Lesson 17 Apply Rounding

Warm-up Notice and Wonder: Plane Altitudes

What do you notice? What do you wonder?

Altitude is the vertical distance from sea level. Here are the altitudes of ten planes.

plane	altitude (feet)	rounded to the nearest thousand
WN11	$35, 625$
SK51	$28, 999$
VT35	$15, 450$
BQ64	$36, 000$
AL16	$31, 000$
AB25	$35, 175$
CL48	$16, 600$
WN90	$30, 775$
NM44	$30, 245$

Which planes are flying at about 30,000 feet? Explain or show your reasoning.
Planes flying over the same area need to stay at least 1,000 feet apart in altitude.
Mai said that one way to tell if planes are too close is to round each plane’s altitude to the nearest thousand. Do you agree that this is a reliable strategy?
In the last column, round each altitude to the nearest thousand. Use the rounded values to explain why or why not.

Use the altitude data table from earlier for the following problems.

Look at the column showing exact altitudes.
- Find two or more numbers that are within 1,000 feet of one another. Mark them with a circle or a color.
- Find another set of numbers that are within 1,000 feet of one another. Mark them with a square or a different color.
- Based on what you just did, which planes are too close to one another?
Repeat what you just did with the rounded numbers in the last column. If we look there, which planes are too close to one another?
Which set of altitude data should air traffic controllers use to keep airplanes safe while in the air? Explain your reasoning.
Are there better ways to round these altitudes, or should we not round at all? Explain or show your reasoning.

In some countries, cell phone use is allowed on a flight only when the plane is at a certain altitude, usually around 40,000 feet.

Here are six planes and their altitudes.

Jada says the passengers in all planes except for plane F can use their phones.

Elena says only those in B and D can do so.

Do you agree with either of them? Explain your reasoning.

When rounded to the nearest 1,000, Airplane X is flying at 30,000 feet, Airplane Y at 31,000 feet, and Airplane Z at 32,000 feet.

Could Airplanes X and Y be within 1,000 feet of each other? If you think so, give some examples. If you don’t think so, explain why not.
Explain why Airplanes X and Z could not be within 1,000 feet of each other. Use a number line if you find it helpful.