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Common Core MathKindergartenGeometry

K.G.6: Compose Simple Shapes into Larger Shapes

Also written as K.G.B.6 and CCSS.MATH.CONTENT.K.G.B.6 · Cluster: Analyze, compare, create, and compose shapes.

Make Graph PaperAll 22 Kindergarten Math Standards

The Official Wording

Compose simple shapes to form larger shapes. For example, "Can you join these two triangles with full sides touching to make a rectangle?"

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

What K.G.6 Means in Plain English

Kindergartners fit small shapes together to make a bigger one. Two square tiles pushed side to side make a rectangle, and two triangles from a cut square, joined along their long sides, make the square again. The rule is that whole sides touch, not just corners.

Pattern blocks are the classic material: six green triangles cover a yellow hexagon, two trapezoids do too. Children discover that the same big shape can be made several ways. In 1st grade composing extends to half-circles, quarter-circles and solids like cubes and cones (1.G.2).

K.G.6 I Can Statements

  • I can put two shapes together to make a new shape.
  • I can join shapes so their whole sides touch.
  • I can tell which shapes I used to make a bigger one.

K.G.6 Worked Example

Two paper triangles becoming a square, with the one way of joining them that works and the ways that do not.

Problem

Here are two triangles cut from one square. Can you join them, full sides touching, to make the square again?

Two triangles make a square
  1. Look at each triangle. Each one has a long side and two shorter sides.2 triangles, 1 long side each
  2. Try the short sides together first. The shape has a notch and points sticking out, so it is not a square.a shape with a gap, not it
  3. Turn one triangle around and slide the two long sides together until they touch along their whole length.long side against long side
  4. Count the new shape. Four sides, four corners, all the sides the same.4 sides, 4 corners: a square
AnswerJoined along their long sides, the two triangles make a square.

Check it: Lay the original square tile on top. If the two triangles disappear underneath it exactly, with no paper showing, the full sides are touching.

Common Mistakes with K.G.6

Corners touching instead of sides

Two triangles meet at a single point, making a bow tie, not a square

Try this: Run a finger along the seam. It should travel the whole length of a side, not stop at a single point.

Overlapping the pieces

One triangle sits partly on top of the other to “make it fit”

Try this: Trace the target shape on paper and ask the child to fill it like a puzzle, flat, with every piece showing.

Giving up after one try

“They do not make a square.” after the short sides are tried once

Try this: Ask which side has not been tried yet, and have the child flip or turn one piece before testing the join again.

Where K.G.6 Fits

Comes BeforeK.G.2Name a shape in any orientation, which matters once pieces get turned.K.G.4Count sides and corners, which is how the new shape gets its name.
AlongsideK.G.5Build shapes from sticks and clay and draw shapes.
Comes Next1.G.2Compose flat and solid shapes into a composite shape, and build from the composite.1.G.3Split circles and rectangles into halves and fourths, the reverse of composing.2.G.2Partition a rectangle into rows and columns of same-size squares.

Practice K.G.6

Graph Paper GeneratorFree ToolLarge-square grid paper for drawing the joins: students color two squares side by side and outline the rectangle they make, or cut a square along its diagonal and glue the two triangles back together.Large squaresOne page
Make Graph Paper
Math Worksheet GeneratorFree ToolKindergarten shape pages: which two shapes make this one? Students draw the line that splits a square into two triangles or a rectangle into two squares.KindergartenShapesAnswer key
Make a Worksheet

Quick Check

  1. Two squares are pushed together with their whole sides touching. What shape do they make?
  2. You have two triangles cut from a square. Which sides should touch to make the square again?
  3. Dev puts six small triangles together with their sides touching and gets one big shape with six sides. What is it?

K.G.6: Other Names

K.G.6K.G.B.6CCSS.MATH.CONTENT.K.G.B.6

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.