Lesson 12 Compare Multi-digit Numbers

- Let’s compare large numbers.

Warm-up Which One Doesn’t Belong: Friendly Numbers

Which one doesn’t belong?

1,395
3,095
9,530
30,195

Activity 1 Which is Greater?

Your teacher will give you a set of cards, each with a single digit, 0–9.

image of cards with numbers 2,7, and 8 on them.

Problem 1

Use the cards for 2, 7, and 8 to make two different three-digit numbers. Use < or > to compare them.

Problem 2

Now include the digit 1 to make two different four-digit numbers. Compare the numbers.

$,$ $,$

Problem 3

Shuffle the cards. Repeat what you did earlier with new cards.

Four-digit numbers
$_{,}$ $_{,}$
Five-digit numbers
- $_{,}$ $_{,}$
Six-digit numbers
$_{,}$ $_{,}$

Problem 4

For each pair you compared, how did you decide which number is greater?

Activity 2 Incomplete Numbers

Problem 1

Here are two numbers. In both, the missing digit is the same number.

$1 7 6 2$

Han says the numbers can’t be compared because they are incomplete.
Clare says the second number is greater, no matter what the missing digit is.

Do you agree with either one of them? Explain your reasoning.

Problem 2

Here are some pairs of numbers. The numbers in each pair are missing the same digit. Can you tell which number is greater? Be prepared to explain your reasoning.

$4 9$
$3 9$
$1, 7 2$
$1, 8 5$
$8, 1 6$
$5, 8 2$
$2 7, 9 5$
$2, 7 4 5$
$9 0, 1 6 5$
$9 0, 0 6 4$

Activity 3 Is It Possible?

Each of the following pairs of numbers is missing the same digit but in different places.
Your teacher will assign a digit to you. Use it as the missing digit and decide if each comparison statement is true.
1. $, 9 9 9 >, 5 0 0$
2. $1 5, 2 0 > 1 5, 0 2$
3. $4, 7 0 0 < 7, 4 0 0$
4. $1 5, 0 0 0 > 5 1, 0 0 0$
Here are two numbers, each with the same missing digit.
$4, 3 0 0 3, 4 0 0$
Choose a digit to complete the numbers and show where they would be on the number line.
Is it possible to fill in the two blanks with the same digit to make each statement true? If you think so, give at least one example of what the digits could be. If not, explain why it is not possible.
1. $4, 3 0 0$ is less than $3, 4 0 0$ .
2. $4, 3 0 0$ is less than $3, 4 0 0$ .

Practice Problem

Problem 1

Jada writes the same digit in the two blanks to make the statement true. Which digits could she write?

$6, 4 3 2 < 6 5, 9 8$