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Middle school math requires many different and sometimes difficult concepts. Below are links to programs that can help you complete many tasks as well assist you in learning concepts that you are working on! These links will open in a new window and this website will stay open in the background. Thank you to The Shodor Education Foundation, Inc © Copyright 1997-2001 for the development and use of the activities! Areas of Study: Number and Operation ConceptsConvert fractions to decimals and decimals to fractions Play a generalized version of connect four, gaining the chance to place a piece on the board by simplifying a fraction. Parameters: Level of difficulty of fractions to simplify Learn about classifying numbers into various categories through answering questions about Venn Diagrams Learn about number patterns in sequences and recursions by specifying a starting number, multiplier and add-on Color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that are multiples of the number rolled, thereby practicing multiplication tables investigating number patterns, and investigating fractal patterns. Color numbers in Pascal's Triangle by rolling a number and then clicking on all entries that have the same remainder when divided by the number rolled, thereby practicing multiplication tables, investigating number patterns, and investigating fractal patterns Learn about modular arithmetic operations through working with various types of clocks. Parameters: Number of hours on the clock Practice simple arithmetic skills by encoding and decoding messages using an affine cipher Practice reasoning and arithmetic skills by decoding messages to determine the form for an affine cipher. Step through the tortoise and hare race, based on Zeno's paradox, to learn about the multiplication of fractions and about convergence of an infinite sequence of numbers Learn about fractions between 0 and 1 by repeatedly deleting portions of a line segment, also learning about properties of fractal objects. Parameter: fraction of the segment to be deleted each time. Geometry and Measurement ConceptsStudents are shown shapes on a grid after setting the perimeter and asked to calculate areas of the shapes Students are shown shapes on a grid after setting the area and asked to calculate perimeters of the shapes Students are shown shapes on a grid and asked to calculate areas and perimeters of the shapes Students explore the world of translations, reflections, and rotations in the Cartesian coordinate system by transforming squares, triangles and parallelograms. Parameters: Shape, x or y translation, x or y reflection, angle of rotation An expanded version of TransmoGrapher which allows reflections across any line and rotations about any point. It also allows the user to specify the vertices of the polygon used. Parameters: Polygon, x or y translation, line of reflection, angle of rotation, point to rotate about Students practice their knowledge of acute, obtuse and alternate angles Students learn about areas of triangles and about the Cartesian coordinate system through experimenting with triangles drawn on a grid Students find the length of a side of a right triangle by using the Pythagorean Theorem, and then check their answers Students learn about how the Pythagorean Theorem works, through investigating the standard geometric proof. Parameters: Sizes of the legs of the triangle. Students learn about tessellation on quadrilateral figures by dynamically changing the shape of the quadrilateral through dragging corners Students deform a triangle, rectangle or hexagon to form a polygon that tiles the plane. Corners of the polygons may be dragged, and corresponding edges of the polygons may be dragged. Parameters: Colors, starting polygon Students manipulate dimensions of polyhedra, and watch how the surface area and volume change. Parameters: Type of polyhedron, length, width and height Students step through the generation of a Hilbert Curve -- a fractal made from deforming a line by bending it, allowing them to explore number patterns in sequences and geometric properties of fractals Students 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 Students step through the generation of the Koch Snowflake -- a fractal made from deforming the sides of a triangle, allowing them to explore number patterns in sequences and geometric properties of fractals. Students step through the generation of Sierpinski's Triangle -- a fractal made from subdividing a triangle into four smaller triangles and cutting the middle one out, allowing them to explore number patterns in sequences and geometric properties of fractals Students step through the generation of Sierpinski's Carpet -- a fractal made from subdividing a square into nine smaller squares and cutting the middle one out, allowing them to explore number patterns in sequences and geometric properties of fractals Students play the Chaos Game by experimenting with probabilities, and they learn about an apparently random process with a not-so-random, geometric fractal result Students investigate the fractal dimensions of several line- deformation fractals Students generate complicated geometric fractals by specifying starting polygon and scale factor Students create their own fractals by specifying a "line deformation rule" and stepping through the generation of a geometric fractal. Parameters: Grid type, number of bending points on the line Students enter a complex value for c in the form of an ordered pair of real numbers. The applet draws the fractal Julia set for that seed value Students investigate the relationships between the Mandelbrot set and Julia sets by clicking and zooming Function and Algebra ConceptsThis activity allows the manipulation of a linear function of the form f(x)=mx+b and encourages the user to explore the relationship between slope and intercept in the cartesian