CH 1 NOTES Variables, Function Patterns, Graphs Winter,

CH 1-1 Using Variables Background: In STEM careers, it is typical to make observations of an event and try to explain a relationship to describe that event. Ex. a nurse monitoring a patient’s heart rate after giving that patient some medication. Vocabulary: STEM career: Any career involving Science, Technology, Engineering and Math. Variable: a symbol representing any number. Ex. x, y, n Expression: a phrase, with variables and any mathematical operators (EXCEPT the = sign!) Equation: expression written WITH the = sign

CH 1-1 Using Variables How To Use Them: Ex.1: State whether each one below is a variable, expression, or equation. a) z° variable (measured in degrees) b) z°+5s expression c) 2x expression d) 2x=6 equation e) b (cm) variable (measured in cm)

CH 1-1 Using Variables How To Use Them Cont.: Ex.2 Write an expression for the following data collected by an accountant: Answer: h = hours worked (define your variable) $7.50∙h Hours Worked (h)Pay ($/hr) 1$7.50∙1 2$7.50∙2 3$7.50∙3 ANSWER: _________________

CH 1-1 Using Variables How to Use It Cont.: Before we can “translate” words into algebraic expressions, let’s review some definitions from elementary school: Sum/More than tells us to: _________________ Difference tells us to: _______________________ Product tells us to: _________________________ Times tells us to: ___________________________ Quotient tells us to: ________________________ Is tells us to: ______________________________ Can you think of any others?

CH 1-1 Using Variables How to Use Them Cont.: Ex.3 Write an algebraic expression for each phrase. a) p multiplied by 3 3p b) n less 7 n-7 c) 3 plus m 3+m NOTE: MAKE SURE YOU WRITE THINGS EXACTLY IN THE ORDER GIVEN!!!!!

CH 1-1 Using Variables NOW, YOU DO ODDS, #’s 1-9 IN 10 MINUTES! READY……. SET…….. GO!

CH 1-1 Using Variables How to Use It Cont.: Ex. 4 Define a variable and write an algebraic expression for each phrase. a) the sum of 4 and a number define variable: n= number write expression: 4+ n b) 3 increased by a number define variable: x= number write expression: 3 + x

CH 1-1 Using Variables NOW, YOU DO ODDS, #’s IN 10 MINUTES! READY……. SET…….. GO!

CH 1-1 Using Variables How to Use It Cont.: Ex. 5 Define a variable and write an algebraic expression to model each situation. a) The number of gal of water used to water trees is 30 times the number of trees. define variable: y = number of gallons of water used x = number of trees write expression: y = 30∙x b) What is the cost of buying several pairs of jeans at $32.95 per pair? define variable: z = total cost, t = number of pairs of jeans write expression: z = 32.95∙t

CH 1-1 Using Variables Think About It: WOULD YOU RATHER WRITE: The number of gal of water used to water trees is 30 times the number of trees. OR: y = 30∙x ???????????????? Algebra lets you take shortcuts!!!!!!

CH 1-1 Using Variables NOW, YOU DO ODDS, #’s IN 10 MINUTES! READY……. SET…….. GO!

CH 1-2 Order of Operations Background: If we don’t all agree on the order of simplifying expressions, we will all have different answers! Scientists and Mathematicians gathered and decided on PEMDAS. Vocabulary: PEMDAS: Please Excuse My Dear Aunt Sally

CH 1-2 Order of Operations Please (Parentheses first) Excuse (Exponents/Powers next) My (Multiply next) Dear (Division next) Aunt (Add next) Sally (Subtract last)

CH 1-2 Order of Operations How to Use It: Ex. 1 Simplify each expression. a) ( )/8 P ( ) /8 P&E (49-9)/8 E (40)/8 M (none in this problem) D (40)/8 = 5 A (none in this problem) S (none in this problem) b) ( *8)/(8+9) P ( *8) /(8+9) P&E (100 – 32)/ (8+9) E (68)/(17) M (none in this problem) D 68/17 = 4 A (none in this problem) S (none in this problem)

CH 1-2 Order of Operations NOW, YOU DO ODDS IN YOUR BOOK, PAGE 12 ODDS #’s 1-39 ANSWERS ON PAGE 836!!!!!! READY……. SET…….. GO!

Ch 1-3 Exploring Real Numbers Background: All numbers are not created equally. John Venn, this statistician dude from 1880 England, came up with a way to classify all numbers. Vocabulary: Natural #s: “Counting numbers” 1,2,3,….. Whole #s: “Counting #’s plus 0” 0,1,2,3,…… Integers: All - and + whole numbers …-3,-2,-1,0,1,2,3,… Rational #s: All fractions or decimals, but denominator ≠0. All fractions are terminating or repeating or ⅛ Irrational #s: All the weird stuff: √, i, non-repeating, non- terminated fractions, Π, etc.

Vocabulary Continued: Real #s: all rational numbers and irrational numbers. Venn Diagram: A circle diagram that shows how sets of things are related.Real Numbers Ch 1-3 Exploring Real Numbers Rational NumbersIrrational Numbers 0.755/8-2/ Integers Whole Numbers √10 √2/3 π √ ….. i Nat # 1,2

Ch 1-3 Exploring Real Numbers How To Use Them: Ex.1 Name the set(s) of numbers to which each number belongs. a rational number, real number b. 8 whole number, natural number, integer, rational, & real c. √7 irrational number, real number d rational number, real number

CH 1-3 Exploring Real Numbers NOW, YOU DO EVENS #2 - #8, and 26 & 28 READY……. SET…….. GO!

Ch 1-3 Exploring Real Numbers Vocabulary Contd: Counterexample: An example that proves a statement false. Ex. 2 Everyone in this room has dark hair. Counterexample: Ron and Christen have light colored hair. Ex.3 True or False: All negative numbers are integers. False: -1/2 is a negative RATIONAL number Now YOU try #’s 10 & 12!

Ch 1-3 Exploring Real Numbers Vocabulary Contd: Inequality: Statement that compares the value of two expressions using symbols. Less than is < Greater than is > Ex. 4 Use to compare these expressions. a) _____ > b) 3/8 ________ 9/16 3/8 (0.375) < 9/16 (0.5625)

CH 1-3 Exploring Real Numbers NOW, YOU DO EVENS: #14- #24 READY……. SET…….. GO!

Ch 1-3 Exploring Real Numbers Vocabulary Contd: Absolute Value: The absolute value of a number is the distance it is from 0. We write |-3| with absolute value bars. Ex. 5 Find the absolute value of the following numbers. a) |-5.44| 5.44 b) |3| 3 Now, you do #s 30 & 32