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BASIC ALGEBRA/GEOMETRY, Lenox Memorial High School

There are  178 + 2(0.5) = 179  class meetings in the school year:

first 2 21 21.5                 44.5
second       15 14 14           43
third           5 15 21.5 3     44.5
fourth                 13 20 14 47

Algebra Table of Contents

  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  xmxn = xm+n
    practice with  (xm)n = xmn
  46. practice with  xm/xn = xm-n
    practice with  x-p = 1/xp
  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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