Students will apply their problem-solving skills as they measure circular objects and make connections to planets.
For each group:
- Planet Cutouts
- Measuring devices
measuring tape, string
or yarn, etc.)
For each student:
Background for Teachers
This activity encourages students to apply their problem-solving skills
to measurement as they measure circular objects and make connections to
the planets. Measuring circular objects can sometimes be challenging.
One way to measure the circumference of an object is to use a piece of
yarn or string. Measure around the object using the yarn. Then lay the
yarn against a ruler to find the correct distance. Once the circumference
is found, the diameter can be found by dividing the circumference by π.
Likewise, if the diameter of an object is known, the circumference can be
found by using the formula: c = π x d.
The interrelationship between circumference and diameter allows us
to make valuable conjectures in science. Astronomers measure the
diameter of distant objects in space and then use the c = π x d formula to
estimate that object's circumference and architects must use the
relationship of circumference and diameter whenever creating circular
Vocabulary terms used in this lesson:
circumference - The perimeter of a circle.
diameter - A chord that goes through the center of a circle.
metric system - A system of measurement based on tens. The basic
unit of length is the meter. The basic unit of mass is the gram. The
basic unit of capacity is the liter.
pi - The ratio of the circumference of any circle to its diameter,
approximately equal to 3.14.
Intended Learning Outcomes
5. Make mathematical connections.
Invitation to Learn
Hold up an object 1 cm in diameter. Show the students that the
diameter of this object is 1 cm and explain that it represents Mercury.
Have a quick scavenger hunt to find objects that represent Jupiter, Pluto,
and Earth. Students search the room and record objects in their journal.
Jupiter: 28.6 cm
Pluto: 0.5 cm
Earth: 2.5 cm
- Divide the class into nine groups for this activity.
- Give the It's All Relative 1 worksheet to each student.
- Display a packet of Planet Cutouts. In each packet are cutouts for
the nine planets, but they are not labeled. Each planet has a line
drawn through the center of it (the diameter) and we know (from
our worksheets) the circumference of each planet. Is there any
way we can figure out what planet each circle corresponds to? Allow the students to discuss their strategies in their groups. Then
hand out one set of cutouts and several measurement supplies to
each group and encourage them to match each cutout to the
- Circle around the room as students work on this problem. Make
sure that students understand the connection between diameter
and circumference (c = π x d) and that they are using metric units
- Once groups have made the connections, have them complete the
blank column on the It's All Relative 1 worksheet. After all groups
have matched the circles to the planets, go around the room and
have groups quickly present the strategies they used while you
check for understanding.
- Yellow helium balloon
on a string
For each group:
- Roll of toilet paper
For each student:
- Assign a planet to each group. Have each student record their
assigned planet on the top of their It's All Relative 2 worksheet.
Tell the students that they will now use their planet to construct a
class-sized scale model of the solar system.
- Display the sun (helium balloon). Ask the students the
- Is the sun accurately drawn to scale? (No)
- What are some of the problems with the size of this sun?
(It's too small. A sun accurately drawn to scale would fit
more than 1,000,000 Earth's inside it. It's three-dimensional
and our planets are only two-dimensional. A scale model of
the sun would have a diameter of 270 cm.)
- What is true about the sun? (It's yellow in appearance. It
contains helium. It is the center of our solar system., etc.)
- Once you have resolved the sun-scale issue, tell the students
that we need to figure out how far each planet is from the sun.
- Direct the student's attention to the It's All Relative 2 worksheet.
Tell each group to find his/her planet and practice reading the
actual distance from the sun (e.g., "Jupiter is seven hundred
seventy eight million, four hundred twelve thousand, ten
kilometers from the sun."). This is a good opportunity to teach
students not to use the word "and" when reading whole numbers.
- Ask students to convert the distance from the sun to a form of
scientific notation using a base of 106. Once students have
completed the measurement for their planet, encourage them to do
the same for the other planets.
Note: What the students are doing here is not technically referred
to as scientific notation. True scientific notation would be
written with whole numbers between 0 and 10.
- As a class, divide the prefix of each scientific notation by 30 to
find the number of toilet paper sheets from the sun.
- Hand out a roll of toilet paper to each group. Model how to count
and cut sheets. You may also want to model how to make
estimates for partial sheets. Encourage students to be very
accurate in their measurements by using various estimation
- Find a large open area outside. Place the sun at the center of the
model. Have groups stand around the sun and roll their toilet
paper outward. Students tape their planet cutouts to the end of
each toilet paper roll.
- After the model is constructed, students write a reflective journal
piece about what they learned from this activity.
- Students create a scale object for the planetoids Quaoar and Sedna
- Create a scale model of the sun using yellow chart paper and art
supplies at home.
- Circulate around the room and make informal assessments while
the students work. Make sure you aren't moving too quickly
through this activity and that the students understand why this
activity requires so many steps. You may wish to take notes on
specific misconceptions or questions that arise. You can address these questions at the end of the lesson.
- It's All Relative worksheets.
- You may choose to assign one of the curriculum extensions as an