Download Geometry - Bunker R-III School District

Geometry
Rationale: The district mathematics curriculum respects the importance of mathematical
literacy for all students. The curriculum, based on upon National Council of Teachers of
Mathematics Standards as well as Missouri Show-Me Standards and Grade Level
Expectations, is student-centered and will allow students to explore, discover, conjecture,
and apply mathematics. To facilitate student learning, teachers utilize a variety of
techniques such as direct instruction, cooperative learning, and appropriate use of
computers and calculators. Through numerous and interrelated mathematical
experiences, students will work to attain the following goals:
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Become mathematical problem-solvers,
Communicate mathematically,
Reason mathematically,
Connect mathematics to their daily lives,
Develop confidence in their own abilities to do mathematics, and
Appreciate and understand the role of mathematics in real-world situations.
The district’s mathematics curriculum has a multi-faceted focus, including problem
solving, critical thinking, computation, and the integration of technology. These
components and goals are an important part of each student’s educational experience.
They provide the coherent viewpoint that mathematics is more than a body of knowledge;
it is a way of thinking.
Description: Geometry is designed for any student regardless of his or her high school
path. This is the study of Euclidean Geometry and will include: congruence, parallel
lines, perpendicular lines, angles, triangles, polygons, proofs, logic and basic
trigonometric functions.
Major Instructional Goals:
Number and Operations
Students will:
 Understand numbers, ways of representing numbers, relationships among
numbers and number systems
o Use real numbers to solve problems
o Use a variety of representations to demonstrate an understanding of very
large and very small numbers
 Understand meanings of operations and how they relate to one another
o Apply properties of exponents to simply expressions or solve equations
o Apply operations to real numbers, using mental computation or penciland-paper calculations for simple cases and technology for more
complicated cases
 Compute fluently and make reasonable estimates
o Judge the reasonableness of numerical computations and their results
o Solve problems involving proportions
Algebraic Relationships
Students will:
 Understand patterns, relations and functions
o Generalize patterns using explicitly or recursively defined functions
o Compare and contrast various forms of representations of patterns
o Understand and compare the properties of linear, exponential and
quadratic functions (include domain and range)
o Describe the effects of parameter changes on quadratic and exponential
functions
 Represent and analyze mathematical situations and structures using algebraic
symbols
o Use symbolic algebra to represent and solve problems that involve
quadratic relationships, including recursive relationships
o Describe and use algebraic manipulations, including factoring and rules
integer exponents
o Use and solve equivalent forms of equations and inequalities (piece-wise
and quadratic)
o Use and solve systems of linear equations or inequalities with 2 variables
 Use mathematical models to represent and understand quantitative relationships
o Identify quantitative relationships and determine the type(s) of functions
that might model the situation to solve the problem
 Analyze change in various contexts
o Analyze quadratic functions by investigating rates of change, intercepts
and zeros
Geometric and Spatial Relationships
Students will:
 Analyze characteristics and properties of two- and three-dimensional geometric
shapes and develop mathematical arguments about geometric relationships
o Use inductive and deductive reasoning to establish the validity of
geometric conjectures, proved theorems and critique arguments made by
others
o Apply relationships among surface areas and among volumes of similar
objects
 Specify locations and describe spatial relationships using coordinate geometry
and other representational systems
o Make conjectures and solve problems involving 2-dimensional objects
represented with Cartesian coordinates
 Apply transformations and use symmetry to analyze mathematical situations
o Use and apply constructions to represent translations, reflections, rotations
and dilations of objects
o Translate, dilate and reflect quadratic and exponential functions
o Identify types of symmetries of 2- and 3-dimensional figures
 Use visualization, spatial reasoning and geometric modeling to solve problems
o Draw representations of 3-dimensional geometric objects using a variety
of tools
o Draw or use visual models to represent and solve problems
Measurement
Students will:
 Apply appropriate techniques, tools and formulas to determine measurements
o Solve problems of angle measure of parallel lines cut by a transversal
o Determine the surface area and volume of geometric figures, including
cones, spheres and cylinders
o Analyze effects of computation on precision
Data and Probability
Students will:
 Formulate questions that can be addressed with data and collect, organize and
display relevant data to answer them
o Formulate questions, design studies and collect data about a characteristic
o Select, create and use appropriate graphical representation of data
 Select and use appropriate statistical methods to analyze data
o Apply statistical concepts to solve problems and distinguish between a
statistic and a parameter
o Given one-variable quantitative data, display the distribution and describe
its shape
o Display and analyze bivariate data where one variable is categorical and
the other is numerical
 Develop and evaluate inferences and predictions that are based on data
o Describe how sample statistics reflect eh values of population parameters
and use sampling distributions as the basis for informal inference
 Understand and apply basic concepts of probability
o Describe the concepts of sample space and probability distribution
o Use and describe the concepts of conditional probability and independent
events