Function, Product, and Mean in Mathematics

Recognize math's exact meanings for words used loosely in everyday life.

Mathematics depends on precise definitions, so common words take on fixed meanings. A 'function' is a rule that assigns exactly one output to each input; in daily speech, function just means purpose. A 'product' is the result of multiplication, not something sold in a store. The 'mean' is the arithmetic average, found by adding values and dividing by how many there are; it has nothing to do with being unkind. 'Range' is the difference between the largest and smallest values in a data set, and 'odd' describes integers not divisible by two.

Worked example: 'Find the mean of the products of each pair: (2, 3) and (4, 5). ' The products are 6 and 20. Their mean is (6 + 20) / 2 = 13. A student who misreads either word solves the wrong problem. In math, a word problem is a vocabulary test before it is a calculation.

• 1A function assigns exactly one output to each input.
• 2A product is the result of multiplication.
• 3The mean is the average; the range is max minus min.