Lesson 14

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.

• “Contemos a saltos usando números grandes. Haremos tres rondas” // “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.
• “Cuenten de 1,000 en 1,000, empezando en 85,000” // “Count by 1,000, starting at 85,000.”
• Stop counting and recording at 115,000.
• “Cuenten de 10,000 en 10,000, empezando en 80,000” // “Count by 10,000, starting at 80,000.”
• Stop counting and recording at 230,000.
• “Cuenten de 100,000 en 100,000, empezando en 0” // “Count by 100,000, starting at 0.”
• Stop counting and recording at 400,000.

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

• “El primer conjunto de números muestra ‘múltiplos de 1,000’. El segundo conjunto muestra ‘múltiplos de 10,000’ y el tercer conjunto muestra ‘múltiplos de 100,000’” // “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’.”
• “¿Cómo sabemos que 85,000 es un múltiplo de 1,000?” // “How do we know that 85,000 is a multiple of 1,000?” (\(85 \times 1,\!000 = 85,\!000\))
• “¿Cómo sabemos que 90,000 es un múltiplo de 10,000?” // “How do we know that 90,000 is a multiple of 10,000?” (\(9 \times 10,\!000 = 90,\!000\))
• “¿Puede un múltiplo de 1,000 ser también múltiplo de 10,000? Si creen que sí, muestren algunos ejemplos” // “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.)
• “¿Puede un múltiplo de 10,000 ser también múltiplo de 100,000? Muestren algunos ejemplos” // “Can a multiple of 10,000 also be a multiple of 100,000? Show examples.” (Yes, for example, 100,000 and 200,000)
• “¿Puede un múltiplo de 100,000 ser también múltiplo de 1,000? Muestren algunos ejemplos” // “Can a multiple of 100,000 also be a multiple of 1,000? Show examples.” (Yes, for example, 100,000)

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.

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

• Groups of 4
• “Miren las rectas numéricas que hay alrededor del salón. ¿Qué observan acerca de ellas? ¿Qué se preguntan?” // “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.
• “¿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.

• “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.

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

• “Piensa en tus números, ¿entre cuáles dos números está cada uno?” // “Between which two numbers does each of your numbers fall?”
• “Piensa en cada número, ¿cuál recta numérica tiene extremos que están cerca de él?” // “Which number lines have endpoints close to each number?”

• 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.

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).

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

• “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

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.

• 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.