Practice Abstraction Level in Math
Use these practice problems to test your method after reviewing the concept explanation and worked examples.
Quick Recap
The degree of generality at which a mathematical concept or expression is stated, ranging from specific numerical cases to fully universal symbolic forms.
2+3=5 is concrete. a+b=b+a is abstract. 'Groups have associativity' is more abstract.
Example 1
easyRank from most concrete to most abstract: 3 + 5 = 8, a + b = b + a, x + 5 = 8.
Example 2
mediumExplain why (a+b)^2 = a^2 + 2ab + b^2 is more useful than 5^2 = 25.
Example 3
easyWhich is more abstract: 'the area of a 3×5 rectangle is 15' or 'A = lw'?
Example 4
mediumWhat abstraction level jump occurs from 'triple any number and add one' to f(x) = 3x + 1?