Examples:

tally count  Marks such as //// //// used to keep track of an amount to be counted.

tangent  Intersecting at exactly one point.

term  In an algebraic expression or equation, a number or a product of a number and one or more variables.  For example, the terms of the expression 5y + 3k – 8 are 5y, 3k, and 8.  A variable term is a term that contains at least one variable.  For example, in the equation 4b – 8 = b + 5, 4b and b are variable terms.  A constant term is a term that does not contain a variable.  For example, in the equation 4b – 8 = b + 5, 8 and 5 are constant terms.  See also like terms.

terminating decimal  A decimal which ends; a repeating decimal in which the repeating digit is 0.  For example, 0.5 and 0.125 are terminating decimals.  See decimal.

tessellation  An arrangement of closed shapes that covers a surface completely without overlaps or gaps.  See also tile.

test number  A number used to replace a variable in an equation when using the trial-and-error method for finding a solution.  Test numbers are useful when trying to “close in” on the exact solution of an equation.

tetrahedron  See regular polyhedron.

theorem  A mathematical statement that can be proved to be true (or, sometimes, a statement that is proposed and needs to be proved).  For example, the Pythagorean Theorem states that if the legs of a right triangle have lengths a and b, and the hypotenuse has a length c, then a˛ + b˛ = c˛.

three-dimensional (3-D)  Not lying completely within a single flat surface.  Three-dimensional objects have depth, or thickness, as well as length and width.

tile  A shape used in a tessellation.  If only one shape is repeated in a tessellation, the tessellation is called a same-tile tessellation.

tiling  Covering a surface with uniform shapes so there are no gaps or overlaps, except possibly gaps around the edges.  Also called a tessellation.

time graph  A graph that is constructed from a time story and shows what has happened through a progression of time.

top-heavy fraction  A fraction that names a number greater than or equal to 1; a fraction whose numerator is equal to or greater than its denominator.  Examples of top-heavy fractions are 7/3, 5/5, 9/7, and 16/4.  Also called improper fraction.

topography  The surface features of a region or country; rivers, mountains, plains, and so on.

topological property  See topology.

topological transformation  See topology.

topologically equivalent  In topology, a term for shapes that can be transformed into each other with a topological transformation.  See also genus.

topology  A modern branch of mathematics that deals, among other things, with the properties of geometric objects that remain the same when the objects are changed by certain operations, such as shrinking, stretching, or twisting.  Tearing, breaking, poking holes, and “sticking together” are not permitted.  Transformations that follow these rules are called topological transformations.  Properties of a figure that a not changed by topological transformations are called topological properties.  Examples of topological properties include the order of points on a curve and the number of holes in a shape (its genus).

township  A square land unit 6 miles on each side (area 36 square miles).

transformation  An operation on a geometric figure that produces a new figure, called the image, from the original figure, called the preimage.  Transformations are sometimes thought of as “motions” that move a figure from one place to another, and possible change its size or shape.

transformation geometry  The study of transformations.

translation  A transformation in which a figure “slides” along a line.

translation tessellation  A tessellation created by translating (sliding) curves from one side of a figure (such as a square) to the opposite side.  The resulting figure is then translated to create the interlocking pieces in the tessellation.

transparent mirror  A piece of transparent plastic used to draw and study reflections.

transversal  A line which intersects two or more other lines.

trapezoid  A quadrilateral with exactly one pair of parallel sides.

tree diagram  A tool used to solve probability problems in which there is a series of events.  The tree diagram in the margin represents a situation where the first event has 4 possible outcomes and the second event has 2 possible outcomes.

trial-and-error method  A method for finding the solution of an equation by trying several test numbers.

triangle  A polygon with three sides.  An equilateral triangle has three sides of the same length.  An isosceles triangle has two sides of the same length.  A scalene triangle has no sides of the same length.

triangular numbers  Figurate numbers that can be shown by a triangular arrangement of dots.

trillion  A digit or digits followed by 12 whole-number places.  One trillion written in number form is 1,000,000,000,000 or 1012.

truncate  To discard all digits to the right of a particular place; to slice off a piece of a pyramid or cone.

turn-around fact  See arithmetic fact.

twin primes  Two prime numbers that are separated by just one composite number.  For example, 3 and 5 are twin primes, because they are separated by the composite number 4.  The numbers 11 and 13 are also twin primes.

two-dimensional (2-D)  Lying completely within a plane.  Two-dimensional objects have length and width but not thickness.