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Domain and Range for a segmentAlgebra IDrag point C along segment AB to watch the domain and range appear on the axes. Drag the endpoints of the segment to try a new problem.7/9/2014
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Domain and Range for a set of pointsAlgebra I Drag the gray point over points A, B, C, D, and E to watch the domain and range for each point appear on the axes. Students move the points to try a new problem.7/8/2014
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Domain and range for functionsAlgebra I/Algebra IIInput a function, as well as left and right bounds for the functions. Drag the point along the function and watch as the domain and range are traced along the axes.
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Domain and range open endedAlgebra I/Algebra IIEnter a starting point for A. Drag point A to trace a relation, function, or shape. Watch as the domain and range are traced along the axes.Challenge students to trace a relation that has a given domain and range.
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Absolute Value GraphingAlgebra I/IIMove sliders a, h, and k. How do each of these change the graph? Reset slider values. Turn on the trace tool. As I move slider a a function family is created. What is the same and what is different about the graphs in this family? Reset sliders and clear trace. Repeat for sliders h and k.How is the graph changing as I change the parameter value? How is this reflected in the equation? For function families, what is the same and what is different about each graph?9/4/2014
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Inverse Functions PracticeAlgebra IIEnter a function into the input box for f(x). Move points A, B, and C so that they will be on the inverse function. The purpose of this step is to help you visualize what the inverse function will look like. Find the inverse function by showing work on your paper. Then type the inverse function into the f-inverse input box, and press enter to see if your function is correct.11/20/2014
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Square Root and Cube Root GraphsAlgebra IIClick the boxes to show either the square root or cube root function. Move points A, B, and C so that they are on the function (they will turn blue). Then move points A, B, and C according to the transformation given by your teacher. Type the transformed function into the input box, and press enter to see if your function is correct.11/21/2014
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Parent Graphs and function transformationsAlgebra II and Trig/Math AnalysisSelect a parent graph. Drag the sliders to view how the function is transformed. Turn on the trace feature to see a family of graphs.What effect on a parent graph does each parameter have? What does the b parameter do to a graph, and which parent graphs does this apply to?6/30/2014
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Inverse FunctionsAlgebra II and Trig/Math AnalysisThis tool will trace a function and the inverse relation. Represent your function by choosing its coordinates to be (a, f(a)), and for the inverse relation (f(a),a).What is relationship between the graph of a function and its inverse relation? How can we predict when a function will have an inverse function? If I know a point on the original function, what point will be on the inverse function?7/4/2014
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Cubics and Quartics (Easier version)Algebra II/Math AnalysisGeogebra Book: Find the equation of the cubic function that goes through each point. For pages 4-5, you can drag the intercepts to create a new function, and then find its equation.
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Tangent line to a functionCalculusInput a function. Drag slider a to see a dynamic tangent line.When will this line have a slope of zero? When will this line have a positive or negative slope? When will this line be above the function? Below the function?6/30/2014
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Tangent line approximationCalculusInput a function, x-coordinate for point of tangency, and an x-value for tangent line approximation. Zoom in on the point of tangency to see a visual representation on what happens. Check the values of the coordinates on the right to make use of the values.When is the tangent line approximation an overestimate/underestimate of the true value of the function? What does it depend on ? 6/30/2014
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Average value of a functionCalculusInput a function, lower limit, and upper limit of integration. Check the "show congruent area" box to view the corresponding rectange. Have students predict the average value or height of the rectangle.How can we get an average value of zero? 6/30/2014
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Graph of derivative functionCalculusDrag point A along function f, or hit the play button. Watch as point B traces out the graph of the derivative.When will the slope of the tangent line be positive, negative, or zero? When is the slope increasing or decreasing? Are there any values for which the slope doesn't exist or will approach infinity? How will this impact the graph of the derivative function?7/14/2014
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Definition of derivative at a given valueCalculusInput a function, a fixed point (a,f(a)) and a starting location for your moving points. Drag the moving point towards the fixed point. Use the values of the coordinates to find the slope of the secant line. How can I get a better approximation of the slope of the tangent line? Students should be able to tell you to drag the moving point as close to the fixed point as possible to get the best estimate.8/7/2014
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Topic CourseDescriptionPossible questions to ask students Date Added/Modified
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Coordinate Transformation Rules
GeometryInput point A. Write the coordinates of point B as a function of the coordinates of point A. Use the coordinate rules for reflection, translation, rotation, or dilation.After typing in a rule such as (a,b) goes to (b,-a), have students predict what the relationship will be between the two objects that will be traced.6/30/2014
