“Why is sigma notation useful?” and “Where is it actually used?” are questions answered in this program. Shows how calculators use sigma notation to determine trigonometric ratios and examines the various patterns present in Pascal’s triangle.
Grade levels: Senior High (10-12)
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Fundamental Counting Principle and Permutations
Stereos, clothes shopping, blood types, batting orders, telephone numbers and postal codes are topics used to demonstrate the fundamental counting principle. Students are introduced to permutations in a very general way.
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Sequences and Series: Review
This review of arithmetic and geometric sequences and series uses several common-sense approaches and formula manipulation to work with the patterns and relationships in a string of numbers.
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Permutations with Restrictions
Saddling up horses for a trail ride introduces permutations with restrictions. Formulas and common-sense approaches are used to solve permutation problems, including circular and ring permutations.
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Physical Properties of Conic Sections
Explores the topology of the double-napped cone and, through computer technology and graphics, demonstrates conditions necessary to produce the conic sections and their degenerates.
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Combinations
Choices pervade our lives. From concrete examples to questions with restrictions, students count choices and solve problems involving combinations. Practical and technological examples are included.
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Division of Polynomial Functions and Their Graphs
Historical anecdotes intersperse the teaching of long division with linear and nonlinear divisors. The concept of synthetic division is also presented, along with a strategy for finding missing coefficients.
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Sketching and Graphing Exponential Functions
Students learn to recognize the general characteristics of the graphs of exponential functions with various bases. Situations involving exponential growth and decay are explored. Students solve and verify exponential equations.
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The Remainder and Factor Theorems
The Remainder Theorem is illustrated, proven, and then used to prove the Factor Theorem.
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Exponential Growth and Decay
Through a variety of real world applications, this program explores the concepts of exponential growth and decay. Examples include carbon dating, bacterial growth, DNA splicing and the effect of the bubonic plague on current world populations.