Lesson 15

The purpose of this Choral Count is for students to practice counting by 10 and 100 and notice patterns in the count. These understandings help students develop fluency and will help students see that multiples of 100 are also multiples of 10, and prepare them to round large numbers to the nearest ten and hundred.

• “Contemos de 10 en 10, empezando en 0” // “Count by 10, starting at 0.”
• Record as students count.
• Stop counting and recording at 200.
• “Contemos de 100 en 100, empezando en 0” // “Count by 100, starting at 0.”
• Record as students count.
• Stop counting and recording at 900.

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

• “¿Por qué 100 y 200 aparecen en ambos conteos?” // “Why do 100 and 200 show up in both of these counts?” (You say 100 and 200 when you are counting by tens or hundreds. You can think of 100 as 10 tens or 200 as 20 tens. 100 and 200 are multiples of 10 and multiples of 100.)

The purpose of this activity is for students to round given numbers to the nearest ten and hundred and see that the result can be the same for some numbers. Students think about what it means to round a number that is exactly halfway between two tens or two hundreds and are introduced in the synthesis to the convention that these numbers are rounded up (MP3).

• Groups of 2
• “Redondeemos algunos números a la decena más cercana y a la centena más cercana. Recuerden que ‘redondeen a la decena (o centena) más cercana’ es otra forma de decir que encuentren el múltiplo de 10 (o de 100) más cercano” // “Let’s round some numbers to the nearest ten and the nearest hundred. Remember ‘round to the nearest ten (or hundred)’ is another way of saying find the nearest multiple of 10 (or 100).”

• “Completen la tabla con su compañero” // “Work with your partner to complete the table.”
• 3–5 minutes: partner work time
• Monitor for students who notice 97 and 601 round to the same number whether rounding to the nearest ten or the nearest hundred.
• Select previously identified students to share their responses.
• “¿Por qué 97, al igual que 601, se redondea a un mismo número cuando lo redondeamos a la decena y a la centena más cercanas?” // “Why did 97 and 601 round to the same number when we rounded to the nearest ten and the nearest hundred?” (The closest multiple of 10 was also a multiple of 100. 100 and 600 are multiples of 100, but they are also multiples of 10.)
• “Completen el segundo problema con su compañero. Expliquen cómo razonaron” // “Complete the second problem with your partner. Explain your reasoning.”
• 3–5 minutes: partner work time
• Monitor for the following in student explanations to share in the synthesis:
  • 415 is halfway between 410 and 420.
  • 415 is the same distance from 410 and 420.
  • 415 has two closest multiples of 10: 410 and 420.
  • 750 is halfway between 700 and 800.
  • 750 is the same distance from 700 and 800.
  • 750 has two closest multiples of 100: 700 and 800.

• Select previously identified students to share their responses.
• “Kiran y Priya tienen razón. No hay solo un múltiplo de 10 que sea el más cercano a 415 porque este número está justo en el medio de dos múltiplos de 10. No hay solo un  múltiplo de 100 que sea el más cercano a 750 porque este número está justo en el medio de dos múltiplos de 100” // “Kiran and Priya are correct. There isn’t one closest multiple of 10 to 415 because it’s right in the middle of two multiples of 10. There isn’t a closest multiple of 100 to 750 because it’s right in the middle of two multiples of 100.”
• “En casos como este, redondeamos hacia arriba. Por ejemplo, 415 está en el medio entre 410 y 420. Entonces para redondear a 415 a la decena más cercana, lo redondeamos hacia arriba, a 420” // “In cases like this, we round up. For example, since 415 is halfway between 410 and 420, we would round up to 420 to round 415 to the nearest ten.”
• “Como 750 está en el medio entre 700 y 800, lo redondeamos hacia arriba, a 800” // “Since 750 is halfway between 700 and 800, we would round up to 800.”
• “En ambos casos podríamos decidir hacerlo de la otra forma, pero es útil que todos hagamos lo mismo en estas situaciones” // ”In both of these situations we could go the other way, but it is helpful if we all do the same thing in these situations.”

The purpose of this activity is for students to practice rounding to the nearest ten and hundred in context. Students work with numbers from a previous lesson to estimate the total number of students in a school. They learn that how you round (to the nearest ten or hundred) can give different estimates for the same situation.

• Groups of 2
• “Repasemos el número de estudiantes que había en los distintos lugares de la escuela. Vamos a redondear números para ayudarle a Andre y a Lin a estimar cuántas personas había en toda la escuela. Andre planea redondear los números a la centena más cercana. Lin planea redondearlos a la decena más cercana” // “Let’s revisit the number of students in different areas in a school. We’re going to use rounding to help Andre and Lin make an estimate of the number of people in the whole school. Andre plans to round the numbers to the nearest hundred. Lin plans to round them to the nearest ten.”
• “Hagan una predicción. ¿Cuál estimación va a ser mayor? Prepárense para explicar cómo razonaron” // “Make a prediction: Whose estimate is going to be greater? Be prepared to explain your reasoning.”
• 30 seconds: quiet think time
• Share responses.

• “Completen la tabla y el último problema con su compañero” // “Work with your partner to complete the table and the last problem.”
• 7–10 minutes: partner work time

• Invite students to share their observations about the completed table, including whether it matched their predictions.
• “Al estimar un total, redondear a la decena más cercana puede darnos un resultado distinto al de redondear a la centena más cercana. Si redondean para estimar un total, ¿redondearían a la decena más cercana o a la centena más cercana?” // “When we are estimating a total, rounding to the nearest ten or the nearest hundred can give us different results. If you were rounding to estimate a total, would you round to the nearest ten or nearest hundred?” (The nearest ten because you get an estimate that’s closer to the total. The nearest hundred because multiples of 100 are easier to work with.)
• “Tengan estas ideas presentes mientras redondean para hacer estimaciones en las próximas lecciones” // “Keep these ideas in mind as you use rounding to estimate in future lessons.”