following examples:
Bells Corners
9,977
Wild Rose
8,031
Taber
8,163
Beauceville
6,226
Kirkland Lake
7,775
Round Beauceville’s population 6226 to the nearest TEN.
We identify the 6 digit in the ONES. It is 5 or greater, so we round the 2 digit UP to 3.
The rounded number is 6230.
Round Taber’s population of 8163 to the nearest TEN.
We identify the 3 digit in the ONES. It is 4 or less, so we keep the 6 digit the SAME and round DOWN.
The rounded number is 8160.
Round Beauceville’s population 6226 to the nearest HUNDRED.
We identify the 2 digit in the TENS. It is 4 or less, so we keep the 2 digit in the HUNDREDS place value the SAME, and round DOWN.
The rounded number is 6 200.
Round Taber’s population of 8 163 to the nearest HUNDRED.
We identify the 6 digit in the TENS. It is 5 or greater, so we round the 1 digit in the HUNDREDS place value UP by one to 2.
The rounded answer is 8 200.
Round Beauceville’s population 6 226 to the nearest THOUSAND.
We identify the 2 digit in the HUNDREDS. It is 4 or less, so we round the 6 digit in the THOUSANDS DOWN so it stays the same.
The rounded answer is 6 000.
Round Taber’s population 8 163 to the nearest THOUSAND.
We identify the 1 digit in the HUNDREDS. It is 4 or less, so we round the 8 digit in the THOUSANDS DOWN so it stays the same.
The rounded answer is 8 000.
Round Kirkland Lake’s population 7 775 to the nearest THOUSAND.
We identify the 7 digit in the HUNDREDS. It is 5 or more, so we round the 7 digit in the THOUSANDS UP by 1.
The rounded answer is 8 000.
Similarly, round Bells Corners 9 977 population to the nearest THOUSAND
We identify the 9 digit in the HUNDREDS. It is 5 or more, so we round the 9 digit in the THOUSANDS UP by 1.
The rounded answer is 10 000.
If we round Bells Corners 9 977 population to the nearest HUNDREDS, we identify the 7 digit in the TENS and notice it is 5 or more, so we round the 9 digit in the HUNDREDS UP by 1.
The rounded answer is 10 000.
If we want to round the 9977 population of Bells Corners to the nearest TENS, we have to round the 77 in 9,977. You round up, if the number you are rounding is followed by 5, 6, 7, 8, or 9. You round down, if the number you are rounding is followed by 4, 3, 2, 1 or 0. Therefore, the number 77 will be rounded up to 80.
9,977 rounded to the nearest tens is 9980.
Take the populations of the 10 cities you chose to order.
- Round each population to the nearest TEN.
- Round each population to the nearest HUNDRED.
- Round each population to the nearest THOUSAND.
Rounding gives us a sense of the general magnitude or size according to the place value.
For example, if you were describing Banff’s population of 7,502 in a conversation, you would likely round its population to the nearest thousand or hundred.
Usually, people don’t remember the exact number unless they refer to the specific number in a report or table (even though every individual counted is equally as important).
Similarly, if you attended a professional sports championship finals game, you or a sportscaster would estimate the attendance in the thousands, maybe ten thousand.
Access the following episode of Homework Zone, where teacher Shahana demonstrates how to round 4-digit whole numbers.
Task 3: Ordering populations
Find out which of your 10 cities from Task 1 are in Ontario and which are outside of Ontario. Record the province. Use rounding to the nearest thousand and/or hundred to organize the cities in a Venn diagram or Carroll chart.
For example, for a Carroll diagram you could organize cities into categories that have populations that are equal to or smaller than 8,500 and those larger than 8,500, as well as cities in Ontario and cities outside of Ontario.
| In Ontario | Outside Ontario | |
|---|---|---|
| populations equal to or smaller than 8,500 | ||
| populations larger than 8,500 |
Task 4: Differences
In this task, you will practice subtracting whole numbers, up to 10,000.
For each city whose populations you chose to order, find the difference between its population and 10,000. How many more people would have to live there for the city’s population to reach 10,000?
Using Bells Corners population of 9,977, find the difference between this number and 10,000.
The key word in this question is difference which means to subtract.
One method used to subtract is the concept of borrowing.
We borrow from the place value to the left because it is a larger number than the number we are working with.
We start with the SMALLEST place value (furthest to the right).
Since we have 0 ONES, we must borrow from the TENS, but since it too has 0 TENS, we must move to the HUNDREDS.
Since it too has 0 HUNDREDS, we must move to the THOUSANDS, but it too has 0 THOUSANDS.
We then have to move to the TEN THOUSANDS, which has a 1 digit which means 1 TEN THOUSANDS and has a value of 10,000.
The following image displays 10,000 − 9,977 using the process of borrowing.
Description
On the top row of the equation, the zero in the ones place has a red line through it and a small, red number ten above it. To the left, in the tens place value, the zero is struck with a red line and a small, red nine is added above it. The same has been done for the zeros in the hundred and thousands place value. The 1 in the ten thousands place has been struck with a red line and a small, red zero is above it.
The difference is 23. In other words, the difference between the population of Bells Corners (9,977) and 10,000 is 23.
Consolidation
Practice
Select one province outside of Ontario and find the populations of 5 city/towns with populations less than or equal to 10,000.
Complete 3 of the following tasks:
- Write each population in its expanded form. Use a place value chart that includes ten thousand and order the populations from largest to smallest.
- Round each population to the nearest thousand, hundred, and ten.
- Choose 2 towns/cities and find the difference between each township population and 10,000.
- Next, with those same two towns/cities, find the difference between their populations (for example, to find the difference between Bells Corners 9,977 and Sooke 6,145.
- For each city with a population of under 7,000, find the change in population if your school visited it (for example 452 plus 6,145). For the 10 city/towns you chose, find its closest neighbouring large city with a population greater than 10,000.
Reflection
As you read through these descriptions, which sentence best describes how you are feeling about your understanding of this learning activity? Press the button that is beside this sentence.
I feel...
Now, record your ideas using a voice recorder, speech-to-text, or writing tool.