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~ Chapter 1 ~

Algebra I. Algebra I. Lesson 1-1 Using Variables Lesson 1-2 Exponents & Order of Operations Lesson 1-3 Exploring Real Numbers Lesson 1-4 Adding Real Numbers Lesson 1-5 Subtracting Real Numbers Lesson 1-6 Multiplying & Dividing Real Numbers Lesson 1-7 The Distributive Property

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~ Chapter 1 ~

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  1. Algebra I Algebra I Lesson 1-1 Using Variables Lesson 1-2 Exponents & Order of Operations Lesson 1-3 Exploring Real Numbers Lesson 1-4 Adding Real Numbers Lesson 1-5 Subtracting Real Numbers Lesson 1-6 Multiplying & Dividing Real Numbers Lesson 1-7 The Distributive Property Lesson 1-8 Properties of Real Numbers Lesson 1-9 Graphing Data on the Coordinate Plane Chapter Review ~ Chapter 1 ~ Tools of Algebra

  2. Lesson 1-1 Using Variables Chap 1 Diagnosing Readiness Answers Main Menu

  3. Lesson 1-1 • Variable – a symbol that represents one or more numbers. Examples – x, y, q, r, s, n … • Algebraic Expression – a mathematical phrase that can include numbers, variable, and operation symbols. (no equal sign) Examples ~ 2n , 4+8 , n , 27x – 4y … 9 Using Variables Notes Main Menu

  4. Lesson 1-1 Using Variables Lesson 1-1 Notes • Writing an Algebraic Expression • Add – Terms -> sum, altogether, more than, • greater than… • Subtract – terms -> difference, minus, • less than… • Multiply – terms -> product, times, • multiplied by, twice, triple… • Divide – terms -> quotient, divided by, • half, third… • Writing an Algebraic Expression • Add – Terms -> sum, altogether, more than, greater than… • Subtract – terms -> difference, minus, • less than… • Multiply – terms -> product, times, • multiplied by, twice, triple… • Divide – terms -> quotient, divided by, • half, third… Using Variables Notes Main Menu

  5. Lesson 1-1 Examples: Five more than a number n + 5 The difference of five and a number 5 - x Five less than x x - 5 The product of five and a number 5n The quotient of a number and five n ÷ 5 Using Variables Notes Main Menu

  6. Lesson 1-1 • More complex algebraic expressions: • Two times a number plus five • 2n + 5 • Seven less than five times a number • 5x - 7 • Four more than the quotient of a number and six • (n ÷ 6) + 4 Using Variables Notes Main Menu

  7. Lesson 1-1 • Equation – a mathematical sentence that uses an equal sign. (Ex: 2+3 = 5, 4x=8,…) • Open sentence – an equation that contains one or more variables. (Ex: 2x=8, 3x+2y = 10) Writing an Equation Track One Media sells all CD’s for $12 each. Write an equation for the total cost of a given number of CD’s. Know: The total cost is 12 times the number of CD’s Define:Let n = of CD’s Let c = total cost Write: c = 12n or 12n = c Using Variables Notes Main Menu

  8. Lesson 1-1 Using Variables Notes Know: Number of hours times 8 equals the total pay Define: Let n = number of hours Let t = total pay Write: 8n = t or t = 8n Main Menu

  9. Lesson 1-1 the quotient of 6.3 and b 6.3 ÷ b s minus ten s - 10 9 less than a number n - 9 The sum of twice a number and thirty-one 2x + 31 The product of one half of a number and one fourth of the same number ½ n ( ¼ n) Using Variables Notes – Practice Problems Main Menu

  10. Lesson 1-1 Using Variables Practice 1-1 ~ all ~ Homework Main Menu

  11. Lesson 1-2 Exponents & Order of Operations Daily Math Review Main Menu

  12. Lesson 1-1 Using Variables Homework - Answers ?????? Questions ??????? Main Menu

  13. Lesson 1-2 • Simplify – replace an expression with its simplest name or form. • Exponents – A number that shows repeated multiplication. (In 24 ~ 4 is the exponent) • Base – The number that is multiplied repeatedly in a power. (In 24 ~ 2 is the base) • Power – has two parts, a base and an exponent, and has the form an. • Order of operations – GEMS – (1) grouping symbols; (2) Exponents; (3) Multiply & Divide (left to right) (4) Subtract & Add (left to right) Exponents & Order of Operations Notes Main Menu

