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Ratios & Percentages:

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!

 

 

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Supplies:

Paper and pencil | Calculator

Atlas with a U.S. map and a map of Rhode Island

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 2 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:

 

  1. The height of a human (6 feet) in proportion to the area in square feet of the state of Rhode Island.

 

  1. The weight of a human (150 pounds) in proportion to the weight of the planet Earth.

 

  1. The height of a human (6 feet) in proportion to the Earth's annual orbit around the sun.

 

 

 

The 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)

 

150 : ________________

 

 

 

        6 feet : (Earth's orbit in feet)

 

6 : ________________

 

 

 

 

 

By Susan Darst Williams www.AfterSchoolTreats.com Math 2010

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