Shared Gizmo List: Geometry

2016 VA Standards of Learning
Geometry

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Shared by a science teacher.

G.1 Logic

Biconditional Statements Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form.
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Conditional Statements Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form.
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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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G.3 Symmetry and Transformations

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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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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Slope Explore the slope of a line, and learn how to calculate slope. Adjust the line by moving points that are on the line, and see how its slope changes.
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Holiday Snowflake Designer Fold paper and cut in a certain way to make symmetrical snowflakes with six sides (similar to what can be found in nature) or with eight sides (an easier folding method). This simulation allows you to cut virtual paper on the computer screen with round dot or square dot "scissors" of various sizes before using physical paper.
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Dilations Dilate a figure and investigate its resized image. See how scaling a figure affects the coordinates of its vertices, both in (x, y) form and in matrix form.
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Rotations, Reflections, and Translations Rotate, reflect, and translate a figure in the plane. Compare the translated figure to the original figure.
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Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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G.4 Constructions

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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Constructing Parallel and Perpendicular Lines Construct parallel and perpendicular lines using a straightedge and compass. Use step-by-step explanations and feedback to develop understanding of the construction.
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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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G.5 Triangles: Lengths of sides and measures of angles

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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G.6 Congruent Triangles

Congruence in Right Triangles Apply constraints to two right triangles. Then drag their vertices around under those conditions. Determine under what conditions the triangles are guaranteed to be congruent.
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Proving Triangles Congruent Apply constraints to two triangles. Then drag the vertices of the triangles around and determine which constraints guarantee congruence.
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G.7 Similar Triangles

Similar Figures Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.
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G.8 Right Triangles

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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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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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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Pythagorean Theorem with a Geoboard Build right triangles in an interactive geoboard and build squares on the sides of the triangles to discover the Pythagorean Theorem.
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Cosine Function Compare the graph of the cosine function with the graph of the angle on the unit circle. Drag a point along the cosine curve and see the corresponding angle on the unit circle.
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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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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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Tangent Function Compare the graph of the tangent function with the graph of the angle on the unit circle. Drag a point along the tangent curve and see the corresponding angle on the unit circle.
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G.10 Angles of convex 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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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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G.11 Properties of Circles

Inscribed Angles Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
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G.12 Equations of Circles

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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G.14 Apply the concepts of similarity to 2D or 3D geometric figures

Perimeters and Areas of Similar Figures Manipulate two similar figures and vary the scale factor to see what changes are possible under similarity. Explore how the perimeters and areas of two similar figures compare.
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Similar Figures Vary the scale factor and rotation of an image and compare it to the preimage. Determine how the angle measures and side lengths of the two figures are related.
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Prisms and Cylinders Vary the height and base-edge or radius length of a prism or cylinder and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of an oblique prism or cylinder to the volume of a right prism or cylinder.
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