# Lesson 14

Multiples of 10,000 and 100,000

## Warm-up: Choral Count: Multiples of 1,000, 10,000, and 100,000 (10 minutes)

### Narrative

The purpose of this Choral Count is to familiarize students with multiples of 1,000, 10,000, and 100,000 and to notice patterns in the count. These understandings help students develop fluency and will be helpful later in this lesson when students locate large numbers on number lines and identify multiples of 10,000 and 100,000 that are near those numbers.

### Launch

• “Let’s count by some large numbers. We’ll do three rounds.”
• Prepare to record three rounds of counting: by 1,000, 10,000, and 100,000. Record the count by 10,000 on a number line.
• “Count by 1,000, starting at 85,000.”
• Stop counting and recording at 115,000.
• “Count by 10,000, starting at 80,000.”
• Stop counting and recording at 230,000.
• “Count by 100,000, starting at 0.”
• Stop counting and recording at 400,000.

### Activity

• “What patterns do you see?”
• 1–2 minutes: quiet think time
• Record responses.

### Student Response

For access, consult one of our IM Certified Partners.

### Activity Synthesis

• “The first set of numbers shows ‘multiples of 1,000.’ The second set shows ‘multiples of 10,000,’ and the third set shows ‘multiples of 100,000’.”
• “How do we know that 85,000 is a multiple of 1,000?” ($$85 \times 1,\!000 = 85,\!000$$)
• “How do we know that 90,000 is a multiple of 10,000?” ($$9 \times 10,\!000 = 90,\!000$$)
• “Can a multiple of 1,000 also be a multiple of 10,000? If you think so, show some examples.” (Yes, for example, 80,000 and 120,000 are multiples of 1,000 and 10,000. They show up on both lists.)
• “Can a multiple of 10,000 also be a multiple of 100,000? Show examples.” (Yes, for example, 100,000 and 200,000)
• “Can a multiple of 100,000 also be a multiple of 1,000? Show examples.” (Yes, for example, 100,000)

## Activity 1: On Which Line Do They Belong? (20 minutes)

### Narrative

In this activity, students locate five- and six-digit numbers on a series of number lines. The endpoints of each number line are multiples of 100,000, and the space between them is partitioned into ten equal intervals. As they locate the numbers, students recognize each tick mark as a multiple of 10,000 (MP7). Later in the activity, students use a number line to name multiples of 10,000 that are near given five-digit numbers.

Prior to the lesson, create number lines from the blackline master and post them around the room for students to visit during the activity.

Engagement: Develop Effort and Persistence. Differentiate the degree of difficulty or complexity. Some students may benefit from practicing with more accessible values first. For example, display a 100200 number line with ten tick marks, and invite students to discuss multiples of 10 and 100 that they see. Help them articulate a strategy to place 182 on the number line. Encourage students to draw connections to this work as you introduce the 100,000200,000 number line.
Supports accessibility for: Conceptual Processing, Language, Attention

### Required Materials

Materials to Gather

Materials to Copy

• On Which Line Do They Belong? (0-700,000 number line)

### Required Preparation

• Create number lines from the blackline master and post them around the room before the activity.

### Launch

• Groups of 4
• “Take a look at the number lines around the room. What do you notice about them? What do you wonder?”
• 30 seconds: quiet think time
• Share responses.
• Display a number line with 100,000 at one end and 200,000 at the other.
• “Do you see multiples of 100,000 in this number line?” (Yes, 100,000 and 200,000)
• “Do you see multiples of 10,000?” (Yes, each tick mark is a multiple of 10,000.) “Let’s name them!” (100,000, 110,000, . . . , 200,000)
• Label the first few tick marks.
• “Do you see multiples of 1,000?” (No, they’re not marked.) “If they were marked, what might they look like?” (10 tiny, equal spaces between each pair of tick marks)]
• “Can you estimate where 113,500 goes on the number line?” (Between the second and third tick marks, but closer to the first tick mark. Or between 110,000 and 120,000, but closer to 110,000.)
• Assign one set of numbers (A, B, C, D, or E) to each group of 4.
• Give 4 stickers and 4 sticky notes to each group.

