Vocab

=Year 7 (Revise in Year 8)= algebra brackets commutative equals (=) equation expression evaluate prove simplify, simplest form solution (of an equation) solve (an equation) squared substitute symbol term therefore ( ∴   ) unknown value variable verify

=Year 8= Algebra Equations, formulae and identities algebraic expression collect like terms formula, formulae linear equation linear expression multiply out (expressions) prove, proof transform verify

=A - Z Maths Vocab= ** Absolute value ** A number's distance from zero (0) on a number line. The absolute value of both 4, written |4|, and negative 4, written |-4|, equals 4.

An angle with a measure of less than 90 degrees.
 * Acute Angle **

The number (0), that is, adding 0 does not change a number's vale (e.g., 5 + 0 = 5).
 * Additive identity **

A number and its additive inverse have a sum of zero (0) (e.g., in the equation 3 + -3 = 0, 3 and -3 are additive inverses of each other).
 * Additive inverse property **

A mathematical sequence in which two expressions are connected by an equality symbol.
 * Algebraic equation **

A mathematical sentence in which two expressions are connected by an equality symbol.
 * Algebraic expression **

An expression containing numbers and variables (e.g., 7x), and operations that involve numbers and variables (e.g., 2//x// + //y// or 3//a// - 4). Algebraic expressions do not contain equality or inequality symbols.
 * Algebraic order of operations **

A mathematical expression that contains variables and describes a pattern or relationship.
 * Algebraic rule **

The shape made by two rays extending from a common end point, the vertex. Measures of angles are described using the degree system.
 * Angle **

The inside region of a two-dimensional figure measured in square units (e.g., a rectangle with sides of 4 units by 6 units contains 24 square units or has an area 24 square units).
 * Area **

The way in which three or more numbers are grouped for addition or multiplication does not change their sum or product (e.g., 2 + 3 = 3 +2 or 4 x 7 = 7 x 4).
 * Associative property **

The horizontal and vertical number lines used in a rectangular graph or coordinate grid system.
 * Axes **

** Base ** The line or plane upon which a figure is thought of as a resting.

** Break ** A zigzag on the line of the //x//- or //y//-axis in a line or a bar graph indicating that the data being displayed does not include all of the values that exist on the number line being used. Also called a //Squiggle.//

** Capacity ** The amount of space that can be filled. Both capacity and volume are used to measure three-dimensional spaces; how ever, capacity usually refers to fluids, whereas volume usually refers to solids.

The perimeter of a circle is called its circumference.
 * Circumference **

A two-dimensional figure whose beginning and ending points meet, such that the plane in which the figure lies is divided into two parts---the part inside the figure and the part outside the figure (e.g., circles, squares, rectangles).
 * Closed figure **

The order in which two numbers are added or multiplied does not change their sum or product (e.g., 2 + 3 = 3 +2 or 4 x 7 = 7 x 4).
 * Commutative property **

Two angles, the sum of which is exactly 90 degrees.
 * Complementary angles **

A whole number that has no more than two factors.
 * Composite **

Having a definite for or relating to an actual thing.
 * Concrete representations of numbers **

Figures or objects that are the same shape and the same size.
 * Congruent **

A network of evenly spaced, parallel horizontal and vertical lines especially designed for locating points, displaying data, or drawing maps.
 * Coordinate grid or system **

Numbers that correspond to points on a graph in the form (//x, y).//
 * Coordinates **

The units of measure developed and used in the United States. Customary units for length are inches, feet, yards and miles. Customary units for volume are cubic inches, cubic feet, and cubic yards. Customary units for capacity or fluid ounces, cups, pints, quarts, and gallons.
 * Customary units **

** Data displays ** Different ways of displaying data in tables, charts, or graphs, including pictographs, circle graphs, single, double, or triple bar and line graphs, histograms, stem-and-leaf plots, and scatter plots.

Any number written with a decimal point in the number. A decimal number falls between two whole numbers (e.g., 1.5 falls between 1 and 2). Decimal numbers smaller than 1 are sometimes called decimal fractions (e.g., five-tenths is written 0.5).
 * Decimal number **

A line segment from any point on the circle passing through the center to another point on the circle.
 * Diameter **

Obtaining the measure of an object by using measuring devices, either standard devices of the customary or metric systems, or nonstandard devices such as a paper clip or pencil.
 * Direct measure **

For any real numbers //a, b,// and //x, x//(//a + b) = ax + bx.//
 * Distributive property **

** Effects of operations ** The results of applying an operation to given numbers (e.g., adding two whole numbers results in a number greater than or equal to the original numbers).

