Interactivate: Standard Expectation

42 items total

Organization: National Council of Teachers of Mathematics
Grade Band: Grades 9 - 12
Standard Goal: Algebra Standard

Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.
Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.
Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations.
Use symbolic algebra to represent and explain mathematical relationships.
Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluencyâmentally or with paper and pencil in simple cases and using technology in all cases.
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Judge the meaning, utility, and reasonableness of the results of symbol manipulations, including those carried out by technology.

Introduction to Fractals: Infinity, Self-Similarity and Recursion	Lesson: Introduces students to the ideas involved in understanding fractals.
Function Flyer	Activity: 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.
InteGreat!	Activity: InteGreat! allows the user to visually explore the idea of integration through approximating the integral value with partitions. The activity integrates a function and displays the value of the definite integral as well as overlays the specified number of partitions on the graph of the function. The user controls the number of partitions and the upper and lower limits.
The Mandelbrot Set	Activity: Investigate the relationships between the famous Mandelbrot Set fractal and Julia sets by clicking and zooming.

Understand the meaning of equivalent forms of expressions, equations, inequalities, and relations.

Impossible Graphs	Lesson: Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.
Reading Graphs	Lesson: Demonstrates the connections between formulas, graphs and words.
Conic Flyer	Activity: 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.

Use a variety of symbolic representations, including recursive and parametric equations, for functions and relations.

Spy Game	Lesson: Students will learn about modular arithmetic in order to decipher encrypted messages.
Another Hilbert Curve Generator	Activity: Students work step-by-step through the generation of a different Hilbert-like Curve (a fractal made from deforming a line by bending it), allowing them to explore number patterns in sequences and geometric properties of fractals.
Cantor's Comb	Activity: Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, and also learn about properties of fractals. Parameter: fraction of the segment to be deleted each time.
Hilbert Curve Generator	Activity: Step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, and explore number patterns in sequences and geometric properties of fractals.
Recursion	Activity: Graph recursive functions by defining f(0)=C and defining f(n) based on f(n-1).
The Mandelbrot Set	Activity: Investigate the relationships between the famous Mandelbrot Set fractal and Julia sets by clicking and zooming.
Tortoise and Hare Race	Activity: Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence and limits to an infinite sequence.

Use symbolic algebra to represent and explain mathematical relationships.

Cartesian Coordinate System	Lesson: Introduces students to plotting points on the Cartesian coordinate system -- an alternative to "Graphing and the Coordinate Plane."
Functions and the Vertical Line Test	Lesson: Introduces students to the vertical line test for graphs of functions.
Graphs and Functions	Lesson: Demonstrates the connections between formulas and graphs.
Introduction to Functions	Lesson: Introduces the basic ideas needed for understanding functions.
More Complicated Functions: Introduction to Linear Functions	Lesson: Introduces the basic ideas needed for understanding linear functions.
Practicing Arithmetic	Lesson: Students practice arithmetic skills. Can be tailored for practice of all types of single operation arithmetic ranging from simple addition to operations with integers and decimals.
Reading Graphs	Lesson: Demonstrates the connections between formulas, graphs and words.
Algebra Four	Activity: 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.
Algebra Quiz	Activity: 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.
Data Flyer	Activity: 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.
Function Flyer	Activity: 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.
Function Machine	Activity: 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.
Linear Function Machine	Activity: 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.
Number Cruncher	Activity: 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 on without at least having two data points.
Positive Linear Function Machine	Activity: Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs.
Slope Slider	Activity: Manipulate a linear function of the form f(x)=mx+b using slider bars. Explore the relationship between slope and intercept in the Cartesian coordinate system.
Tables and Chairs	Activity: Explore rectangular and straight-line arrangements of tables, calculating the number of chairs needed to surround different arrangements thereby exploring perimeter concepts. Tables and Chairs is one of the Interactivate assessment explorers.
Whole Number Cruncher	Activity: 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.

Write equivalent forms of equations, inequalities, and systems of equations and solve them with fluencyâmentally or with paper and pencil in simple cases and using technology in all cases.

Impossible Graphs	Lesson: Teaches distinguishing between possible and impossible graphs of functions as well as causes of graphical impossibility.
Reading Graphs	Lesson: Demonstrates the connections between formulas, graphs and words.
Algebra Four	Activity: 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.
Algebra Quiz	Activity: 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.
Function Machine	Activity: 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.
Linear Function Machine	Activity: 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.
Number Cruncher	Activity: 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 on without at least having two data points.
Positive Linear Function Machine	Activity: Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs.
Tables and Chairs	Activity: Explore rectangular and straight-line arrangements of tables, calculating the number of chairs needed to surround different arrangements thereby exploring perimeter concepts. Tables and Chairs is one of the Interactivate assessment explorers.
Whole Number Cruncher	Activity: 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.