Learn about graphing polynomials. The shape of the curve changes as the constants are adjusted. View the curves for the individual terms (e.g. y=bx ) to see how they add to generate the polynomial curve.
Embedded from http://phet.colorado.edu/en/simulation/equation-grapher
Powerpoint with activating lesson, lesson, and references to assessments (GPS Georgia Mathematics I: Test Prep and Practice) for Unit 1, Lesson 1 for Math I.
Concepts: Family of Functions: Linear, Absolute Value, Quadratic, Cubic, Radical, and Rational
How do we represent functions using function notation?
How do we graph and write equation for each of the Family of Functions?
How do we graph transformations of functions?
What are the characteristics of a function and how do you use them?
How do we use graphs and tables to investigate behavior of functions?
How do we recognize sequences as functions with domains that are whole numbers?
How do constant rates of change compare to variable rates of change within the Family of Functions?
How do we determine graphically and algebraically whether a function has symmetry and whether it is odd, even, or neither?
How do we interpret an equation in x, and its solutions as f(x) = g(x) and show where they intersect? Identify functions by graph and equation B. Identify critical points and slope
C. Identify characteristics: Domain and range, zeros and intercepts, max and min, end behavior, and increase and decrease
C. Graph equation
D. Write equations from graph
E. Identify parent graphs.
Provides step-by-step feedback for students as they learn to model integer addition and subtraction with pictures. A hands-on experience that allows students to master the reasoning behind the "add the opposite" method for subtracting integers while developing fluency with addition.
This is a collection of interactive Excel spreadsheets or Excelets for use in mathematics and general chemistry. Many of the spreadsheets come with discovery-based activities. A number of Excelets support the introduction of mathematical modeling concepts. The user changes a variable and the spreadsheet changes in numerical, graphical, and/or even symbolic form (equations). Through the use of numerical experimentation and "what if" scenarios, we have a powerful learning tool for students using readily available off-the-shelf software. All of this is done computationally with no use of programming, no macros or Visual Basics for Applications, VBA.
In 1936 Alan Turing, a British Mathematician, came up with an idea for an imaginary machine that could carry out all kinds of computations on numbers and symbols. He believed that if you could write down a set of rules describing your computation his machine could faithfully carry it out. Turing's Machine is the cornerstone of the modern theory of computation and computability even though it was invented nine years before the creation of the first electronic digital computer.