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# Geometry Technology

A description of useful geometry applets & applications

by

Tweet## Sarah Giddings

on 7 May 2010#### Transcript of Geometry Technology

#16 - Interactive Surface Area and Volume #7 - Geometer's Sketchpad Website: http://www.shodor.org/interactivate/activities/SurfaceAreaAndVolume/

Summary:

Students can interact with rectangular and triangular prisms by changing the length, width, and height using sliders and rotating the figure to see all the different faces. This ability to change the length, width, and height provides students both the surface area and volume of the 3-d shapes. Students can use these interactive features to predict both the formula for surface area and volume of these prisms.

Website: http://www.dynamicgeometry.com/

Summary:

Geometer Sketchpad gives students' a wealth of opportunities to create any geometric shape using a variety of drawing and measurement tools. The program provides a great opportunity for students to quickly adapt shapes to explore new problems and make conjectures about mathematical ideas. This program can be especially useful for proofs of the Pythagorean Theorem and informal proofs of congruence theorems such as SSS or SAS.

#4 - Geogebra Website: http://www.geogebra.org/cms/

Summary:

Geogebra is a free download with the ability to create graphs and math presentations for students. The graphing capabilities of this program allow students to create functions that they can see in front of them with greater visual abilities than a graphing calculator.

Geometry Applets and Applications! This presentation will show a set of applets and applications that can be implemented into a Geometry curriculum looking to use more technology. Each applet is aimed at either introducing students to a new concept, getting the students' to make an important conjecture, or is setup as an assessment of a unit. #6 - Complex Area Problems using Google Earth Website: http://realworldmath.org/Real_World_Math/Complex_Area_Problems.html

Summary:

Students can use Google Earth to predict the measurement of aerial snap shots of pieces of the Earth. Students will take their prior knowledge of composite area to find the area of irregular shapes formed by property lines or other formations. Students will explore various snap shots of local properties or fields to expand on their knowledge of composite area.

#2 - Measuring Angles Website: http://e-learningforkids.org/Courses/EN/M1108/index.html

Summary:

This geometry applet was created to help students' learn how to use a protractor. This applet saves teachers from having to teach students one on one by giving them a tutorial of how to read an angle and a protractor. Students will line up the protractor, choose whether the angle is obtuse or acute and provide the measurement for real world applications.

#1 - Measuring Distance Website: http://e-learningforkids.org/Courses/EN/M1106/index.html

Summary:

This applet allows students to use technology to explore how to set up and read a ruler. It provides students a tutorial of how to use both centimeters and inches to measure lines and eventually real world figures. After the tutorial, students will be able to apply their knowledge to a game set up by the applet. #19 - Google Sketchup Website: http://sketchup.google.com/

Summary:

This website allows students to download software to create 3-d models of the prisms and pyramids we discussed in class. Students can make an architectural design of any of the shapes we learned about in class. You can choose the shapes length, width, and height along with any aesthetic features to make the model come to life. Students can then present their models to their classmates.

#10 - Geoboard Website: http://nlvm.usu.edu/en/nav/frames_asid_279_g_4_t_3.html?open=activities&from=topic_t_3.html

Summary:

This applet is a virtual geoboard for students to create any 2-d polygon using a set of rubber bands. Besides letting the students create their own polygon of their choosing, the program also gives the students a set of directives in which to explore using the geoboard. For example, it may ask students to create multiple shapes with the same area or to find two different polygons with the same perimeter.

#15 - Tesselations Website: http://nlvm.usu.edu/en/nav/frames_asid_163_g_4_t_3.html?open=activities&from=topic_t_3.html

Summary:

Rather than having students create their own shapes for a tessellation, you can have students use any polygon to create a virtual tessellation that they can print out when complete. Students can use the applet as a way to quickly maneuver the shapes around without having to manually create multiple shapes or models. The applet allows students to save time in creating a geometric piece of art.

