Geometry Honors
Recommended Prerequisite: Algebra I
Grades Offered: 9-12
Credit: 1/2-1
SDE Course Code: 3108
MNPS Course Code: MTH4212
Course Description:
Geometry develops the concepts of plane, solid, and coordinate geometry through the use of proofs, both deductive and inductive, while simultaneously developing logical thought and reasoning processes.
Outline of Content:
Number Sense and Number Theory
· The student will recognize, order, represent, and graph rational and irrational numbers.
° Demonstrating an understanding of the relative size of rational and irrational numbers by …
§ Matching a given irrational number to the appropriate point on a number line.
§ Ordering a set of rational and irrational numbers.
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Estimation, Measurement, and Computation
· The student will apply appropriate units of measurement; develop effective estimation and computation strategies for solving real-world problems involving length, are, and volume; and choose appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance.
° Using concepts of length, area, and volume to estimate and solve real-world problems by …
§ Determining the perimeter or area of a triangle or rectangle when the dimensions are given as binomials in one variable.
§ Determining the perimeter or area of a triangle or rectangle in a real-world situation given the dimensions expressed as linear algebraic expressions in one variable.
§ Determining the volume or surface area of a rectangular solid in a real-world situation.
° Applying measurement concepts and relationships in algebraic and geometric problem-solving situations where appropriate to determine the length, perimeter, area, surface area, and volume for two- and three-dimensional figures in real world situations.
° Choosing appropriate techniques and tools to measure quantities in order to meet specifications for precision, accuracy, and tolerance.
Patterns, Functions, and Algebraic Thinking
· The student will recognize, extend, and create, and analyze a variety of geometric, spatial, and numerical patterns; solve real-world problems related to algebra and geometry; and use properties of various geometric figures to analyze and solve problems.
° Recognizing, extending, and creating geometric, spatial, and numerical patterns to:
§ Extend a geometric pattern.
° Analyzing mathematical patterns related to algebra and geometry in real-world problem solving to:
§ Solve multi-step linear equations applied to geometric figures.
§ Solve systems of two linear equations with integral coefficients to find length, width, perimeter, and area of geometric figures.
§ Solve systems of two linear equations with integral coefficients to determine if the lines are parallel, intersecting, or coinciding.
§ Choose the equations of parallel or perpendicular lines given either the coordinates or the graphs.
§ Apply the concept of rate of change from a pattern of data.
° Solving problems in number theory, geometry, probability and statistics, and measurement and estimation using algebraic thinking and symbolism by …
§ Applying ratio and proportion to problems involving polygons.
§ Applying the triangle inequality property to determine if a triangle exits and to order by size both its angles and sides.
§ Identifying by graphical representation the inequality that represents the possible lengths of the third side of a triangle when given the other two sides.
§ Determining the perimeter, area, surface area, or volume given the ratio of two similar geometric figures.
§ Applying the Triangle Sum or Exterior Angle Theorems to determine the measures of the angles of a triangle when the angle measures are expressed algebraically.
§ Applying the properties of angels, arcs, chords, tangents and/or secants to solve problems.
§ Determining the equation of a circle given the graph of the circle or the coordinates of important points (e.g., center, endpoints of diameter).
° Applying coordinate geometry to analyze and solve problems by …
§ Determining the slope given the graph of a linear equation.
§ Determining the distance, midpoint, or slope when given the coordinates of two points.
Statistics and Probability
· The student will investigate, explore, and apply geometric representations to calculate theoretical probability.
° Applying geometric representations to calculate theoretical probability by …
§ Making a prediction from a geometric representation of a real-world data set.
§ Determining the probability of an even using a spinner and a circle graph.
§ Determining the probability of an event represented as a subset of the area of a two-dimensional geometric figure.
§
Spatial Sense and Geometric Concepts
· The student will investigate, model, and apply geometric properties and relationships and use indirect reasoning to make conjectures; deductive reasoning to draw conclusions; and both inductive and deductive reasoning to establish the truth of statements.
° Analyzing relationships among corresponding parts of similar and congruent figures by …
§ Comparing congruence or similarity between triangles or quadrilaterals given a diagram.
