Common Core State Standards
Functions
Linear, Quadratic, and Exponential Models
Construct and compare linear, quadratic, and exponential models and solve problems
Lessons (10)
Introduces students to a geometric derivation of the conic sections.
Students will graph input/output pairs from a simple linear function in order to gain an understanding of basic linear functions.
Students learn basic ideas about graphing points on the coordinate plane.
Demonstrates the connections between formulas and graphs.
Introduces students to arithmetic and geometric sequences. Students explore further through producing sequences by varying the starting number, multiplier, and add-on.
Introduces the basic ideas needed for understanding linear functions.
Introduces the basic ideas needed for understanding functions.
Demonstrates the connections between formulas, graphs and words.
Students learn to identify a variety of patterns using sequences and tessellations.
Introduces students to the vertical line test for graphs of functions.
Activities (14)
Manipulate different types of conic section equations on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph. Choose from vertical or horizontal parabola, circle, ellipse, and vertical or horizontal hyperbola.
Enter a set of data points, then derive a function to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.
A more advanced version of Slope Slider, this activity allows the manipulation of the constants and coefficients in any function thereby encouraging the user to explore the effects on the graph of the function by changing those numbers.
Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs. Function Machine is one of the Interactivate assessment explorers.
Students can create graphs of functions entered as algebraic expressions -- similar to a graphing calculator.
Create graphs of functions and sets of ordered pairs on the same coordinate plane. This is like a graphing calculator with advanced viewing options.
Students investigate linear functions by trying to guess the slope and intercept from inputs and outputs. Linear Function Machine is one of the Interactivate assessment explorers.
Enter a set of data points and a function or multiple functions, then manipulate those functions to fit those points. Manipulate the function on a coordinate plane using slider bars. Learn how each constant and coefficient affects the resulting graph.
Similar to the original "Function Machine" but lists input and output in a table and will not let the user attempt to guess the rule without having at least two data points. Number Cruncher is one of the Interactivate assessment explorers.
Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs. Positive Linear Function Machine is one of the Interactivate assessment explorers.
Learn about number patterns in sequences and recursions by specifying a starting number, multiplier, and add-on. The numbers in the sequence are displayed on a graph, and they are also listed below the graph.
Similar to other "flyers", Slope Slider uses slider bars to explore the effect of the multiplier and constant on a linear function of the form f(x)=mx+b. Explore the relationship between slope and intercept in the Cartesian coordinate system.
Give input to the Whole Number Cruncher and try to guess what it did from the output it generates. This activity only generates multiplication and addition functions to avoid outputting any negative numbers. Whole Number Cruncher is one of the Interactivate assessment explorers.
Students create linear inequalities and systems of linear inequalities on a coordinate plane. This is like a graphing calculator with advanced viewing options.