BASIC ALGEBRA/GEOMETRY, Lenox Memorial High School

1. Introductions, syllabus, start-up
2. expressions versus sentences
3. addition
4. multiplication
5. divisibility
6. basic properties of zero and one
7. deciding if a number is a whole number, an integer, etc.
8. addition of signed numbers
9. subtraction of signed numbers
   mixed addition and subtraction of signed numbers
10. fractions with a denominator of 2 to decimal form
    the average of two signed numbers
11. the average of three signed numbers
12. identifying place values
    multiplying by powers of ten
13. changing decimals to fractions
    multiplying and dividing decimals by powers of ten
14. changing decimals to percents
    changing percents to decimals
15. introduction to sets
16. interval and list notation
17. introduction to variables
18. going from a sequence of operations to an expression
    going from an expression to a sequence of operations
19. solving simple sentences by inspection
    "undoing" a sequence of operations
20. solving for a particular variable
21. Getting bigger? Getting smaller?
22. scientific notation
23. rewriting fractions as a whole number plus a fraction
    locating fractions on a number line
24. fractions involving zero
    finding reciprocals
25. determining if a product is positive or negative
    multiplying and dividing fractions
26. practice with the form  a(b/c)
27. more practice with the form  a(b/c)
28. renaming fractional expressions
    practice with multiples
29. finding least common multiples
    renaming fractions with a specified denominator
30. practice with factors
    adding and subtracting fractions
31. adding and subtracting simple fractions with variables
32. divisibility equivalences
    identifying inequalities as true or false
33. bigger, smaller, greater, lesser
34. practice with the phrases "at least" and "at most"
    identifying inequalities with variables as true or false
35. solving equations of the form xy = 0
    recognizing zero and one
36. writing fractions in simplest form
    rounding decimals to a specified number of places
37. Tables of Unit Conversion Information
    classifying units as length, time, volume, weight/mass
    practice with unit abbreviations
38. practice with unit names
    practice with unit conversion information
39. one-step conversions
40. multi-step conversions
41. rate problems
42. practice with exponents
43. practice with order of operations
44. basic exponent practice with fractions
45. practice with  x^mxⁿ = x^m+n
    practice with  (x^m)ⁿ = x^mn
46. practice with  x^m/xⁿ = x^m-n
    practice with  x ^-p = 1/x ^p
47. one-step exponent law practice
48. multi-step exponent law practice
49. practice with radicals
50. approximating radicals
51. practice with  x  and  -x
    practice with products of signed variables
52. practice with the distributive law
53. equal or opposites?
54. recognizing the patterns xⁿ and (-x)ⁿ
    
55. writing expressions in the form kxⁿ
56. writing more complicated expressions in the form kxⁿ
57. writing quite complicated expressions in the form kxⁿ
58. identifying variable parts and coefficients of terms
    combining like terms
59. simplifying expressions like -a(3b - 2c - d)
60. basic FOIL
61. more complicated FOIL
62. simplifying  (a + b)²  and  (a - b)²
63. simplifying expressions like (a - b)(c + d - e)
64. practice with the mathematical words and, or, and is equivalent to
65. recognizing products and sums; identifying factors and terms
    identifying common factors
66. factoring simple expressions
    listing all the factors of a whole number
67. finding the greatest common factor of 2 or 3 numbers
    finding the greatest common factor of variable expressions
68. factoring out the greatest common factor
69. practice with the Addition Property of Equality
    practice with the Multiplication Property of Equality
70. solving simple linear equations with integer coefficients
71. solving more complicated linear equations with integer coefficients
72. solving linear equations involving fractions
73. solving linear equations, all mixed up
74. simple word problems resulting in linear equations
75. solving simple linear inequalities with integer coefficients
76. solving linear inequalities with integer coefficients
77. solving linear inequalities involving fractions
78. simplifying basic absolute value expressions
79. determining the sign (plus or minus) of absolute value expressions
    solving simple absolute value sentences
80. solving sentences like 2x - 1 = ±5
81. Additional Practice
82. solving absolute value equations
83. solving absolute value inequalities involving "less than"
84. solving absolute value inequalities involving "greater than"
85. solving absolute value sentences (all types)
86. identifying perfect squares
    writing expressions in the form A²
87. factoring a difference of squares
88. solving simple equations involving perfect squares
89. solving more complicated equations involving perfect squares
90. translating simple mathematical phrases
91. word problems involving perfect squares
92. basic concepts involved in factoring trinomials
93. factoring x² + bx + c,   c > 0
94. factoring x² + bx + c,   c < 0
95. factoring trinomials, all mixed up
96. identifying quadratic equations
97. writing quadratic equations in standard form
    solving simple quadratic equations by factoring
98. factoring ax² + bx + c
99. solving more complicated quadratic equations by factoring
100. multiplying and dividing fractions with variables
101. writing expressions involving percent increase and decrease
102. calculating percent increase and decrease
103. problems involving percent increase and decrease
104. more problems involving percent increase and decrease
105. locating points in quadrants and on axes
106. practice with points
107. the Pythagorean Theorem
108. the distance formula
109. the midpoint formula
110. introduction to equations and inequalities in two variables
111. adding and subtracting fractions with variables
112. introduction to the slope of a line
113. practice with slope
114. finding equations of lines
115. point-slope form
116. horizontal and vertical lines
117. parallel and perpendicular lines
118. introduction to functions
119. introduction to function notation
120. more practice with function notation
121. Dividing polynomials by monomials
122. introduction to the quadratic formula
123. choosing the best method to solve a quadratic equation
124. mixture problems
125. work problems
126. Points, Lines, and Planes
127. Segments, Rays, Angles
128. Introduction to Polygons
129. Sum of Angles in a Triangle
130. Constructions
131. More Terminology for Segments and Angles
132. Angles: Complementary, Supplementary, Vertical and Linear Pairs
133. Triangle Congruence
134. Parallel Lines
135. Quadrilaterals
136. Parallelograms and Negating Sentences
137. Introduction to Area and Perimeter
138. Area Formulas: Triangle, Parallelogram, Trapezoid
139. Area of a Rhombus
140. Similarity, Ratios, and Proportions
141. Two Special Triangles
142. Circles and related terminology (center, radius, diameter, chord, secant, tangent, concentric)
143. Arcs, Central Angles, and Chords
144. Inscribed Angles and Intercepted Arcs
145. Arc Lengths and Areas of Sectors
146. Geometric Probability
147. Introduction to Solids
148. Prisms
149. Pyramids
150. Cylinders and Cones
151. Spheres
152. Projections and Cross-Sections
153. Reflections/Translations
154. Rotations/Dilations
155. Composition of Mappings
156. Symmetry: Line, Point, Rotational
157. Vertex-Edge Graphs
158. Applications of Vertex-Edge Graphs
159. basic probability concepts
160. more probability concepts
161. probability tree diagrams
162. mean, median, and mode
163. measures of spread
164. graphical representations for data (scatterplot, table, line graphs)
165. graphical representations for data (stem-and-leaf plots)
166. graphical representations for data (box-and-whisker plots)
167. lines of best fit
168. First Quarter Midterm
169. First Quarter Final
170. Second Quarter Midterm
171. Second Quarter Final
172. Third Quarter Midterm
173. Third Quarter Final
174. Fourth Quarter Midterm
175. Fourth Quarter Final
176. (final exams)
177. (final exams)
178. (final exams)
179. (final exams)

© 2004–2007 Carol J.V. Fisher

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