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Transformations ReviewGeometryDrag any point to decide if it is dependent or independent. If it is a dependent point, what is the relationship to the independent point? Turn on the trace feature to see the relationship more clearly.6/30/2014
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DilationsGeometryDrag the points for the center of dilation or the vertices of preimage triangle. Use the table to check values, and make predictions for unknown valuesIf I know the side lengths of both triangles, how to do I find the dilation factor? If I know the dilation factor and a side of a triangle from the preimage or image, how do I find other sides?7/4/2014
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Trigonometric Ratios IntroGeometryUse this tool to check ratios of sides of right triangles. The diagram shows a set of 3 similar right triangles, so students can check a certain ratio for each to see that they are the same. This tool is best viewed using the Geogebra program, not a browser, so download from the linked site if possible.Find any needed side lengths, and record on the whiteboard or on your paper. Use the spreadsheet to find the ratio of the adjacent side over the hypotenuse for each triangle. What do you notice? Repeat this for the opposite side over the adjacent side. What do you notice? Change the angle using the slider. What predictions can you make about ratios of side lengths?7/4/2014
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Parabola from focus and directrix
GeometryDrag point B or select "animate" to see the graph of the parabola appear. Drag the focus or directrix to a new location to find another parabola.How can I change the focus or directrix to make the parabola wider? Narrower?7/4/2014
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Triangle area given coordinatesGeometryEnter the coordinates of the vertices of the triangle. Discuss what the enclosing rectangle will look like, and reveal this rectangle. Find the area using the subtraction method. Reveal area to check answer.What are the coordinates of the enclosing rectangle? What is the area of each non-included right triangle? How do I use these areas to help me find the area of my triangle? Can you find another triangle that has this same area? Can you find 3 different triangles that all have an area of 50?7/6/2014
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Exploring Parallel and Perpendicular LinesGeometryInput points A and B to create a line. Input point C so that C is not collinear with A and B. Find an equation of the line through point C that is parallel or perpendicular to line AB. You can input the equation in slope intercept, point slope, or standard form.How do I know that the lines are parallel or perpendicular?
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Pythagorean Theorem Practice and ProofGeometryGeogebra Book: Page 1 can be animated so students can make observations. Pages 2-4 Students can compare areas to observe Pythagorean Theorem. Page 5 is dynamic, so size of squares and triangles can be changed in order to verify Pythagorean Theorem.3-act Worksheet11/25/2014
Original Source with cut-outs
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Angle Pairs on transversalGeometryGeogebra Book: Each page shows the measurements for an angle pair formed when a transversal intersects a pair of parallell lines. Use to reinforce relationships and vocabulary.11/6/2014
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Triangle Transformation ActivityGeometryGeogebra Book: One of the three triangles is independent, and the other two are dependent. Determine the independent triangle. Identify the type of transformations that map the independent triangle onto the dependent triangles. Write as a coordinate rule as well.10/27/2014
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Coordinate Transformation Rules
GeometryGeogebra Book: Pages 1,3,4 can be used to review translations and reflections. For page 2, input a coordinate rule that relates point B to point A. Drag point A around the screen. Describe how the location of point B relates to point A. Make predictions about the location of point A or B, then move point A to the appropriate location to confirm your guesses.10/3/2014
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Exploring Trigonometric RatiosGeometryDrag points A and B to change the angle measures and side lengths of the given triangle. Check the boxes to the right to see the trigonometric ratios of the acute angles A and B. Observe how the ratios change as you change the measurements of the triangle.1. As an acute angle of a right triangle approaches 90 degrees, what happens to the value of the sine ratio? 2. How can we make cos(B) as large as possible? As small as possible? 3. How can we make tan(A)<1?1/1/2015
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Dilations and Area ExplorationGeometry1/6/2015
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angles in standard positionTrigonometryInput positive and negative angles in degrees, view the graph of the angle in standard position What will the angle look like? Where will it terminate? What other angles will have the same graph? Is this a positive or negative angle measure? How do you know? 6/29/2014
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Angles in standard position-dynamic versionTrigonometryTurn on animation. Watch as the terminal ray rotates in the counterclockwise direction. Turn off animation. What is the true angle measure? Geogebra only measures angles up to 360 degrees.How do you find the true angle measure? How many rotations/revolutions? In what quadrant does/will an angle terminate?7/2/2014
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Modeling tides with trig functions
TrigonometryGeogebra Book: Find an equation for the trigonometric function that goes through the given points that model high and low tides over a 24 hour period. Page 4 includes the data from the Rabbit and Fox problem from Illustrative Mathematics.10/9/2014
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