St a y co nn ect ed!
These Big Id eas will
help you underst and
how t h e m at h you
st u d y in hi gh school
BIGideas
These Big Ideas are the organizing ideas for the study of im portant areas of mathematics: algebra,
geometry, and statistics.A,
Algebra
Pr o p er t ies- In th e tra n s itio n fro m a rith m e tic to a lg e b r a , a tte n tio n shifts fro m a rith m e tic o p e ra tio n s
(addition, subtraction, m ultiplication, a nd division) to use o f the properties of these
operations. - All of the facts of arithmetic and algebra follow from certain properties.
Variable - Quantities are used to form expressions, equations, and inequalities.
- A n e xp re s s io n refers to a q u a n tity b u t d o e s n o t m a k e a sta te m e n t a b o u t it. A n e q u a tio n (or
a n in e q u a lity ) is a sta te m e n t a b o u t the q u a n titie s it m ention s. - Using variables in place of numbers in equations (or inequalities) allows the statement of
relationships a m o n g num bers that are unknow n o r unspecified.
Eq u i v a l e n c e - A single quantity may be represented by many different expressions.
- The facts about a quantity may be expressed by many different equations (or inequalities).
So l v i n g Eq u a t i o n s & I n e q u a l i t i e s - S o lv in g a n e q u a tio n is th e p ro c e s s o f re w ritin g th e e q u a tio n to m a k e w h a t it s a y s a b o u t its
variable(s) as simple as possible. - Properties of numbers and equality can be used to transform an equation (or inequality) into
e q u iv a le n t, s im p le r e q u a tio n s (or in e q u a litie s ) in o rd e r to fin d solu tio n s. - Useful information about equations and inequalities (including solutions) can be found by
analyzing graphs or tables. - The numbers and types of solutions vary predictably, based on the type of equation.
Pr o p o r t i o n al i t y - Two quantities are proportional if they have the same ratio in each instance where they are
measured together. - Two quantities are inversely p ro p o rtio n a l if they have the same product in each instance
where they are measured together.
Fu n ct i o n - A fu n c tio n is a re la tio n s h ip b e tw e e n v a r ia b le s in which each value of the input variable is
associated with a unique value of the output variable. - Functions can be represented in a variety of ways, such as graphs, tables, equations, or
w o r d s. E ach re p re s e n ta tio n is p a rtic u la rly useful in c e rta in situations. - Some important families of functions are developed through transformations of the simplest
form o f the function. - N ew functions can be made from other functions by applying arithmetic operations or by
applying one function to the output of another.
Modeling - M any real-world mathematical problems can be represented algebraically. These
representations can lea d to a lg e b ra ic solutions. - A function that models a real-world situation can be used to make estimates or predictions
about future occurrences.