Integrated Algebra Course Outline					Last Updated: June 26, 2007

I. Operations
1. How do we use the symbols of algebra and the order of operations to evaluate numerical expressions?
2. How do we add and subtract within the set of signed numbers?
3. How do we multiply and divide signed numbers?
4. How do we evaluate algebraic expressions using given numerical values from the set of integers?
5. How do we determine if a number is a solution of an open sentence?
6. How do we translate an English sentence into an algebraic expression?
7. What are the properties of Real numbers?
8. What are the properties of an operation defined by a table?
9. Review
10. Test

II. Solving Equations
11. How do we solve an equation of the type ?
12. How do we solve an equation of the type ?
13. How do we solve equations of the type ?
14. What is meant by the distributive property?
15. How do we add monomials and add polynomials?
16. How do we subtract monomials and subtract polynomials?
17. How do we solve equations containing like terms on one side of the equal sign?
18. How do we solve equations which contain variables on both sides of the equal sign?
19. How do we solve equations containing parentheses?
20. Review
21. Test

III. Verbal Problems
22. How can we solve a literal equation?
23. How can we solve verbal number problems using equations?
24. How do we solve problems involving consecutive integer problems?
25. How do we solve problems involving consecutive even or odd integers?
26. How do we solve more complex verbal problems leading to linear equations?
27. How do we solve verbal problems involving objects moving in opposite directions using a linear equation?
28. How do we solve verbal problems involving objects moving in the same direction?
29. How do we solve verbal problems involving coin/value leading to linear equations in one variable?
30. How do we solve verbal problems involving proportions that lead to linear equations?
31. How do we solve verbal problems involving finding percent of a number?
32. How do we solve more difficult verbal problems involving percentage using equations?
33. Review
34. Test

IV. Inequalities/Polynomials
35. How do we solve a linear inequality in one variable?
36. How do we solve an inequality using more than one property of inequality?
37. How can we solve a verbal problem which leads to an inequality?
38. How do we multiply monomials?
39. How do we divide monomials?
40. What is the meaning of a negative exponent and a zero exponent?
41. How do we use scientific notation to compute products and quotients?
42. How do we multiply a polynomial by a monomial?
43. How do we divide a polynomial by a monomial?
44. How do we find the product of polynomials?
45. Review
46. Test

V. Perimeter, Area, Volume, Surface Area
47. What is meant by the perimeter of triangles, squares and rectangles?
How do we find the area of a rectangle and a square?
48. How do we find the area of parallelograms and triangles?
49. How do we find the area of a trapezoid?
50. How do we find the circumference of a circle?
How do we find the area of a circle?
51. How can we find the area of complex figures?
52. How do we find the surface area of a solid figure?
53. What is meant by the volume of a rectangular solid and a cube?
54. What is meant by the volume of prisms, pyramids, right circular cylinders, cones and spheres?
55. What is meant by the volume of prisms, pyramids, right circular cylinders, cones and spheres?
56. What is the effect of changing a linear dimension of a figure on its perimeter, area or volume?
57. Review
58. Test

VI. Factoring
59. What is meant by factoring?
60. How do we factor quadratic trinomials (only for a=1)?
61. How do we factor the difference of two squares?
62. How can algebraic expressions be factored completely?
63. Test

VII. Algebraic Fractions
64. How can we reduce fractions?
65. How can we reduce algebraic factions involving polynomials?
66. How can we multiply and divide fractions containing monomial expressions?
67. How do we multiply and divide fractions containing polynomial expressions?
68. How can we combine fractions with like and unlike monomial denominators?
69. How can we combine fractions with like polynomial denominators?
70. How can we solve equations with fractional coefficients?
71. Review
72. Test

VIII. Quadratic Equations
73. How do we solve a quadratic equation?
74. How do we solve a quadratic equation?
75. How do we solve more difficult quadratic equations?
76. How do we solve verbal problems leading to a quadratic equation?
77. How do we solve consecutive integer problems leading to a quadratic equation?
78. How do we solve area problems leading to a quadratic equation?
79. Review
80. Test

