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Activity 1

20 mins

Card Sort: Large Numbers

Standards Alignment

Building On

Addressing

Instructional Routines

Card Sort

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

To Copy (from Blackline Masters)

Card Sort Large Numbers Cards

Activity Narrative

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 Activity 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).

Representation: Access for Perception. Synthesis: Use base-ten blocks to demonstrate the relationship between the value of the same digit in different numbers. For example, represent 200 with two large square blocks and 2,000 with two large cubes.
Supports accessibility for: Conceptual Processing, Visual-Spatial Processing

Launch

Groups of 2
Give each group a set of cards.
“Read the directions for the first two problems and explain them to your partner in your own words.”
Collect explanations and clarify any confusion about directions.

Activity

“Work with your partner to sort your cards into categories in a way that makes sense to you.”
5 minutes: partner and group work time on the first two problems
As students work, monitor for students who use place-value language such as: “value of the digit”, “ten times”, “thousands”, “ten-thousands”, and “hundred-thousands”.
Invite 2–3 previously identified groups to share how they sorted their cards.
Record any place-value language students use to describe how they sorted the numbers and display for all to see.
“Now work independently to write the numbers in the next problem in expanded form. Then talk with your partner about the value of the digits.”
3 minutes: independent work time
5 minutes: partner work time
Monitor for students who:
- Accurately write the numbers in expanded form.
- Describe the relationship between the value of the digits in multiplicative terms (“ten times”).

Student Task Statement

Your teacher will give you a set of cards that show multi-digit numbers.

Sort the cards into categories in a way that makes sense to you. Be ready to explain the meaning of your categories.
Join with another group and explain how you sorted your cards.
Write each number in expanded form.
1. 4,620
2. 46,200
3. 462,000
Write the value of the 4 in each number.
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?

Activity Synthesis

Invite previously selected students to share their expressions in expanded form and what they noticed about the value of the 4.
“What do you notice about the value of the 6 in each number? The value of the 2?” (The value of the 6 is different in each number. It is first 600, then 6,000, then 60,000.)
Students may talk about the number of zeros in each number. Shift their focus to the place value of the 6— hundreds, thousands, ten-thousands.
“How is the value of the 2 in 46,200 related to the value of the 2 in 462,000?” (The value of the 2 in 462,000 is 2,000 and the same digit in 46,200 has a value of 200. 2,000 is ten times the value 200.)
“What multiplication equation could we write to represent the relationship between the 2 in 46,200 and 462,000?” ()
“We can also write this equation using division: .”

Activity 2

15 mins

Expand Large Numbers

Standards Alignment

Building On

Addressing

Instructional Routines

None

First time implementing?

Learn how to use instructional routines to facilitate problem-based learning!

Materials

None

Activity Narrative

In this activity, students read, write, and analyze multi-digit numbers and use expanded form to describe the relationship between the digits. The numbers in the activity are designed to highlight common errors in reading and writing large numbers. Students encounter numbers with the digit zero in the ten-thousands place and think about how to represent this in expanded and word forms.

MLR2 Collect and Display. Synthesis: Direct attention to words collected and displayed from the previous activity. Invite students to borrow language from the display as needed, and update it throughout the lesson.
Advances: Conversing, Reading

Launch

Groups of 2
“Read the heading in each column and look in the table for examples of each form of number.”
1 minute: quiet think time
1 minute: partner discussion
Share and record responses from students. Clarify any misunderstanding about each number form. Record on chart for future reference if needed.

Activity

“Work independently on the first three problems. Then find 2 classmates to work on the last problem with.”
10 minutes: work time

Student Task Statement

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

number	expanded form	word form
784,003

		eight hundred three thousand, ninety-nine
310,060
		nine hundred thirty-four thousand, nine hundred

Choose 2 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.
Find 2 classmates who chose different numbers than you. 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 _______________.
- The 3 in _______________ is ten times the value of the 3 in _______________.

Activity Synthesis

See Lesson Synthesis.

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Lesson 9

Same Digit, Different Value

Warm-up

True or False: Expanded Expressions

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Student Response

Advancing Student Thinking

Are You Ready for More?

Activity Synthesis

Activity 1

Card Sort: Large Numbers

Standards Alignment

4.NBT.A.1

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Activity 2

Expand Large Numbers

Standards Alignment

4.NBT.A.1

Instructional Routines

First time implementing?

Materials

Activity Narrative

Launch

Activity

Student Task Statement

Activity Synthesis

Lesson Synthesis

Have a correction or suggestion?

Standards Alignment

4.NBT.A.2

Student Response

Advancing Student Thinking

Are You Ready for More?

Student Response

Advancing Student Thinking

Are You Ready for More?

4.NBT.A.2

4.NBT.A.2