Shared Gizmo List: Georgia GSE Geometry

aligned to the Georgia Standards of Excellence
Geometry

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Shared by an elementary school math and science teacher.

Unit One

Parallel, Intersecting, and Skew Lines Explore the properties of intersecting, parallel, and skew lines as well as lines in the plane. Rotate the plane and lines in three-dimensional space to ensure a full understanding of these objects.
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Investigating Angle Theorems Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
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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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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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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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Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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Reflections Reshape and resize a figure and examine how its reflection changes in response. Move the line of reflection and explore how the reflection is translated.
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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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Rock Art (Transformations) Create your own rock art with ancient symbols. Each symbol can be translated, rotated, and reflected. After exploring each type of transformation, see if you can use them to match ancient rock paintings.
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Unit Two

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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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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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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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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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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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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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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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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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 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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Parallelogram Conditions Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram.
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Special Parallelograms Apply constraints to a parallelogram and experiment with the resulting figure. What type of shape can you be sure that you have under each condition?
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Unit Three

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 Four

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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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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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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Circumference and Area of Circles Resize a circle and compare its radius, circumference, and area.
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Pyramids and Cones Vary the height and base-edge or radius length of a pyramid or cone and examine how its three-dimensional representation changes. Determine the area of the base and the volume of the solid. Compare the volume of a skew pyramid or cone to the volume of a right pyramid or cone.
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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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Unit Five

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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Unit Six

Spin the Big Wheel! (Probability) Step right up! Spin the big wheel! Each spin can result in no prize, a small prize, or a big prize. The wheel can be spun by 1, 10, or 100 players. Results are recorded on a frequency table or a circle graph. You can also design your own wheel and a sign that describes the probabilities for your wheel.
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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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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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Theoretical and Experimental Probability Experiment with spinners and compare the experimental probability of a particular outcome 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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