Counting Methods Unit Plan
Introduction to Counting Methods
General Outcome: Develop critical thinking skills related to uncertainty.
SO4. Solve problems that involve the fundamental counting principle. [PS, R, V]
4.1 Represent and solve counting problems, using a graphic organizer.
4.2 Generalize, using inductive reasoning, the fundamental counting principle.
4.3 Identify and explain assumptions made in solving a counting problem.
4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.
4.2 Generalize, using inductive reasoning, the fundamental counting principle.
4.3 Identify and explain assumptions made in solving a counting problem.
4.4 Solve a contextual counting problem, using the fundamental counting principle, and explain the reasoning.
SO5. Solve problems that involve permutations. [ME, PS, R, T, V]
(It is intended that circular permutations not be included.)
5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation.
5.2 Determine, with or without technology, the value of a factorial.
5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and denominator.
5.4 Solve an equation that involves factorials.
5.5 Determine the number of permutations of n elements taken r at a time.
5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.
5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.
5.8 Generalize strategies for determining the number of permutations of n elements taken r at a time.
5.9 Solve a contextual problem that involves probability and permutations.
5.1 Represent the number of arrangements of n elements taken n at a time, using factorial notation.
5.2 Determine, with or without technology, the value of a factorial.
5.3 Simplify a numeric or an algebraic fraction that contains factorials in both the numerator and denominator.
5.4 Solve an equation that involves factorials.
5.5 Determine the number of permutations of n elements taken r at a time.
5.6 Determine the number of permutations of n elements taken n at a time where some elements are not distinct.
5.7 Explain, using examples, the effect on the total number of permutations of n elements when two or more elements are identical.
5.8 Generalize strategies for determining the number of permutations of n elements taken r at a time.
5.9 Solve a contextual problem that involves probability and permutations.
SO6. Solve problems that involve combinations. [ME, PS, R, T, V]
6.1 Explain, using examples, why order is or is not important when solving problems that involve permutations or combinations.
6.2 Determine the number of combinations of n elements taken r at a time.
6.3 Generalize strategies for determining the number of combinations of n elements taken r at a time.
6.4 Solve a contextual problem that involves combinations and probability.
6.2 Determine the number of combinations of n elements taken r at a time.
6.3 Generalize strategies for determining the number of combinations of n elements taken r at a time.
6.4 Solve a contextual problem that involves combinations and probability.
Mathematical Processes
- Connections [CN] Students are expected to make connections among mathematical ideas, other concepts in mathematics, everyday experiences and other disciplines
- Problem Solving [PS] Students are expected to develop and apply new mathematical knowledge through problem solving
- Reasoning [R] Students are expected to develop mathematical reasoning
- Visualization [V] Students are expected to develop visualization skills to assist in processing information, making connections and solving problems.
- Mental Estimation [ME] Students are expected to demonstrate fluency with mental mathematics and estimation.
- Technology [T] Students are expected to select and use technology as a tool for learning and for solving problems