Common or Vulgar Fractions
Material:
Ten metal or plastic circles in square metal or plastic frames. The first
circle is whole, the second is divided into 2 halves, the third into 3 thirds,
and so on to the tenth circle which is divided into 10 tenths. Each
fraction of the circle has a small knob for handling. They should be
kept in one line on a shelf if possible.
Exercise 1: Introduction
The teacher sets the set of fraction frames out in a line on a table.
The first exercise is for small group of children. The teacher directs
them to remove all the fractions of the circles and then replace them in the
empty frames. All the fractions of the same size should be put in the
same frame. It is easy to see the difference between halves and thirds,
but more difficult to recognize the difference between ninths and tenths.
Exercise 2: Learning the Names
The teacher takes the half, third and quarters frames to the table.
The teacher presents the names half, third, etc., by the three period lesson.
Take halves, thirds, and quarters to a child's table. You might have
2 or 3 children who have done exercise 1 and would be ready to learn the names.
For the first period say, "When the whole is divided into 2 equal pieces,
each piece is called a half." Stress the fact that the 2 halves are
equal. To prove it to them you can superimpose the 2 halves showing
that one fits over the other exactly. They are divided into 2 equal
pieces each piece is called a half.
Take the third frame and say, "Here, the whole is divided into 3 equal pieces,
so each piece is called a third." Superimpose the pieces to show that
they are exactly the same size.
Do the same with the quarters, "If the whole is divided into 4 equal pieces,
each piece is called a quarter."
Proceed to teach the names using the three period lesson. Keeping the fractions
in their frames, point at the individual sections and review, "This is half...
a third...a quarter." Repeat if necessary.
The teacher continues with the second period.
"Who could give me a quarter?"
"Would someone hand me a third?"
"Who could give me a half?"
When the children show that they have made the connection between the name
and the fraction, the teacher proceeds with the third period.
The teacher takes a fraction out of its frame and asks, "How much is this?"
The children tell her the names.
To summarize, the teacher points to the fractions and reviews, "Today, we
learned one half, one third, and one quarter." On the other days more names
can be introduced. Eventually any piece can be taken out of the frame
and the child can identify it, i.e. 1/7 th, 1/10th, etc. As a variation
the teacher can ask the child to hand her a fraction, "Give me 1/5th."
When the children are familiar with the names, the teacher can take a number
of quantities. For example, 3/5 ths. The teacher can point out
that she has taken out three fifths. Next, she can take out a different
quantity, for example, 5/8ths and ask the child how much it is. Other
quantities can be taken out and identified.
For variations, the teacher can ask the child to make a quantity when the
teacher states the number.