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Monday, July 14, 2014

Essential Questions for Algebra 2

Pssst....Anna....here's what we have so far.

Sequences and Series
  • What kinds of patterns commonly arise in our world? 
  • Why is it sometimes desirable to describe a pattern mathematically? 
  • When we notice a real-world or mathematical pattern, what are some different ways in which we can describe it? 
  • How is it possible to keep getting closer and closer to something, but never actually touch it? 
Probability and Statistics
  • How can I use probability and statistics to make predictions and decisions that will benefit me in life?
  • How should I interpret statistical information about myself and that I see in the news?
  • What is the bell curve, why does it appear in many aspects of society, why is understanding it so important to our society?
  • What are are some more sophisticated ways of counting, and when are they useful?
Intro to Functions
  • How are functions used to represent/simulate the world we live in, and why are they so important?
  • How do functions help us to make the best decision?
  • What are some different kinds of functions, and what sorts of real-world situations can they model?
  • Why is the idea of "inverse" so important in mathematics?
Quadratics
  • How are quadratic functions used to understand/represent the Universe we live in?
  • How can writing a mathematical statement in different but equivalent ways highlight its various features?
  • Often, solving problems involves making choices. How can we make smart choices for any problem?
Polynomials
  • How are polynomial functions used to understand/represent the Universe we live in?
  • How are all the different representations of a polynomial function related?
Rationals
  • How are rational functions and different types of variation used to understand/represent the Universe we live in?
  • How is it possible to keep getting closer and closer to something, but never actually touch it?
Radicals
  • How are radical functions used to understand/represent the Universe we live in?
  • How can something that "doesn't exist" affect our world?
  • How can we make sense of exponents that are not integers?
Exponentials and Logs
  • How are exponential and logarithmic functions used to understand/represent the Universe we live in?
  • Why does the graph of an exponential function have its shape? How is it possible to get closer and closer to something and never touch it?
  • Why is the idea of "inverse" important in mathematics?
Modeling with Data
  • How do you decide if a mathematical model is "good"?
  • How can we use existing measurements to make predictions?
  • What are some possible pitfalls of using mathematical models to make predictions?