CC.2.2.A.2

HALVES, THIRDS, AND FOURTHS

If a shape is partitioned into two equal shares, the shares can be described as halves.
One of the shares can be described as half of the whole shape.
The whole shape can be described as two halves.

If a shape is partitioned into three equal shares, the shares can be described as thirds.
One of the shares can be described as a third of the whole shape.
The whole shape can be described as three thirds.

If a shape is partitioned into four equal shares, the shares can be described as fourths.
One of the shares can be described as a fourth of the whole shape.
The whole shape can be described as four fourths.

Equal shares of identical wholes are the same size,
but not necessarily the same shape.

Sometimes it is easy to see if shares of a shape are the same size.
The square on the left is partitioned into three same size shares, or three thirds.
The square on the right is partitioned into three shares which are not the same size; it is not partitioned into thirds.

Example:

The two shares on the right appear to be the same size.
Is the longer share on the left the same size as each share on the right?

By cutting the longer share into pieces, it can be seen that the longer share is the same size as each of the shares on the right.

So, the square is partitioned into three equal shares.
This means each share is a third of the whole square.
So, yes, the square is partitioned into three thirds - even though the shares are shaped differently.

Partitioning Shapes

Pennsylvania Core Standards: CC.2.2.A.2

Use the understanding of fractions to partition shapes into halves, quarters, and thirds

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