Math 87

Math 87

2nd or 3rd Edition

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Course Content

Lessons Status
1

Introduction: Prerequisites for the Course – How to Use the Math Book – Expectations of Students

2

Lesson 1: Explanation of the Numbers – Arithmetic Using Whole Numbers – Working with Decimals Using Money – Evaluating Expressions Using Variables

3

Lesson 2: Defining Operations and Inverse Operations – Explaining What a Sequence Is

4

Lesson 3: Solving Equations Containing Missing Numbers, Using Addition, Subtraction, Multiplication or Division

5

Lesson 4: What Is a Number Line and How Can You Use It? – Comparing Numbers

6

Lesson 5: Learning Whole Number Place Values & How to Read and Write Whole Numbers

7

Lesson 6: Defining and Working with Numerical Factors – Explaining What Is Meant by Divisibility – Testing for Divisibility

8

Lesson 7: Space, Planes, Points, and Lines – How Angles Are Formed – Defining Types of Angles

9

Lesson 8: Working with Fractions and Percents as Parts of the Whole – Break Down of Measurements on a US Standard Ruler

10

Lesson 9: Working with the Addition, Subtraction, and Multiplication of Fractions and Their Reciprocals

11

Lesson 10: Defining a Mixed Number Using a Long Division Problem – Describing Improper Fractions

12

Investigation 1: Using Manipulatives to Depict Fractions and Percents

13

Lesson 11: Identifying and Solving Word Problems Dealing with Combining (Adding) and Separating (Subtracting)

14

Lesson 12: Recognizing Problems Dealing with “Comparing” – Solving Elapsed-Time Word Problems

15

Lesson 13: Word Problems Dealing with “Equal Groups”

16

Lesson 14: Word Problems Dealing with “Parts of the Whole”

17

Lesson 15: Recognizing Equivalent Fractions – How to Reduce Fractions (Part I)

18

Lesson 16: Studying the US Customary System (In Lesson 32 We Will Study the Metric System)

19

Lesson 17: Using a Protractor to Measure Angles

20

Lesson 18: Studying Polygons and Similar vs. Congruent Figures

21

Lesson 19: What Is a Perimeter? How Do We Measure It?

22

Lesson 20: Learning How “Exponents” Work with “Bases” – Finding Areas of Rectangular Shapes (Part I) – Finding Square Roots

23

Investigation 2: Working with a Compass and a Straight Edge (Part I)

24

Lesson 21: The Difference Between Prime and Composite Numbers – Defining Prime Factorization – Creating a Factor Tree

25

Lesson 22: Word Problems Involving Finding a Fraction of Something – Converting Percent to a Fraction

26

Lesson 23: Working with Word Problems Involving Mixed Number Fractions or Percents

27

Lesson 24: More on Reducing Fractions (Part II)

28

Lesson 25: How to Divide Fractions

29

Lesson 26: How to Multiply or Divide Mixed Numbers

30

Lesson 27: Defining What “Multiples” Are – Finding a “Least Common Multiple” (Lcm) – Using “Equivalents” by Division

31

Lesson 28: Solving Multiple-step Word Problems – Finding the Average (Part I)

32

Lesson 29: Rounding Whole & Mixed Numbers – Estimating an Answer

33

Lesson 30: Finding a Common Denominator – Adding or Subtracting Fractions That Do Not Have Common Denominators

34

Investigation 3: Working with the Coordinate Plane

35

Lesson 31: How to Read and Write Decimal Numbers

36

Lesson 32: The Metric System (US Customary System Was in Lesson 16)

37

Lesson 33: Using Place Value to Compare Decimals – How to Round Decimals

38

Lesson 34: Placing Decimal Numbers on a Number Line

39

Lesson 35: How to Add, Subtract, Multiply, and Divide Decimal Numbers

40

Lesson 36: Definition of a “Ratio” – Defining and Working with “Simple Probability”

41

Lesson 37: Formula for Finding the Area of a Triangle – Finding the Area of Rectangular Shaped Objects (Part II)

42

Lesson 38: How to Read and Interpret Graphs

43

Lesson 39: Defining a “Proportion”- Working with Proportions

44

Lesson 40: The Sum of the Measure of the Angles of Any Triangle Always Equal 180 Degrees – Explaining the Measure of Complementary & Supplementary Angles

45

Investigation 4: Working with Stem-and-Leaf & Box-and-Whisker Plots

46

Lesson 41: Recognizing Which Formula to Use and How to Use It – What Is the Distributive Property?

