B. Number · Number Sense: Numbers to 10 000, Fractions and Decimal Tenths

Place Value: Thousands, Hundreds, Tens and Ones

B1.1About 35 minutes

Learning goals

I can tell the value of each digit in a number up to 10 000.
I can show a number with base-ten blocks or a place value chart.
I can write a number in expanded form, like 3000 + 400 + 20 + 5.
I can explain why each place is worth 10 times the place to its right.

Words to know

place value
The value of a digit depends on its place. In 5300, the 5 means 5000.

value
How much a digit is worth in its place.

expanded form
A number written as the sum of the values of its digits: 2604 = 2000 + 600 + 4.

standard form
The usual way to write a number with digits: 2604.

placeholder
A zero that holds a place so the other digits stay in the right spots.

Remember from Grade 3

In Grade 3 you used hundreds, tens and ones. In 346, the 3 means 3 hundreds (300), the 4 means 4 tens (40) and the 6 means 6 ones. Now we add one more place on the left: the thousands.

Same digit, different value

Look at the digit 7 in these numbers:

7 → seven ones (7)
72 → seven tens (70)
715 → seven hundreds (700)
7154 → seven thousands (7000)

The digit is the same, but its place changes its value. That's why we call it place value.

Ten thousands	Thousands	Hundreds	Tens	Ones
	7	1	5	4
	3	0	8	2
1	0	0	0	0

A place value chart. 7154 has 7 thousands, 1 hundred, 5 tens and 4 ones. 3082 has 0 hundreds. 10 000 has 1 ten thousand.

Base-ten blocks

Base-ten blocks help us see the places:

a small unit cube is 1
a rod is 10 units: 10
a flat is 10 rods: 100
a big cube is 10 flats: 1000

Here is 2345 in blocks.

2 big cubes (thousands), 3 flats (hundreds), 4 rods (tens) and 5 units (ones) make 2345.

The "times 10" pattern

Each place is worth 10 times the place to its right:

10 ones = 1 ten
10 tens = 1 hundred
10 hundreds = 1 thousand
10 thousands = 1 ten thousand (10 000)

This pattern keeps going forever, which is why our number system can show any number with just ten digits!

Each place is worth 10 times the place to its right. Follow the arrows from the ones all the way to ten thousands.

Worked example

Example 1: Value of each digit

What is the value of each digit in 8506?

8 is in the thousands place: 8000.
5 is in the hundreds place: 500.
0 is in the tens place: 0. It holds the tens place.
6 is in the ones place: 6.

8506 = 8000 + 500 + 6. This is called expanded form.

Worked example

Example 2: From expanded form to standard form

Write 4000 + 60 + 3 in standard form.

4000 → 4 in the thousands place.
There are no hundreds, so write 0 in the hundreds place.
60 → 6 in the tens place. 3 → 3 in the ones place.

4063

Worked example

Example 3: 10, 100 or 1000 more

What is 1000 more than 5274? What is 100 less?

1000 more: only the thousands digit changes. 5 becomes 6: 6274.
100 less: only the hundreds digit changes. 2 becomes 1: 5174.

1000 more is 6274. 100 less is 5174.

Finger trick

Read each digit's place before you say its value. Put your finger under the digit, then slide right and count the places after it: 0 places after it means ones, 1 means tens, 2 means hundreds, 3 means thousands.

Just for fun

Q: Why was the digit 5 so happy to move into the thousands place?

A: It got a big raise. It went from being worth 5 to being worth 5000!

Hands-on activity

Place value mat and digit cards

You need: 4 sheets of paper, 10 small pieces of paper, a marker, and a timer (optional).

Label the 4 sheets Thousands, Hundreds, Tens, Ones. Lay them in a row on the floor or table, in that order from left to right.
Write the digits 0 to 9 on the small papers, one digit on each. Turn them face down and mix them up.
Pick 4 cards and place one on each sheet. Read the number out loud.
Say the value of each digit ("The 6 is worth 600") and write the number in expanded form.
Your grown-up says "Make it 1000 more!" or "Make it 10 less!" Change the right card and read the new number.

Math talk: "Which card changed? Why didn't the others change?" (Note: going past 9 or below 0 in one place needs a trade. If that happens, talk about it together!)

Your turn

What is the value of the 4 in 4719?

What is the value of the 4 in 7149?

Write 6352 in expanded form.

Write 9000 + 70 + 1 in standard form.

How many blocks of each kind do you need to show 3208?

What is 1000 more than 4627?

How many thousands make 10 000?

More practice: warm-up

What digit is in the hundreds place of 2853?

What digit is in the thousands place of 6091?

Write 5000 + 400 + 30 + 2 in standard form.

What is the value of the 9 in 9000?

What is 10 more than 3460?

More practice: on your own

Write 7036 in expanded form.

What is 100 less than 8215?

In 5555, how many times bigger is the value of the first 5 than the second 5?

Write the number: 6 thousands, 4 tens, 9 ones.

What is 1000 less than 10 000?

Challenge

I have 4 digits. My thousands digit is 3. My hundreds digit is double my thousands digit. My tens digit is 0. My ones digit is 1 more than my hundreds digit. What number am I?

What is 10 more than 4995? Explain what happens to the digits.

Nia says the 0 in 2059 doesn't matter, so 2059 is the same as 259. Is she right? Explain.

Check your understanding

Quiz

What is the value of the 3 in 3816?

Which is 5000 + 200 + 7 in standard form?

What is 100 more than 6950?

Which number has a 6 in the tens place?

10 hundreds is the same as...

Which is the expanded form of 4082?

For parents and teachers

Big idea: Place value is the key to all work with whole numbers (and, later this year, decimals). Each place is worth 10 times the place to its right. This lesson supports B1.1 (represent numbers to 10 000 using tools and strategies).

Common difficulties:

Confusing the digit and its value (saying the 3 in 3816 is worth 3). Ask: "What place is it in? So what is it worth?"
Dropping zeros in standard form (4000 + 60 + 3 written as 463). Use the four-column place value mat.
Changing more than one digit when finding 100 more or 1000 more. Point out that usually only one digit changes, unless a place goes past 9.

How to help: If you don't have base-ten blocks, use money: $1000 can be shown with ten $100 bills (play money or drawings). Ask quick questions in the car: "What's 1000 more than 2026? 10 less than 5000?"