K–2Geometry & TopologyLesson available
Shapes
Recognising, naming, sorting and building two- and three-dimensional shapes by their attributes, such as number of sides and corners and whether faces are flat or curved.
math.geom.shapes
Builds on
No prerequisites — start here!
You will learn to
- Name and describe circles, triangles, squares, rectangles, cubes, cylinders, cones and spheres, whatever their size or orientation.
- Sort shapes by attributes such as the number of sides or corners, and explain the sorting rule.
- Compose larger shapes from smaller ones and decompose shapes into parts.
Definition
- A triangle is a closed flat shape with three straight sides.
- A side is a straight edge of a flat shape; a corner (vertex) is where two sides meet.
- A square is a rectangle whose four sides all have the same length.
Theorem
- Turning or moving a shape does not change what shape it is.
- Every square is a rectangle, but not every rectangle is a square.
Common misconceptions
- Thinking a square turned onto a corner is no longer a square.
- Believing a triangle must have a flat bottom or equal sides.
- Treating colour or size as part of what makes a shape a triangle or a square.
Leads to
Optional discoveries
- Sets Sorting shapes into overlapping groups, such as 'four-sided' and 'red', leads to Venn diagrams.
- Surfaces, polyhedra and the Euler characteristic Counting the corners, edges and faces of solid shapes leads to Euler's formula V − E + F = 2, one of the founding results of topology.Wonder Trail →