47

Lesson 42: What Is a “Repeating Decimal”? What Is a “Repetend”?

48

Lesson 43: How to Convert Decimals to Fractions and Vice-Versa – How to Convert Percents to Decimals

49

Lesson 44: Several Ways to Reflect Answers to Division Problems

50

Lesson 45: How to Divide by a Decimal Number

51

Lesson 46: Calculating Unit Prices as Rates & How to Calculate Sales Tax

52

Lesson 47: Working with the Powers of 10 and Expanded Notation – Multiplying and Dividing by the Powers of 10

53

Lesson 48: Creating Equivalent Values of a Fraction and Its Decimal and Percent Formats

54

Lesson 49: Introduction to Adding and Simplifying Mixed Numbers

55

Lesson 50: Cancelling and Converting Units and Unit Multipliers When Working with Fractions

56

Investigation 5: How to Create Different Types of Graphs

57

Lesson 51: How to Work with Very Large or Very Small Numbers Using Scientific Notation

58

Lesson 52: The Importance of the Order of Operations – Review of the Order of Operations

59

Lesson 53: Word Problems Involving the Multiplication of Rates

60

Lesson 54: Word Problems Using Ratios

61

Lesson 55: Working with the Average (Part II)

62

Lesson 56: Converting (When Needed), Subtracting, and Simplifying Mixed Measures

63

Lesson 57: Working with Negative Exponents and Using Scientific Notation for Very Small Numbers

64

Lesson 58: Working with Lines of Symmetry – Definition & Introduction to a Function (Part I)

65

Lesson 59: Review of Integers – Definition of Absolute Value of Numbers – Placing Numbers on the Numbers Line

66

Lesson 60: Working with Fractional Parts of a Number (Part I) – Word Problems Involving Percents of Numbers (Part I)

67

Investigation 6: How We Classify Quadrilaterals

68

Lesson 61: Calculating the Area and Angles of a Parallelogram

69

Lesson 62: How We Classify Triangles

70

Lesson 63: What Are the Various Forms of “Symbols of Inclusion”

71

Lesson 64: Several Rules for Adding Signed Numbers

72

Lesson 65: How to Solve Some Ratio Word Problems Using the Total

73

Lesson 66: The Relationship Between the Circumference of a Circle, Its Radius, Its Diameter, and “Pi”

74

Lesson 67: Defining Geometric Solids Using a Venn Diagram

75

Lesson 68: Using the Thought Process of Algebraic Addition to Simplify Difficult Expressions

76

Lesson 69: Another Review of Using Scientific Notation

77

Lesson 70: Introduction to Measuring Volume of Some Geometric Solids

78

Investigation 7: Since the Word “Equation” Means “Equal,” What Is Meant by a “Balanced Equation”?

79

Lesson 71: Solving Word Problems Using a Fraction to Help Find the “Whole”

80

Lesson 72: Solving Word Problems Using Both Ratio and Proportion

81

Lesson 73: Rules for the Multiplication and Division of Signed Numbers

82

Lesson 74: Word Problems Involving Decimal or Fractional Parts of a Number (Part II)

83

Lesson 75: Finding the Area of a Complex Figure and a Trapezoid

84

Lesson 76: Defining and Simplifying a Complex Fraction

85

Lesson 77: Word Problems Involving Percent of a Number (Part II)

86

Lesson 78: How to Graph an “Inequality”

87

Lesson 79: Encountering “Insufficient Information” – Using Quantitative Comparisons

88

Lesson 80: Identifying Geometric Transformations

89

Investigation 8: Working with a Straight-edge and Compass (Part II)

90

Lesson 81: Working with Using Proportions to Solve Percent Word Problems

91

Lesson 82: Calculating the Area of a Circle

92

Lesson 83: How to Multiply Powers of 10 – How to Multiply Numbers In Scientific Notation

