2.G.3: Partition Shapes into Halves, Thirds and Fourths
Also written as 2.G.A.3 and CCSS.MATH.CONTENT.2.G.A.3 · Cluster: Reason with shapes and their attributes.
The Official Wording
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.
Common Core State Standards, Grade 2, Geometry · Read it at the source · Checked October 14, 2026
What 2.G.3 Means in Plain English
Second graders split circles and rectangles into 2, 3 or 4 equal shares and name them: a half of the pizza, a third of the pan, two halves make the whole. A rectangle cut into fourths as strips or as a cross gives equal shares of different shapes.
Thirds are new. First grade did halves and fourths (1.G.3). No fraction symbols appear yet, only words, and the whole is always a shape. In 3rd grade one share gets written as 1/3 (3.NF.1) and the shares are described as equal areas (3.G.2).
2.G.3 I Can Statements
- I can split a circle or rectangle into halves, thirds or fourths.
- I can describe a share as a half, a third or a fourth.
- I can show that equal shares can have different shapes.
2.G.3 Worked Example
One pan of brownies cut into fourths two different ways, with the words for the pieces and the whole, and a reason the pieces are equal.
Cut a rectangular pan of brownies into fourths for four friends. Then show a different way to cut fourths, and tell whether the shares are still equal.
- Fourths means four equal shares. Cut the pan in half, then cut each half in half the same direction.4 equal strips. Each strip is a fourth of the pan.
- Say the pieces and the whole with the fraction words.One piece is a fourth. Four fourths make the whole pan.
- Another way: cut once across and once down. Four pieces again, each one a fourth, but shaped like a smaller pan.4 equal pieces, each a fourth
- A strip and one of the smaller rectangles are different shapes, but each is one of four equal shares of the same pan. Same amount of brownie.Equal shares need not be the same shape
Check it: Fold a paper pan into strips and another into the cross cut. Cut one strip in half and lay the two halves side by side on one small rectangle: they cover it exactly.
Common Mistakes with 2.G.3
Unequal pieces called halves
A rectangle cut off-center into a big piece and a small piece, both called a half
Try this: Fold the paper so the two pieces lie on top of each other. If one sticks out, the pieces are not halves.
Thirds drawn as a cross
A circle split by two crossing lines and labeled thirds, which makes four pieces
Try this: Count the pieces aloud after cutting. Thirds means exactly three equal pieces, so a circle needs three lines from the center.
Different shape means different size
“The strip is bigger than the square piece.” when both are a fourth of the same pan
Try this: Cut the strip in half and rearrange the two halves onto the square piece. They cover it exactly, so the shares are equal.
Where 2.G.3 Fits
Practice 2.G.3
Quick Check
- A pizza is cut into 3 equal pieces. What is each piece called, and how many make the whole pizza?
- A rectangle is cut into 4 equal strips. Another rectangle the same size is cut into 4 equal squares. Does a strip hold more than a square?
- Jo folds a paper circle in half and then in half again. How many equal shares does she have, and what is each called?