Abstraction Level Math Example 3

Follow the full solution, then compare it with the other examples linked below.

Example 3

easy
Which is more abstract: 'the area of a 3×5 rectangle is 15' or 'A=lwA = lw'?

Solution

  1. 1
    'A=lwA = lw' is more abstract — it works for any length and width.
  2. 2
    'Area = 15' is a specific case of A=lwA = lw with l=3,w=5l=3, w=5.

Answer

A=lwA = lw is more abstract.
The formula A=lwA = lw is a general relationship, while '15 square units' is one instance. Moving from specific to general is the essence of algebraic abstraction.

About Abstraction Level

The degree of generality at which a mathematical concept or expression is stated, ranging from specific numerical cases to fully universal symbolic forms.

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More Abstraction Level Examples

Example 1 easy

Rank from most concrete to most abstract: [formula], [formula], [formula].

Example 2 medium

Explain why [formula] is more useful than [formula].

Example 4 medium

What abstraction level jump occurs from 'triple any number and add one' to [formula]?

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Related Concepts

VariablesGeneralization