### Activity

• “Work with your group to locate each number on the right number line. Use a sticker to mark the location on the number line and use a sticky note to label it. Then, complete the last problem.”
• 8–10 minutes: group work time
• Monitor for the ways students locate their numbers and how they determine the multiples of 10,000 in the last problem.

### Student Facing

Your teacher will assign a set of numbers to you.

A B C D 140,261 100,025 486,840 676,850 450,099 414,500 128,201 379,900 158,002 42,326 99,982 428,950 194,030 658,340 541,700 621,035 215,300 499,600 608,720 644,700
1. Several number lines are posted around the room. Work with your group to decide on which number line each number should go.

Then, estimate the location of the number on that line, put a dot sticker to mark it, and label it with the number.

2. Look at the number line that represents 0 to 100,000 and has two points on it.

1. Name two multiples of 10,000 that are closest to each point.
2. Of the two multiples of 10,000 you named, which one is the nearest to each point?

### Student Response

For access, consult one of our IM Certified Partners.

Students may decide to place all numbers in their assigned set on the same number line. Consider asking:

• “Between which two numbers does each of your numbers fall?”
• “Which number lines have endpoints close to each number?”

### Activity Synthesis

• Select students to explain how they identified which number line to use and where to put the dot sticker to represent each number. Highlight explanations that are based on place-value reasoning:
• To identify the right number line, we’d look at the digit in the hundred-thousands place. If it didn’t have a digit there, it goes on the first number line.
• To locate the point, we’d look at the digit in the ten-thousands place. For 379,000, it is the 7 in the ten-thousands place, so we’d count 7 tick marks from 300,000. The dot would be close to the eighth tick mark because 79,000 is close to 80,000.
• Briefly discuss how students identified the nearest multiple of 10,000 for 42,326 and 99,982.
• Keep the number lines displayed for the next activity.

## Activity 2: Closer to Some Multiple (15 minutes)

### Narrative

In this activity, students identify the nearest multiples of 10,000 and 100,000 for the six-digit numbers they saw in the first activity. They may do so by using the number lines from earlier, but they may also start to notice a pattern in the relationship between the numbers and the nearest multiples without the number lines (MP7).

MLR8 Discussion Supports. Display sentence frames to support small-group discussion: “I noticed _____ so I . . .” and “I agree/disagree because . . . .”

### Launch

• Groups of 2 or 4
• Display number line with endpoints of 100,000 and 200,000.

### Activity

• “Take a few quiet minutes to work on the activity. Then, share your responses with your group.”
• 6–7 minutes: independent work time
• 3–4 minutes: group discussion

### Student Facing

Use the number line that represents the numbers between 100,000 and 200,000 for this activity.

1. Name the multiple of 10,000 that is the nearest to each number. (Leave the last column blank for now.)
number nearest multiple of 10,000 $$\phantom{nearest multiple}$$
100,025
128,201
140,261
158,002
194,030
2. Here is the number line with 215,300 shown on it. Which multiple of 100,000 is the nearest to 215,300?

3. Label the last column in the table “nearest multiple of 100,000.” Then, name the nearest multiple of 100,000 for each number in the table.

### Student Response

For access, consult one of our IM Certified Partners.

Students may see that the nearest multiples of 10,000 for a number are the two tick marks surrounding the point but may be unsure what numbers they represent. Ask them to recall what each tick mark represents on this set of number lines and urge them to count the marks.

### Activity Synthesis

• Display the blank table from the activity. Invite students to share their responses to complete the table. Discuss any disagreements.
• Invite students to share how they identified the nearest multiples of 10,000 and 100,000.
• If no students mentioned that they examined the location of each point visually and decided the closest tick marks on the number line, ask them about it.

## Lesson Synthesis

### Lesson Synthesis

“Today we learned to identify multiples of 10,000 and 100,000 that are close to a number.”

Ask students to write a six-digit number.

“Which two multiples of 10,000 are closest to your number? Of the two, which one is the nearest?”

“Which two multiples of 100,000 are closest to your number? Which one is the nearest?”