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Common Core Math3rd GradeGeometry

3.G.2: Partition Shapes into Equal Areas

Also written as 3.G.A.2 and CCSS.MATH.CONTENT.3.G.A.2 · Cluster: Reason with shapes and their attributes.

Make 3.G.2 Graph PaperAll 25 3rd Grade Math Standards

The Official Wording

Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole. For example, partition a shape into 4 parts with equal area, and describe the area of each part as 1/4 of the area of the shape.

Common Core State Standards, Grade 3, Geometry · Read it at the source · Checked October 14, 2026

What 3.G.2 Means in Plain English

Third graders cut a shape into parts that cover the same space and name one part with a fraction. A 4 by 4 square cut into 4 pieces of 4 squares is in fourths, and each piece is 1/4 of the area, even when the pieces are different shapes.

Second grade cut shapes into halves, thirds and fourths and named them in words (2.G.3). Now each part gets a unit fraction (3.NF.1), and equal means equal area, checked by counting squares (3.MD.6). In 4th grade unit fractions add back up: 1/4 + 1/4 + 1/4 = 3/4 (4.NF.3).

3.G.2 I Can Statements

  • I can split a shape into parts with equal area.
  • I can name one equal part with a unit fraction like 1/4.
  • I can show that equal parts can have different shapes.

3.G.2 Worked Example

One square cake on grid paper, cut three different ways by three students and checked by counting squares.

Problem

A square cake drawn on grid paper is 4 squares by 4 squares. Ella cuts it into 4 strips, Max into 4 small squares, and Rosa into 4 L-shaped pieces that spin around the middle. Did everyone cut fourths? What fraction of the cake is one piece?

Three ways to cut a cake into fourths
  1. Count the whole cake first.4 × 4 = 16 squares
  2. Four equal pieces of 16 squares means each piece must have 4 squares.16 ÷ 4 = 4 squares per piece
  3. Ella’s strips are 1 square wide and 4 long.4, 4, 4, 4
  4. Max’s small squares are 2 by 2.4, 4, 4, 4
  5. Rosa’s pieces look different, so count each one: 3 squares along the edge and 1 in the middle.4, 4, 4, 4
  6. Every piece covers 4 of the 16 squares, so every piece is one of four equal parts.each piece = 1/4 of the cake
AnswerYes, all three cut fourths. Each piece is 1/4 of the cake’s area, 4 of its 16 squares.

Check it: Put the four pieces of any cut back together: 4 + 4 + 4 + 4 = 16, the whole cake, with nothing missing and nothing left over.

Common Mistakes with 3.G.2

Four pieces, not four equal pieces

A rectangle cut into 4 pieces of different sizes, each one labeled 1/4

Try this: Count the squares in every piece before naming it. The fraction name only fits when all the pieces cover the same area.

Different shapes mean different sizes

Rosa’s L-shaped pieces rejected as fourths because they do not look like each other

Try this: Count the squares in each L-shaped piece. Four squares each means equal area, so each piece is still 1/4.

Naming the part by the number of cuts

A strip cut with 3 lines into 4 parts and called thirds

Try this: Count the parts, not the lines. Three cuts across a strip make four equal parts, and each one is 1/4.

Where 3.G.2 Fits

Comes Before2.G.3Split circles and rectangles into halves, thirds and fourths and name the shares in words.2.G.2Split a rectangle into rows and columns of same-size squares.
Alongside3.NF.1Know 1/4 as one of four equal parts of a whole.3.MD.6Measure areas by counting unit squares.
Comes Next4.NF.3Add and subtract fractions as joining and separating parts of the same whole.

Practice 3.G.2

Graph Paper GeneratorFree ToolDraw a 4 by 4 or a 6 by 4 rectangle and find as many ways as possible to cut it into equal parts, counting the squares in each.Large squaresOne pagePrint
Make Graph Paper

Quick Check

  1. A rectangle is cut into 6 parts with equal area. What fraction of the area is one part?
  2. A 2 by 6 rectangle on grid paper is cut into 3 parts with equal area. How many squares are in each part?
  3. A circle is cut into 4 pieces: two big ones and two small ones. Is each piece 1/4 of the circle?

3.G.2: Other Names

3.G.23.G.A.2CCSS.MATH.CONTENT.3.G.A.2

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.