Shared Gizmo List: Accel Math 1

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Algebra IAlgebra IIGeometry

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Shared by a high school math and science teacher in Georgia.

UNIT 1 QUADRATICS

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 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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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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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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TRIANGLES UNIT 5

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

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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UNIT 4 STAT

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

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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Dividing Exponential Expressions Choose the correct steps to divide exponential expressions. Use the 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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Polygons

Polygon Angle Sum Derive the sum of the angles of a polygon by dividing the polygon into triangles and summing their angles. Vary the number of sides and determine how the sum of the angles changes. Dilate the polygon to see that the sum is unchanged.
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Classifying Triangles Place constraints on a triangle and determine what classifications must apply to the triangle.
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Triangle Angle Sum Measure the interior angles of a triangle and find the sum. Examine whether that sum is the same for all triangles. Also, discover how the measure of an exterior angle relates to the interior angle measures.
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Triangle Inequalities Discover the inequalities related to the side lengths and angle measures of a triangle. Reshape and resize the triangle to confirm that these properties are true for all triangles.
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Segment and Angle Bisectors Explore the special properties of a point that lies on the perpendicular bisector of a segment, and of a point that lies on an angle bisector. Manipulate the point, the segment, and the angle to see that these properties are always true.
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Isosceles and Equilateral Triangles Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles.
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Concurrent Lines, Medians, and Altitudes Explore the relationships between perpendicular bisectors, the circumscribed circle, angle bisectors, the inscribed circle, altitudes, and medians using a triangle that can be resized and reshaped.
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Factoring Special Products Choose the correct steps to factor a polynomial involving perfect-square binomials, differences of squares, or constant factors. Use the feedback to diagnose incorrect steps.
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Modeling the Factorization of ax2+bx+c Factor a polynomial with a leading coefficient greater than 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
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Addition and Subtraction of Functions Explore the graphs of two polynomials and the graph of their sum or difference. Vary the coefficients in the polynomials and investigate how the graphs change in response.
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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.
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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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