Pre-Algebra CHAPTER 1: TOOLS FOR ALGEBRA AND GEOMETRY
Chapter 1: WRITE THIS DOWN IN YOUR PLANNER 1-2 PEMDAS and Divisibility Rules FRIDAY - QUIZ 1A 1-3 Variables and Expressions 1-4 Variables and Equations 1-5 Distribution Property FRIDAY - Quiz 1B 1-7 Ordered Pairs 1-8 Solving Equations Using Inverse Operations FRIDAY - Quiz 1C 1-9 Inequalities 1-10 Gathering and Recording Data FRIDAY - Chapter 1 Test
1.2 Order of Operations OBJ: To re-examine the basic tools for Algebra: To choose the appropriate method of computation To use variables and algebraic properties
1.2 Order of Operations P Parenthesis E Exponents M Multiply D- Divide A Add S - Subtract Example: 5(2+6) 8 x 4 = 5(8) 8 x 4 = 40 32= Answer = 8
PEMDAS (Order of Operations) Parentheses 3(5 + 4) = Exponents 6-2² Mult./Div. Family Order of Operations PEMDAS Add/Sub. Family
Divisibility Rules CHAPTER 1
1-3 Variables and Expressions OBJ: To evaluat e exp ression s co n t ain in g var iab les an d t ran slat e ver b al p h rases in t o algeb raic exp ression s. War m -up : Find t h e value o f each exp ressions: 1. 72 + 12 = 35 + 7 2. 54 42 7 = 3. 36 9 3= 4. 37 + 38 = 30 5 5. 3[(18 3) + 4(5 + 7)] = Answers: 1. 2 2. 48 3. 12 4. 3 5. 189 Vocabulary Quiz - FRIDAY
1-3 Variables and Expressions Not es: Expression An expression is a phrase, a sentence fragment. You simplify an expression. An expression has no relation symbol. 1. a number less than five = 5 - x 2. five less than a number = x - 5 Vocabulary Quiz - FRIDAY
Math Vocabulary Mathematics (math) is the study of numbers, quantities, shapes, and space using mathematical processes, rules, and symbols. CHAPTER 1 Vocabulary Quiz - FRIDAY
Math Vocabulary Vocabulary Quiz - FRIDAY
Math Vocabulary Algorithm: A step-by-step mathematical procedure used to find an answer. Vocabulary Quiz - FRIDAY
Math Vocabulary Coefficient A number that multiplies a variable. For example, 9 is the coefficient in 9x. Vocabulary Quiz - FRIDAY
Math Vocabulary Denominator The bottom number in a fraction. The denominator represents the number of parts into which the whole is divided. For example, 6 is the denominator in the fraction. Vocabulary Quiz - FRIDAY
Math Vocabulary Equation A mathematical statement used to show that two expressions are equal. It contains an equals sign. For example, 16-9 = 7 (the expression 16-9 and the expression 7 are equal). Vocabulary Quiz - FRIDAY
Math Vocabulary Greatest Common Factor (greatest common divisor) The largest number that will divide two or more other numbers equally. For example, the greatest common factor of 32 and 48 is 16. Vocabulary Quiz - FRIDAY
Math Vocabulary Improper Fraction (mixed fractions) A fraction that has a larger numerator than denominator. For example, is an improper fraction. Vocabulary Quiz - FRIDAY
Math Vocabulary Inverse Operations Opposite or reverse operations. Addition and subtraction are inverse operations, as are multiplication and division. Vocabulary Quiz - FRIDAY
Math Vocabulary Negative Number A number that is less than zero. A minus sign is used to show that a number is negative. For example, -12 is a negative number. Vocabulary Quiz - FRIDAY
Math Vocabulary Numerator The top number in a fraction. The numerator represents the number of parts of the whole. For example, 5 is the numerator in the fraction. Vocabulary Quiz - FRIDAY
Math Vocabulary Ordinal Number A number that shows place or position, as in 2nd place. Vocabulary Quiz - FRIDAY
Math Vocabulary Positive Number A number that is greater than zero. While a minus sign is used to signify a negative number, the absence of a minus sign signifies a positive number. Vocabulary Quiz - FRIDAY
Math Vocabulary Prime Number A number that can be divided evenly only by itself and 1. For example, 7 is a prime number. Vocabulary Quiz - FRIDAY
Math Vocabulary Square Number A number that results from multiplying another number by itself. For example, 49 is the square of 7 (7 x 7 = 49). 49 7 x 7 Vocabulary Quiz - FRIDAY
Math Vocabulary Square Root of a Number A number that is multiplied by itself to produce a square number. For example, 7 is the square root of 49. It is designated by the symbol. Vocabulary Quiz - FRIDAY
Math Vocabulary Variable A quantity that can change or vary, taking on different values. It is typically represented by a letter of the alphabet. For example x is the variable in 9x (x can be any number that is being multiplied by 9). Vocabulary Quiz - FRIDAY
