Hone

Lessons · Teaching · classifying shapes, and the angles inside them

Shapes are classified by what they must have, not what they look like

A square is a rectangle, because a rectangle is any quadrilateral with four right angles and a square has four. Classification is by properties, and the categories nest: every square is a rectangle, every rectangle a parallelogram, every parallelogram a quadrilateral.

Hone is a place to practise a career, one idea a day. This is one of its lessons, written out in full and free to read without an account.

In beta. This lesson was written for Hone and has not yet been checked by a state certification officer. Practice material, not professional advice. What that means.

What it is for

A child says a square stops being a square when you turn it forty-five degrees, because they learned the picture rather than the properties. And 'is a square a rectangle?' is the question that reveals whether a teacher learned the same way.

How to think about it

For any shape, list what must be true: number of sides, which sides are equal, which are parallel, which angles are right. Compare that list to the definitions rather than to a remembered picture. Orientation is never part of a definition.

Worked example

Every square is a rectangle, and not every rectangle is a square
Nesting runs one way. The special case belongs to the general one.
Angles in any triangle add to 180 degrees; in any quadrilateral, 360
True for every one of them, however odd the shape looks.
A right angle is 90 degrees, acute is less, obtuse is more than 90 and less than 180
Three words that an examination uses and expects back.
A shape turned on its corner has not changed what it is
Orientation appears in no definition of anything.

Your turn

Name the total of the angles inside any triangle, in degrees.

The angles in a triangle add to  degrees

The trap

Teaching a diamond as a shape. It is a square or a rhombus that has been rotated, and calling the rotation a new shape is exactly the misconception that makes classification fail.

Next in Teaching

Every Teaching lesson on one page

Practise classifying shapes, and the angles inside them on HoneA question on it now, a real problem where there is one, and it is remembered for review. Free, no email needed.