Shared Gizmo List: Georgia Pre Calculus

aligned to the Georgia Standards of Excellence
Pre-Calculus

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Shared by an elementary school math and science teacher.

Unit 1: Conics

Ellipses Compare the equation of an ellipse to its graph. Vary the terms of the equation of the ellipse and examine how the graph changes in response. Drag the vertices and foci, explore their Pythagorean relationship, and discover the string property.
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Hyperbolas Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola. Examine how the graph of the hyperbola and its asymptotes changes in response.
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Unit 2: Trigonometric Functions

Sine Function Compare the graph of the sine function with the graph of the angle on the unit circle. Drag a point along the sine curve and see the corresponding angle on the unit circle.
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Unit 3: Trigonometry of General Triangles

Similarity in Right Triangles Divide a right triangle at the altitude to the hypotenuse to get two similar right triangles. Explore the relationship between the two triangles.
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Sine, Cosine, and Tangent Ratios Reshape and resize a right triangle and examine how the sine of angle A, the cosine of angle A, and the tangent of angle A change.
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Pythagorean Theorem Explore the Pythagorean Theorem using a dynamic right triangle. Examine a visual, geometric application of the Pythagorean Theorem, using the areas of squares on the sides of the triangle.
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Unit 4: Trigonometric Identities

Simplifying Trigonometric Expressions Choose the correct steps to simplify a trigonometric function. Use step-by-step feedback to diagnose incorrect steps.
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Sum and Difference Identities for Sine and Cosine Choose the correct steps to evaluate a trigonometric expression using sum and difference identities. Use step-by-step feedback to diagnose incorrect steps.
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Unit 5: Matrices

Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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Unit 6: Vectors

Points in the Complex Plane Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
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Points in the Complex Plane Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
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Points in the Complex Plane Identify the imaginary and real coordinates of a point in the complex plane. Drag the point in the plane and investigate how the coordinates change in response.
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Vectors Manipulate the magnitudes and directions of two vectors to generate a sum and learn vector addition. The x and y components can be displayed, along with the dot product of the two vectors.
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2D Collisions Investigate elastic collisions in two dimensions using two frictionless pucks. The mass, velocity, and initial position of each puck can be modified to create a variety of scenarios.
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Adding Vectors Move, rotate, and resize two vectors in a plane. Find their resultant, both graphically and by direct computation.
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Unit 7: Probability

Independent and Dependent Events Compare the theoretical and experimental probabilities of drawing colored marbles from a bag. Record results of successive draws to find the experimental probability. Perform the drawings with replacement of the marbles to study independent events, or without replacement to explore dependent events.
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Permutations and Combinations Experiment with permutations and combinations of a number of letters represented by letter tiles selected at random from a box. Count the permutations and combinations using a dynamic tree diagram, a dynamic list of permutations, and a dynamic computation by the counting principle.
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Probability Simulations Experiment with spinners and compare the experimental probability of particular outcomes to the theoretical probability. Select the number of spinners, the number of sections on a spinner, and a favorable outcome of a spin. Then tally the number of favorable outcomes.
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Geometric Probability Randomly throw darts at a target and see what percent are "hits." Vary the size of the target and repeat the experiment. Study the relationship between the area of the target and the percent of darts that strike it
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