2nd Grade · 2.G.A.1

Pentagons and hexagons in 2nd grade

Pentagons and hexagons are flat shapes with straight sides: a pentagon has 5 sides, and a hexagon has 6. In 2nd grade, your child names shapes by counting their sides and corners. Identifying shapes this way covers triangles, quadrilaterals, pentagons and hexagons. Your child also learns to recognize a cube.

What the standard says

The official Common Core wording, quoted exactly. The plain version follows.

2.G.A.1 Recognize and draw shapes having specified attributes, such as a given number of angles or a given number of equal faces. Identify triangles, quadrilaterals, pentagons, hexagons, and cubes.

What it means, in plain words

A polygon is a flat, closed shape made of straight sides. Closed means there are no gaps: the sides join all the way around. A corner, also called an angle, is where two sides meet. Polygons are named by how many sides they have. A triangle has 3, a quadrilateral has 4, a pentagon has 5 and a hexagon has 6. Every polygon has as many corners as sides.

Pentagons and hexagons do not have to look like the pictures in books. A pentagon does not have to look like the outline of a house, and a hexagon does not have to look like a honeycomb cell. A 6-sided shape with sides of different lengths is still a hexagon. Turning a shape or making it bigger does not change its name either. Only the count matters.

2nd grade also adds the cube, a solid shape with 6 faces. A face is a flat side of a solid shape. All 6 faces of a cube are squares of the same size, like the faces of a die from a board game.

Your child should be able to:

Name triangles, quadrilaterals, pentagons and hexagons by counting sides or corners
Recognize a pentagon or a hexagon that is turned or has sides of different lengths
Draw a shape with a given number of sides or corners
Recognize a cube by its 6 square faces

Example

A closed shape has 6 straight sides, and no two sides are the same length. Is it a hexagon?

Count the sides: there are 6.
A hexagon is any closed shape with 6 straight sides.
The lengths of the sides do not matter, so yes, the shape is a hexagon.

Example

Which of these is a polygon: a circle, a triangle or a shape with one curved side?

A polygon is closed and has only straight sides.
A circle has no straight sides, so it is not a polygon.
The shape with a curved side is not a polygon either.
Only the triangle is a polygon.

Where children usually get stuck

Your child says a long, lopsided 6-sided shape is not a hexagon, because hexagons look like a honeycomb cell.
Most pictures of hexagons show one with equal sides. The child learned the picture, not the rule about counting sides.
What helps. Draw three very different 6-sided shapes together. Count the sides of each one and say "hexagon" out loud every time.
Your child counts the sides of a pentagon and gets 4 or 6.
The child starts counting at any side and loses track of where the count began, so a side gets skipped or counted twice.
What helps. Put a small dot on the first side before counting. Stop when your child is back at the dot.
Your child calls a cube a square.
The child sees one face, which is a square, and names that. A cube is a solid shape with 6 square faces.
What helps. Hold a box shaped like a cube, or a die, and touch each face as you count them together. Then trace one face on paper to show the flat square.

Try four practice questions

Real 2nd grade questions from our question bank, easiest first. Answer them right here, check each one, and see a worked solution for any question.

1Warm-up
Which object is shaped like a cube?
A
B
C
D
Show the answer and how to solve it
The building block is the cube. It is the only object that has six flat square faces, all the same size.
1. 1Look at the four objects. To find the cube, check each one for six flat square faces, all the same size.
2. 2The basketball has a curved surface and no flat faces — it is not a cube.
3. 3The traffic cone has one flat circle on the bottom and a curved surface that comes to a point. It has no square faces, so it is not a cube.
4. 4The marble is round all over — it has a curved surface and no flat faces at all. It is not a cube.
5. 5The building block has six flat square faces, all the same size. That makes it a cube.
Common mistake. A common mistake is picking the basketball or marble because they look like solid objects. A cube must have flat SQUARE faces — a curved surface rules those out completely.
The idea underneath. A cube is a special box where every face is a square AND all six faces are exactly the same size. Other shapes can have flat faces too, but they are only cubes when every face is a square.
2On level
Devontae was asked to draw a closed polygon with 4 corners. Devontae's drawing is shown below.
What does Devontae need to do to follow the directions?
A
Remove 1 corner.
B
Add 2 corners.
C
Add 1 corner.
D
It is already correct.
Show the answer and how to solve it
The answer is "Add 1 corner." Devontae's polygon has 3 corners, but the directions asked for 4, so Devontae needs 1 more corner.
1. 1Look at Devontae's drawing on the dot grid. Count each corner of the polygon, one at a time.
2. 2Devontae's polygon has 3 corners.
3. 3The directions asked for 4 corners. Devontae's polygon has only 3. So Devontae needs to add 1 more corner to the polygon.
4. 4The answer is "Add 1 corner."
Common mistake. A common mistake is confusing sides with corners or missing a corner while counting. Touch each corner with your finger as you go around the shape to make sure you count every one.
The idea underneath. In a closed polygon, the number of corners equals the number of straight sides. Counting one helps you check the other.
3On level
Which statement best describes this shape?
A
It is not a cube — it has triangular faces.
B
It is not a cube — it has a curved surface.
C
It is not a cube — the faces are rectangles, not squares.
D
It is a cube — all 6 faces are equal squares.
Show the answer and how to solve it
The shape is a cube because all 6 faces are equal squares.
1. 1Look at the 3D shape and check what shape each face is.
2. 2This shape has 6 equal square faces. All the faces are the same size and shape.
3. 3For a shape to be a cube, all 6 faces must be EQUAL SQUARES. Since this shape has 6 equal square faces, it is a cube.
4. 4The correct statement is: "It is a cube — all 6 faces are equal squares."
Common mistake. A common mistake is being unsure whether a shape is a cube without checking that ALL 6 faces look the same. When all 6 faces are equal squares, it really is a cube.
The idea underneath. A cube is a special kind of box shape where all the edges are the same length, so every face is an equal square.
4Stretch
Carlos put these shapes in his group of shapes with 4 corners. One shape does NOT belong. Which shape should be removed?
A
B
C
D
Show the answer and how to solve it
The pentagon does not belong because it has 5 corners, not 4. Carlos should remove the pentagon.
1. 1Carlos wants shapes with 4 corners in his group. Look at each shape and count its corners carefully.
2. 2Three of the shapes have 4 corners: the kite, the scalene trapezoid, and the right trapezoid. They all belong in Carlos's group.
3. 3The other shape is a pentagon. A pentagon has 5 corners, not 4. So the pentagon does NOT belong in a group of 4-corner shapes.
4. 4Carlos should remove the pentagon from his group.
Common mistake. A common mistake is to count corners too quickly, especially on rotated shapes. Pick a starting corner and count around the shape one corner at a time so you do not miss any.
The idea underneath. A polygon's number of corners (vertices) is the same as its number of sides. To check whether a shape fits in a group of shapes with 4 corners, count carefully — go around the shape and touch each corner exactly once.