  14. Lesson 1-2 Simplifying a Numerical Expression 25 – 8 * 2 + 32 14 + 2 * 4 – 22 3 + 5 – 6 ÷ 2 6 – 10 ÷ 5 Exponents & Order of Operations 3 2 4 1 18 3 2 4 1 18 Notes 2 3 1 5 2 1 4 Main Menu

  15. Lesson 1-2 Evaluating an Algebraic Expression 3a – 23 ÷ b for a = 7 and b = 4 3 * 7 – 23 ÷ 4 Example: A shirt costs $22.85 plus sales tax. What is the total cost of the shirt? Expression - p + p * r ( p = price; r = tax) c = $22.85 + $22.85(0.07) = $22.85 + $1.5995 = c = $24.45 Exponents & Order of Operations 2 4 3 1 19 Notes Main Menu

  16. Lesson 1-2 3 * 6 – 42 ÷ 2 4 * 7 + 4 ÷ 22 53 + 90 ÷ 10 Evaluate the following for c = 2 and d = 5 4c – 2d ÷ c c4 – d * 2 3 6 d + 6c ÷ 4 40 – d2 + cd * 3 8 45 Exponents & Order of Operations Practice Main Menu

  17. Lesson 1-2 Expressions with parenthesis 15(13 – 7) ÷ (8 - 5) (5 + 3) ÷ 2 + (52 – 3) 15(6) ÷ (3) (8) ÷ 2 + (25 – 3) 90 ÷ 3 4 + 22 30 26 Expressions with Exponents (cd)2 for c = 7 & d = 19 (7 * 19)2 (133)2 = 17,689 Exponents & Order of Operations Notes Main Menu

  18. Lesson 1-2 m2n for m = 5 & n = 4 52 * 4 = 25 * 4 = 100 Evaluate the following for m=3, q=4, p=7 qp2 + q2p m(pq)2 4*72 + 42*7 3(7*4)2 4*49 + 16*7 3(28)2 196 + 112 = 308 3(784) = 2,352 Simplifying an expression 2[(13-7)2 ÷3] 24 Exponents & Order of Operations Notes Main Menu

  19. Lesson 1-2 5[4 + 3(22+1)] 28 ÷ [(19 -7) ÷ 3] 5[4 + 3(4+1)] 28 ÷ [(12) ÷ 3] 5[4 + 3(5)] 28 ÷ [4] = 7 5[4 + 15] 5[19] = 95 9 + [4 – (10 – 9)2]3 9 + [4 – (1)2]3 9 + [4 – 1]3 9 + [3]3 9 + 27 = 36 Exponents & Order of Operations Practice Main Menu

  20. Lesson 1-2 Exponents & Order of Operations Practice 1-2 ~ even ~ Homework Main Menu

  21. Lesson 1-3 Exploring Real Numbers Daily Math Review Main Menu

  22. Lesson 1-2 ?????? Questions ??????? Exponents & Order of Operations Homework - Answers ?????? Questions ??????? Main Menu

  23. Lesson 1-3 Natural Numbers – counting numbers ~ 1, 2, 3… (not 0) Whole Numbers – non-negative integers ~ 0, 1, 2, 3, 4… Integers – whole #’s & their opposites ~ …-2, -1,0,1,2… Rational Numbers – numbers that can be written as a/b where b ≠ 0. Decimal form is a terminating or repeating decimal. Irrational Numbers – numbers that cannot be expressed in the form a/b where a & b are integers. (Ex ~ π, √10, 0.101001000…) Classify the following -12 -4.67 integer, rational number rational number 5 5/12 natural number, whole number, rational number integer, rational number Exploring Real Numbers Notes Main Menu

