Week 7 of 10

Geometry Explorer

Students explore 2D and 3D shapes by their attributes - sides, corners, faces, edges, and vertices - and discover lines of symmetry by folding shapes so both halves match.

Estimated time: 45-60 minutes
Grade range: Grades 2-5
Skill focus: 2D shapes, 3D shapes, Sides and corners, Faces and edges, Symmetry
Theme: Geometry Explorer: mapping the world of shapes

The story

You're the newest Geometry Explorer, and the map in front of you is covered in shapes nobody has named yet. Some are flat, like the tiles on a floor; others are solid, like blocks you can hold. Your explorer's toolkit is simple: count the sides, count the corners, count the faces and edges - and fold to find hidden symmetry. Every shape you describe correctly gets pinned to the map.

What you'll learn

Name 2D shapes by counting their sides and corners (a triangle has 3 sides and 3 corners).
Describe 3D shapes by their faces, edges, and vertices (a cube has 6 faces, 12 edges, 8 vertices).
Find a line of symmetry by folding a shape so both halves match exactly.

Key ideas

2D shapes are flat; we count their sides and corners.
3D shapes are solid; we count their faces, edges, and vertices.
A shape has a line of symmetry when it can be folded into two matching halves.

Words to know

2D shape: A flat shape with length and width, like a triangle or square.
3D shape: A solid shape you can hold, like a cube or sphere.
Side: A straight edge of a 2D shape.
Vertex (corner): A point where two or more sides or edges meet.
Face: A flat surface of a 3D shape.
Edge: The line where two faces of a 3D shape meet.
Line of symmetry: A fold line that splits a shape into two matching halves.

The lesson

Flat shapes are called 2D (two-dimensional). We identify them by counting sides (the straight edges) and corners, also called vertices (where two sides meet). A triangle has 3 sides and 3 corners; a square has 4 equal sides and 4 corners; a pentagon has 5 sides and 5 corners.

Solid shapes are 3D (three-dimensional) - you can hold them. We describe them by faces (the flat surfaces), edges (where two faces meet), and vertices (the pointed corners). A cube has 6 square faces, 12 edges, and 8 vertices. A rectangular box (rectangular prism) has the same counts but its faces are rectangles.

2D and 3D shapes are related: the faces of a 3D shape are 2D shapes. A cube's faces are squares; a can (cylinder) has two circle faces. Knowing your flat shapes helps you describe the solids they build.

A shape has a line of symmetry if you can fold it so the two halves land exactly on top of each other. A square has 4 lines of symmetry; a rectangle has 2; a heart has 1 (straight down the middle). Folding is the surest test: if the halves don't match, that fold isn't a line of symmetry.

Worked examples

How many sides and corners does a hexagon have?

6 sides and 6 corners

'Hex' means six. A hexagon has 6 straight sides, and each pair of sides meets at a corner, so it has 6 corners too.

How many faces, edges, and vertices does a cube have?

6 faces, 12 edges, 8 vertices

A cube is like a box with 6 square faces. Each place where two faces meet is an edge (12 of them), and each pointed corner is a vertex (8 of them).

How many lines of symmetry does a rectangle (not a square) have?

You can fold a rectangle in half top-to-bottom and left-to-right and both halves match, but the diagonal folds do not match - so there are 2 lines of symmetry.

Try it: interactive practice

This is the week's practice game. Work through it right here - try each step yourself, then check your thinking.

Activity

Sort and Fold the Shapes

Sorting by dimension and counting attributes turns shape names into something you can reason about, and the fold tool makes symmetry a thing you see rather than memorize.

Question 1 of 7

Which shape has exactly 3 sides and 3 corners?

Hands-on challenge

Build and Fold Shapes

What you need

Paper
Scissors
Shape nets to fold (optional)
Pencil

Steps

1
Cut out 2D shapes from paper and fold each one to find all its lines of symmetry; mark each fold line with a pencil.
2
Build a cube or box from a net (a flattened pattern) and count its faces, edges, and vertices as you fold it up.
3
Make a shape chart listing each shape and its attributes.

You've got it when: Your chart correctly lists sides/corners for flat shapes and faces/edges/vertices for solids, and your folded shapes show their true lines of symmetry.

Checkpoint

Quick checks before you move on. Try each one first, then reveal the answer.

1
What 2D shape has 4 equal sides and 4 corners?
Show answer
A square.
2
How many edges does a cube have?
Show answer
12 edges.
3
How many lines of symmetry does a square have?
Show answer
4 (two through the middles of the sides and two through the corners).

Think about it

How are 2D and 3D shapes connected? Pick a 3D shape and describe the 2D shapes you see in its faces.

Challenge problem

A shape has 5 faces, 8 edges, and 5 vertices. One face is a square and the rest are triangles. What 3D shape is it?

Show hint

Picture a shape with a flat bottom and triangle sides that meet at a single point on top.

Show answer

A square pyramid. Its square base plus four triangular faces make 5 faces, and the base's corners plus the top point make 5 vertices.

Extension · go further

Design a symmetrical butterfly or mask by drawing one half, folding, and tracing so both sides match. Then mark its line of symmetry.

Finished the lesson, activity, and challenge? Mark this week complete to track your progress through the 10-week course.