Vocabulary Variables & Patterns Number Properties and Algebraic Equations

Variable A quantity that can change: a letter is used to represent a variable #1 DefinitionDrawing/Example X 15 + n 8p variables = x, n, p

Coordinate Graph A graph using pairs of related values that shows a relationship between an independent variable (x-axis) and dependent variable (y-axis) #2 DefinitionDrawing/Example Time (minutes) Laps around pool Mark’s laps around his pool (6,15)

Dependent Variable Value of this variable depends upon or is determined by the other variable (called the independent variable) It is labeled on the y-axis #3 DefinitionDrawing/Example The cost of a long distance phone call (dependent variable) DEPENDS on how long you talk (independent variable)

Y-Axis the number line that is VERTICAL on a coordinate graph #4 DefinitionDrawing/Example Y-AXIS

Independent Variable #5 DefinitionDrawing/Example This variable’s value determines the value of the other variable, called the dependent variable. It is labeled on the x-axis. The number of people that register for a bike tour (independent variable) determines the cost for renting bikes (dependent variable).

X-Axis the number line that is HORIZONTAL on a coordinate graph #6 DefinitionDrawing/Example X-AXIS

Scale the equal- spaced labeling used on each axis of a coordinate grid #7 DefinitionDrawing/Example the x-axis scale is by 2’s -- the y-axis scale is by 5’s. 0

Coordinate Pair (x, y) an ordered pair of numbers used to locate a point on a coordinate graph 1 st number – (x-coordinate) 2 nd number – (y-coordinate) #8 DefinitionDrawing/Example Time (minutes) Laps around pool Mark’s laps around his pool The coordinate (6,15) means that in 6 minutes, he did 15 laps. (6,15)

Rule a summary of a predictable relationship that tells how to find the value of a variable. *Written in words! #9 DefinitionDrawing/Example distance is the rate times time (d = r t)

Equation a rule containing, numbers,variables, and symbols that represent a mathematical relationship #10 DefinitionDrawing/Example d = r t (distance = rate times time) OR C = ∏ d (Circumference of a circle = pi times diameter)

Expression #11 DefinitionDrawing/Example Represents a quantity *Written using numbers, variables, and symbols 4 + t X – 5 6p 12 r

Coefficient #12 DefinitionDrawing/Example A number or symbol multiplied with a variable 4m *4 is the coefficient 6t *6 is the coefficient

Inverse Operations #13 DefinitionDrawing/Example Math operations that undo each other Addition – subtraction Multiplication – division Ex. X + 5 = – 5 x = 3 *subtracting 5 is the inverse of adding 5

Commutative Property #14 DefinitionDrawing/Example Says changing the order does not change the sum or product = x = x ● 5 = 5 ● 4 5 ● p = p ● 5

Associative Property #15 DefinitionDrawing/Example Says changing the grouping does not change the sum or product 4 + (7 + 9) = (4 + 7) (2 + x) = (3 + 2) + x (6 ● 2) ● 8 = 6 ● (2 ●8) ( 3 ● t) ● 5 = 3 ● ( t ● 5)

Distributive Property #16 DefinitionDrawing/Example The product of a number times a sum is equal to the sum of the products of that number and each addend 5 ● (6 + 11) = (5 ● 6) + (5 ● 11) 4 ● ( 3 + x) = ( 4 ● 3) + (4 ● x)