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Same Digit, Different Value

Grade 4: Unit 4: Lesson 9

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Lesson Purpose

The purpose of this lesson is to describe the value of a digit in one place as having ten times the

value of the same digit in a place to its right.

Lesson Narrative

This lesson shifts the focus from reading and writing numbers to describing the multiplicative

relationship between place values in a multi-digit number. In previous lessons, students used base-

ten blocks to represent large numbers, and wrote numbers in expanded form. In this lesson, they

use their developing understanding of the value of a digit to begin to articulate that a digit in one

place is ten times the value as the same digit in a place to its right. The syntheses in this lesson help students connect the language of “ten times the value” to equations to help them represent this concept.

Learning Goals

• Describe that the value of a digit in one place represents ten times what it represents in the

place to its right.

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Let’s describe the relationship between the digits in multi-digit numbers.

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True or False: Expanded Expressions

Warm-Up

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Decide if each statement is true or false. Be prepared to explain your reasoning.

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Let’s Talk About It!

How can you explain your answer without finding the value of both sides?

What form is used to represent the numbers in this True or False?

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Card Sort: Large Numbers

Activity 1

Card Sort

In this activity, students sort a set of multi-digit numbers and describe the place-value relationships

they notice in the sorted numbers. They analyze numbers that have the same digits and write the

numbers in expanded form, highlighting the value of each digit. Students then describe

relationships they see between the digits in each number.

For example, students may note that the value of the 2 in 46,200 is 200, in 462,000 it is 2,000, and

that 2,000 is ten times as much as 200. In the synthesis, they learn that the observed relationship

can be expressed with multiplication and division equations, such as ,

, or other equivalent equations.

When students sort the cards, they look for how the numbers are the same and different, including

their overall value or the digits that make up the numbers (MP7).

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Your teacher will give you and your partner a set of cards with multi-digit numbers on them.

a. Sort the cards in a way that makes sense to you. Be prepared to explain your reasoning.

b. Join with another group and explain how you sorted your cards.

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Write each number in expanded form.

Write the value of the 4 in each number.

a. 4,620

b. 46,200

c. 462,000

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Compare the value of the 4 in two of the numbers. Write two statements to describe what you notice about the values.

How is the value of the 2 in 46,200 related to the value of the 2 in 462,000?

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Let’s Talk About It!

What do you notice about the value of the 6 in each number? The value of the 2?

How is the value of the 2 in 46,200 related to the value of the 2 in 462,000?

What multiplication equation could we write to represent the relationship between the 2 in 46,200 and 462,000?

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Expand Large Numbers

Activity 2

MLR2: Collect and Display

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Express each number in standard form, expanded form, and word form.

Choose two numbers from the table to make this statement true:

The 3 in _____ is ten times the value of the 3 in____ .

Explain why you chose those numbers.

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Find two classmates who chose different numbers than you did. Record their numbers. Take turns sharing your completed statements and explaining your reasoning.

◦ The 3 in____ is ten times the value of the 3 in____ .

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Let’s Talk About It!

Which value is ten times another value?

How does this help you determine what numbers can you include in the statement, ‘The 3 in_______________ is ten times the value of the 3 in _______________.’?

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Lesson Synthesis

Share with a neighbor something you learned about the relationship between digits from today’s lesson.

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The Value of Digits

Cool-Down

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Here are two numbers: 531,690 and 58,487.

a. Write each number in expanded form.

b. Write a multiplication equation to represent the relationship between the digit 5 in both numbers.

Cool-Down: The Value of Digits

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