It's All Relative
Today's snack: Since we're working with ratios and percentages
today, let's make a snack with one part that changes drastically in size in
relationship to the other parts. Let's
make Microwave S'Mores and watch that marshmallow grow in its ratio of size,
bigtime! Break a graham cracker into two squares. Place one square on a plate.
Place one Hershey's miniature chocolate bar, or one section of a Hershey bar,
on top. Place one large marshmallow on top of the chocolate. Now microwave for
one minute on high power. Be sure to watch the marshmallow! Its proportion
changes, all right: it may double in size! If that's true, then it has
increased by a 2:1 ratio. When the minute's up, take your concoction out of the
microwave, and smash down the other graham-cracker half on top, sandwich-form.
Mmmm!!! It's out-of-proportion good!
Paper and pencil | Calculator
Atlas with a U.S. map and a map of
Poster or encyclopedia article showing
our galaxy with the Sun and planets
The "E" encyclopedia with a listing
for the Earth
Or: a search engine such as www.google.com
It's alllllll relative! No,
we're not talking about your relatives - your grandparents, aunts and uncles
and so forth. We're talking about how everything in the universe relates to
other things in the universe.
Everything can be understood based on how it relates
to something else. Is it larger? Smaller? Heavier? Lighter? More colorful?
Faster? Slower? On and on the comparisons go.
Proportion means how things compare,
one to another, in any number of measurements. When we say that a basketball is
bigger than a golf ball, we are comparing their proportions.
Ratio is the means of comparing
those things. We express a ratio in math with two numbers separated by a colon
or a slash. When you look at a ratio, you know how many times the second number
will go into the first. So if two balls are in a 5:2 ratio, the first one is
proportionately 2½ times bigger than the second one. In a 1:4 ratio, the first
number is only one-fourth as big as the second number.
Whenever you estimate something, you're working with
proportions. You can come fairly close when the objects you're comparing are
concrete - visible and easily understood. It gets a lot tougher when you're
dealing with things that are too small to see - like microscopic things - or
too large to see - like the stars.
You'll soon find out, though, that with a little
math work, you can measure the proportions of things, and know a little more
about them, and a little more precisely, too.
How good are you at figuring out
proportions to begin with? Take this quiz and choose one answer:
Q. The size of a human cell, in
proportion to the human body, is the same ratio as:
- The height of a human (6
feet) in proportion to the area in square feet of the state of Rhode
- The weight of a human (150
pounds) in proportion to the weight of the planet Earth.
- The height of a human (6
feet) in proportion to the Earth's annual orbit around the sun.
correct answer is (a). How did you do? Is a human cell a lot bigger, or a lot
smaller, than you thought?
Now use your reference books to find out:
the area in square miles of Rhode Island
x 5,280 x 5,280 (to figure it in square feet)
the weight of the Earth in pounds
the distance of the Earth's orbit around the sun, expressed in miles, and
multiplied by 5,280, the number of feet in one mile, to find out how many feet
the orbit is.
Now express all these as ratios:
1 square mile : (Rhode Island's area in square feet)
1 : ________________
150 pounds : (the weight of the Earth in pounds)
6 feet : (Earth's orbit in feet)