Alaska Performance Standards
Grade 9
Functions and Relationships
The student demonstrates conceptual understanding of functions, patterns, or sequences including those represented in real-world situations.
Lessons (13)
Introduces students to a geometric derivation of the conic sections.
This lesson utilizes the concepts of cross-sections of three-dimensional figures to demonstrate the derivation of two-dimensional shapes.
Explores derivatives and the idea of infinity using a geometric interpretation of slope.
Students will graph input/output pairs from a simple linear function in order to gain an understanding of basic linear functions.
Demonstrates the connections between formulas and graphs.
Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.
Introduces students to the ideas involved in understanding fractals.
Introduces the basic ideas needed for understanding linear functions.
Introduces the basic ideas needed for understanding functions.
Introduces students to graphing in the Polar coordinate plane
Demonstrates the connections between formulas, graphs and words.
Introduction to various algorithms for solving single-variable, linear equations.
Introduces students to the vertical line test for graphs of functions.
Activities (25)
Students play a generalized version of connect four, gaining the chance to place a piece on the board by solving an algebraic equation. Parameters: Level of difficulty of equations to solve and type of problem. Algebra Four is one of the Interactivate assessment games.
Test your algebra skills by answering questions. This quiz asks you to solve algebraic linear and quadratic equations of one variable. Choose difficulty level, question types, and time limit. Algebra Quiz is one of the Interactivate assessment quizzes.
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.
Explore cross sections of different geometric solids: cone, double cone, cylinder, pyramid, and prism. Manipulate the cross section with slider bars, and see how the graphical representation changes.
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.
View the graph and the equation of the line tangent to any function at any point on the function.
This activity helps you understand how to balance an equation. You input the term and the operation. The activity uses that term and operates on both sides of the equation. It then displays the resulting equation. Equation Solver is one of the Interactivate assessment explorers.
Students play a generalized version of connect four, gaining the chance to place a piece after simplifying fractions, converting fractions to decimals and percentages, and answering algebra questions involving fractions. Choose difficulty level, question types, and time. Fraction Four is one of the Interactivate assessment games.
Test your fraction skills by answering questions. This quiz asks you to simplify fractions, convert fractions to decimals and percentages, and answer algebra questions involving fractions. Choose difficulty level, question types, and time. Fraction Quiz is one of the Interactivate assessment quizzes.
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.
This applet allows the user to make observations about the relationship between speed and position and how both of these are affected by initial velocity and the incline on which the biker is traveling.
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.
This activity allows the user to explore the polar coordinate system. The applet is similar to GraphIt, but instead allows users to explore the representation of a function in the polar coordinate system.
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.
Review the properties of functions by looking at ten different curves and deciding whether or not they meet the criteria for a graph of a function. This activity simply displays the curves - it does not quiz the user.
Graph recursive functions by defining f(0)=C and defining f(n) based on f(n-1).
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.
Enter two complex numbers (z and c) as ordered pairs of real numbers, then click a button to iterate step by step. The iterates are graphed in the x-y plane and printed out in table form. This is an introduction to the idea of prisoners/escapees in iterated functions and the calculation of fractal Julia sets.
Learn about the vertical line test for functions by trying to connect points in the plane to build a function. When you have connected all of the points, you will be told if your graph is a valid graph of a function. Vertical Line Test is one of the Interactivate assessment explorers.
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.