Geometry

Prerequisite: 1st year Algebra

1. The student understands and applies the concepts and procedures of mathematics.

• 1. understands how changes in dimension affect perimeter, area, and volume
• 2. measures objects and events directly or uses indirect methods (such as find the volume of a cone, given its height and diameter)
• 3. calculates rate and other derived and indirect measurements.
• 4. understands that the precision and accuracy of measurement is affected by the measurement tools and calculating procedures.
• 5. compares, describes, and classifies 2- and 3-dimensional geometric figures.
• 6. constructs geometric models and scale drawings using tools as appropriate (for example, in designing a house plan or building a model of a bridge)
• 7. understands and uses coordinate grids
• 8. identifies simple differences between geometric properties of a plane and a sphere
• 9. understands and uses properties of symmetry, similarity, and congruence
• 10. understands and constructs multiple geometric transformations using combinations of translation, reflection, or rotation
• 11. uses a variety of tools and technologies to perform geometric constructions
• 12. recognizes, creates, extends, and generalizes patterns, sequences, and series
• 13. understands, develops, and expresses rules describing patterns
• 14. represents situations that involve variable quantities with expressions, formulas and equations, and inequalities
• 15. evaluates and simplifies expressions
• 16. creates and solves equations and inequalities

2. The student uses mathematics to define and solve problems.

• 1. searches systematically for patterns in complex situations
• 2. analyzes and uses multiple strategies
• 3. identifies questions to be answered in complex situations
• 4. defines problems in complex situations
• 5. identifies the unknowns in complex situations

3. The student uses mathematical reasoning

• 1. interprets and integrates information from multiple sources
• 2. validates thinking and mathematical ideas using models, known facts, patterns, relationships, counter-examples, and proportional reasoning.
• 3. makes and explains conjectures and inferences based on analysis of problem situations
• 4. tests conjectures and inferences by formulating a proof or by constructing a counter-example
• 5. supports arguments and justifies results using inductive and deductive reasoning

4. The student communicates knowledge and understanding in both everyday and mathematical language.

• 1. expresses complex ideas and situations using mathematical language and notation in appropriate and efficient forms
• 2. expresses or presents mathematical ideas clearly and effectively using both everyday and mathematical language appropriate to audience

5. The student understands how mathematical ideas connect within mathematics, to other subject areas, and to real-life situations.

• 1. extends mathematical patterns and ideas to other disciplines
• 2. recognizes the extensive use of mathematics outside the classroom
• 3. identifies situations in which mathematics can be used to solve problems with local, national, or international implications (such as in calculating resources necessary for interstate highway maintenance)
• 4. investigates the mathematical knowledge and training requirements for occupational/career areas of interest