Geometry and Measurement Topics


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Alpine Cyclist

Problem Solving

	Description:	Design a mountain race course that meets length and slope specifications using Pythagorean Theorem, slope, and scale.


Ancient Pyramid	Problem Solving

	Description:	Build a pyramid that meets volume and surface area specifications.

Area	Concept Development

	Description:	Learn that area is the size of the region enclosed within a plane figure. Understand how to calculate area and derive area formulas for common shapes.

Bisection

Concept Development

	Description:	Understand and learn how to construct points, segments, and rays of bisection.

Circumference

Concept Development

	Description:	Investigate and learn how to calculate circumference.

Congruent Polygons

Concept Development

	Description:	Investigate congruency properties for line segments, angles, and polygons.

Congruent Line Segments & Angles

Concept Development

	Description:	Examine how congruent angles have the same measure and learn how to construct congruent angles.

Diagonals of a Polygon

Concept Development

	Description:	Explore how diagonals of a polygon join two nonconsecutive vertices and how to calculate the number of diagonals in a polygon.

Flight Planning

Problem Solving

	Description:	Plan an optimal flight route that minimizes time and delay using algebraic equations, measurement, and fractions.

Measurement

Concept Development

	Description:	Investigate how measurement is the assignment of values using units and explore how measurement can be found using instruments or obtained using calculations.

Package Sorting

Problem Solving

	Description:	Program a scanner to recognize packages according to characteristic shape properties using sides, angles, and diagonals.

Perimeter

Concept Development

	Description:	Examine how perimeter is the distance around a shape or figure and investigate perimiter formulas for some common shapes.

Perpendicular Lines

Concept Development

	Description:	Explore how perpendicular lines intersect to form right angles and how the slopes of perpendicular lines equals negative one.

Pythagorean Theorem

Concept Development

Description:

Learn that the Pythagorean Theorem describes the relationship between the lengths of the sides of a right triangle. Discover visual and algebraic proofs. Apply the Pythagorean Formula to find missing side lengths. Derive the distance formula for points in the coordinate plane.

Radius

Concept Development

	Description:	Understand how radius is the distance from the center of a circle to any point on the circle.

Regular Polygons

Concept Development

	Description:	Understand that regular polygons are plane figures that are equilateral and equiangular.

Similar Figures

Concept Development

	Description:	Explore the angle and side congruency of similar shapes.

Surface Area

Concept Development

	Description:	Investigate surface area as the total area of the surface of a space figure. Derive surface area formulas for common three dimensional figures.

Triangles: Angle Sum Theorem

Concept Development

	Description:	Discover that the angles in a triangle always sum to 180°. Prove the Triangle Sum Theorem visually and algebraically. Use the Triangle Sum Theorem to find missing angles in simple and compound triangles.

Triangles: Classifying

Concept Development

	Description:	Understand that triangles can be classified by their sides and angles. Investigate and explore scalene, equilateral, isosceles, obtuse, right, and acute triangles.

Volume

Concept Development

	Description:	Examine volume as the interior space of a three dimensional figure and derive volume formulas for common objects.