In this activity, students learn about the Burj Khalifa, the tallest highrise in the world, and calculate the distance scaled by a climber given a rate (828 meters in 6 hours) and some amounts of time. Students may approach each question in different ways, with or without using a unit rate.

• To find the distance climbed in 2 hours, students are likely to divide both the total distance climbed and the total number of hours by 3. 
• To find the distance climbed in 5 hours, they are likely to divide the total distance by 6 to find the rate per hour and multiply it by 5. 
• To find the distance climbed in the last 15 minutes, students are likely to multiply the rate per hour by (or divide it by 4), recognizing that to climb “at the same rate” means the distance covered in any 1 hour or any 15-minute period is the same throughout the climb. Though less likely, some students may find the distance climbed in hours and subtract it from 828 meters, the distance climbed in 6 hours. 

Monitor for students who approach the task in different ways or use different representations to reason, and select them to share later.

Invite students who use different strategies to briefly share their work. Focus the discussion on when it might be helpful to find the unit rate (the number of meters climbed per hour). Because an amount of time is specified in each question, we can multiply the given amount of time by the number of meters climbed per hour to find the heights climbed.

In this activity, students determine how long it would take to wash all of the 24,348 windows of the Burj Khalifa given a specific rate of work by a window-washing crew. 

The total number of windows is not a multiple of the number of windows in the given ratio (15 windows in 18 minutes). This may motivate some students to identify the rate for washing 1 window and scale that number. It may prompt other students to reason less directly. Monitor for students who apply their understanding of equivalent ratios in different ways. Here are some likely approaches, from less direct to more direct:

• Use the equivalent ratio of 10 windows in 12 minutes to find the time for washing 24,350 windows (the nearest multiple of 10) and then subtract the time for washing 2 windows. 
• Find the number of windows that can be washed in 1 minute and divide 24,348 by that number.
• Find how many groups of 15 windows are in 24,348 and multiply that number by 18.
• Find the time for washing 1 window and then multiply it by 24,348.

Regardless of the strategy used, students should be encouraged to explain the quantity they are calculating—such as windows washed per minute, minutes to wash 1 window, minutes to wash 10 windows, and so on—and how they plan to use it.

Because not all the necessary information is given up front and no solution pathway is suggested, students have an opportunity to make sense of the problem and persevere in solving it (MP1). Students who find the amount of time for washing the nearest multiple of 10 or 5 windows also practice considering the level of precision that is appropriate in the context of the problem (MP6).

Invite previously selected students to share their responses and reasoning. Sequence the discussion of the strategies in the order listed in the Activity Narrative. 

Connect the different responses to the learning goals by asking questions such as:

• “One strategy we saw involves dividing 24,238 by 15. What does the result represent in this situation?” (how many groups of 15 windows are on the Burj Khalifa) “How does it help us?” (We know it takes 18 minutes to wash 15 windows, so we can multiply the number of groups of 15 windows by 18 to answer the question.)
• “Dividing 15 by 18 gives . What does that value represent in this situation?” (windows washed in 1 minute)
• “Dividing 18 by 15 gives 1.2 or . What does that value represent?” (minutes needed to wash 1 window)
• “To find the amount of time for washing a given number of windows, which unit rate is more convenient or useful to know: windows washed in 1 minute or minutes needed to wash 1 window?” 

Highlight that the window per minute and minutes per window are the two unit rates associated with the ratio 15 windows to 18 minutes.

If time permits, ask students to consider what 29,217.6 minutes mean in terms of normal work days. Students may point out that there are 1,440 minutes in a 24-hour day but dividing the minutes of window washing by 1,440 would not represent the number of normal work days. When students interpret the result of their calculations in context, they practice reasoning quantitatively and abstractly (MP2).