Return to Mathematics IndexHistory Of Our Solar System on a Time Line

Richard Murray Gage Park High School

5630 South Rockwell

Chicago IL 60629

(312)535-9230Objectives:

The Students will be able to use ratios.Materials Needed:

Tape measure or a length of rope, Masking tape and a marker or chalk. A space

that has a 100 feet in a straight line (like a hall way or a sidewalk). A

calculator should be used for all calculations.Strategy:

In the class room you discuss with your students the concept of what does a

billion years mean. Develop the idea with the students that they need to

compare a billion years to something that they are familiar with. Suggest that

they compare 4.5 billion years that the Earth has been around to a 100 feet

length. Draw a line on the board and tell the students that this line will

represent the start of the Earth to present time. Ask the students where on

this line did the dinosaurs exist. Most students will make choices around the

midpoint. Note the students choices on the board, come back to these estimates

after the students have done the calculation and have plotted points.

Discuss with the class that ratios are comparison of two numbers. Ratios can be

written as fractions. The comparison that is being made is that of Distance

over Time, that is 100 feet over 4,500 million years. Pass out a sheet that has

various geological time periods listed. For example the Paleocene period was 65

million years ago. Set up the proportion 100/4500= x/65. When this proportion

has been solved for "x", what has been solve is where 65 million will be

position on the 100 foot line. "x" represents a distance on the time line.

Some examples of times to find would be 200 million years ago. The proportion

to write is 100/4500 = x/200. The answer will be 4.44. This means that 200

million years ago will be 4.44 feet from the end of the line that represents

present time. Homo Sapiens appears on Earth 350,000 years ago, where will this

date appear on this time line. Set up the following proportion 100/4500 =

x/.35. The answer is .0077 of a foot. Mankind's appearance on Earth cannot be

measured within a framework of a 100 foot line. If you want the appearances of

man to be represented by one inch of a line, then the proportion you need to set

up to determine the length of the line is 1/.35 = x/4500. The line would have to

be 12857 inches long or 1071 feet long.

Time Periods:

Cambrain period 550 My (million Years) ago. This period is known for the

earliest fossils including trilobites.

Ordovician period 500 My ago. The early evolution of fishes.

Triassic period 250 My ago. The rise of the dinosaurs.

Jurassic period 210 My ago. This is the dinosaur heyday.

Cretaceous period 150 My ago. The climax of the dinosaur reign.

Have the students calculate where geological time periods would exist on the

time line and have them mark these on line. Have them write about what they

discovered in doing this exercise.Performance Assessment:

Direct observation of the students setting up the ratios and getting the right

value and the plotting of the value on the line.

Have the students draw a 30 centimeter line. This line will represent an amount

of time (the last fifty years, last 2000 years...). Have the students place

dates on the line.

Another ratio problem that the students could do to see if they got the

connection between ratio's and drawing to scale is creating a model of the Sun

and planets. If the Sun's diameter is compared to 10 feet, what is the heights

of other planets.