1-3 Variables and Expressions Assignment: p. 19 (11-14, 16 26 EVEN)
1-4 Properties OBJ: To id en t if y p rop ert ies of ad d it ion an d m u lt ip licat ion and use t hem t o solve prob lem s. War m -up : Evaluat e each expression if : a= 4, b= 2, and c= 3 1. a + bc 2. 4a + b b 3. ac b 4. 7a (2c + b) Answers: 1. 10 2. 20 3. 6 4. 20 Vocabulary Quiz - FRIDAY
1-4 Properties Notes:
1-4 Properties Notes:
1-4 Properties Notes:
1-4 Propert ies Assignment: p 25 (16-48 x4)
1-5 Distributive Property OBJ: To sim p lif y alg eb raic exp ression s u sin g t h e d ist ribut ive p ropert y War m -up: Nam e t h e p ro p er t y: 1. (ab)c = a(bc) 2. (7 + 4) 0 = 0 Answers: 1. Associative Prop. Of Mult. 2. Mult. Prop. Of Zero Vocabulary Quiz - FRIDAY
1-5 Distribution Property NOTES: The Distributive Property is an algebra property which is used to multiply a single term and two or more terms inside a set of parentheses. Take a look at the problem below. 2(3 + x) 2(3) + 2(x) 6 + 2x
1-5 Distribution Property Notes:
1-5 Distibution Property Assignment: p 28 (15-33 x3)
1-6 Variables and Equations OBJ: To id en t if y an d solve op en sen t en ces War m -up: Sim p lif y each exp ressio n: 1. 4q + q 2. 4m + 6m + 3 3. 24a + a + 16 4. 9(r + 7) + 12r 5. 6(x + y) + 4(2x + 3y) Answers: 1. 5q 2. 10m + 3 3. 25a + 16 4. 21r + 63 5. 14x + 18y Vocabulary Quiz - FRIDAY
Chapter 1 Update! 1-2 PEMDAS and Divisibility Rules FRIDAY - QUIZ 1A (DONE) 1-3 Variables and Expressions 1-4 Properties 1-5 Distribution Property FRIDAY - Quiz 1B (DONE) 1-6 Variables and Equations 1-8 Solving Equations Using Inverse Operations FRIDAY - Quiz 1C (THIS FRIDAY) 1-9 Inequalities 1-10 Gathering and Recording Data FRIDAY - Chapter 1 Test (NEXT FRIDAY!)
1-6 Variables and Equations Notes: ADDING yo ur like t er m s
1-6 Variables and Equations Determine which equation is true by replacing the variable with -1. A. 5 + x = 4 B. 5 + x = 5 C. 5 + x = 9 D. 5 + x = 10 Which of the numbers is the solution of x 4 2 = 5? A. 32 B. 28 C. 26 D. 30 Determine which equation is true by replacing the variable with 3. A. 6x + 4 = 16 B. 3x + 1 = 10 C. 6x = 8 D. 2x + 2 = 8 Solve 11 = 2m - 3 mentally. A. 4 B. 22 C. 7 D. 12
1-6 Variables and Equations Assignment: p 34 (15-33 x3)
1-8 Solving Equations OBJ: To u se inverse op erat ion s t o solve eq u at ion s an d solve problem s using equat ions War m -up: Writ e each as an alg eb raic exp ression. 1) t h e dif f er ence o f 10 an d 5 2) t h e quot ient o f 14 an d 7 3) u decr eased by 17 4) half o f 14 5) x incr eased by 6 6) t h e pr oduct o f x an d 7 7) t h e sum o f q an d 8 8) 6 squar ed 9) t w ice q 10) t h e pr oduct o f 8 an d 12 Answers: 1) 10-5 2) 14/7 3) u 17 4) 14/2 5) x + 6 6) x 7 7) q + 8 8) 6² Equation Quiz - FRIDAY
1-8 Solving Equations Notes: Using Inverse Operations Just like with PEMDAS M/D House A/S House The operation that reverses the effect of another operation. Example: Addition and subtraction are inverse operations Another Example: Multiplication and division are inverse operations. So lve f or var iab le using INVERSE OPERATIONS
1-8 Solving Equations Assignment: p 44 (12-13 & 18-39 x3)
1-9 Inequalities OBJ: To w rit e an d solve in eq u alit ies War m -up: Writ e each as an alg eb raic exp ression. 1) 5 + r = 7 2) 34 = 2x 3) 2 = 4) 4.37 = y 9.32 5) d + 48 = 55 Answers: 1) r = 2 2) x = 17 3) w = 24 4) y = 13.69 5) d = 7 Equation Quiz - FRIDAY
Weekly Schedule Monday 1.9 Inequalities Tuesday Quiz Reviews Block Review Math Lab Friday Chapter 1 Test PROGRESS REPORTS NEXT WEEK!
1-9 Inequalities Notes: Solve INEQUALITIES
1-9 Inequalities x > 2 Graphing the Inequality: Draw your number line --------I--------------I-----------------I-------- 1 2 3 Mark this point with the appropriate notation (an open dot indicating that the point x = 2 was NOT included in the solution) Then you'd shade everything to the right, because "greater than" meant "everything off to the right". The steps for graphing two-variable linear inequalities are very much the same.
1-9 Inequalities Assignment: p 48 (13-21 ALL & 22-26 Even s - GRAPH EACH ANSWER)
Math Lab Chapter 1 Review Section A (IND) p58 (9-35 ODD) Section B (ME) p 60 (63 68 ALL) Section C (GROUP) p 58-59 (30-49 & 56-62)