GoalUse paper folding to see that 1 fold, 2 folds and 3 folds make halves, fourths and eighths.
New words
fold · to bend paper so that the edges match exactlycrease · the line left on paper after it is foldedequal parts · parts that are exactly the same size
Explanation
When we fold paper so that the edges match, the crease cuts the paper into equal parts. One fold makes 2 equal parts, and each part is 1/2. Fold again and the paper has 4 equal parts, each 1/4. A third fold makes 8 equal parts, each 1/8. Every new fold cuts each part in half, so the number of parts doubles: 2, 4, 8. Now think about the half of the paper. After one fold it is 1 part, after two folds it is 2 parts, and after three folds it is 4 parts. So 1/2 = 2/4 = 4/8. Be careful: a fold is fair only when the two sides match exactly. If one side is bigger, the parts are not equal, and they are not halves.
Folds
Equal parts
One part
Half of the paper
1
2
1/2
1 part
2
4
1/4
2 parts
3
8
1/8
4 parts
Worked examples
Nour folds a rectangular napkin once so that the corners meet. The crease makes 2 equal parts, and each part is 1/2 of the napkin.
She folds it in half again in the same way. Now the napkin has 4 equal strips, and each strip is 1/4. The first half is now 2 strips, so 1/2 = 2/4.
She makes a third fold across the napkin. Now there are 4 columns and 2 rows, which is 8 equal parts, each 1/8. A half of the napkin is 4 of these parts, so 1/2 = 4/8.
Class activity
Paper fold stories. Take three strips of paper of the same size. Fold the first in half once, the second in half twice and the third in half three times. Open them, count the equal parts and shade half of each strip. Make up a short story for each strip, such as a scarf folded for the market. Write the fraction you shaded each time.
Practice
1
Hana folds a sheet of paper in half and then in half again. How many equal parts are there, and what fraction is one part?
There are 4 equal parts. Each part is 1/4.
2
She shades 2 of the 4 parts. What fraction is shaded? Is it equal to one half?
2/4 is shaded. Yes, 2 is half of 4, so 2/4 = 1/2.
3
Seif folds a paper strip three times and shades it as shown. Write the fraction shaded and say which simpler fraction it equals.
4 of 8 parts are shaded, so the fraction is 4/8, and 4/8 = 1/2.
4
Karim folds a paper so that one part is bigger than the other. Can he call each part 1/2? Why?
No. Halves must be equal parts. If one part is bigger, the parts are not equal.
5
A paper is folded into 8 equal parts. How many parts make one half of the paper?
