## How Much Time Do We Need?

- Lesson

Students consider the amount of time that space travelers need to travel to the four terrestrial planets. Students also think about what kinds of events might occur on Earth while the space travelers are on their journey.

**Getting Started**

The terrestrial planets are the four innermost planets in the solar system: Mercury, Venus, Earth, and Mars. They are called terrestrial because they have a rocky, compact surface like the Earth's. Jupiter, Saturn, Uranus, and Neptune are known as Jovian, or Jupiter-like, planets because they are gigantic planets when compared with Earth and have a gaseous nature like Jupiter's. Jovian planets are sometimes called the gas giants. Pluto is not a member of either group. Its composition is unknown, but it is probably composed mostly of rock, ice, and frozen gases.

**Developing the Activity**

Present the following scenario to students:

Since humankind wants to know more about each of our planetary neighbors, we need to plan our travel to the planets. Select one terrestrial planet and one Jovian planet. Plan trips to the two planets and to Pluto. Describe the speed of your spacecraft as well as the time required to reach the planet, stay one Earth year to explore it, and return to Earth. You may assume that advances will be made in the development of spacecraft and that speeds up to 50,000 miles per hour will be possible.

As a class, you will need to determine a Launch Day for all missions. Based upon that Launch Day, on what date will you arrive at the targeted planet? On what date will you return from each mission?

These questions will require that students convert such time intervals as 10.2 years into years and days. When the conversion results in a part of a day, round the value to the nearest day. Students may not be familiar with thinking about a date in the year as having an ordinal value in relation to the year; for example, 1 July is the 183rd day of the year. Locate a reference calendar where the ordinal value is given along with the date. Remind students they may not necessarily be beginning with 1 January, however. Launch could be on any day of the year. Since the year 2008 is a leap year, students need to use 366 days for that year as well as other leap years spent traveling to other planets.

Each member of the mission team should write about one of the trips to a planet. The description should include the launch date, the destination, the speed of travel, the time to reach the planet, the date of arrival, and the date the crew returned to Earth.

To this point in the lesson, students have been considering space travel from the perspective of what happens to the space traveler on the journey. But while the space travelers are visiting distant planets, life continues on its usual course at home on planet Earth. Students should be familiar with the aspect of all travel from their previous experiences. While they are away from home, life goes on; on their return, they need time to catch up on all the news and events. Occasionally, an event occurs while they are gone that has a profound effect on them when they return.

**Extending the Activity**

Return the students to their mission teams. Tell them to imagine that their team was actually sent on a mission to their selected terrestrial planet. They know their launch data and have computed the duration of their trip and the date of their return. Although NASA kept the crew members posted on the news, they have missed many important events, both personal and public.

Each mission team serves as the ground crew for a space-traveling counterpart. The ground crew's task is to debrief the astronauts on their return to Earth.

Each ground crew makes a list of important events that the astronaut crew should know about on its return. Of course, the names and some of the events will be fictitious, but they should be plausible for the time that passed on the journey. Be certain to include the results of regularly occurring events. Such personal events as graduations for family members should be mentioned, too. Sports events, such as the Olympics, the Super Bowl, and the World Series, maybe important events for some students.

**Closing the Activity **

Students present the briefings they have written for the returning astronauts. These reports could take many forms. Some mission teams may make time lines. Others may present their briefing as a newscast. They might use technology to support their presentation. Another team member may make a scrapbook. Do not place limits on their creativity.

All students should take time to reflect on the mathematics of this lesson. The calendar, the time conversions, the distances in space, and the speeds required to complete space travel are all important concepts for students to think about as they construct their understanding of the world and the mathematics that describes it.

- Paper (to be used as a journal)

### Space Shuttle

### Learning Objectives

- Calculate the amount of time needed to travel to the four terrestrial planets
- Convert time intervals, such as 10.2 years, into years and days
- Reflect upon events that would occur on Earth while the space travelers are on their journey

### Common Core State Standards – Mathematics

Grade 6, Ratio & Proportion

- CCSS.Math.Content.6.RP.A.2

Understand the concept of a unit rate a/b associated with a ratio a:b with b ≠ 0, and use rate language in the context of a ratio relationship. For example, ''This recipe has a ratio of 3 cups of flour to 4 cups of sugar, so there is 3/4 cup of flour for each cup of sugar.'' ''We paid $75 for 15 hamburgers, which is a rate of $5 per hamburger.''

Grade 7, Ratio & Proportion

- CCSS.Math.Content.7.RP.A.1

Compute unit rates associated with ratios of fractions, including ratios of lengths, areas and other quantities measured in like or different units. For example, if a person walks 1/2 mile in each 1/4 hour, compute the unit rate as the complex fraction (1/2)/(1/4) miles per hour, equivalently 2 miles per hour.