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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
“Miren las rectas numéricas que hay alrededor del salón. ¿Qué observan? ¿Qué se preguntan?” // “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.
“¿Ven múltiplos de 100,000 en esta recta numérica?” // “Do you see multiples of 100,000 in this number line?” (Yes, 100,000 and 200,000)
“¿Ven múltiplos de 10,000?” // “Do you see multiples of 10,000?” (Yes, each tick mark is a multiple of 10,000.) “¡Nombrémoslos!” // “Let’s name them!” (100,000, 110,000, . . . , 200,000)
Label the first few tick marks.
“¿Ven múltiplos de 1,000?” // “Do you see multiples of 1,000?” (No, they’re not marked.) “Si estuvieran marcados, ¿cómo se verían?” // “If they were marked, what might they look like?” (10 tiny, equal spaces between each pair of tick marks)]
“¿Pueden estimar en qué lugar de la recta numérica está ubicado 113,500?” // “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

“Con su grupo, ubiquen cada número en la recta numérica correcta. Usen una calcomanía para marcar la ubicación en la recta numérica y usen una nota adhesiva para escribir el número que corresponde. Después completen el último problema” // “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.

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: “Observé _____, entonces yo . . .” // “I noticed _____ so I . . .” and “Estoy de acuerdo / en desacuerdo porque . . .” // “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

“En silencio, trabajen unos minutos en la actividad. Luego, compartan sus respuestas con su grupo” // “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

Para esta actividad, usa la recta numérica que representa los números entre 100,000 y 200,000.

En cada caso, nombra el múltiplo de 10,000 que está más cerca del número (por ahora no llenes la última columna).

número	múltiplo de 10,000 que está más cerca
100,025
128,201
140,261
158,002
194,030

Esta recta numérica muestra 215,300. ¿Qué múltiplo de 100,000 es el más cercano a 215,300?
Marca la última columna de la tabla con las palabras “múltiplo de 100,000 que está más cerca”. Después, nombra el múltiplo de 100,000 que está más cerca de cada número de la tabla.

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.

Su profesor les va a asignar un conjunto de números.

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

Hay varias rectas numéricas puestas alrededor del salón. En grupo, decidan en cuál recta numérica debe ir cada número.

Estimen la ubicación del número en la recta, pongan una calcomanía de punto para marcarlo y escriban el número debajo de la calcomanía.
Miren la recta numérica que representa los números de 0 a 100,000 y que tiene 2 puntos.
1. Nombren los 2 múltiplos de 10,000 que están más cerca de cada punto.
2. De los 2 múltiplos de 10,000 que nombraron, ¿cuál está más cerca de cada punto?