Math Investigations

Help with Opening PDF Files

Chapter 1

Part 1: For the problem in the Teacher's Edition, page 2

Students can practice their research skills by finding facts about outer space that contain numbers greater than ten million. Or you can provide them with the data sheet with information about Orbiting the Sun found on the Activity page (PDF file).

If you use the data that we have provided, ask the students which column in the table has data with numbers greater than ten million. They should see that the column headed Distance Traveled in One Complete Orbit of the Sun contains numbers greater than ten million and the column headed Amount of Time for One Complete Orbit of the Sun does not contain numbers greater than ten million. Explain to students that they may use the numbers from the last column to create facts that contain numbers greater than ten million.

Have students share their facts and point out the digit that they underlined that is in the ten millions place.

If students have looked up their own data, have them share what they have found. Have them show the numbers greater than ten million and the digit that was underlined. Students could also give facts to each other without the underlining to give students an opportunity to find the digit in the ten millions place in a number found by another student.

Part 2: Be an Investigator

A good time to do this investigation is after Lesson 4 on rounding and estimating numbers.

Materials

  • thin cardboard or newspapers (some planets will have a diameter of almost 1 meter)
  • scissors
  • string
  • centimeter rulers or metersticks

Introduction to the Investigation

Introduce the investigation by reading aloud the letter on the first page of the Description of Investigation and Student Report (PDF file), having one of your students read the letter aloud, or having the students read the letter individually.

We have intentionally given the students too much information. You might want to ask them which information will be helpful to them in doing the investigation. Review rounding numbers to the nearest thousand if you feel your students need it. You might want to brainstorm with them ways they could create a circle with a given diameter.

Put students in groups of two to four students to work on the investigation. Provide students with the Description of Investigation and Student Report (PDF file).

Working on the Investigation

Allow students to explore different ways to make the circles. Some groups might use a pencil with a string attached. Others might try to find an object that has a diameter that is close to the one they are looking for and trace around the object. When everyone is finished, have the students share with each other the method they used to create their circular models.

Answers:

Diameter of the Planets


Name of Planet Actual Diameter Diameter for Model in Centimeters
( 1 cm = 1000 mi)
Mercury 3,030 miles 3 centimeters
Venus 7,520 miles 8 centimeters
Earth 7,925 miles 8 centimeters
Mars 4,225 miles 4 centimeters
Jupiter 88,730 miles 89 centimeters
Saturn 75,000 miles 75 centimeters
Uranus 31,440 miles 31 centimeters
Neptune 30,200 miles 30 centimeters
Pluto 1,865 miles 2 centimeters

Letter

The letter back to Sky Smith gives students an opportunity to write about what they have done, thus communicating about mathematics.

Extending the Investigation

Have students put the planets in order from least diameter to greatest diameter.

Answer: Pluto, Mercury, Mars, Venus, Earth, Neptune, Uranus, Saturn, Jupiter


Houghton Mifflin Math Grade 6