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Common Core Math1st GradeGeometry

1.G.1: Defining and Non-Defining Attributes of Shapes

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

Make a 1.G.1 WorksheetAll 21 1st Grade Math Standards

The Official Wording

Distinguish between defining attributes (e.g., triangles are closed and three-sided) versus non-defining attributes (e.g., color, orientation, overall size); build and draw shapes to possess defining attributes.

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

What 1.G.1 Means in Plain English

First graders separate what makes a shape what it is from what does not. A triangle must be closed with three straight sides. Color, size and the way it points never matter. Then they build and draw shapes that follow those rules, like a triangle from three sticks.

The goal is to judge by rules, not looks: a triangle tipped on its point or stretched long and thin is still a triangle, and a three-sided shape with a gap is not. In 2nd grade, students draw shapes to a given number of angles or faces (2.G.1).

1.G.1 I Can Statements

  • I can tell which features make a shape a triangle.
  • I can say that color and size do not change a shape.
  • I can build and draw a shape that follows the rules.

1.G.1 Worked Example

Three shapes that all look a bit like triangles, sorted by the rules instead of by looks, then one built from sticks.

Problem

Shape A is a huge blue triangle standing on its point. Shape B has three sides, but one is curved. Shape C has three straight sides with a gap at one corner. Which are triangles?

Which of these is a triangle?
  1. Start with the rule that makes a triangle a triangle: three straight sides, three corners, closed all the way around.triangle: 3 straight sides, 3 corners, closed
  2. Shape A: count three straight sides and three corners, and it is closed. Its size, its color and the way it points do not count.A: a triangle
  3. Shape B has three sides, but one of them bends like the crust on a slice of pizza.B: not a triangle, one side is not straight
  4. Shape C has three straight sides, but two of them do not meet. Trace it with a finger and you fall out through the gap.C: not a triangle, it is not closed
  5. Now build one: three craft sticks, each end touching another, no gaps. Turn it any way, it stays a triangle.3 sticks, 3 corners, closed: a triangle in any position
AnswerOnly shape A is a triangle. B has a curved side and C is open. A’s size, color and tilt do not matter.

Check it: Ask what would turn B and C into triangles: straighten the curved side, close the gap. If every fix is about sides or closing, the child is reasoning with defining attributes.

Common Mistakes with 1.G.1

A turned shape loses its name

A square resting on one corner called a diamond, not a square

Try this: Turn a paper square slowly in front of the class and count its sides and corners at each stop: nothing changes.

Only the picture-book triangle counts

A long, thin triangle rejected because “triangles look like a mountain”

Try this: Build skinny, wide and lopsided triangles from straws, then ask the child to count the sides of each before deciding.

Sorting by color or size

“These go together because they are all red.” when the task was to sort by shape

Try this: Ask whether the shape would still have the same name if it were painted blue or made giant, then sort again by sides.

Where 1.G.1 Fits

Comes BeforeK.G.2Name shapes correctly whatever their size or the way they face.K.G.4Describe shapes by their parts, like the number of sides and corners.
Alongside1.G.2Put shapes together to make a new shape, then build from the new one.
Comes Next2.G.1Recognize and draw shapes with a given number of angles or equal faces.3.G.1Group shapes by shared attributes, like rhombuses, rectangles and squares as quadrilaterals.

Practice 1.G.1

Math Worksheet GeneratorFree Tool1st grade shape pages with an answer key. Ask students to circle every triangle, then write the rule each skipped shape breaks: not closed, or not three straight sides.Grade 1ShapesAnswer key
Make a Worksheet
Graph Paper GeneratorFree ToolLarge squares to draw on: a triangle with one long side, a rectangle twice as long as it is tall, a square tipped onto a corner, each labeled with its number of sides.Large squaresOne pagePrint
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Quick Check

  1. Jada says a shape is a rectangle because it is blue. Is that a good reason?
  2. A shape has three straight sides, but two of them do not meet. Is it a triangle?
  3. You turn a square so it stands on one corner. What shape is it now?

1.G.1: Other Names

1.G.11.G.A.1CCSS.MATH.CONTENT.1.G.A.1

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.