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Common Core Math1st GradeGeometry

1.G.3: Partition Shapes into Halves and Fourths

Also written as 1.G.A.3 and CCSS.MATH.CONTENT.1.G.A.3 · Cluster: Reason with shapes and their attributes.

Download the Fraction ChartAll 21 1st Grade Math Standards

The Official Wording

Partition circles and rectangles into two and four equal shares, describe the shares using the words halves, fourths, and quarters, and use the phrases half of, fourth of, and quarter of. Describe the whole as two of, or four of the shares. Understand for these examples that decomposing into more equal shares creates smaller shares.

Common Core State Standards, Grade 1, Geometry · Read it at the source · Checked October 14, 2026

What 1.G.3 Means in Plain English

First graders fold and cut circles and rectangles into two or four equal shares and name them: half of the sandwich, a fourth of the paper pizza, a quarter of the cracker. They also name the whole by its shares, like two halves or four quarters.

The surprising idea is that more pieces means smaller pieces: a fourth is less than a half, though 4 is more than 2. Shares must be equal, or they are not halves. In 2nd grade thirds join in (2.G.3), and 3rd grade writes a share as 1/4 (3.NF.1).

1.G.3 I Can Statements

  • I can split a circle or rectangle into two equal shares.
  • I can name a share as a half, a fourth or a quarter.
  • I can explain why a fourth is smaller than a half.

1.G.3 Worked Example

A paper pizza folded once for two friends and again for four, with the share words said out loud at each fold.

Problem

Two friends share a paper pizza. Then two more friends arrive. Fold it into fair shares both times, and say whether each friend got more the first time or the second.

One paper pizza, halves then fourths
  1. Fold the circle so the edges meet exactly all the way around, then open it. The fold runs through the middle.1 fold, 2 equal shares
  2. Each share is a half. Say the share and the whole.Each piece is half of the pizza. Two halves make the whole pizza.
  3. Now there are four friends. Fold the pizza in half, then in half again with the edges matching, and open it.2 folds that cross in the middle, 4 equal shares
  4. Each share is a fourth, also called a quarter.A fourth of the pizza, a quarter of the pizza. Four fourths make the whole pizza.
  5. Lay one fourth on top of one half. The half sticks out past it.a half is bigger than a fourth
AnswerEach friend got half of the pizza when two shared, and a quarter when four shared. More shares means smaller shares, so the first time was more.

Check it: Lay two of the quarters side by side on one half. They cover it exactly, so the folds really made equal shares.

Common Mistakes with 1.G.3

Two pieces, but not halves

A rectangle cut near one end into a big piece and a sliver, both called halves

Try this: Ask which piece the child would want if it were a cookie. If one is worth choosing, the pieces are not halves.

More pieces means bigger pieces

“I want fourths, because 4 is more than 2.”

Try this: Cut two same-size paper circles, one into halves and one into fourths, and lay a fourth on a half so the difference shows.

Cutting a circle like a loaf of bread

A circle cut into four with three side-by-side cuts, so the middle pieces are much bigger than the end pieces

Try this: Fold the circle in half and in half again, then cut on the folds, which always cross at the middle.

Where 1.G.3 Fits

Comes BeforeK.G.6Join simple shapes to make larger ones, the move this standard runs in reverse.
Alongside1.G.2Put shapes together, like two half-circles into a circle.1.MD.3Tell time to the half hour, when the long hand has gone halfway around.
Comes Next2.G.3Partition circles and rectangles into halves, thirds and fourths.3.NF.1Write one of b equal parts of a whole as the fraction 1/b.

Practice 1.G.3

Graph Paper GeneratorFree ToolDraw a rectangle 4 squares long and 2 squares tall, then cut it into halves and fourths along the lines. Each half holds 4 squares and each fourth holds 2, so the shares are equal.Large squaresOne page
Make Graph Paper

Quick Check

  1. A sandwich is cut into 2 equal pieces. What is each piece called?
  2. Would you get more cracker with half of it or a quarter of it?
  3. Leo cuts a square into 4 pieces, but one piece is much bigger than the others. Are the pieces fourths?

1.G.3: Other Names

1.G.31.G.A.3CCSS.MATH.CONTENT.1.G.A.3

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved. Official wording from the Common Core State Standards PDFs at corestandards.org, last checked October 14, 2026. The explanation, I can statements, example, mistakes and practice on this page are EMStudio’s own, written beside the official wording. They are not part of the standard.