  24. Lesson 1-3 • Counterexample – Any example that proves a statement false… • All Whole numbers are rational numbers T or F • All integers are whole numbers. T or F • The square of a number is always greater than the number. T or F • All whole numbers are integers. T or F • No fractions are whole numbers. T or F • Inequality • (>, <, ≥ , ≤ , ≠ ~ used to compare the value of two expressions) • Ordering fractions • Write fractions as a decimal and then compare • Find the common denominator, convert, and then compare • Absolute value – distance a number is from 0. l-19l = 19 l22l = 22 Exploring Real Numbers Notes Main Menu

  25. Lesson 1-4 • Identity Property of Addition - n + 0 = n, for every real number n. • Inverse Property of Addition – n + (-n) = 0 • (additive inverse is the opposite of a number) • Rules for Adding • Numbers with the same signs – add and keep the sign. • Numbers with different signs – subtract, answer takes the sign of the number with the greatest absolute value. • Examples • -7 + (-4) -26.3 + 8.9 • -11 -17.4 • -3/4 + (-1/2) 8/9 + (-5/6) • -1 ¼ 1/18 Adding Real Numbers Notes Main Menu

  26. Lesson 1-4 & 1-5 Evaluating Expressions -n + 8.9 for n = -2.3 t + (-4.3) for t = -7.1 11.2 -11.4 Matrix 29.3 3.1 -3 -3.9 14.6 1.2 + -4 2 12.1 3.3 2.7 -5 Subtracting Real Numbers Leave, change, opposite… (then use the rules for addition) 3 – 5 = 3 + (-5) = -2 3-(-5) = 3 + 5 = 8 ¾ - (-11/12) = Adding & Subtracting Real Numbers Notes Main Menu

  27. Lesson 1-5 Absolute Values l 5-11 l = l 7 – 8 l = Evaluating Expressions -a – b for a = -3 & b = -5 -(-3) – (-5) = 3 + 5 = 8 Subtract with Matrices -3 4 _ -5 -6 0 -1 -9 -4 Subtracting Real Numbers Notes Main Menu

  28. Lesson 1-3, 1-4, & 1-5 Real Numbers Practice 1-3 - every 3rd problem Practice 1-4 – every 3rd problem Practice 1-5 – every 3rd problem & #35 Homework Main Menu

  29. Lesson 1-4 Adding Real Numbers Daily Math Review Main Menu

  30. Lesson 1-3 & 1-4 Real Numbers Homework - Answers Main Menu

  31. Lesson 1-5 Real Numbers Homework - Answers ?????? Questions ??????? Main Menu

  32. Lesson 1-6 • Identity Property of Multiplication ~ 1 * n = n • Multiplication Property of Zero ~ n * 0 = 0 • Multiplication Property of -1 ~ -1 * n = -n • Rules for Multiplying & Dividing • Like/same signs – answer is positive. • Different signs – answer is negative. • Simplifying Expressions • -6 * -5 = -2( -15/3) = -2.7 * 4.1 = • 30 10 -11.07 • -43 (-2)4 -(3/4)2 • -(4*4*4) (-2)(-2)(-2)(-2) -( ¾ * ¾) • -64 16 -9/16 Multiplying & Dividing Real Numbers Notes Main Menu

  33. Lesson 1-6 Evaluating Expressions -(cd) (-2)(-3)(cd) for c= -8 and d= -7 -(-8*(-7)) (-2)(-3)(-8*(-7)) -56 336 3x ÷ 2z + y ÷ 10 2z+x/2y for x = 8, y = -5, & z = -3 3(8) ÷ 2(-3) + (-5) ÷ 10 [2(-3) + (8)]/2(-5) 24 ÷ (-6) + (-5/10)[-6 + 8]/-10 -4 + (-1/2) 2/-10 -4 ½ - 1/5 Inverse Property of Multiplication ~ a ≠ 0, a (1/a) = 1 x/y x = -3/4 and y = -5/2 -3/4 ÷ (-5/2) (the reciprocal or multiplicative inverse is used) -3/4 x (-2/5) = 6/20 = 3/10 Multiplying & Dividing Real Numbers Notes Main Menu

