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 to make scale models.Materials Needed:

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

where distance can be measured in a straight line (like a hallway or a

sidewalk). A calculator should be used for all calculations.Strategy:

In the classroom you discuss with your students what a billion years mean.

Develop the idea with the students that they need to compare a billion years to

something they are familiar with. Suggest that they compare the 4.5 billion

years the Earth has been around to 100 feet or 100 meters.

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 on the 100 foot (meter) line.

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

written as a fraction. The comparison that is being made is that of Distance

over Time; that is, 100 feet (100 meters) 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 solved is where 65

million would be positioned 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/0.35.

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

within a frame work of a 100 foot line. If you want man's time on Earth 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 1/0.35 = x/4500. The line would have to be

12857 inches long or 1071 feet long (about a quarter of a mile).

Time Periods:

Cambrain period 550 My (million Year) 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 decline of the dinosaur reign.

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

time line and have them mark these on the 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 ratios and drawing-to-scale is creating a model of the Sun

and planets. If the sun diameter is compared to 10 feet, what are the heights

of other planets?