The Power of 2.

Here’s another way to learn about fractions and fractional equivalents as well as an introduction to how a computer counts.

Reczniki papierowe

Paper Towel (Photo credit: Wikipedia)

Materials:

  • Paper towel or napkin or sheet of paper
  • Magic marker, pens and pencils, or crayons
  • Optional: scissors

Instructions:

  • Have your grandchild fold a paper towel in half.
  • Have them press down on the fold to make a neat fold line that is easy to see.
  • Have them unfold and draw along the fold line with a magic marker
  • Have them count how many sections the paper towel has now (2 sections)
  • Ask your grandchild what fraction or part of the whole towel is one section (one-half)
  • Fold the towel in half again, then, fold in half again. Press down on folds.
  • Open up the towel and draw along the fold lines.
  • Have them count how many sections of the towel there are now (four).
  • Ask your grandchild what part of the towel is one section (one-fourth).
  • Ask your grandchild what part of the towel is two sections (two-fourths or one-half).
  • Refold the first two folds and fold in half again. Unfold and draw lines on the towel. They will now have 8 sections.
  • One section is one-eighth. Two are one-fourth of the towel. Four are one-half of the towel.
  • Refold and fold in half again. When you open up the towel and draw all the lines, you will have sixteen sections.
  • One section is one-sixteenth. Two is one-eighth. Four is one-fourth. Eight is one-half.
  • Optional: Use different colored pencils, markers or crayons to draw the fold lines.
  • Optional: After two or three folds, tear or cut apart two sections and lay them on top of the matching larger section to show how two quarters (2/4), for instance, is the same size as one-half (1/2).
  • Optional: write the fraction in one of the sections each time you unfold from a new fold. That is, write the fraction 1/2 on one section after the first fold. As you continue with more folds, your grandchild will see how one-half becomes two quarters, and 1/4 becomes two eighths.

What Should Happen?

Before their eyes, your grandchildren will see how a whole can be divided into even pieces.

They are seeing another way to show that some fractions are equivalent.

Two-fourths, for instance, is the same size as one-half of the towel.

They are also being introduced to an important concept in computers, the sequence, 1, 2, 4, 8, 16, or the power of 2.

That is, each time your grandchild folds the towel in half again, they are doubling the number of sections in the towel.

Computers work by testing whether a circuit is on or off.

So, the only numbers available to work with are 0 (off) and 1 (on) and arithmetic with those two numbers.

Computer memory is measured using a binary numbering system.

Starting with a byte, for 8 bits (a bit is one of those circuits that is on or off), memory is measured by kilobyte, or, roughly one thousand, but, more accurately 1,024 bytes, or megabytes (approximately one million bytes or 1,048,576), then gigabytes (one billion) and terabytes (one trillion).

Eventually, your grandchildren will start learning about exponents.

They tell us how many times a number is multiplied by itself.

2 to the power of 1, for instance, is 2 x 1 which equals 2, or 21.

2 to the power of 2 is 2 x 2 which equals 4, or 22.

2 to the power of 3 is 2 x 2 x 2 which equals 8 or 23.

This is important in the computer field because 2s that are multiplied a lot get unwieldy.

Thus, we shorten 1,024 to 1K (rounding off to 1,000, where K, or kilo, means 1,000).

But, 1K is also 2 to the power of 10, or 2 multiplied by itself 10 times, or 210.

That is the power of 2.

And, you thought it was just a paper towel.

 Thanks to babycenter.com for this suggestion.

This article first appeared on grandmotherdiaries.com.

 

Carol Covin, Granny-Guru

Author, “Who Gets to Name Grandma? The Wisdom of Mothers and Grandmothers”

http://newgrandmas.com

 

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