An increase in size in all directions by a uniform amount.
 * Enlargement **

A mathematical sentence (e.g., 2//x// = 10) that equates one expression (2//x//) to another expression (10).
 * Equation **

Expressions that have the same value but are represented in a different format using the properties of numbers [e.g., //ax + bx = (a +b)x].//
 * Equivalent expressions **

Expressions that have the same value but are represented in a different format using the properties of numbers [e.g., //ax + bx = (a + b)x].//
 * Equivalent forms of a number **

The use of rounding and/or other strategies to determine a reasonably accurate approximation, without calculating an exact answer.
 * Estimation **

Substitute numbers for the variables and follow the operation symbols to find the numerical value of the expression.
 * Evaluate an expression **

Directions requesting a written description of the procedures for finding the solution to the problem presented.
 * Explain in words **

The number of times the base occurs as a factor. For example, 2^3 is the exponential form of 2x2x2. The numeral two (2) is called the base, and the numeral three (3) is called the exponent.
 * Exponent (exponential form)**

A collection of numbers, symbols, and/or operation signs that stands for a number.
 * Expression **

To estimate or infer a value or quantity beyond the known range.
 * Extrapolate **

** Face ** One of the plane surfaces bounding a three-dimensional figure (a side).

A number or expression that divides exactly another number (e.g., 1,2,3,4,5,10, and 20 are factors of 20).
 * Factor **

A graph having definable limits.
 * Finite graph **

** Flip ** A transformation that produces the mirror image of a geometric figure. Also called a [|//**reflection.**//]

Any part of a whole is called a fraction (e.g., one-half written in fractional form is 1/2.
 * Fraction **

The relationship between two sets (e.g., sets of numbers) in which each element of one set has one assigned element in the other set. See [|**//Pattern//**]
 * Function **

A table of //x-// and //y-//values (ordered pairs) that represents the function, pattern, relationship, or sequence between the two variables.
 * Function table **

** Grid ** A network of evenly spaced, parallel horizontal and vertical lines.

** Height ** A line segment extending from the vertex or apex of a figure to its base and forming a right angle with the base or basal plane.

A proposition or supposition developed to provide a basis for further investigation or research.
 * Hypothesis **

** Indirect measure ** Obtaining the measurement of an object through the known measure of another object.

A sentence that states one expression is greater than or equal to, less than, less than or equal to another expression (e.g., a does not = 5 or x < 7 ).
 * Inequality **

The numbers in the set {...,-4, -3, -2, -1, 0, 1, 2, 3, 4,...}.
 * Integers **

The value of a variable when all other variables in the equation equal zero (0). On a graph, the values where a function crosses the axes.
 * Intercept **

The point at which two lines meet.
 * Intersection **

An action that cancels a previously applied action. For example, subtraction is the inverse operation of addition.
 * Inverse operation **

A real number that can not be expressed as a ratio of two numbers (e.g., 20=2(//w//+4) + 2//w// and //y// = 3//x// + 4).
 * Irrational number **

** Labels (for a graph)** The titles given to a graph, the axes of a graph, or to the scales on the axes of a graph.

A one-dimensional measure that is the measurable property of line segments, The chance that something is likely to happen. [|//**See Probability.**//]
 * Length **
 * Likelihood **

A straight line that is endless in length.
 * Line **

A portion of a line that has a defined beginning and end (e.g., the line segment AB is between point A and point B).
 * Line segment **

An algebraic equation in which the variable quantify or quantities are in the first power and the graph is a straight line (e.g., 20 = 2(w + 4) + 2//w// and //y// = 3//x// + 4).
 * Linear equation **

** Mean ** The arithmetic average of a set of ordered numbers where half of the numbers are above the median and half are below it.

The middle point of a set of ordered numbers where half are below it.
 * Median **

The units of measure developed in Europe and used in most of the world. Like the decimal system, the metric system uses the base 10. Metric units for length are millimeters, centimeters, meters, kilometers. Metric units for weight are milligrams, grams, and kilograms. Metric units for volume are cubic millimeters, cubic centimeters, and cubic meters. Metric units for capacity are milliliters, centiliters, liters, and kiloliters.
 * Metric units **

The point on a line segment that divides it into two equal parts.
 * Midpoint of a line segment **

The score or data point found most often in a set of numbers.
 * Mode **

The numbers that result from multiplying a given number by the set of whole numbers (e.g., the multiples of 15 are 0, 15, 30, 45, 60, 75, etc....).
 * Multiples **

The number one (1), that is, multiplying by 1 does not change a number's value (e.g., 5 x 1= 5).
 * Multiplicative identity **

**Multiplicative inverse** (reciprocal) Any two numbers with a product of 1. (e.g., 4 and 1/4).

**Natural numbers** (counting numbers) The numbers in the set {1, 2, 3, 4, 5, ...}.

Used in scientific notation to designate a number smaller than one (1) (e.g., 3.45 x 10^-2 equals0.0345).
 * Negative exponent **

