FTCE Middle Grades Math 5-9 (025) key terms

Any number that can be written as a fraction with an integer numerator and a nonzero integer denominator. Its decimal form either terminates or repeats, as with 3/4, −7, and 0.25.

A real number that cannot be expressed as a ratio of two integers. Its decimal expansion never terminates and never repeats, as in the cases of pi, the square root of 2, and e.

The distance of a number from zero on the number line, which is always nonnegative. Written |x|, it equals x when x is zero or positive and −x when x is negative.

The unique expression of a whole number greater than one as a product of prime numbers, such as 60 = 2 squared times 3 times 5. It supports work with common factors and multiples.

The smallest positive number that is a multiple of two or more given whole numbers. For 6 and 8 the least common multiple is 24, and it serves as a common denominator.

The largest whole number that divides two or more given numbers with no remainder; for 18 and 24 it is 6. It is used to simplify fractions and factor expressions.

A comparison of two quantities by division, written as a to b, a:b, or a/b. A rate is a special ratio that compares quantities measured in different units.

A number from the set of whole numbers and their opposites: ..., −2, −1, 0, 1, 2, .... Integers have no fractional or decimal part and are closed under addition, subtraction, and multiplication.

The agreed sequence for evaluating expressions: grouping symbols first, then exponents, then multiplication and division left to right, then addition and subtraction left to right, often remembered as PEMDAS.

A value that, when multiplied by itself, produces the original number; the square root of 49 is 7 because 7 times 7 equals 49. Every positive number has one positive and one negative square root.

A letter or symbol that stands for a quantity whose value is unknown or may change within an expression, equation, or formula, such as x in 3x + 5.

The numerical factor that multiplies a variable in an algebraic term. In the term −7x squared, the coefficient is −7, while in x the coefficient is understood to be 1.

An equation whose graph is a straight line because each variable appears only to the first power and no variables are multiplied together. An example is 2x + 3y = 12.

A measure of how steep a line is, computed as the change in y divided by the change in x between two points on the line. Horizontal lines have a slope of zero.

The point where a graph crosses the vertical axis, which happens where x equals zero. In the form y = mx + b, the value b gives the y-intercept.

A rule that assigns to each allowed input exactly one output. A relation stops being a function when a single input is paired with two or more different outputs.

Two or more linear equations considered together, where a solution is an ordered pair or set of values satisfying all equations at once. Graphically the solution is where the lines intersect.

A mathematical statement comparing two expressions using the symbols <, >, ≤, or ≥. Its solutions form a range of values, and multiplying or dividing by a negative number reverses the symbol.

The total distance around the boundary of a two-dimensional figure, found by adding the lengths of its sides. For a rectangle the formula is 2 times the sum of length and width.

The distance around a circle, calculated as 2 times pi times the radius or as pi times the diameter. Pi is the constant ratio of a circle's circumference to its diameter.

The number of square units needed to cover a two-dimensional region, reported in units such as square centimeters. Each shape has its own formula, such as length times width for rectangles.

The amount of space a three-dimensional solid occupies, measured in cubic units. For a rectangular prism it is length times width times height.

The combined area of every face and curved surface of a three-dimensional figure, measured in square units. It answers questions about how much material is needed to cover a solid.

The relationship stating that in a right triangle the square of the hypotenuse equals the sum of the squares of the two legs, written a squared plus b squared equals c squared.

Figures that share the same shape but not necessarily the same size. Their corresponding angles are equal and their corresponding side lengths are proportional.

The ratio comparing a length in an image, model, or drawing to the matching length in the original. It multiplies lengths once but multiplies areas by its square.

Two angles whose measures add up to 180 degrees. They need not be next to each other, though adjacent supplementary angles form a straight line.

A change to a figure's position, size, or orientation on the coordinate plane, produced by a translation, rotation, reflection, or dilation. Translations, rotations, and reflections preserve shape and size.

The arithmetic average of a data set, found by adding all the values and dividing by how many values there are. Outliers can pull the mean noticeably toward them.

The middle value of a data set arranged in order, or the average of the two middle values when the number of values is even. It is resistant to the pull of outliers.

The difference between the greatest and least values in a data set. It is a quick measure of spread, but it depends on only two values and ignores the rest.

The difference between the third quartile and the first quartile of a data set, describing how spread out the middle half of the values is. It is often paired with a box plot.

A number between 0 and 1 expressing how likely an event is. When outcomes are equally likely, it equals the number of favorable outcomes divided by the total number of outcomes.

The complete set of all possible outcomes of a probability experiment. For a single roll of a standard number cube, the sample space is the numbers 1 through 6.

A graph that displays paired quantitative data as points on a coordinate plane, used to look for patterns such as positive or negative association, clusters, and outliers.

Ongoing checks of student understanding carried out during instruction, such as exit tickets or quick quizzes, used to adjust teaching rather than to assign a grade.

An evaluation given at the end of a unit, course, or term to measure what students have learned overall. Results are typically graded and reported to students and families.

Planning that adapts content, process, or product to students' readiness, interests, and learning profiles while keeping the same core learning goals for everyone.

A physical object such as fraction circles, tiles, or blocks that students handle to build concrete understanding of a mathematical idea before working with symbols.

Temporary instructional support, such as worked examples, guiding prompts, or visual models, that is gradually withdrawn as learners become able to work independently.

A scoring guide that lists criteria and describes levels of performance, used to judge open-ended work consistently and to communicate expectations clearly to students in advance.