Lesson 11

The purpose of this warm-up is to elicit the idea that many different questions could be asked about this situation involving time, which will be useful when students solve problems in a later activity. 

• Groups of 2
• Display the situation.
• “¿Qué observan? ¿Qué se preguntan?” // “What do you notice? What do you wonder?”
• 1 minute: quiet think time

• “Discutan con su compañero lo que pensaron” // “Discuss your thinking with your partner.”
• 1 minute: partner discussion
• Share and record responses.

• “Agreguémosle tiempos a la situación de Han. ¿Qué tiempos podríamos agregar?” // “Let’s add times to Han’s situation. What times could we add?” (The time he started or finished dinner. The amount of time he was on the bus. How long he waited for the bus. The time his band practice started.)
• “¿Qué tipo de preguntas podríamos hacer sobre esta situación?” // “What kinds of questions could we ask about this situation?”

The purpose of this activity is for students to solve problems involving addition and subtraction of time intervals when given times on a clock. Students may choose to show or explain their reasoning in any way, but the clocks are given to encourage use of that representation. Monitor for different ways that students represent their thinking, particularly differences in strategies when the problem involves time crossing the hour mark and when it doesn’t.

• Display students’ ideas from the lesson synthesis in the previous lesson.

• Groups of 2
• Display the clocks showing when Han got on and off the bus.
• “Ahora tenemos más información sobre el viaje de Han en bus al ensayo de la banda” // “Now we have more information about Han’s bus ride to band practice.”
• “¿A qué hora pudo haber cenando Han? ¿A qué hora piensas que empieza el ensayo de la banda?” // “What time could Han have been eating dinner? What time do you think band practice might start?” (Han could have eaten dinner at 5:00. Band practice might start at 6:45 since we know he had to hurry to get there.)
• 1 minute: partner discussion
• Share responses.

• “Ahora tómense un momento para resolver estos dos problemas” // “Now take some time to solve these two problems.”
• 5 minutes: partner work time
• Consider asking:
  • “¿A qué hora _____ sube al bus? o ¿A qué hora _____ baja del bus?” // “What time did _____ get on [or off] the bus?”
  • “¿Cómo podrían mostrar sus ideas en el reloj?” // “How could you show your ideas on the clock?”
• Monitor for students who used different strategies to solve the two problems, or those who noticed that the time crossed the hour mark in the first problem but not in the second.

• Select previously identified students to share their responses and reasoning.
• “Observamos que cuando el tiempo no se pasa de la hora en la que estamos, podemos simplemente sumar o restar el número de minutos, como hicimos aquí con \(36 - 32=4\). Cuando en un problema el tiempo se pasa de la hora, necesitamos asegurarnos de saber en qué hora estamos” // “We noticed that when the time does not cross the hour, we can just add or subtract the number of minutes, such as \(36 - 32=4\) here. When the time does cross the hour in a problem, we need to make sure to keep track of what hour we are in.” 

The purpose of this activity is for students to solve problems involving addition and subtraction of time intervals in minutes. Students fill a name and activity into each problem before they solve it using any representation that makes sense to them. The synthesis draws attention to the different types of problems that have been solved. Students need to read and think carefully about the given information and the unknown, which differ in most of the situations, in order to decide which calculations to perform (MP2).

• Groups of 2
• “Hemos resuelto problemas sobre tomar el bus. ¿En qué otras actividades harían seguimiento de la hora al minuto más cercano?” // “We have been solving problems about riding the bus. What are some other activities where you would keep track of the time to the nearest minute?” (recess, TV time, baking or cooking time, class time)
• 1 minute: partner discussion
• Share and record responses. Keep displayed for ideas to use in the activity.

• “Con su compañero, llenen los espacios de cada problema con un nombre y una actividad. Después, resuelvan cada problema” // “Work with your partner to fill in a name and activity for each problem. Then, solve the problem.”
• 10 minutes: partner work time

• For each problem, invite groups to share what they filled in and how they solved the problem.
• Keep the problems displayed.
• “¿En qué se parecen estos problemas?” // “How are these problems alike?” (They are all about doing an activity for a certain amount of time.)
• “¿En qué son diferentes?” // “How are they different?” (They are about different activities and give different kinds of information. Sometimes we know the start time and end time. Other times we know either the start time or end time, and how much time passed. We are solving for different things.)
• Highlight ideas about how the problems had different unknowns (start, end, and time that passed).