Examples:

face  A flat surface on a 3-dimensional shape.

fact  See arithmetic fact.

fact family  A group of addition or multiplication facts together with the related subtraction or division facts.  For example, 5 + 6 = 11, 6 + 5 = 11, 11 – 5 = 6, and 11 – 6 = 5 form an addition fact family.  5 * 7 = 35, 7 * 5 = 35, 35/7 = 5, and 35/5 = 7 form a multiplication fact family.

factor (noun)  A number that is multiplied by another number.  Factors may be whole numbers or rational numbers expressed as fractions or decimals.  For example, 4, 3, and 2 are factors of 24, because 4 * 3 * 2 = 24, 0.5 and 25 are factors in 0.5 * 25; ½ and 9 are factors in ½ * 9; and –2 and –5 are factors in –2 * (-5).  See also multiplication.

factor (verb)  To represent a quantity as a product of factors.  For example, 20 factors to 4 * 5; 3x + 6 factors to 3(x + 2).factorial  The product of a natural number n and all natural numbers smaller than n, written n!  For example:

            3! = 3 * 2 * 1 = 6                                3! is read as “three factorial.”

            4! = 4 * 3 * 2 * 1 = 24                        4! is read as “four factorial.”

For any number N,

            N! – N * (N – 1) * (N – 2) *…* 1     N! is read a “N factorial.”

factor of a whole number n  A whole number, which, when multiplied by another whole number, results in the number n.  The whole number n is divisible by its factors.  For example, 4 and 7 are factors of 28 because 4 * 7 = 28, and 28 is divisible by 4 and 7.

factor pair  Two whole-number factors of a number n whose product is the number n.  A number may have more than one factor pair.  For example, the factor pairs for 21 are 1 and 21, and 3 and 7.

factor rainbow  A way of showing factor pairs in a list of all the factors of a number.  This can be helpful in checking whether a list of factors is correct.

factor string  A name for a number written as a product of at least two whole-number factors.  For example, a factor string for the number 24 is 2 * 3 * 4.  This factor string has three factors, so its length is 3.  The number 1 is never part of a factor string.  For example, 1 * 2 * 3 * 4 is not a factor string for 24.

factor tree  A method used to obtain the prime factorization of a number.  The original number is represented as a product of factors, and each of those factors is represented as a product of factors, and so on, until the factor string consists of prime numbers.

fair  A coin or die is said to be fair if, over a large number of tosses, the results are consistent with the predictions of probability.  On a fair coin, heads and tails should come up about equally often; the six sides of a fair die should come up about equally often.

fair game  A game in which each player has the same chance of winning.  If any player has an advantage, or disadvantage (for example, by playing first), then the game is not fair.

fathom  A unit of measure equivalent to 6 feet; used mainly by people who work with boats and ships to measure depths under water and lengths of cables and cords.

figurate numbers  Numbers which can be shown by dots arranged in specific geometric patterns.  For example, rectangular numbers, square numbers, and triangular numbers are examples of figurate numbers.

formula  A general rule for finding the value of something.  A formula is usually written as an equation with variables representing unknown quantities.  For example, a formula for distance traveled at a constant rate of speed is d = r * t, where d stands for distance, r for rate, and t for time.

fraction  A number in the form a/b, where a and b are whole numbers and b is not 0.  Fractions are used to name part of a whole object or part of a whole collection of objects, or to compare two quantities.  A fraction can represent division; for example 2/3 can be thought of as 2 divided by 3.

frequency  The number of times an event or value occurs in a set of data.

friction  A surface resistance to motion.

fulcrum  A point on a mobile at which a rod is suspended; in general, the point or place around which a lever pivots.  See also mobile.

function machine  An imaginary machine that processes numbers according to a certain rule.  A number (input) is put into the machine and is transformed into a second number (output) by application of the rule.

furlong  A unit of distance most commonly used in horse racing.  There are 40 furlongs in 5 miles.