MTEL Math Elementary (68) key terms

The value a digit has because of its position in a numeral; in 4,706 the 7 means 700 because it sits in the hundreds place, while the 4 means 4,000.

A positional system that groups quantities in powers of ten, so each place is worth ten times the place to its right and regrouping moves value between adjacent places.

A way of writing a number as the sum of the values of its digits, such as 3,052 = 3,000 + 50 + 2, which makes place value explicit.

Trading one unit in a place for ten units in the place to its right, or the reverse, to carry or borrow during addition and subtraction.

A step-by-step procedure that works for all numbers of a given operation, such as lining up place values and carrying when adding multi-digit whole numbers.

The separate products formed when multiplying by each place value of a factor, later added together; for 23 × 4 the parts are 80 and 12.

A whole number that divides another number with no remainder; 1, 2, 3, 4, 6, and 12 are all factors of 12.

The result of multiplying a whole number by any counting number; the multiples of 6 include 6, 12, 18, 24, and so on without end.

A whole number greater than 1 whose only whole-number factors are 1 and itself, such as 2, 3, 5, 7, and 11.

A whole number greater than 1 that has at least one factor other than 1 and itself, such as 9, which equals 3 × 3.

Writing a composite number as a product of primes; 60 = 2 × 2 × 3 × 5, and the result is unique apart from order.

The largest number that divides two or more given numbers evenly; the greatest common factor of 18 and 24 is 6.

The smallest nonzero number that is a multiple of two or more given numbers; the least common multiple of 4 and 6 is 12.

Fractions that name the same amount even though their numerators and denominators differ, such as 1/2, 2/4, and 5/10.

A fraction written so the numerator and denominator share no common factor other than 1; 6/8 in simplest form is 3/4.

A shared multiple of the denominators of two or more fractions, needed so the fractions can be compared or added and subtracted.

A base-ten numeral using a decimal point to mark the ones place, so digits to the right record tenths, hundredths, thousandths, and smaller parts of one.

A ratio out of 100, so 35% means 35 per 100, which equals 0.35 and the fraction 35/100.

A comparison of two quantities by division; a ratio of 3 to 4 can be written 3:4 or 3/4 and describes a multiplicative relationship.

A rate expressed per one unit of the second quantity, such as 45 miles per hour or $2.50 per pound, found by dividing the two measures.

Any of the whole numbers together with their negatives, such as −7, 0, and 12, but not fractions or decimals.

The distance of a number from zero on the number line, always zero or positive; both 6 and −6 have absolute value 6.

A straight line marked with evenly spaced points representing numbers, used to compare values, show order, and model addition and subtraction.

A statement describing how each term in a sequence is produced from earlier terms, such as add 4 each time or multiply by 3.

A number pattern in which the same amount is added to each term to get the next, as in 5, 9, 13, 17, where the common difference is 4.

A number pattern in which each term is multiplied by the same factor to get the next, as in 2, 6, 18, 54, where the ratio is 3.

A letter or symbol that stands for an unknown or changing number in an expression or equation, such as n in 3n + 5.

A mathematical phrase combining numbers, variables, and operation signs without an equals sign, such as 4x − 7 or 2(a + 3).

A statement that two expressions have the same value, joined by an equals sign, such as 2x + 1 = 11, which is true only for certain values.

An operation that undoes another, such as addition and subtraction or multiplication and division, used to isolate a variable when solving equations.

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.

The rule that multiplying a sum by a number gives the same result as multiplying each addend separately and adding, as in 4(2 + 5) = 8 + 20.

A rule that assigns exactly one output value to each input value, often shown in a table, graph, or equation such as y = 2x + 1.

A grid formed by a horizontal x-axis and vertical y-axis meeting at the origin, used to graph ordered pairs and show relationships between two quantities.

Two numbers written in a fixed order, (x, y), locating a point on the coordinate plane by its horizontal and vertical positions from the origin.

A closed plane figure made of straight line segments that meet only at endpoints, such as triangles, quadrilaterals, pentagons, and hexagons.

A polygon with exactly four sides and four angles; squares, rectangles, parallelograms, trapezoids, and rhombuses are all quadrilaterals.

A quadrilateral with two pairs of parallel sides, whose opposite sides and opposite angles are equal, and whose area equals base times height.

The total distance around the outside of a closed figure, found by adding the lengths of all its sides.

The number of unit squares needed to cover a flat region, measured in square units; a rectangle's area equals length times width.

The amount of space a solid figure occupies, measured in cubic units; a rectangular prism's volume equals length times width times height.

The total area of all the faces of a three-dimensional figure, found by adding the areas of each face, measured in square units.

Having exactly the same size and shape, so one figure can be moved onto the other by turns, flips, or slides without changing dimensions.

Figures with the same shape but not necessarily the same size, whose corresponding angles are equal and whose corresponding side lengths share a constant ratio.

A line that divides a figure into two halves that match exactly when the figure is folded along that line.

A move that changes a figure's position or size on a plane, including translations (slides), reflections (flips), rotations (turns), and dilations (resizings).

The ratio that compares a length in a scale drawing or similar figure to the corresponding length in the original, such as 1 inch to 5 feet.

Changing a measurement from one unit to another by multiplying by a ratio equal to one, such as 3 feet per yard or 1,000 milliliters per liter.

The balance-point average of a data set, found by adding all values and dividing the sum by the number of values.

The middle value of a data set arranged in order; with an even number of values it is the mean of the two middle values.

The value that appears most often in a data set; a set may have one mode, several modes, or none at all.

The spread of a data set, found by subtracting the least value from the greatest value.

A value far from the rest of the data that can pull the mean noticeably while affecting the median very little.

A number from 0 to 1 describing how likely an event is, often computed for equally likely outcomes as favorable outcomes divided by total outcomes.

The set of all possible outcomes of an experiment, such as the six results of rolling one number cube.

The event consisting of all outcomes in the sample space that are not in a given event; its probability equals 1 minus the event's probability.

A display that places a mark above a number line for each data value, showing how often each value occurs and revealing clusters or gaps.

A bar graph for numerical data grouped into equal intervals, where bar height shows frequency and bars touch to signal a continuous scale.