coordinate system. Students can plot ordered pairs of numbers, either as a scatter plot or with the dots connected Students can create graphs of functions by entering formulas -- similar to a graphing calculator Students can graph functions and sets of ordered pairs on the same coordinate plane -- similar to a graphing calculator Students investigate the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted Students investigate the first quadrant of the Cartesian coordinate system through identifying the coordinates of points, or requesting that a particular point be plotted Students investigate very simple functions by trying to guess the algebraic form from inputs and outputs Students investigate linear functions by trying to guess the slope and intercept from inputs and outputs Students investigate linear functions with positive slopes by trying to guess the slope and intercept from inputs and outputs Students learn about the vertical line test for functions by trying to connect points in the plane to build a function Drills students on whether a curve satisfies the properties of functions Students 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 Probability and Data Analysis ConceptsStudents can view histograms for either built-in or user-specified data, and experiment with how the size of the class intervals influences the perceptions. Parameters: Data sets, class sizes Students view piecharts. Parameters: Number of sectors, size of sector as a percent Students view stem-and-leaf plots of their data, and then get to practice finding means, medians and modes. Parameters: Data Students can view boxplots for either built in or user-specified data, and experiment with outliers. Parameters: Data sets, definition of outliers Two players each roll a die, and the lucky player moves one step to the finish. Parameters: what rolls win and how many steps to the finish line N players roll two dice, the lucky player moves one step to the finish, or everybody moves one step and the lucky player moves two steps to the finish. Parameters: the number of players, number of trials and length of the race Three players play games of chance using dice, cards, spinners or coin tosses, to compare theoretical and experimental probabilities. Parameters: Type of game for each player, number of trials Students can create a game spinner with one to twelve sectors to look at experimental and theoretical probabilities. Parameters: Number of sectors, number of trials Students can create a game spinner with variable sized sectors to look at experimental and theoretical probabilities. Parameters: Sizes of sectors, number of sectors, number of trials Students choose between three boxes and choose one marble from the box to look at conditional probabilities. Parameters: Number of trials Students learn about sampling with and without replacement by modeling drawing marbles from a bag. Parameters: Number and color of marbles in the bag, replacement rule Students choose one of three doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Staying or switching between the two remaining doors Students run a simulation to mimic the simple monty hall activity with multiple trials. Parameters: Number of doors, number of trials, staying or switching between the two remaining doors Students choose one of N doors to experimentally determine the odds of winning the grand prize behind one of the doors, as in the TV program "Let's Make a Deal." Parameters: Number of doors, number of trials, staying or switching between the two remaining doors Students experiment with the outcome distribution for a roll of two dice by playing a dice throwing game. Parameters: Which player wins on which rolls Students learn about expected value and payoff for an event that will occur with a known probability, by playing a game in which the payoff is earnings from stocks. Parameters: Probability of receiving cash, cash amounts, number of trials Students click to build dot plots of data and view how the mean, median, and mode change as numbers are added to the plot. Parameters: Range for observations Students enter data and view the mean, median, variance and standard deviation of the data set. Parameters: Number of observations, range for observations, which statistics to view, identifiers for the data Students can change the standard deviation of the graphed normal distribution to create a new distribution, allowing them to observe properties like how well the histogram fits the curve and how areas under the curve correspond to the probability that a number is selected. Parameters: standard deviation, number of trials, class intervals Students can change the median standard deviation of the graphed normal distribution to create a skewed distribution, allowing them to observe properties like what it means for the mean, median, and mode to be different. Parameters: median, standard deviation, number of trials, class intervals Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will burn Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Probability that a tree will set fire to each of its eight neighbors Students run a simulation of how a fire will spread through a stand of trees, learning about probability and chaos. Parameters: Forest density, wind direction, size of forest Students run the classic game of life, learning about probabilities, chaos and simulation. Parameters: Type of world, types of "life," rules for living Similar to Life with fewer options for creatures and world configuration Students experiment with a simple ecosystem consisting of grass, rabbits and wolves, learning about probabilities, chaos and simulation Students play the Chaos Game by experimenting with probabilities, and they learn about an apparently random process with a not-so-random, geometric fractal result Students experiment with a simulation to get an approximation of Pi
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