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Math 8 1st Trimester Lesson Schedule: September 2014 Grading Period: week #1 Monday Tuesday Wednesday Thursday Friday 1 2 3 4 5 Day 2 Day 3 Day 4 School Year: Day 1 No School Labor Day First Day of School Discuss: - Classroom Rules - Math Procedures - Common Core: pilot - Intro to Quizzles ClassWork: groups Worksheet: Math 2 Part I Review Test: #1-17 Practice: finish worksheet Discuss: Discuss: - worksheet - Intro to Quizzles - worksheet - Placement Test ClassWork: groups ClassWork: Worksheet: Math 2 Part II Review Test: #1-16 Placement Test Practice: finish worksheet Practice: finish past worksheets Finish Placement Test Vocabulary variable - a letter used to represent a number constant - any number (whole, integer, fraction, decimal, etc. ) numerical expression – contains only constants and/or math operations algebraic expression - numbers and/or variables in a math sentence evaluate - find the value; replace the variables in an expression, then simplify to find the numerical value Replacement Set - a set of numbers that can be substituted for a variable Real numbers - the set of all numbers that can be represented on a number line absolute value - distance from zero (distance is always positive): 3 3 ; 3 3 opposites - two numbers whose sum equals zero: 3 (3) 0 x ( x) 0 are called Additive Inverses additive inverses - a number and its opposite; same distance from zero and have the same absolute value reciprocals - two numbers whose product is 1; 1 2 1 2 3 4 4 1 are called Multiplicative Inverses 3 multiplicative inverses - a number and its reciprocal BASE exp onent power - repeated multiplication 23 2 2 2 8 BASE - the number to be multiplied exponent - the raised number that tells how many factors of the base to multiply Number Sets - Natural numbers (counting numbers) 1,2,3,… Whole numbers 0,1,2,3,… Integers …-3, -2, -1, 0-, 1 ,2 , 3,… Rational numbers: any number that can be represented as a Quotient of two Integers Irational numbers: numbers that are NOT rational R Real numbers: all possible numbers (Rational and Irrational numbers) N W I Q square root - a number that is multiplied by itself to form a product = radical radicand - the quantity under the square root symbol radicand principal square root - the “positive” square root negative root both roots perfect square - a number whose positive square root is a whole number 9 3 16 4 25 5 etc. 1, 4,9,16, 25,36, 49,64,81,100,... 1 1 4 2 cube root - a number that is raised to the third power to form a product 3 because 8 2 2 8 3 3 8 2 (2)3 8 terminating decimal - has a finite number of digits after the decimal point examples: .2 1.75 repeating decimal - has a block of one or more digits after the decimal point that repeat continuously (not all of them zero’s) examples: 0.3 2.45 repetend = the block of repeating digits counterexample - an example that disproves a statement or shows the statement is false closure - a set of numbers is said to be closed, or to have closure, under an operation if the result of the operation on any two numbers in the set is also in that set of numbers. order of operations - G E M/D A/S the order in which to do math operations in an expression Grouping symbols; Exponents; Multiply or Divide (left to right); Add or Subtract (left to right) Step 1: perform operations inside the Grouping Symbols work inside outward N ( ) [ ] { } D Parentheses brackets braces fraction bar square root absolute value Step 2: evaluate powers Step 3: perform multiplication or division from left to right Step 4: perform addition or subtraction from left to right term - a constant; or a variable; or a product of constants & variables or a quotient of constants & variables ; terms are separated by + and signs like terms - terms that have the same variable parts 6.2 x 2 y3 z ; 3 x3 ; 2 x3 2 2 3 x y z 3 = same variable with the exact same exponents by those variables 2;7 constants are Like Terms! coefficient - the numerical factor; the number that the variable is multiplied by; the number in front of the variable -------------------------------------------------------------------------------------------------------------------------------Other important vocabulary from Pre-Algebra: = 2x 7 equation - a number sentence which states two expressions are equal: 17 solution - the value of the variable that makes a true open sentence or equation Inequality - algebraic expressions that are NOT equal: > greater than greater than or equal to less than less than or equal to not equal to Domain - the set of all "x" coordinates; the set of numbers that a variable may represent (Replacement Set) Range - the set of all "y" coordinates; the "value" of the expression Function - a rule that establishes a relationship between two quantities (numbers), the input and the output. The input is the set of all x-coordinates and the output is the set of all y-coordinates. There is exactly one output for each input (each x-coordinate can have only one y-coordinates). formula - an algebraic equation that states a rule about relationships Formulas: A = lw P = 2l + D = rt C = np Area of a Rectangle = length x width 2w Perimeter of a Rectangle = (2 x length) + (2 x width) Distance traveled = rate x time traveled Cost = number of items x price per item linear - first degree equation; x1 (the exponent on the "x" is one and the graph is a line): y 2 x 7