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Developing Algebraic Expressions to Represent Geometric Properties

The student will investigate patterns to make conjectures.

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Developing Algebraic Expressions to Represent Geometric Properties of Polygons

Given numerical and/or geometric patterns that represent geometric properties of polygons, the student will develop algebraic expressions that represent the geometric properties.

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Developing Algebraic Expressions to Represent Geometric Properties of Angle Relationships in Polygons

Given numerical and/or geometric patterns that represent geometric properties of angle relationships in polygons, the student will investigate patterns to make conjectures about interior and exterior angles of polygons.

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Applying Pythagorean Triples to Solve Problems

Given verbal and pictorial representations of problem situations, the student will apply patterns from right triangles whose sides are Pythagorean Triples to solve the problems.

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Introduction to Coordinate Geometry

The students will use multiple representations of undefined terms on a coordinate plane to solve problems.

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Coordinate Geometry: Parallel and Perpendicular Lines

Given characteristics of two lines, such as slopes and equations, the student will determine whether the lines are parallel, perpendicular, or neither.

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Coordinate Geometry: Special Segments

The student will derive and use the slope and midpoint formulas to verify geometric relationship that include parallelism and perpendicularity of lines. Then, the student will determine an equation of a line parallel or perpendicular to a given line.

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Coordinate Geometry: Length and Distance

Given coordinates of points, the student will use the distance formula to solve problems involving length and distance.

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Coordinate Geometry: Slope

Given coordinate points, the student will use slope formulas to solve problems.

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Describing and Drawing Cross Sections

Given a verbal and/or pictorial description of the intersection of a plane with various three-dimensional geometric figures, the student will describe and/or draw the intersection.

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Determining Area: Composite Figures

Given information about composite fiugres, the student will determine the area of composite 2-dimensional figures comprised of a combination of triangles and parallelograms using appropriate units of measure.

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Determining Arc Length

Given a problem situation involving sectors of circles, the student will use proportional reasoning to solve the problem.

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Using The Pythagorean Theorem

The student will use triangle relationships to prove the Pythagorean Theorem and solve problems.

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Applying Geometric Probability

The student will find the area of polygons and circles. Then, the student will use probability to solve real-world problems.

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Determining the Surface Area of Cones and Cylinders

Given a problem involving cones or cylinders, the student will find the surface area using appropriate units of measure.

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Determining the Volume of Cones and Cylinders

Given a problem involving cones or cylinders, the student will find the volume using appropriate units of measure.

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Determining the Surface Area and Volume of Spheres

Given a problem involving spheres, the student will find the surface area and volume.

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Determining the Surface Area and Volume of Composite Figures

Given a problem involving composite figures made from prisms, pyramids, spheres, cones, and/or cylinders, the student will find the surface area and volume of the composite figure.

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Making Conjectures about Parallel and Perpendicular Lines

The student will verify theorems about angles formed by parallel lines cut by a transversal and apply these relationships to solve problems.

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Making and Verifying Conjectures About Triangles

Given examples of triangles and their component parts, the student will use explorations and concrete models to verify and apply the Triangle Inequality theorem and find the sum of interior angles.