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Common Core Math1st GradeGeometry

1.G.2: Compose Shapes to Make New Shapes

Also written as 1.G.A.2 and CCSS.MATH.CONTENT.1.G.A.2 · Cluster: Reason with shapes and their attributes.

Make Graph Paper for ShapesAll 21 1st Grade Math Standards

The Official Wording

Compose two-dimensional shapes (rectangles, squares, trapezoids, triangles, half-circles, and quarter-circles) or three-dimensional shapes (cubes, right rectangular prisms, right circular cones, and right circular cylinders) to create a composite shape, and compose new shapes from the composite shape.

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

What 1.G.2 Means in Plain English

First graders put shapes together into a new one and then use that new shape as a building piece. Two square tiles make a rectangle, two rectangles make a bigger square. The same works in solids: two cubes make a brick shape, and bricks stack into a wall.

The piece list grows: half-circles, quarter-circles, trapezoids, and solids like cones and cylinders. A cone on a cylinder makes a tower. In 2nd grade the move runs backwards: a rectangle is split into rows and columns of equal squares (2.G.2).

1.G.2 I Can Statements

  • I can put shapes together to make a new shape.
  • I can use a shape I built to build a bigger one.
  • I can tell which smaller shapes make up a bigger shape.

1.G.2 Worked Example

Four square tiles built up in two stages, so the rectangle made first becomes a single piece in the second build.

Problem

Use four square tiles, all the same size. Make a rectangle, then use rectangles as your pieces to make a bigger square.

Squares to a rectangle, rectangles to a square
  1. Push two square tiles together so one whole side of each touches.2 squares = 1 rectangle
  2. Make a second rectangle the same way with the other two tiles.4 squares, 2 rectangles
  3. Now treat each rectangle as one piece. Lay one rectangle above the other, long side against long side.2 rectangles = 1 big square
  4. Check the new shape: four square corners, and every side is two tiles long.a big square, 2 tiles on every side
  5. Name the parts both ways, big to small and small to big.1 big square = 2 rectangles = 4 small squares
AnswerTwo squares make a rectangle, and two of those rectangles make a square twice as wide as one tile.

Check it: Lay the two rectangles end to end instead. That makes a long rectangle four tiles long, not a square, so the way the pieces join decides the new shape.

Common Mistakes with 1.G.2

Starting over from the small pieces

Asked to build with two rectangles, the child pulls them apart and starts again from loose squares

Try this: Tape each composite together so it moves as one piece, then ask for a new shape made from the taped pieces only.

Naming the parts, not the new shape

“It’s two squares.” when asked what shape the two squares make

Try this: Run a finger around the outside edge only, counting sides and corners aloud, and name the shape that outline makes.

Stacking on a point or a curve

A tower that keeps falling because the cone is at the bottom or the cylinder lies on its side

Try this: Ask which faces are flat and which are curved or pointed, then stack only flat face to flat face.

Where 1.G.2 Fits

Comes BeforeK.G.6Join simple shapes to make a larger shape.
Alongside1.G.1Tell the attributes that make a shape what it is, which is how the new shape gets its name.1.G.3Split circles and rectangles into halves and fourths, the reverse of putting shapes together.
Comes Next2.G.2Partition a rectangle into rows and columns of same-size squares and count them.3.MD.5Understand area as the number of unit squares that cover a shape.

Practice 1.G.2

Graph Paper GeneratorFree ToolLarge squares stand in for tiles. Students outline two squares to make a rectangle, then two rectangles to make a square, coloring each stage differently so both builds show.Large squaresOne pagePrint
Make Graph Paper
Math Worksheet GeneratorFree Tool1st grade shape pages with an answer key: which shapes make this one? Keep pattern blocks on the table so students build each answer before they draw it.Grade 1ShapesAnswer key
Make a Worksheet

Quick Check

  1. How many half-circles does it take to make a whole circle?
  2. Kai makes a rectangle from two squares, then makes another one just like it. What can he build from the two rectangles?
  3. Which solid goes on top of a cylinder to make a tower with a pointed roof?

1.G.2: Other Names

1.G.21.G.A.2CCSS.MATH.CONTENT.1.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.