Lesson 10

The purpose of this Choral Count is to invite students to practice counting times by 15 minutes and notice patterns in the count. This will be helpful later in this section when students will solve problems involving addition and subtraction of time intervals.

Students have an opportunity to notice regularity through repeated reasoning (MP8) as they count by 15 minutes over a span of 3 hours.

• “Contemos de 15 minutos en 15 minutos, empezando en las 12:00” // “Count by 15 minutes, starting at 12:00.”
• Record as students count. Record times in the count in a single column.
• Stop counting and recording at 3:00.

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

• “¿Cuánto tiempo transcurrió entre la 1:15 y la 1:45?” // “How much time passed between 1:15 and 1:45?” (30 minutes) “¿Entre la 1:15 y las 2:30?” // “1:15 and 2:30?” (75 minutes)
• Consider asking:
  • “¿Quién puede describir el patrón con otras palabras?” // “Who can restate the pattern in different words?”
  • “¿Alguien quiere compartir otra observación sobre por qué ocurre ese patrón aquí?” // “Does anyone want to add an observation on why that pattern is happening here?”
  • “¿Están de acuerdo o en desacuerdo? ¿Por qué?” // “Do you agree or disagree? Why?”

In this activity, students solve problems involving elapsed time in a way that makes sense to them. Although the problem type may be new, students can reason about them using their understanding of time and of addition and subtraction. They can also support their reasoning by drawing on a clock.

In each problem, students are given a start time and an elapsed time of 24 minutes. To find each end time, students may:

• use words to describe their thinking
• write a series of numbers and symbols to show how 24 minutes is added to the start time
• create a table to track changes in time from the start time to 24 minutes later
• show incremental “jumps” that add up to 24 minutes on the clock
• use a linear representation to show incremental changes from the start time to 24 minutes later

To elicit and discuss as many possible strategies and representations for reasoning about the problems, significant time is allocated for this activity. Students may choose to use any of the strategies or representations they see here to solve elapsed time problems in future lessons.

When they determine what time different events occurred based on the initial time and the 24 minutes of elapsed time students reason abstractly and quantitatively(MP2).

• Groups of 2
• “¿Alguna vez han viajado en un bus? ¿Cuándo o dónde?” // “Have you ever ridden a bus? When or where?” (I ride a school bus to school. I ride the city bus with my parents. I rode a bus at the airport to get to our car in the parking lot.)
• “¿Qué cosas necesitan saber cuando viajan en un bus?” // “What are some things you need to know about when you ride the bus?” (What time will the bus come? How often does the bus come? Where does the bus pick you up? Where are you getting off? How long will your bus ride take? How much does the bus cost?)
• 1–2 minutes: partner discussion
• Share and record responses.

• “Ahora resuelvan los problemas sobre los viajes en bus de Kiran y de Elena. Muestren cómo pensaron y háganlo de una forma que tenga sentido para ustedes” // “Now solve the problems about Kiran and Elena riding the bus. Show your thinking in any way that makes sense to you.”
• 8–10 minutes: independent work time
• As students work, consider asking:
  • “¿Cómo se muestran en su trabajo los 24 minutos que Kiran o Elena esperaron?” // “How does your work show the 24 minutes Kiran or Elena waited?”
  • “¿Cómo muestra su trabajo la hora a la que llegó el bus?” // “How does your work show the time the bus arrived?”
  • “¿Cómo supieron si el bus llegó antes o después de las 4:00?” // “How did you know it would be before or after 4:00 when the bus arrived?”
• Monitor for and identify students who use the strategies listed in the activity narrative.

If students say they aren’t sure how to show their thinking, consider asking:

• “¿De qué se trata el problema?” // “What is the problem about?”
• “¿Qué representaciones que hayamos usado con la suma y la resta podrías usar aquí para mostrar cómo pensaste?” // “What representations have we used with addition and subtraction that could be used here to show your thinking?”

• Select previously identified students to share their responses in any order. Display or record their representations for all to see.
• “En el problema de Elena, ¿cómo nos ayuda cada una de las estrategias a ver que el bus llegará después de las 4:00?” // “In Elena’s problem, how does each of the strategies help us see that the bus would come after 4:00?” (If we add the minutes and get a sum that is more than 60, we know that it’s a new hour. On the clock, we can see that there are only 15 minutes until 4:00, so 24 minutes would be past 4:00.)

In this activity, students encounter another type of elapsed-time problem in which the start and end times are given but the elapsed time is not. Students consider possible strategies they saw earlier that could be used to find elapsed time. Although they are not required to solve the problem, students may choose to do so as they think about ways to reason abstractly and quantitatively about the solution (MP2).

• Groups of 2
• Read the problem as a class.
• “¿En qué se parece este problema a los que vimos antes?” // “How is this problem like the ones we saw earlier?” (They are all about the passing of time and are related to riding the bus. The start time is given in all of them.) “¿En qué es diferente?” // “How is this one different?” (The arrival time is given here, and the amount of time that has passed is missing.)
• 1 minute: quiet think time
• Share responses.

• “¿Cómo resolverían este problema? Expliquen qué estrategias o representaciones que hayan visto antes pueden ser útiles para resolver un problema como este” // “How would you solve this problem? Explain which strategies or representations you saw earlier that would be useful for solving a problem like this.”
• 5–7 minutes: independent work time

• Invite students to share their reasoning and strategies. Display or record different representations for all to see.