Paper-folding and fractions

 

Paper-folding can be used effectively in the development of fraction concepts. The teacher and the children fold a sheet of paper in two and discuss the equality of the parts. The concept of half can then be introduced and the children can colour half of the piece of paper. The same activity can be done with quarters by folding the paper a second time. Is there more than one way to fold a piece of paper in half? in quarters? The children will have to consider the size of the unit.

Comparison of fractions

Which is bigger, a half or a quarter? By how much?
Children show how much bigger the half is and discuss how they found out.
Which is bigger, a half or three quarters? By how much? Which is smaller?

Equivalence of fractions

Which is bigger, a half or two quarters?
This can also be done by re-folding and discussing eighths.
Which is bigger 3/4 or 5/8 ?
Which is smaller, 1/2 or 3/8 ?
Which is bigger, 2/4 or 4/8 ?
Similar work can be done with thirds and sixths. Folding becomes difficult for fifths and tenths so it is best to develop the concept with fraction families that are easy to fold. However, similar work can be done on squared paper.

Addition and subtraction within fraction families

Add 3/4 and 1/8 ; add 1/3 and 1/6

 

Cross-folding

To compare fractions from different families it is necessary to use cross-folding.
Fold one sheet to illustrate quarters and thirds. Fold one direction for quarters, the other direction for thirds.

Which is bigger, a quarter or a third? Why?
How many equal parts is the unit divided into?
How many in one third? One quarter?
Which is bigger, two thirds or three quarters? one third or two quarters?

 

Addition

Add a half and a third. Fold the sheet into two halves in one direction,
and three thirds in the other direction.

How many equal parts?
How many equal parts in one half?
How many equal parts in one third?
How many in a half and a third?

 

Subtraction

Subtract two thirds from three quarters by folding in two directions.

How many equal parts?
How many equal parts in three quarters?
How many equal parts in two thirds?
How many left when two thirds are removed from three quarters?

 

Multiplication

Fold a sheet of paper into halves in one direction and into thirds in the other direction.

How many equal parts?
How many equal parts in one third?
How many in half of one third?


Use the same method to find:

a) two thirds of three quarters
b) three quarters of two thirds

Are they the same?

Use the same method to find three fifths of a third.