§ Solving problems involving complementary, supplementary, congruent, vertical, or adjacent angles given angle measures expressed algebraically.
§ Solving problems involving the angles formed when parallel lines are cut by transversals.
° Applying geometric properties of solids, polygons, and circles to real-world problems.
§ Applying the reflexive, transitive, or symmetric properties of equality.
§ Applying properties of quadrilaterals to solve real-world problems given a diagram.
§ Solving real-world problems using measures of interior and exterior angles of regular polygons.
§ Determining which three-dimensional solid is represented by a given net.
§ Determining the area of shaded regions involving circles and polygons.
§ Solving problems using the properties of angles, arcs, chords, tangents, and secants.
§ Finding the area of a sector or segment of a circle given a diagram.
° Justifying conclusions using deductive reasoning to
§ Determine whether triangles in a diagram are congruent because the ASA, SSS, AAS, SAS, or hypotenuse-leg theorems apply to the given situation.
§ Determine if a triangle is acute, obtuse, or right given the lengths of the sides of a triangle.
° Using inductive reasoning to make conjectures.
° Communicating position using spatial sense of two- and three-dimensional coordinate systems.
° Demonstrating an understanding of transformations of geometric figures by …
§ Determining whether a figure has been translated, dilated, reflected, or rotated given a diagram.
§ Choosing the three-dimensional geometric object that has been rotated or reflected given a diagram.
° Applying right triangle relationships including the Pythagorean Theorem, the distance formula, and trigonometric ratios.
§ Determining the length of the missing side of a right triangle.
§ Determining the trigonometric ratio of a right triangle needed to solve a real-world problem given a diagram.
§ Solving real-world problems using 30-60-90 and 45-45-90 degree triangles.
° Demonstrating understanding of geometric properties of congruence, similarity, perpendicularity, and parallelism.
° Recognizing and articulating relationships among families of geometric figures (e.g. quadrilaterals, prisms)
° Using indirect and deductive reasoning to establish the truth of a statement
Reading: The student will develop appropriate reading strategies for understanding mathematical texts as well as variety of sources including maps, charts, graphs, and technical writings.
Writing: The student will write regularly using correct mathematical symbols and terminology. Suggested written assignments include: descriptions, comparisons, and logically ordered processes.
Additional Course Requirements:
All honors courses must include – multiple assessments exemplifying coursework (such as short-answer, constructed-response prompts, performance-based tasks, open-ended questions, essays, original or creative interpretations, authentic products, portfolios, and analytic writing). Additionally, an honors course shall include:
- The four following components:
- Integrating appropriate technology into the course using a graphing or scientific calculators or other technologies (Sketchpad, Cabri, etc.)
- Completing projects that apply course curriculum to relevant or real-world situations.
- May include oral presentations or other modes of sharing findings.
- Participating in extensive opportunities for problem-solving experiences through imagination, critical analysis, and application.
- Engaging in extended reading assignments that connect with the specified curriculum (such as Flatland, Alice in Wonderland, etc.)
- A choice of one of the following components:
- Completing research-based writing assignments that address and extend the course curriculum.
- Conducting open-ended investigations in which the student selects the questions and designs the research.
- Completing writing assignments that demonstrates a variety of modes, purposes, and styles.
- Employing deeper exploration of the culture, values, and history of the discipline.
- Participating in job shadowing experiences with presentations which connect class study to the world of work.
Standard Links:
MNPS Standards:
http://www.mnps.org/PageFactory.aspx?PageID=3403
State Standards:
http://www.state.tn.us/education/ci/cistandards2001/math/cimath.htm
Textbooks:
Larson, Boswell, Stiff, Geometry: Applying, Reasoning, Measuring, Evanston, IL: McDougal-Littell, 2005. (Adopted: 2005)
Online Textbook:
http://www.classzone.com/books/geometry/index.cfm
Required Resources:
TI-83+ or TI-84+ graphing calculator or any scientific calculator
Graph paper, rulers, protractors
Compass or Geometer’s Sketchpad/Cabri software
Recommended Resources:
A variety of manipulatives: polydrons, models of geometric solids, tangrams, miras, geoboards, etc.
Geometer’s Sketchpad or Cabri software