  34. Lesson 1-8 Properties of Real Numbers Notes Main Menu

  35. Lesson 1-7 Distributive Property ~ a(b + c) = ab + ac; (b + c)a = ba + ca a(b – c) = ab – ac; (b – c)a = ba – ca Simplifying Expressions 13(103) = 13(100 + 3) 24(98) = = 13(100) + 13(3) = 1300 + 39 = 1339 6(m + 5) 2(3-7t) (0.4 + 1.1c)(3) 6m + 30 6 – 14t 1.2 + 3.3c Terms, constants, and coefficients… 6a2 – 5ab + 3b – 12 (a2, ab, and b are all unlike terms) Like terms are combined to simplify an expression… 3x2 + 5x2 7y + 6y -9w3 - 3w3 The Distributive Property Notes Main Menu

  36. Lesson 1-6 & 1-7 Writing an Expression… -2 times the quantity t plus 7 -2(t + 7) The product of 14 and the quantity 8 plus w 14(8 + w) Multiplying & Dividing Real Number & The Distributive Property Notes & Homework Main Menu

  37. Lesson 1-8 Commutative Property of Addition ~ a + b = b + a Commutative Property of Multiplication ~ a * b = b * a Associative Property of Addition ~ (a + b) + c = a + (b + c) Associative Property of Multiplication ~ (a * b) * c = a * (b * c) Identity Property of Addition ~ a + 0 = a Identity Property of Multiplication ~ a * 1 = a Inverse Property of Addition ~ a + (-a) = 0 Inverse Property of Multiplication ~ a (1/a) = 1 Distributive Property Multiplication Property of Zero Multiplication Property of -1 Identify the property… 9+7 = 7+9 1m = m np = pn 2+0=2 Properties of Real Numbers Notes Main Menu

  38. Lesson 1-8 Using Deductive Reasoning – logically justifying the reason (the why) for each step in simplifying an expression using properties, definitions, or rules. Simplify the expression… Justify each step 7z – 5(3 + z) StepReason 7z – 15 - 5z Distributive Property 7z +(-15) + (-5z) Rules for subtraction 7z + (-5z) + (-15) Commutative property of addition 2z + (-15) addition of like terms 2z – 15 rules for subtraction Properties of Real Numbers Notes Main Menu

  39. Lesson 1-8 & 1-9 2(3t – 1) + 2 StepReason 6t – 2 + 2 Distributive property 6t +(-2) + 2 Rules/defn of subtraction 6t addition Homework Practice 1-7 & 1-8 even;-) Properties of Real Numbers & Graphing on the Coordinate Plane Notes Main Menu

  40. Lesson 1-5 Subtracting Real Numbers Quiz Lesson 1-1 to 1-4 Main Menu

  41. Lesson 1-8 Properties of Real Numbers Notes Main Menu

  42. Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Homework Answers Main Menu

  43. Lesson 1-9 Graphing Data on the Coordinate Plane A coordinate plane has an x-axis (horizontal) and a y-axis (vertical) An ordered pair (x, y) are the numbers that identify the specific location of a point. Graphing on the Coordinate Plane Notes y-axis (0,0) origin origin (-,+) (+,+) Quadrant II Quadrant I x-axis Quadrant IV Quadrant III (+,-) (-,-) Main Menu

  44. Lesson 1-8 & 1-9 Identifying & Graphing Points Use the (x, y) location to identify the location of a point. Graph C(0,3); D (2,4); E(-1,-4); F(-3,0) Quadrant? (-2,0) (4,-1) (-3,-5) (2.7,3.6) Can we find the dimensions of a shape when we graph it? Scatter Plot Graph that relates data of two different sets. Scattered points do not form a line. (Usually graphed in Quadrant I) A trend line can show trend of the data in a scatter plot. Properties of Real Numbers & Graphing on the Coordinate Plane Notes Main Menu

  45. Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Practice Homework Practice 1-8 & 1-9 odd Main Menu

  46. Lesson 1-8 & 1-9 Properties of Real Numbers & Graphing on the Coordinate Plane Homework Answers Main Menu

  47. Daily Math Review Main Menu

  48. Algebra I Algebra I ~ Chapter 1 ~ Chapter Review Main Menu

  49. Algebra I Algebra I ~ Chapter 1 ~ Chapter Review Main Menu

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