Unpacked Content
Knowledge
Students know:
- Distributive Property of multiplication over addition for polynomials.
- The generation pattern for Pascal's Triangle and which binomial expansion term has coefficients corresponding to each row.
- Simplification procedures for expressions involving the number of combinations of n things taken r at a time.
- The patterns of coefficients and exponents in a binomial expansion.
Skills
Students are able to:
- Accurately perform algebraic manipulations on polynomial expressions.
- Generate rows of Pascal's Triangle.
- Accurately perform simplification procedures for expressions involving the number of combinations of n things taken r at a time.
- Apply the patterns of coefficients and exponents to expand any binomial raised to a power.
Understanding
Students understand that:
- Regularities noted in one part of mathematics may also be seen in very different areas of mathematics, (i.e., Pascal's Triangle from counting procedures and the Binomial Theorem). These regularities are useful in computing or manipulating mathematical expressions.
- The regularities that are seen in exponents and coefficients in a binomial expansion will be generalized to all binomials to aid in identifying specific terms.
Vocabulary
- Binomial Theorem
- Pascal's Triangle
- Combinatorial Argument
- Mathematical induction
