Explorations in Explorations in GeometryGeometry

Explorations in Explorations in GeometryGeometry

Group 3:Group 3:Theresa AbromitisTheresa Abromitis

Stephen KishStephen KishKimberly KozarKimberly Kozar

Background Information

Subject: Mathematics (Geometry)

Grade Level: 6th Grade

Standards• “Analyze characteristics and properties of two- and three- dimensional

geometric shapes and develop mathematical arguments about geometric relationships.”

Describe using specific vocabulary and classify relationships among types of triangles, polygons, quadrilaterals (trapezoids, parallelograms, rectangles, rhombi, squares) using their defining properties.

Develop concept of congruence. Describe using specific vocabulary parts of a circle.• “Use visualization, spatial reasoning, and geometric modeling to solve

problems.” Draw geometric objects (squares, triangles and rectangles) with

specified properties, such as side lengths or angle measures . Recognize and apply geometric ideas and relationships in areas outside

the mathematics classroom, such as stained glass windows or quilt patterns.

Standards con’t• The specific technology standards that are addressed through the use

of “Explorations in Geometry” are: Students use technology tools to enhance learning, increase

productivity, and promote creativity. Students use technology resources for solving problems and making

informed decisions.• The specific technology performance indicators that are addressed

through the use of “Explorations in Geometry” are: Use content-specific tools, software, and simulations (e.g.

environmental probes, graphing calculators, exploratory environments, Web tools) to support learning and research.

Apply productivity/multimedia tools and peripherals to support personal productivity, group collaboration, and learning throughout the curriculum.

Goal• The goal of this power point

presentation is for students to comprehend the characteristics and properties of different types of shapes, and apply the information to various activities in order to assess their understanding.

Polygons…Polygons are figures which have three or

more sides. A few examples are:• triangle (3 sides)• rectangle (4 sides)• pentagon (5 sides) • hexagon (6 sides) • octagon (8 sides).

Polygons can be found everywhere.

Polygons…Which one is a triangle? A

rectangle? Pentagon? Hexagon? Octagon?

Polygons…These examples are also known as

regular polygons. Regular means that all of the sides of the figure are the same length.

For a more detailed explanation, visit this website.

Types of Shapes

Polygons are divided into two types of categories:

• Plane Shapes• Geometric Shapes

Plane Shapes

• Circle• Triangle

• Quadrilaterals– Square– Rectangle– Rhombus – Parallelogram– Trapezoid

Plane Shapes• Circle - a closed plane curve

consisting of all points at a given distance from a point within it called the center

• Triangle - a closed plane

figure having three sides and three angles

• Quadrilateral - a plane figure having four sides and four angles

Types of Quadrilaterals• Square - a special

rectangle with 4 equal sides and 4 equal angles (all 90°).

• Rectangle - has 2 pairs of equal sides and 4 equal angles (all 90°).

• Rhombus - has 4 equal sides with opposite sides parallel and opposite angles equal.

Types of Quadrilaterals

• Parallelogram - has opposite sides equal and parallel.

• Trapezium - has one pair of parallel sides of different lengths.

Quadrilaterals

Test your knowledge and complete the chart

Geometric Shapes• Rectangular Prism• Sphere• Cone• Cylinder• Cube • Pyramid

Geometric Shapes• Rectangular Prism – A

solid figure that has two pairs of parallel opposite faces and congruent bases that are all rectangles.

• Sphere – A space figure having all of its points the same distance from the center.

• Cone – a space figure having a circular base and a singular vertex

Geometric Shapes• Cylinder – A three

dimensional figure with two bases that are circles, not polygons, and with sides that are curved, not flat.

• Cube – A three dimensional figure with six matching square faces with three meeting at each vertex.

• Pyramid – A a three dimensional figure with 3 or more triangular faces sharing a common vertex. The base can be any type of polygon.

Test Your KnowledgeYou have successfully reviewed

information regarding various shapes. Try this test to see how much you learned!

On the next page, complete the chart to show many shapes your remember!

Using Shapes in Computer Programs

Next you will see two programs in which you can use the shapes you have learned to create pictures as well as show your understanding.

Please open either Inspiration or Kidspiration and complete the activity.

Additional Resources• http://www.mathleague.com/help/geometry/polygons.htm  • http://www.mathleague.com/help/geometry/3space.htm • http://www.coolmath4kids.com/tesspagl.html   may be able

to get some ideas from this site• http://www.math.com/homeworkhelp/Geometry.html    and

go to polygons• http://nlvm.usu.edu/en/nav/topic_t_3.html   and go to

grades 6-8.  Great visual tasks!!• http://www.gamequarium.com/geometry.html   and go to

Geometric Matching, Assemble the Square and Geo-Matho• http://mathforum.org/dr.math/faq/formulas/faq.figuredef.ht

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