Shared Gizmo List: Math Department Dunwoody High School

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Algebra IAlgebra IICalculusGeometryPre-AlgebraPre-CalculusStatistics

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Pre-Calculus

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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Riemann Sum Approximate the area under a curve in an interval using rectangles. Compare the results of left-hand summation to the results of right-hand summation. Vary the interval and the number of rectangles and explore how the graph of the rectangles and curve change in response.
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Unit Circle (Classic) Explore the relationship between the unit circle and the graphs of the sine, cosine, and tangent functions.
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QUADRATICS

Quadratics in Vertex Form (Classic) Explore the graph of a quadratic of the form y = a(x - h)2 + k. Vary the terms of the equation and explore how the graph changes in response. Calculate the location of the vertex and y-intercepts.
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Roots of a Quadratic Find the root of a quadratic using its graph or the quadratic formula. Explore the graph of the roots and the point of symmetry in the complex plane. Compare the axis of symmetry and graph of the quadratic in the real plane.
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Quadratics in Polynomial Form Compare the graph of a quadratic to its equation in polynomial form. Vary the coefficients of the equation and explore how the graph changes in response.
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System of Two Quadratic Inequalities (Classic) Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response.
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Quadratics in Factored Form Investigate the factors of a quadratic through its graph and through its equation. Vary the roots of the quadratic and examine how the graph and the equation change in response.
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Quadratic Inequalities Find the solution set to a quadratic inequality using its graph. Vary the terms of the inequality and the inequality symbol. Examine how the boundary curve and shaded region change in response.
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Points in the Complex Plane (Classic) 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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RIGHT TRIANGLES AND TRIG RATIOS

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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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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Distance Formula Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.
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CIRCLES UNIT 6

Constructing Congruent Segments and Angles Construct congruent segments and angles using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.
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Perimeter and Area of Rectangles Discover how to find the perimeter and area of a rectangle, and of a square (which is really just a special case of a rectangle).
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Circumference and Area of Circles Resize a circle and compare its radius, circumference, and area.
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Chords and Arcs Explore the relationship between a central angle and the arcs it intercepts. Also explore the relationship between chords and their distance from the circle's center.
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Inscribed Angles Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
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STATS AND PROB UNIT 7

Populations and Samples Compare sample distributions drawn from population distributions. Predict characteristics of a population distribution based on a sample distribution and examine how well a small sample represents a given population.
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Correlation Explore the relationship between the correlation coefficient of a data set and its graph. Fit a line to the data and compare the least-squares fit line.
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Stem-and-Leaf Plots Build a data set and compare the line plot of the data set to the stem-and-leaf plot.
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Box-and-Whisker Plots Construct a box-and-whisker plot to match a line plots, and construct a line plot to match a box-and-whisker plots. Manipulate the line plot and examine how the box-and-whisker plot changes. Then manipulate the box-and-whisker plot and examine how the line plot changes.
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Mean, Median, and Mode Build a data set and find the mean, median, and mode. Explore the mean, median, and mode illustrated as frogs on a seesaw, frogs on a scale, and as frogs stacked under a bar of variable height.
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Polling: City Poll residents in a large city to determine their response to a yes-or-no question. Estimate the actual percentage of yes votes in the whole city. Examine the results of many polls to help assess how reliable the results from a single poll are. See how the normal curve approximates a binomial distribution for large enough polls.
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Exponents

Dividing Exponential Expressions Choose the correct steps to divide exponential expressions. Use the feedback to diagnose incorrect steps.
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Multiplying Exponential Expressions Choose the correct steps to multiply exponential expressions. Use the feedback to diagnose incorrect steps.
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Exponents and Power Rules Choose the correct steps to simplify expressions with exponents using the rules of exponents and powers. Use feedback to diagnose incorrect steps.
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Exponential Functions Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
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Exponential Growth and Decay Explore the graph of the exponential growth or decay function. Vary the initial amount and the rate of growth or decay and investigate the changes to the graph.
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Introduction to Exponential Functions Explore the graph of the exponential function. Vary the initial amount and base of the function. Investigate the changes to the graph.
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Exponential Functions (Classic) Explore the graph of an exponential function. Vary the coefficient and base of the function and investigate the changes to the graph of the function.
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Conics

Circumference and Area of Circles Resize a circle and compare its radius, circumference, and area.
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Circles Compare the graph of a circle with its equation. Vary the terms in the equation and explore how the circle is translated and scaled in response.
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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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Ellipses (Classic) 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. Manipulate 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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Hyperbolas (Classic) Compare the equation of a hyperbola to its graph. Vary the terms of the equation of the hyperbola and examine how the graph of the hyperbola and its asymptotes changes in response. Drag the vertices and foci to discover the string property.
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Parabola with Horizontal Directrix (Classic) Compare the graph of a parabola opening vertically and its directrix to its equation. Vary the terms in the equation and examine how the graph changes in response. Manipulate the focus, directrix, and vertex and discover the string property.
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Parabolas Explore parabolas in a conic section context. Find the relationship among the vertex, focus, and directrix of a parabola, and how that relates to its equation.
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Parabolas (Classic) Compare the graph of a parabola opening horizontally to its equation. Vary the terms in the equation and examine how the graph changes in response. Manipulate the focus, directrix, and vertex and discover the string property.
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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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Ellipses (Classic) 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. Manipulate the vertices and foci, explore their Pythagorean relationship, and discover the string property.
  5 Minute Preview   Lesson Info

Matrix

Logarithmic Functions: Translating and Scaling Vary the values in the equation of a logarithmic function and examine how the graph is translated or scaled. Connect these transformations with the domain of the function, and the asymptote in the graph.
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Solving Linear Systems (Matrices and Special Solutions) Explore systems of linear equations, and how many solutions a system can have. Express systems in matrix form. See how the determinant of the coefficient matrix reveals how many solutions a system of equations has. Also, use a draggable green point to see what it means for an (x, y) point to be a solution of an equation, or of a system of equations.
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Systems of Linear Inequalities (Standard form) (Classic) Compare a system of linear inequalities in standard form to its graph. Vary the coefficients and inequality symbols in the system. Explore how the boundary lines, shaded regions, and the intersection of the shaded regions change in response.
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Linear Programming Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the coefficients of the objective function and vary the constraints. Explore how the graph of the feasible region changes in response.
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Linear Programming (Classic) Use the graph of the feasible region to find the maximum or minimum value of the objective function. Vary the constraints and explore how the graph of the feasible region changes in response.
  5 Minute Preview   Lesson Info