IX. Rational and Irrational Numbers, Pythagorean Theorem, Trigonometry
81. What is the relationship between rational and irrational numbers?
82. How do we simplify radicals with numerical radicands?
83. How do we multiply and divide radicals with numerical radicands?
84. How do we add and subtract radicals?
85. What is the Pythagorean Theorem?
86. What are some applications of the Pythagorean Theorem?
87. What are the trigonometric ratios?
88. How do we use the trigonometric ratios to solve a right triangle problem?
89. How do we apply trigonometric ratios to solve verbal problems?
90. How do we solve trigonometric ratio problems involving the angle of elevation and the angle of depression?
91. Review
92. Test

X. Graphing Linear Equations
93. How can we use the coordinate plane to determine perimeters and areas of geometric figures?
94. How do we find the solutions of a linear equation in two variables?
95. How do we graph a linear equation in two variables?
96. How do we graph lines parallel to the axes?
97. How do we find the slope of a line?
98. How do we identify the slope and y-intercept of a straight line from its equation?
99. How do we graph a linear equation using the slope-intercept method?
100. How do we use a graph to express a linear relationship with a real-world context?
101. What is the relationship between the slopes of two parallel lines?  
102. How do we write the equation of a line?
103. How do we graph the absolute value function: 
104. Review
105. Test

XI. Systems of Equations 
106. How do we find a common solution for a system of two linear equations, with rational coefficients, graphically?
107. How can we use substitution to solve a system of linear equations, with integral coefficients, algebraically?
108. How can we use addition to solve a system of linear equations, with integral coefficients, algebraically?
109. How can we solve a more difficult system of linear equations algebraically?
110. How can we solve a system of more difficult linear equations algebraically?
111. How can we solve verbal problems that lead to solving a system of linear equations algebraically?
112. How do we graph a linear inequality?
113. How can we solve a system of linear inequalities graphically?
114. Review
115. Test

XII. Graphing Quadratics, Quadratic-Linear Systems, Exponential Functions
116. How do we graph a quadratic equation in two variables?
117. How do we graph a quadratic equation in two variables?
118. How can we graphically solve a system of equations involving a parabola and a straight line?
119. How can we solve a quadratic-linear system algebraically for systems with integral solutions only?
120. What is an exponential function?
121. How do we use an exponential function to solve verbal problems?
122. Review 
123. Test

XIII. Probability
124. How can we use a Venn diagram to solve problems?
125. How can we apply probability to problems involving spinners, dice, coins or cards?
126. How can we use tree diagrams and the counting principle to find probabilities of compound events?
127. How do we find conditional probability?
128. How can we find the probability of “A or B” and “A and B”?
129. How do we find probabilities sampling with and without replacement of objects?
130. What do we mean by permutations?
131. How can we count the number of possible arrangements of a set of objects, which are not all different, in a particular order?
132. Review 
133. Test

XIV. Statistics (part I)
134. How do we categorize data?
135. What are the various sampling techniques?
136. How do we determine when collected data or displayed data may be biased?
137. How do we compute the range and measures of central tendency for a given set of data?
138. How does a linear transformation of one-variable data affect the data’s mean, median, mode, and range?
139. How do we compare and contrast the appropriateness of different measures of central tendency for a given set of data?
140. How can we use the five-statistical summary to construct a box-and-whisker plot?
141. Review
142. Test

XV. Statistics (part II)
143. How can we construct frequency tables for intervals of length one and for intervals other than length one?
144. How do we organize data into a histogram?
145. How do we organize data into a cumulative frequency histogram?
146. How can we use a cumulative frequency histogram to determine information on percentile scores, quartile scores, and the median?
147. How do we create a scatter plot of bivariate data?
148. What is the difference between a linear correlation and causation?
149. For a given set of data, how do we manually construct a reasonable line of best fit and determine the equation of that line?
150. How can we use the line of best fit to predict unknown values?
151. How do we evaluate published reports and graphs that are based on data?
152. Review
153. Test