Shared Gizmo List: SDHC High School Math - Geometry Honors

School District of Hillsborough County High School Mathematics Geometry Honors
Geometry

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SDHC High School Math - Geometry Honors

SEMESTER 1

Unit 1 - Geometric Figures and Basic Reasoning

-- GCG 1 of 2 --

Investigating Angle Theorems Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
  5 Minute Preview   Lesson Info

-- GCG 2 of 2 --

Conditional Statements Make a conditional statement from a given fact using word tiles. Use both symbolic form and standard English form.
  5 Minute Preview   Lesson Info
Biconditional Statements Make a biconditional statement from a given definition using word tiles. Use both symbolic form and standard English form.
  Free   Lesson Info

Unit 2 - Distance, Midpoint, and Angle Measurement

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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info

Unit 3 - Angles, Parallel Lines, and Perpendicular Lines

-- GCG 1 of 2 --

Investigating Angle Theorems Explore the properties of complementary, supplementary, vertical, and adjacent angles using a dynamic figure.
  5 Minute Preview   Lesson Info

-- GCG 2 of 2 --

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.
  Free   Lesson Info
Slope-Intercept Form of a Line Compare the slope-intercept form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
  5 Minute Preview   Lesson Info
Point-Slope Form of a Line Compare the point-slope form of a linear equation to its graph. Vary the coefficients and explore how the graph changes in response.
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Unit 4 - Transformations

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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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.
  5 Minute Preview   Lesson Info
Translations Translate a figure horizontally and vertically in the plane and examine the matrix representation of the translation.
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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.
  5 Minute Preview   Lesson Info

Unit 5 - Congruence, Triangles and Proofs

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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Unit 6 - Properties of Triangles

Classifying Triangles Place constraints on a triangle and determine what classifications must apply to the triangle.
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Isosceles and Equilateral Triangles Investigate the graph of a triangle under constraints. Determine which constraints guarantee isosceles or equilateral triangles.
  5 Minute Preview   Lesson Info
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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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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Unit 7 - Quadrilaterals

Parallelogram Conditions Apply constraints to a dynamic quadrilateral. Then drag its vertices around. Determine which constraints guarantee that the quadrilateral is always a parallelogram.
  5 Minute Preview   Lesson Info
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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Classifying Quadrilaterals Apply constraints to a quadrilateral, and then reshape and resize it. Classify the figure by its constraints. Explore the differences between the different kinds of quadrilaterals.
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Unit 8 - Similarity and Polygons

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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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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Unit 9 - Right Angles

-- GCG 1 of 2 --

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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info

-- GCG 2 of 2 --

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.
  5 Minute Preview   Lesson Info

SEMESTER 2

Unit 10 - Trigonometry

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.
  5 Minute Preview   Lesson Info

Unit 11 - 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.
  5 Minute Preview   Lesson Info
Inscribed Angles Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
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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.
  5 Minute Preview   Lesson Info

Unit 12 - Coordinates and Constructions

-- GCG 1 of 2 --

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.
  5 Minute Preview   Lesson Info

-- GCG 2 of 2 --

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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
Inscribed Angles Resize angles inscribed in a circle. Investigate the relationship between inscribed angles and the arcs they intercept.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info

Unit 13 - Area and Perimeter

-- GCG 1 of 2 --

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).
  5 Minute Preview   Lesson Info
Area of Triangles Use a dynamic triangle to explore the area of a triangle. With the help of an animation, see that any triangle is always half of a parallelogram (with the same base and height). Likewise, a similar animation shows the connection between parallelograms and rectangles.
  Free   Lesson Info
Area of Parallelograms Examine and manipulate a parallelogram and find its area. Explore the relationship between the area of a parallelogram and the area of a rectangle using an animation.
  5 Minute Preview   Lesson Info

-- GCG 2 of 2 --

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.
  5 Minute Preview   Lesson Info
Circumference and Area of Circles Resize a circle and compare its radius, circumference, and area.
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Unit 14 - Surface Area and Volume

Surface and Lateral Areas of Prisms and Cylinders Vary the dimensions of a prism or cylinder and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
  5 Minute Preview   Lesson Info
Surface and Lateral Areas of Pyramids and Cones Vary the dimensions of a pyramid or cone and investigate how the surface area changes. Use the dynamic net of the solid to compute the lateral area and the surface area of the solid.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info

Unit 15 - Changing Dimensions

Unit 16 - Systems of Equations and Inequalities

Cat and Mouse (Modeling with Linear Systems) Experiment with a system of two lines representing a cat-and-mouse chase. Adjust the speeds of the cat and mouse and the head start of the mouse, and immediately see the effects on the graph and on the chase. Connect real-world meaning to slope, y-intercept, and the intersection of lines.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
Solving Linear Systems (Slope-Intercept Form) Solve systems of linear equations, given in slope-intercept form, both graphically and algebraically. Use a draggable green point to examine what it means for an (x, y) point to be a solution of one equation, or of a system of two equations.
  5 Minute Preview   Lesson Info
Linear Inequalities in Two Variables Find the solution set to a linear inequality in two variables using the graph of the linear inequality. Vary the terms of the inequality and vary the inequality symbol. Examine how the boundary line and shaded region change in response.
  5 Minute Preview   Lesson Info

Unit 17 - Structures of Expressions

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.
  5 Minute Preview   Lesson Info
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.
  5 Minute Preview   Lesson Info
Modeling the Factorization of x2+bx+c Factor a polynomial with a leading coefficient equal to 1 using an area model. Use step-by-step feedback to diagnose any mistakes.
  5 Minute Preview   Lesson Info