Coordinate and Transformational Geometry
Students understand the connection between algebra and geometry and use the one- and two-dimensional coordinate systems to verify geometric conjectures. Students generate and describe transformations (dilations, translation, reflection, and rotation).
- Determine the coordinates of a point (endpoints are a fractional distance less than 1)
- Identify the sequence of transformations performed for a given pre-image and image (on or off the coordinate plane)
- Identify and distinguish between reflectional and rotational symmetry in a plane figure
Logical Argument and Constructions
Students use process skills with deductive reasoning to understand geometric relationships. Students use constructions to validate conjectures about geometric figures.
- Recognize the connection between a bi-conditional statement and a true conditional statement with a true converse
- Verify the Triangle Inequality Theorem using constructions and apply the theorem to solve problems
Two-Dimensional and Three-Dimensional Figures
Students recognize characteristics and dimensional changes of two- and three-dimensional figures.
- Identify three-dimensional objects generated by rotations of two-dimensional shapes
Students understand geometric relationships and apply theorems and equations about circles.
- Describe radian measure of an angle
- Determine the equation for the graph of a circle
Students understand probability in real-world situations and how to apply independence and dependence of events.
- Develop strategies to use permutations and combinations to solve contextual problems
- Identify whether two events are independent and compute the probability of the two events occurring together with or without replacement
- Apply conditional probability in contextual problems
- Apply independence in contextual problems