B. Number · Number Sense: Numbers to 1000 and Fractions

Place Value: Hundreds, Tens and Ones

B1.5 B1.1About 35 minutes

Learning goals

I can show a number to 1000 with base-ten blocks or a quick drawing.
I can tell the value of each digit in a three-digit number.
I can write a number in expanded form, like 735 = 700 + 30 + 5.
I can explain why we need zero as a placeholder.

Words to know

place value
The value of a digit depends on its place: hundreds, tens or ones.

value
How much a digit is worth. In 735, the 7 has a value of 700.

base-ten blocks
Blocks for showing numbers: a unit is 1, a rod is 10, a flat is 100 and a big cube is 1000.

expanded form
A number written as the sum of its place values, like 735 = 700 + 30 + 5.

standard form
A number written the usual way, with digits, like 735.

placeholder
A zero that holds a place so the other digits stay in the right places, like the 0 in 508.

Remember from Grade 2

In Grade 2 you used hundreds, tens and ones to build numbers to 200. Now you will use them to build any number up to 1000.

Digit detective

Look at the number 555. It has three 5s. Are they all worth the same?

No! One 5 is worth 500, one is worth 50 and one is worth just 5. Where a digit sits tells you how much it is worth. This is called place value.

Base-ten blocks: a unit is 1. A rod is 10 units. A flat is 10 rods, or 100. A big cube is 10 flats, or 1000.

Ten makes the next place

10 ones make 1 ten.
10 tens make 1 hundred.
10 hundreds make 1 thousand.

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

2 hundreds, 4 tens and 6 ones make 246.

Number	Hundreds	Tens	Ones	Expanded form
246	2 → 200	4 → 40	6 → 6	200 + 40 + 6
555	5 → 500	5 → 50	5 → 5	500 + 50 + 5
735	7 → 700	3 → 30	5 → 5	700 + 30 + 5

A place-value chart shows the value of each digit.

Quick drawings

You don't always have blocks. You can draw a quick picture:

a square for each hundred
a line for each ten
a dot for each one

So 3 squares, 2 lines and 4 dots show 324.

Zero holds a place

Look at 508: 5 hundreds, 0 tens and 8 ones. The zero tells us there are no tens. Without it, we would write 58, which is a much smaller number!

5 hundreds, 0 tens and 8 ones make 508. The 0 holds the tens place.

Worked example

Example 1: Read the blocks

A number is made with 3 flats, 1 rod and 9 units. What is the number?

3 flats are 3 hundreds: 300.
1 rod is 1 ten: 10.
9 units are 9 ones: 9.
300 + 10 + 9 = 319.

The number is 319.

Worked example

Example 2: Same digit, different value

What is the value of the 4 in 348? In 483?

In 348 the 4 is in the tens place. 4 tens = 40.
In 483 the 4 is in the hundreds place. 4 hundreds = 400.

40 in 348 and 400 in 483.

Worked example

Example 3: Expanded form and standard form

Write 600 + 7 in standard form. Then write 870 in expanded form.

600 + 7 has 6 hundreds, 0 tens and 7 ones. Write a 0 in the tens place: 607.
870 has 8 hundreds, 7 tens and 0 ones: 800 + 70.

600 + 7 = 607 and 870 = 800 + 70.

Worked example

Example 4: Blocks in a mixed-up order

Leo puts down 8 units, then 2 flats, then 5 rods. He says the number is 825. Is he right?

The order we put blocks down doesn't matter. What matters is what each block is worth.
2 flats = 200, 5 rods = 50, 8 units = 8.
200 + 50 + 8 = 258.

Leo is not right. The number is 258.

Remember

Read a number from left to right: hundreds, then tens, then ones. Always check: How many hundreds? How many tens? How many ones?

Just for fun

Why was the 0 in 508 so proud?

Because without it, 508 would shrink to 58!

Hands-on activity

Roll and build

You need: paper, a pencil, and a die (or 10 small cards with the numbers 0 to 9).

Fold your paper into 3 columns. Label them Hundreds, Tens and Ones.
Roll the die (or pick a card) three times. Write the digits in the hundreds, tens and ones columns, in the order you rolled them.
Draw a quick picture of your number: squares, lines and dots.
Write the number in expanded form and in words. Say it out loud.
Do it 5 times. Which was your biggest number?

Math talk: "What is the value of each digit in my number?"

Your turn

What number has 4 hundreds, 7 tens and 2 ones?

What number has 6 hundreds, 0 tens and 9 ones?

What is the value of the 8 in 685?

What is the value of the 3 in 312?

Write 547 in expanded form.

Write 200 + 90 + 1 in standard form.

How many hundreds make 1000?

More practice: warm-up

How many ones make a ten?

How many tens make a hundred?

Which digit is in the tens place in 864?

What number do 3 flats, 0 rods and 0 units show?

Write 700 + 40 + 2 in standard form.

More practice: on your own

A quick picture has 5 squares, 3 lines and 7 dots. What number is it?

In 777, what is each 7 worth?

Sam writes 400 + 6 as 46. What should he write? Why?

Write 950 in expanded form.

You add one more rod to 358. Which digit changes? What is the new number?

Challenge

I have 6 hundreds. My ones digit is 3. My tens digit is 2 more than my ones digit. What number am I?

What is the greatest three-digit number with a 0 in the tens place and a 9 in the ones place?

Ali has 9 flats, 9 rods and 10 units. What number does he have? Explain.

Check your understanding

Quiz

What is the value of the 6 in 362?

What number has 5 hundreds, 2 tens and 0 ones?

Which is the expanded form of 418?

What is 800 + 3 in standard form?

How many flats make one big cube (1000)?

Which number has a 7 in the hundreds place?

For parents and teachers

Big idea: The value of a digit depends on its place. In our number system each place is worth 10 times the place to its right. The curriculum (B1.5) asks Grade 3 students to use place value to describe and represent numbers in different ways, including with base-ten materials.

Common difficulties:

Forgetting zero as a placeholder (writing 400 + 6 as 46).
Reading blocks in the order they are laid out instead of by value.
Thinking a digit always means the same amount. Ask: "What is this 4 worth here?"

How to help: If you don't have base-ten blocks, quick drawings (squares, lines, dots) work well. You can also use money: $100 bills, $10 bills and $1 coins (play money is fine). Ask questions like "What is the 7 worth in 274?" when you see numbers on signs or price tags.