93

Lesson 84: Definition of, and Rules for, Algebraic Terms

94

Lesson 85: Working with Signed Numbers and Order of Operations – More Work with Functions (Part II)

95

Lesson 86: Review of the “Family of Numbers”

96

Lesson 87: How to Multiply Algebraic Terms

97

Lesson 88: Using Multiple Unit Multipliers – How to Convert Units of Area

98

Lesson 89: Using Diagonals in Quadrilaterals – Defining and Measuring Interior & Exterior Angles

99

Lesson 90: Converting “Mixed Number” Coefficients – Working with “Negative Coefficients”

100

Investigation 9: Learning How to Graph Functions

101

Lesson 91: Evaluating Algebraic Expressions Using Signed Numbers (with or Without Parenthesis)

102

Lesson 92: Word Problems that Use a Percent to Describe a Specified Amount of Increase or Decrease

103

Lesson 93: Simplifying Multiple Step Equations & Multiple Step Inequalities

104

Lesson 94: What Is Compound Probability and How Do We Solve It?

105

Lesson 95: Defining a “Right Solid” and Finding Its Volume

106

Lesson 96: How to Estimate the Measure of an Angle – Using the Distributive Property with Algebraic Terms

107

Lesson 97: Defining “Similar Triangles” – Using “Indirect Measure”

108

Lesson 98: What Is Meant by “Made to Scale” & How Can We Use It in Our Calculations? – Defining a “Scale Factor”

109

Lesson 99: The “Pythagorean Theorem” and Right Triangles – An Algebraic Equation for the “Pythagorean Theorem”

110

Lesson 100: How to Estimate Square Roots – An Introduction to Irrational Numbers

111

Investigation 10: Is There a Difference Between Calculating Probability, Chance, & Odds?

112

Lesson 101: The Language of Algebraic Equations – Translating Phrases into Algebraic Terms

113

Lesson 102: Definition and Application of Transversals – How to Simplify Equations

114

Lesson 103: Working with Powers of Negative Numbers – Dividing and Simplifying Algebraic Terms

115

Lesson 104: Finding Areas of Semi-circles, Lengths of Arcs of Circles, and Areas of Sectors of Circles

116

Lesson 105: How to Find the Surface Area of a Right Solid and the Surface Area of a Sphere – Learning More About “Roots”

117

Lesson 106: Defining and Solving “Literal Equations” – Treating Formulas as “Literal Equations” and Rewriting Them as Necessary

118

Lesson 107: Defining “Slope” – Graphing the “Slant” or “Slope” of a Function

119

Lesson 108: Definition of a “Formula” – How to Manipulate the Variables of a Formula to Solve for the Variable You Want to Find

120

Lesson 109: Solving Equations That Have Exponents of 2

121

Lesson 110: Explaining the Difference Between Simple and Compound Interest – Calculating Successive Discounts

122

Investigation 11: Using the “Scale Factor” In Calculating Surface Area and Volume

123

Lesson 111: Learning How to Divide When Using Scientific Notation

124

Lesson 112: How to Apply the Pythagorean Theorem in Solving Some Real-Life Problems

125

Lesson 113: Calculating and Creating a Formula for the Volume of Pyramids, Cones, and Spheres

126

Lesson 114: Learning How to Graph Linear Inequalities

127

Lesson 115: Finding Volume, Capacity, and Mass Using the Metric System of Measurement

128

Lesson 116: Learning How to Factor Algebraic Expressions Containing One or More Terms – How to Write the Factored Form

129

Lesson 117: Learning About the “Slope-Intercept Form” for Linear Equations – Graphing Linear Equations Using the Slope-Intercept Form

130

Lesson 118: Using a Compass and Straight-edge to Copy Angles and Triangles

131

Lesson 119: Can We Divide by Zero? Why Not?

132

Lesson 120: Introduction to Graphing Non-Linear Equations

133

Investigation 12: One of the Many Proofs of the Pythagorean Theorem

134

Topic A: A Brief Introduction to the “Base 2” Number System – A Review Lesson on Roman Numerals