Early Math · Grades K, 1

Building Shapes: Sides, Corners and Putting Shapes Together

Quick answer

A side is a straight edge, and a corner is where two sides meet. Walking around a flat shape passes one corner after every side, so a shape with straight sides has as many corners as sides: a triangle has 3 of each and a hexagon has 6. Solid shapes have flat faces, curved surfaces and corners of their own. Small shapes fit together to make bigger ones: two triangles make a square, three make a trapezoid, and six make a hexagon.

What you'll learn

  • Count the sides and corners of flat shapes
  • Compare flat and solid shapes by their parts
  • Build and draw shapes
  • Put shapes together to make bigger shapes

Sides and corners

A side is a straight edge. A corner is where two sides meet.

Count the corners A triangle with 3 corners dotted, a square with 4, a rectangle with 4 and a hexagon with 6. 3 corners 4 corners 4 corners 6 corners
Count the corners

Now count the sides. You get the same numbers.

ShapeSidesCorners
triangle3333
square4444
rectangle4444
hexagon6666
circle0000

A circle has no straight sides. Its edge is curved all the way around. It has no corners.

Why sides and corners match

Trace a shape with your finger. Go along a side. You come to a corner. Turn, and a new side starts.

So it goes side, corner, side, corner, all the way around. Each side ends at one corner. That is why the two counts are the same.

Compare shapes

A square and a rectangle are alike. Both have 44 sides and 44 square corners. But a square’s sides are all the same length. A rectangle has two long sides and two short ones.

Solid shapes have parts too.

A cube and its corners A cube with a dot on each of its 8 corners. One corner is at the back, out of sight, and is drawn as an open dot.
A cube and its corners
  • A cube has 66 flat faces. Each face is a square. It has 88 corners.
  • A sphere has no flat faces and no corners. It rolls.
  • A cylinder has 22 flat faces. They are circles. It can roll and stack.
  • A cone has 11 flat face, a circle. It has a point at the top.

Build and draw shapes

You can build a shape with sticks and balls of clay. Each stick is a side. Each ball of clay is a corner.

A triangle takes 33 sticks and 33 balls of clay. A square takes 44 sticks, all the same length.

You can draw a shape, too. Draw straight sides, one after the next. Stop when you get back to where you began.

Join shapes

Small shapes can fit to make a big shape.

Two triangles make a square A triangle with a square corner, plus the same triangle turned upside down, makes a square cut corner to corner. + =
Two triangles make a square

Pattern blocks fit this way too. Three triangles make a trapezoid. Two trapezoids make a hexagon.

Triangles and trapezoids make a hexagon A trapezoid cut into three triangles, and a hexagon cut into two trapezoids.
Triangles and trapezoids make a hexagon

You can join the new shapes, too. Two squares side by side make a rectangle. Stack two cubes to get a tall box.

Worked examples

Common mistakes

Practice problems

  1. How many corners does this shape have?

    How many corners? A pentagon with a dot on each corner.
    How many corners?
    Answer

    55

    Full solution

    Count the dots: 11, 22, 33, 44, 55. It has 55 corners, and 55 sides too.

  2. How many sides does a rectangle have?

    Answer

    44

    Full solution

    Two long sides and two short sides make 44 sides.

  3. What shape do these two triangles make?

    What do they make? A triangle with a square corner, plus the same triangle turned upside down, equals a question mark. + = ?
    What do they make?
    Answer

    A square

    Full solution

    Join the long sides. The new shape has 44 sides the same length. It has 44 square corners. It is a square.

  4. How many triangles make this trapezoid?

    A trapezoid cut into triangles A trapezoid cut into triangles.
    A trapezoid cut into triangles
    Answer

    33

    Full solution

    Count the parts: 11, 22, 33. Each part is a triangle.

  5. How are a square and a rectangle alike?

    Answer

    Both have 44 sides and 44 square corners.

    Full solution

    They have the same sides and corners. One thing is not alike. All 44 sides of a square are the same length.

  6. How many sticks do you need to build a triangle?

    Answer

    33

    Full solution

    Each stick is one side, and a triangle has 33 sides.

  7. Which one can roll, a cube or a sphere?

    Answer

    A sphere

    Full solution

    A sphere is round all over. It has no flat faces. A cube has flat faces, so it sits still.

  8. How many flat faces does a cube have?

    Answer

    66

    Full solution

    Top, bottom, front, back, left and right. That is 66 faces. Each one is a square.

  9. How many trapezoids make a hexagon?

    Answer

    22

    Full solution

    Cut it across the middle. Each half is a trapezoid.

  10. Lily says a circle has 11 side. What went wrong?

    Hint

    Is any part of a circle straight?

    Answer

    A side is straight. A circle has no straight parts. It has 00 sides.

    Full solution

    A side is a straight edge. The edge of a circle is curved all the way around.

    So a circle has no sides and no corners.

Frequently asked questions

What is a side of a shape?

A straight edge. A triangle has 3 sides and a square has 4.

What is a corner of a shape?

The point where two sides meet. Corners are also called vertices.

Why does a shape have as many corners as sides?

Going around the shape, every side ends at a corner, and the next side starts there. So you pass one corner for each side.

What shapes can two triangles make?

Two triangles with a square corner can make a square or a rectangle. Two pattern-block triangles make a rhombus.

How many corners does a cube have?

8: four around the top and four around the bottom. It also has 6 flat faces, all squares.

What to learn next

Standards alignment

This lesson covers the following Common Core State Standards for Mathematics.

  • CCSS.MATH.CONTENT.K.G.B.4GeometryAnalyze and compare two- and three-dimensional shapes, in different sizes and orientations, using informal language to describe their similarities, differences, parts (e.g., number of sides and vertices/"corners") and other attributes (e.g., having sides of equal length).
  • CCSS.MATH.CONTENT.K.G.B.5GeometryModel shapes in the world by building shapes from components (e.g., sticks and clay balls) and drawing shapes.
  • CCSS.MATH.CONTENT.K.G.B.6GeometryCompose simple shapes to form larger shapes.
  • CCSS.MATH.CONTENT.1.G.A.2GeometryCompose 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.
For teachersTick to print a blank worksheet; leave it clear to print the lesson with the full answer key.