Units such as blocks, paper clips, crayons, or pencils that can be used to obtain a measure.
 * Nonstandard units of measure **

A line on which numbers can be written or visualized.
 * Number line **

** Obtuse angle ** An angle with a measure of more than 90 degrees but less than 180 degrees.

The ratio of one event occuring to it not occuring.
 * Odds **

Any mathmatical process, such as addition, subtraction, multiplication, division, exponents, or square roots.
 * Operation **

A method having fewer arithmetic calculations.
 * Operational shortcut **

The location of a single point on a rectangular coordinate system where the digits represent the position relative to the //x//-axis and //y//-axis [e.g., (//x,y//) or (3,4)]
 * Ordered pair **

To arrange data in a display that is meaningful and that assists in the interpretation of the data. See [displays|**//Data displays//**.]
 * Organize data **

** Parallel lines ** Two lines in the same plane that never meet. Also, lines with equal slopes.

** Pattern ** **(relationship)** A predictable or prescribed sequence of numbers, objects, etc. Patterns and relationships may be described or presented using munipulatives, tables, graphics (pictures or drwings), or algebraic rules (functions). Also called a [|__//**Relation.**//__]

A special-case ratio in which the second term is always 100. The ratio is written as a whole number followed by a percent sign (e.g., 25% means the ratio of 25 to 100).
 * Percent **

The length of the boundary around a figure.
 * Perimeter **

Forming a right angle.
 * Perpendicular **

The symbol designating the ratio of the circumference of a circle to its diameter, represented as either 3.17 or 22/7.
 * Pi **

The position of a single digit in a whole number or decimal number containing one or more digits.
 * Place value **

The intersection of a plane and a three-dimensional figure.
 * Planar cross section **

An undefined, two-dimensional (no depth) geometric surface that has no boundries specified. A plane is determined by defining points or lines exisiting on the plane.
 * Plane **

A two-dimensional figure that lies entirely within a single plane.
 * Plane figure **

A location in space that has no length or width.
 * Point **

A closed plane figure whose sides are straight lines and do not cross.
 * Polygon **

Any whole number with only two factors, 1 and itself (e.g., 2, 3, 5, 7, 11, etc.).
 * Prime number **

A three-dimensional figure (polyhedron) with congruent polygonal bases and lateral faces that are all parallelograms.
 * Prism **

The likelihood of an event happening. An impossible event has a probability of zero. An event that will occur with absolute certainty is assigned a probability of one. Every event that is neither certain nor impossible has a probability that is between zero and one, and is obtained by dividing the number of favorable outcomes of an event by the total number of possible outcomes.
 * Probability **

The likelihood of an event happening that is based on experience and observation rather than on theory.
 * Probability, empirical **

The likelihood of an event happening that is based on theory rather than on experience and observation.
 * Probability, theoretical **

A set of steps that demonstrates the truth of a given statement. Each step can be justified with a reason, such as a given, a definition, an axiom, or a previously proven property.
 * Proof **

** Pythagorean theorem ** The square of the hypotenuse (//c//) of a right triangle is equal to the sum of the square of the legs (//a// and //b//), as shown in the equation //c^//2=//a//^2+//b//^2.

** Quadrant ** Any of the four regions formed by the axes in a rectangular coordinate system.

** Radical sign ** The symbol used before a number to show that the number is radicand.

A number that appears with a radical sign.
 * Radicand **

A line segment exrtending from the center of a circle or sphere to a point on the circle or sphere.
 * Radius **

The difference between the highest (H) and the lowest (L) value in a set of data; sometimes calculated as H - L + 1.
 * Range of a set of numbers **

Calculations involving rates, distances, and time intervals, based on the distance, rate, time formula (D = //r t//).
 * Rate/distance **

**Ratio** The compression of two quantities (e.g., the ratio of //a// and //b// is a/b, where b doesn't equal zero).

A real number that can be expressed as a ratio of two integers.
 * Rational number **

A portion of a line that begins at a point and goes on forever in one direction.
 * Ray **

All rational and irrational numbers.
 * Real numbers **

see [|__//**Multiplicative inverse.**//__]
 * Reciprocal **

see [|__//**Flip.**//__]
 * Reflection **

A number or expression is equal to itself (e.g.,//ab// = //ab//).
 * Reflexive axiom of equality **

A polygon that is both quilateral and quiangular.
 * Regular polygon **

see [|__//**Pattern.**//__]
 * Relation (relationship)**

The size of one number in comparison to the size of another number or numbers.
 * Relative size **

**Right angle** An angle whose measure is exactly 90 degrees.

A cylinder in which the bases are parallel circles perpendicular to the side of the cylinder.
 * Right circular cylinder **

Finding the measures of missing sides or angles of a right triangle when given the measures of other sides or angles. See [|__//**Pythagorean theorem.**//__]
 * Right triangle geometry **

The change in //y// going from one point of //y// to another (the horizontal change on the graph.)
 * Rise **

** Rotation ** A transformation of a figure by turning it about a center point or axis. The amount of rotation is usually expressed in the number of degrees (e.g., a 90 degree rotation). Also called a [|__//**Turn.**//__]

**Rule** A mathmatical expression that describes a pattern or relationship, or a written description of the pattern or relationship.

