The purpose of this activity is for students to investigate a situation in which knowing a value to the thousandth place is important. Many high speed athletic events such as sprinting, cycling, downhill skiing, and the luge (studied here), are measured to the thousandth of a second in order to distinguish athletes whose finish times are very close to one another. Students examine the finish times for the luge athletes, introduced in the Warm-up, and what would happen if the times were only measured to the nearest hundredth of a second, tenth of a second, or second.

Students may use number lines to help answer the questions, but as in the previous lesson, will need to think carefully about how to label the number line.

• Ask previously identified students to share their responses.
• “How does rounding the times to the nearest second impact each of the athletes?” (It makes all of the times greater and impossible to distinguish. It impacts the fastest athletes the most as their times are shifted up the most.)
• “How does rounding the times to the nearest tenth of a second impact each of the athletes?” (It makes the times of the 1st, 3rd, and 4th athletes faster and the times of the 2nd and 5th athletes slower. It makes the second athlete tie for second place instead of winning second place.)
• Display the image from the solution or a student generated image.
• “How can you use the number line to find the times to the thousandth of a second that round to 48.85 seconds?” (I can label the tick marks and then take the ones that are closest to 48.85 and the one halfway between 48.84 and 48.85.)

The purpose of this activity is for students to order decimals and examine the effect of rounding on numbers by continuing to use the luge context. In this activity, students investigate the top speeds of the athletes. In this case, the numbers are not listed in decreasing order because the top speeds do not correspond to the fastest times. Students order the top speeds before and after they have been rounded. Then they find a speed between two given speeds when the thousandths place is added. Since the speeds of the riders are not given to the thousandth, students will need to create values for the riders. There is one set of values students could pick, namely 82.804 and 82.805, where there is no value in between to the thousandth. If students choose these values, ask “Are there different possible top speeds for these athletes?”

• “Are there different speeds the athlete at 82.80 mph could have, measured to the nearest thousandth of a mile per hour?” (yes)
• “What is the greatest? The least?” (82.804, 82.795) “What about for the athlete at 82.81? What are their fastest and slowest speeds to the thousandth of a mile per hour?” (82.814, 82.805)
• Invite students to give a possible set of top speeds, to the thousandth of a mile per hour, for athletes 3, 5, and 6.