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Activity 1

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

To Copy (from Blackline Masters)

On Which Line Do They Belong Number Line Template

To Gather

Stickers Sticky notes

Activity 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.

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 100–200 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 make connections to this work as you introduce the 100,000–200,000 number line.
Supports accessibility for: Conceptual Processing, Language, Attention

Launch

Groups of 4
“Take a look at the number lines around the room. What do you notice? 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.

Your teacher will assign a set of numbers to you.

A	140,261	100,025	486,840	676,850
B	450,099	414,500	128,201	379,900
C	158,002	42,326	99,982	428,950
D	194,030	658,340	541,700	621,035
E	215,300	499,600	608,720	644,700

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 the line, put a dot sticker to mark it, and label it with the number.
Look at the number line that represents 0 to 100,000 and has 2 points on it.
1. Name 2 multiples of 10,000 that are closest to each point.
2. Of the 2 multiples of 10,000 you named, which one is the nearest to each point?

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, look at the digit in the hundred-thousands place. If the number didn’t have a digit there, it goes on the first number line.
- To locate the point, look at the digit in the ten-thousands place. For 379,000, it is the 7 in the ten-thousands place, so 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

Standards Alignment

Building On

Addressing

Building Toward

Instructional Routines

None

Materials

None

Activity 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. Students may use number lines, but they may also notice a pattern in the relationship between the numbers and the nearest multiples without using them(MP7).

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

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

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

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
100,025
128,201
140,261
158,002
194,030

Here is the number line that shows 215,300. Which multiple of 100,000 is the nearest to 215,300?
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

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Advancing Student Thinking

Activity Synthesis

Display the blank table from the activity. Invite students to share their responses to complete the table. Discuss any disagreements.
Encourage 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.