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Foundations of Mathematics 20

Foundations of Mathematics 20 is divided into seven units. It meets the required outcomes outlined by Saskatchewan Learning, and is a prerequisite for Foundations of Mathematics 30. Students will require a TI-83 or TI-84 calculator in order to complete this course. This workbook series was developed for use by schools using an individualized, mastery-based learning system, and therefore comes with score keys, tests, and test keys. No additional text is necessary.


Unit 1: Inductive and Deductive Reasoning

At the end of unit one, the student should be able to:

  • understand the difference between inductive and deductive reasoning
  • form and analyze conjectures
  • prove or disprove conjectures to solve problems
  • solve problems using inductive and deductive reasoning
  • analyze and strategize puzzles involving spatial reasoning


Unit 2: Properties of Angles and Triangles

At the end of unit two, the student should be able to:

  • determine the measure of unknown angles using properties of angles formed by parallel lines and transversals
  • determine the measure of unknown angles using angle properties of triangles
  • determine the measure of unknown angles using angle properties of polygons
  • derive proofs based on theorems and postulates about parallel lines and triangles
  • solve problems that involve angles, parallel lines, transversals, and triangles


Unit 3: Proportional Reasoning

At the end of unit three, the student should be able to:

  • solve problems that involve rates
  • solve problems that involve scale factors
  • determine the relationship between scale factors, surface areas, and volumes of similar objects
  • use the relationship between scale factor, surface area, and volume in similar objects to solve problems
  • solve real world problems using the properties of similar triangles


Unit 4: Systems of Linear Inequalities

At the end of unit four, the student should be able to:

  • graph linear inequalities
  • solve problems using linear inequalities in two variables
  • solve problems using systems of inequalities in two variables
  • graph the feasible region of a system of linear inequalities
  • optimize a given objective quantity
  • solve word problems by optimizing the objective quantity


Unit 5: Quadratic Functions

At the end of unit five, the student should be able to demonstrate an understanding of the characteristics of quadratic functions of the form y = a(x - p)2 + q, including:

  • vertex
  • intercepts
  • domain and range
  • axis of symmetry


Unit 6: Trigonometry

At the end of unit six, the student should be able to:

  • completely solve a right triangle
  • understand angle of elevation and angle of depression
  • use the law of sines to solve triangles (determine side lengths and angle measures)
  • use the law of cosines to solve triangles (determine side lengths and angle measures)
  • solve problems by applying the law of sines and the law of cosines
  • determine how many triangles are possible in the ambiguous case of an SSA triangle


Unit 7: Statistical Reasoning

At the end of unit seven, the student should be able to:

  • analyze a numerical data set by creating a grouped frequency distribution table, a histogram, and a frequency polygon
  • use a graphing calculator to analyze data as above
  • calculate the mean, median, and the mode of a numerical data set
  • calculate the range, mean deviation, and standard deviation of a numerical data set
  • understand what it means for data to be normally distributed
  • use a normal curve to estimate the number of data items lying within a specified range
  • use a graphing calculator to draw normal curves
  • convert actual data items to z-scores
  • find the area under the standard normal curve
  • find the probability of events whose outcomes are normally distributed
  • use the area under the standard normal curve to estimate an actual data value
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SAICS has developed Christian curriculum (where none other was available) to match Saskatchewan Learning objectives for high school courses.

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