Week 4 of 10

Place Value City

Students explore how ones, tens, hundreds, and thousands each have a 'street' in a number, write numbers in expanded form, and compare large numbers by checking the biggest place first.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: Ones, tens, hundreds, thousands, Expanded form, Comparing numbers
Theme: Place Value City: every digit lives on its own street

The story

Welcome to Place Value City, where every digit has an address. The ones live on Ones Street, the tens on Tens Avenue, the hundreds on Hundreds Boulevard, and the thousands up on Thousands Hill. Move a digit to a new street and its whole value changes - a 7 on Ones Street is worth 7, but move it to Hundreds Boulevard and it's suddenly worth 700. Today you're the city planner.

What you'll learn

Identify the value of each digit in numbers up to the thousands place.
Write a number in expanded form (2,345 = 2,000 + 300 + 40 + 5) and back again.
Compare four-digit numbers by starting at the largest place value.

Key ideas

Each place is worth ten times the place to its right.
Expanded form shows the value hiding inside every digit.
Comparing starts at the biggest place and moves right until the digits differ.

Words to know

Ones place: The rightmost place, counting single units.
Tens place: The place worth ten times the ones.
Hundreds place: The place worth ten times the tens.
Thousands place: The place worth ten times the hundreds.
Expanded form: A number written as the sum of each digit's value, like 300 + 40 + 5.
Standard form: A number written the normal way, with digits side by side, like 345.

The lesson

In our number system, each place is worth ten times the one to its right. Ones, then tens (ten ones), then hundreds (ten tens), then thousands (ten hundreds). That is why moving a digit one street to the left makes it ten times bigger.

In 2,345 the 2 lives on Thousands Hill and is worth 2,000; the 3 is worth 300; the 4 is worth 40; and the 5 is worth 5. Reading each digit by its street is how you find its true value.

Expanded form writes those values out as a sum: 2,345 = 2,000 + 300 + 40 + 5. It makes the hidden structure visible and is a huge help when adding or subtracting big numbers.

To compare two numbers, start at the biggest place and move right until the digits are different. Comparing 3,412 and 3,398: the thousands tie (3 = 3), but at the hundreds place 4 beats 3, so 3,412 is greater. You never have to check the smaller places once you find a difference.

Worked examples

What is the value of the 6 in 4,682?

600

The 6 sits in the hundreds place (Hundreds Boulevard), so it is worth 6 hundreds, which is 600.

Write 5,207 in expanded form.

5,000 + 200 + 0 + 7

5 thousands + 2 hundreds + 0 tens + 7 ones. The 0 shows there are no tens but keeps the other digits in place.

Compare 3,412 and 3,398.

3,412 > 3,398

Thousands are equal (3 = 3). At the hundreds place, 4 is greater than 3, so 3,412 is the larger number. No need to check tens or ones.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

Build the Address

Placing each digit on the right street makes the abstract idea of place value physical - you see that the same digit means different amounts on different streets.

Build the number 245 using hundreds, tens, and ones.

Hundreds

Tens

Ones

Standard form: 0
Expanded form: 0

Keep going: 0 < 245.

Your number 0 is less than the target 245. Adjust the hundreds, tens, and ones to match.

Hands-on challenge

Place Value Card Flip

What you need

Digit cards 0-9
Paper with labeled place-value columns
Pencil

Steps

1
Make four labeled columns on paper: Thousands, Hundreds, Tens, Ones.
2
Draw digit cards (0-9) and place each one in any column to build a number.
3
Race a partner to build the largest number possible, then say each number in expanded form to prove whose is bigger.

You've got it when: You can build a four-digit number, read the value of every digit, and use expanded form to justify which number is larger.

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
What is the value of the 8 in 8,140?
Show answer
8,000 (it is in the thousands place).
2
Write 3,406 in expanded form.
Show answer
3,000 + 400 + 0 + 6.
3
Which is greater, 6,721 or 6,712?
Show answer
6,721. Thousands and hundreds tie; at the tens place 2 beats 1.

Think about it

Why does the same digit, like 5, mean different amounts in 5,000 and 500 and 50? Explain using the idea of streets or places.

Challenge problem

Use the digits 4, 0, 7, and 2 exactly once each to build the largest possible four-digit number and the smallest possible four-digit number. What is the difference between them?

Show hint

For the largest, put the biggest digits on the left. For the smallest, put small digits left - but a number can't start with 0.

Show answer

Largest is 7,420 and smallest is 2,047. Their difference is 7,420 - 2,047 = 5,373.

Extension · go further

Extend Place Value City to ten-thousands. Build a five-digit number, write it in expanded form, and explain how far away Ten-Thousands Tower is from Ones Street.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.