Capstone Project Part 1: Pick a Topic / Create a Question to Research Choose a topic from the course and ask a driving question (big question or HMW - How Might We... - problem-solving question). Submit your question/topic when completed.

Topics for A (or AB)

Polynomial Expressions within a Geometric Framework Rigid Transformations: Reflections, Translations, and Rotations Dilations Tessellations Similar Triangles Similar Figures Polygons Classifying Quadrilaterals Coordinate proofs of Quadrilaterals Congruent Triangles Geometric Constructions Ratios and Proportions Angle Pair Relationships Parallel Lines Cut by a Transversal Topics for B (or AB)

Right Triangle Trigonometry Pythagorean Theorem Sine and Cosine Functions Special Right Triangles Radians and Degrees Unit circle Circle Theorems Arc Length Area of a Sector Angle Relationships formed by Chords, Secants and Tangents Proof of the Pythagorean Theorem Volume of Cones Volume of Sphere Volume of Cylinder Volume of Prisms Volume of Pyramids Density Independent vs Dependent Events Venn Diagrams Permutations and Combinations Probability Distribution Expected Value Frequency Tables Examples 1. Tessellation Project

You work for an interior design company and have been hired to make an original and unique wall paper design for a hotel lobby. Design a tessellation using slide translations and/or rotations. Present your final product as a presentation, explaining how it was created.

2. Dilation Artists use dilations to enlarge images when painting murals, creating posters and portraits. Find an image to dilate and place it on the coordinate plane. Enlarge the image and identify coordinate points of the pre-image and image. State the scale factor and center of dilation. Be creative with your final product.

3. Carnival Game Design a carnival game that can be used to calculate the theoretical probabilities of winning prizes. Determine the theoretical probability of winning the game using models. Also determine the expected profit for the game.

4. Sandcastle You and two friends decide to take a trip to the beach, and you plan to build a sandcastle. You brought a cylindrical pail, and your friends brought a pyramid mold with a square base and a cone shape mold. Design your sandcastle using these shapes. What is the volume, surface area, and density of your sandcastle?