CCSS.Math.Content.3.G.A.2
The Standard
Partition shapes into parts with equal areas. Express the area of each part as a unit fraction of the whole.
Common Core State Standards for Mathematics · Geometry
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students split rectangles, circles, and other familiar shapes into regions with the same area. They name one region as 1/2, 1/3, 1/4, or another unit fraction of the whole.
What Mastery Looks Like
- Given a shape and a number of parts, students create a valid partition and explain how they know the areas are equal. They label one part with a unit fraction whose denominator matches the total number of equal parts.
Common Misconceptions
- Students may count pieces without checking whether their areas are equal, or use the number of shaded parts as the denominator. They may assume different-looking parts cannot have equal area.
How to Assess It
- Give students a rectangle. Ask: "Partition it two different ways into four equal-area parts, label one part 1/4, and explain why the parts are equal."
Lesson moves
Ways to Teach It
Give pairs paper rectangles to fold into halves, thirds, and fourths, then shade and label one part after each fold.
Show two differently partitioned squares and ask, "Which partitions have equal-area parts, and what evidence supports your answer?"
Play Partition Match: students match shape cards to unit fraction cards, rejecting shapes whose pieces do not have equal area.
Use sandwich diagrams to plan fair shares among two, three, or four children, then name one child’s share as a unit fraction.
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Printable 3.G.A.2 Worksheet
A ready-to-print activity worksheet aligned to CCSS.Math.Content.3.G.A.2, with an answer key for the teacher on its own page. No account needed.
PDF, US Letter, prints cleanly in black and white.
Download the worksheetBefore This Standard
If students are struggling here, check these first.
- CCSS.Math.Content.3.NF.A.1
Students must understand one equal part of a whole as 1/b to name each equal-area shape part as a unit fraction.
- CCSS.Math.Content.2.G.A.3
Equal-share partitioning and fraction names for halves, thirds, and fourths carry into describing each equal-area part as a unit fraction.
- CCSS.Math.Content.3.MD.C.5
Students must understand area as the space inside a shape before judging equal-area parts and naming each as a fraction.
What This Unlocks
Mastery here sets students up for these next.
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- CCSS.Math.Content.1.G.A.3
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,...
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