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Compare Multi-digit Numbers

Grade 4: Unit 4: Lesson 12

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Lesson Purpose

The purpose of this lesson is for students to compare two multi-digit whole numbers within

1,000,000 by reasoning about place value and to explain how they make comparisons.

Lesson Narrative

Previously, students learned to build, read, name, and write multi-digit whole numbers up to six

digits. They also developed an understanding of the relationship between a digit in one place and

the same digit in the place immediately to its right. Through that work, students built their intuition

for the relative size of numbers.

In this lesson, students use their understanding of place value to compare numbers and articulate

how they reason about the size of the numbers. In doing so, they reinforce their understanding of

place value and the base-ten number system (MP7). In communicating their thinking, they also

practice attending to precision (MP6).

Learning Goals

Compare 2 multi-digit whole numbers within 1,000,000 using place value reasoning.

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Let’s compare large numbers.

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Which One Doesn’t Belong: Friendly Numbers

Warm-Up

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Which one doesn’t belong?

A. 1,395

B. 3,095

C. 9,530

D. 30,195

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Let’s Talk About It!

These numbers have mostly the same digits—0, 1, 3, 5, and 9. Are they all the same size?
Which of these is the greatest? How do you know?
The other numbers are all four-digit numbers. How might we compare them?

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Which is Greater?

Activity 1

Number cards 0–10

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

What three-digit numbers can we make with 5, 7, and 3?

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

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Shuffle the cards. Repeat what you did earlier with new cards. For each pair you compared, how did you decide which number is greater?

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Let’s Talk About It!

How did you decide which number is greater? Did you compare every digit?

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Incomplete Numbers

Activity 2

MLR2: Collect and Display

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

Launch

• Groups of 2

• “Let’s look at some other pairs of multi-digit numbers, but this time the numbers are missing a

digit. Can they still be compared?”

Student Work Time;

• “Take a few quiet minutes to think about the first problem. Then, share your thinking with your

partner.”

• 1 minute: independent work time

• 1–2 minutes: partner discussion

• Pause for a whole-class discussion. Invite students to share their responses, hearing first from

those who agree with Han, and then those who agree with Clare.

• “If the missing digit is not the same digit, can we compare the two numbers?” (No) “Why not?”

(Because we don’t know which number has the greater missing digit, so there’s no way to

compare.)

• If not mentioned by students, point out the features of the pair of numbers being compared:

Both are three-digit numbers, both are missing the first digit, and 62 is greater than 17.

• “Let’s compare some other numbers that have a missing digit.”

• 5 minutes: partner work time

• Monitor for students who use place-value language to explain their thinking.

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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.

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Let’s Talk About It!

Share your explanations

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Is It Possible?

Activity 3

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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.

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Here are two numbers, each with the same missing digit.

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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.

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Let’s Talk About It!

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Lesson Synthesis

Suppose a classmate says that we can’t compare and because a digit is missing from each. How might you convince them that it can be done? Write down what you might say to that classmate.

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Two Numbers To Compare

Cool-Down

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Here are two numbers, each with the same digit missing in different places.

a. If the missing digit in both numbers is 1, which number will be greater: the first or the second?

b. Name all the digits from 0 to 9 that will make the second number greater. Explain how you know.

Cool-Down: Two Numbers To Compare

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