The change in //x// going from one point of //y// to another (the horizontal change on the graph).
 * Run **

**Scale model** A model or drwaing based on a ratio of the dimensions for the model and the actual object it represents (e.g., a map). The numeric values assigned to the axes of a graph.
 * Scales **

A graph of data points, usually from an experiment, that is used to observe the relationship between two variables.
 * Scatter plot **

A shorthand method of writing very large or very small numbers using exponents in which a number is expressed as the product of a power of 10 and a number that is greater than or equal to one (1) and less than 10 (e.g.,7.59 x 10^5=759,000). It is based on the idea that is easier to read exponents than it is to count zeros. If a number is already a power of 10, it is simply written 10^27 instead of 1 x 10^27.
 * Scientific notation **

An ordered list with either a constant difference (arithmetic) or a constant ratio (geomtric).
 * Sequence **

The edge of a geometric figure (e.g., a triangle has three sides).
 * Side **

Two figures that are the same shape, have corresponding, congruent angles, and having coorisponding sides that are proportional in length.
 * Similar figures **

Figures that are the same shape are similar; they are not necessarily the same size or in the same position.
 * Similarity **

** Slide ** To move along in constant contract with the surface in a vertical, horizontal, or diagonal direction. Also called a [|__//**Translation.**//__]

The incline of a line, defined by the ratio of the change in units on the vertical axis to the change in one unit on the horizontal axis.
 * Slope **

Three-dimensional figures that completely enclose a portion of space (e.g., a reatangularsolid, cube, sphere, right circular cylindar, right ciscular cone, and regular square pyramid).
 * Solid figures **

Relationships of figures existing or happening in space.
 * Spatial relationships **

A positive real number that can be multiplied by itself to produce a given number (e.g., the square root of 144 is 12, or =12).
 * Square root **

see [|__//**Break.**//__]
 * Squiggle **

The measurement of an object by using accepted measuring devices and units of the customary or metric system.
 * Standard units of measure **

An angle whose measure is exactly 180 degrees.
 * Straight angle **

Two angles, the sum of which is exactly 180 degrees.
 * Supplementary angles **

The sum of the area of the faces of the figure that create the geometric solid.
 * Surface area of a geometric solid **

A symbol or set of symbols expressing a mathmatical quantity or operation (e.g., 2//x// is equal to two times //x//).
 * Symbolic expression **

Being expressed by symbols (e.g., circles shaded to represent 1/4, or variables used to represent quantities).
 * Symbolic representations of numbers **

When a line can be drawn through the center of a figure such that the two halves are congruent.
 * Symmetry **

A group of two or more equations that share variables. The solution to a system of equations is an ordered number set that makes all of the equations true.
 * Systems of equations **

** Tessellation ** A covering of a plane with congruent copies of the same pattern with no holes and no overlaps, like floor tiles. Transformation ** An operation on a geometric figure by which another image is created. Common transformations include flips, slides, and turns. Transitive property ** When the first element has a particular relationship to a third element that in turn has the same relationship to a third element, the first has this same relationship to the third element (e.g., if //a = b// and //b = c,// then //a = c//)//.// Identity and equality are transitive relationships. Translation ** see __//**[|Slide.]**//__ Tree diagram ** A diagram in which all the possible outcomes of a given event are displayed.

see [|__//**Rotation.**//__]
 * Turn **

**Unorganized data** Data that are presented in a random manner.

** Variable ** Any symbol that could represent a number. Vertex ** The common endpoint from which two rays begin (i.e., the vertex of an angle) or the point where two lines intersect; the point on a triangle or pyramid opposite to and farthest from the base. Vertical angles ** The oppisite angles formed when two lines intersect. Volume ** The amount of space occupied in three dimensions and expressed in cubic units. Both capacity and volume are used to measure empty spaces; however, capacity usually refers to fluids, whereas volume usually refers to solids. Weight ** Measures that represent the force that attracts an object to the center of Earth. In the customary system, the basic unit of weight is the pound. Whole numbers ** The numbers in the set {0, 1, 2, 3, 4,...}. x-intercept ** The value of //x// on a graph when //y// is zero (0). The //x//-axis is the horizontal number line on a rectangular coordinate system. y-intercept ** The value of //y// on a graph when //x// is zero (0). The //y//-axis is the vertical number line on a rectangular coordinate system.