Lesson 12

The purpose of this warm-up is to invite students to share what they know about 1 hour and its relationship with other units of time. The work here prepares students to convert units of time and solve problems later in the lesson.

• Display “1 hour”.
• “What do you know about 1 hour?”
• 1 minute: quiet think time

• Record responses.

• “Other than using hours, in what other ways can we measure time?” (minutes, seconds, days, months, years, decades)
• “When might it be more helpful to use hours than to use other units? When might it be more helpful to use minutes or seconds?”

This activity develops students’ understanding of hours and minutes as units of time and helps them to see 1 hour as 60 times as long as 1 minute.

In converting hours into minutes, students may reason additively when the time in hours is a low single-digit number, but are likely to reason multiplicatively when converting, say, 8 or 10 hours into minutes. When they relate the operation of multiplication by 60 to converting hours to minutes, students make use of structure (MP7). To convert fractional numbers of hours (\(\frac{1}{2}, \frac{1}{4}\), and \(\frac{3}{4}\) hour), students might choose to think in multiplicative terms (for instance, \(\frac{1}{2} \times 60\)) but are not expected to do so. Instead they can rely on their prior knowledge about a quarter of an hour and a half of an hour to reason about the number of minutes.

• Groups of 2
• “On a weekday, how do you spend the hours between the time you wake up and the time you go to bed? How much time do you spend getting ready for school, going to school, and at school? How do you spend your time after school?”
• “Take a quick minute to list your usual weekday routine, knowing that it may vary from day to day. You may choose to focus only on one day—say, Monday.” 
• 1–2 minutes: quiet think time
• 1–2 minutes: partner discussion
• “How did you show the amount of time you spend on each activity?” (In hours, in minutes, as intervals of time—for example: 8:30 to 3:30)
• “Let’s look at how Mai spends her day in hours and minutes.”

• 7–8 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for the ways students convert large numbers of hours and fractional hours into minutes.

• Invite selected students to share their responses and reasoning. Start with students who reason additively about the number of minutes in a given number of hours. End with those who frame the relationship between a whole number of hours and the number of minutes in multiplicative terms. 

In this activity, students reason about the number of seconds in given time in minutes. Students see that 1 minute is 60 times as long as 1 second.

• Groups of 2
• “Have you used a timer or a stopwatch to count the number of seconds of doing something? What were you timing?”
• Consider challenging students to do something for a full minute (for instance, holding breath or balancing on one foot) and displaying a timer that shows the second hand or the number of seconds increasing or decreasing.
• “Which one is longer: 1 minute or 1 second? How does 1 minute compare to 1 second?” (One minute is 60 times as long as 1 second.)

• 7–8 minutes: independent work time
• 2–3 minutes: partner discussion
• Monitor for the different ways students find the number of seconds in 10 and 30 minutes and the ways they reason about the last 2 problems.

• Display the table. Invite students to help complete the table by sharing their responses and reasoning. 
• “How did you find the number of seconds in 30 minutes?” (Multiply the number of seconds in 10 minutes by 3, multiply the number seconds in 5 minutes by 6.)
• Select other students to share their reasoning for the problem about commercial breaks. 
• Highlight that we can decompose the number of minutes to find the number of seconds. (For example, \(1\frac{1}{2}\) minutes is 1 minute and \(\frac{1}{2}\) minute or 1 minute and 30 seconds, which is 90 seconds.)