Partition a rectangle into rows and columns of same-size squares, and count to find the total number of squares.

Arkansas Academic Standards:
2.G.A.2

Partition a rectangle into rows and columns of same-size squares and count to find the total number of squares

Arizona Academic Standards:
2.G.A.2

Partition a rectangle into rows and columns of same-size rectangles and count to find the total number of rectangles.

Common Core State Standards:
Math.2.G.2 or 2.G.A.2

Partition a rectangle into rows and columns of same-size squares and count to find the total number of them.

New York State Next Generation Learning Standards:
2.G.2

Partition a rectangle into rows and columns of same-size squares and count to find the total
number of them.

Tennessee Academic Standards:
2.G.A.2

Partition a rectangle into rows and columns of same-sized squares and find the total number of squares.

Alabama Course of Study Standards:
27

Partition circles and rectangles into two, three, or four equal shares. Describe the shares using such terms as
halves, thirds, half of, or a third of, and describe the whole as two halves, three thirds, or four fourths.

Arkansas Academic Standards:
2.G.A.3

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths

Arizona Academic Standards:
2.G.A.3

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, fourths, half of, third of, fourth of, and describe the whole as two halves, three thirds, or four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Common Core State Standards:
Math.2.G.3 or 2.G.A.3

Partition circles and rectangles into two, three, or four equal shares, describe the shares using the words halves, thirds, half of, a third of, etc., and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Georgia Standards of Excellence (GSE):
2.GSR.7.3

Partition circles and rectangles into two, three, or four equal shares. Identify and describe equal-sized parts of the whole using fractional names (“halves,” “thirds,” “fourths”, “half of,” “third of,” “quarter of,” etc.).

North Carolina - Standard Course of Study:
2.G.3

Partition circles and rectangles into two, three, or four equal shares.

Describe the shares using the words halves, thirds, half of, a third of, fourths, fourth of, quarter of.

Describe the whole as two halves, three thirds, four fourths.

Explain that equal shares of identical wholes need not have the same shape.

New York State Next Generation Learning Standards:
2.G.3

Partition circles and rectangles into two, three, or four equal shares. Describe the shares using the words halves, thirds, half of, a third of, etc. Describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Tennessee Academic Standards:
2.G.A.3

Partition circles and rectangles into two, three, and four equal shares, describe the shares using the words halves, thirds, fourths, half of, a third of, and a fourth of, and describe the whole as two halves, three thirds, four fourths. Recognize that equal shares of identical wholes need not have the same shape.

Florida - Benchmarks for Excellent Student Thinking:
MA.2.FR.1.1

Partition circles and rectangles into two, three or four equal-sized parts. Name the parts using appropriate language, and describe the whole as two halves, three thirds or four fourths.

Georgia Standards of Excellence (GSE):
1.GSR.4.3

Partition circles and rectangles
into two and four equal shares.

Georgia Standards of Excellence (GSE):
2.GSR.7.3

Partition circles and rectangles
into two, three, or four equal
shares. Identify and describe
equal-sized parts of the whole
using fractional names (“halves,”
“thirds,” “fourths”, “half of,”
“third of,” “quarter of,” etc.).

Georgia Standards of Excellence (GSE):
2.GSR.7.4

Recognize that equal shares of
identical wholes may be different
shapes within the same whole.

2nd Grade Math - Partitioned Circles & Rectangles Lesson

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.