#12 - Congruent Triangles Website: http://nlvm.usu.edu/en/nav/frames_asid_165_g_1_t_3.html?open=instructions&from=topic_t_3.html

Summary:

In this applet, students are given the chance to create one of three congruence theorems. It also allows students to work with one non-congruence theorem. Students move the side lengths and angles to create two triangles that are either congruent or not. The applet also explains to students what it means if the triangle is created using SAS, SSS, AAS, SSA, etc.

#11 - Isosceles Triangle Website: http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm

Summary:

This basic applet has the sole purpose of students making conjectures about an isosceles triangle. The program actually provides questions for the students to consider as they change the length of the legs and the length of the base of a triangle. Students are asked to measure both the angles and the sides of the triangles to make conjectures about the lengths of the sides and angles being equal.

#5 - Sine, Cosine, and Tangent of an Angle Website: http://www.walter-fendt.de/m14e/sincostan_e.htm

Summary:

The applet for Sine, Cosine, and Tangent of an angle shows students exactly how the unit circle can affect the graph of a trigonometric function. You can move a slider on the unit circle for one of the three trig functions and it will show how the point moves on a graph from 0 to 2 Pi. Students get a visual picture of the sine, cosine, and tangent wave as it moves across a period of 2 Pi.

#17 - Nets Website: http://www.mathsnet.net/geometry/solid/nets.html

Summary:

This applet allows students to see how different 3-D figures are created. Students can use a slider to demonstrate how the faces of the figure, in the form of a net, fold together to make the figure. It would be a good idea to have students predict how they think the faces would form together before you allow the students to move the sliders. After students have observed the figures provided, you can have students use these ideas to create their own nets.

#9 - Circle Properties Website: http://www.mathsnet.net/dynamic/car/circle01.html

Summary

This applet allows for six different properties of a circle to be explored. In each one, you can move the angle, the diameter, radius, etc. to change the circle. As the circle changes, so does the presented property of the circle. It does not tell the students what is changing but rather it implicitly asks the students to make conjectures about the changes that are occurring.

#20 - Interactive Shape Website: http://www.mathsnet.net/shape/index.html

Summary:

This is an application that advertises itself as an online course. In fact, it is a great tool for reviewing many geometric vocabulary and concepts. Students can choose the levels and the type of practice they want to complete. The student can also choose the level of problem that they want to complete (Unit 1, 2, etc). In each case, it gives feedback for the students to receive if the teacher is not around.

#13 - Triangle Explorer Website: http://www.shodor.org/interactivate/activities/TriangleExplorer/

Summary:

This applet is a simple check on finding the area of various triangles. The student can move the triangle to a different space on a coordinate plane. Using the horizontal and vertical distance, the student must predict the area, even though the sides of the triangle don’t perfectly match with the axes. The tool allows students to make their guess and then gives feedback on the correctness of their answer.

#18 - Studyging Polyhedra Website: http://mathforum.org/alejandre/applet.polyhedra.html

Summary:

This applet allows students to explore five different polyhedrons and see how the number of faces, edges, and vertices change. Students have questions to explore about the faces to see how the increase of faces changes the figure. Students can slow down the rotation of the figure to see more clearly the type and number of faces of each shape.

#3 - Interactive Angles Website: http://www.shodor.org/interactivate/activities/Angles/

Summary:

This is an applet that gives students an opportunity to indentify angle vocabulary and the measure of certain angles. Students can choose the difficulty level and can track their own progress on identifying the angles and the composition of the angles. There isn’t anything new to learn about the angles but it should reinforce a lot of the ideas that students have previously learned about angles.

#14 - Squaring the Triangle Website: http://www.shodor.org/interactivate/activities/SquaringTheTriangle/

Summary:

This is an interactive applet that leads to the proof of the Pythagorean Theorem. Students change how long side a and b are. As they change side a and b, the length of side c and the square on side c also change. Students should be able to make conjectures and test multiple examples of why we can take the squares on the legs of a right triangle and add them to make the area of the square on the hypotenuse.

#8 - Circle Circumference and Area Website: http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=206

Summary:

This is a quick applet that allows students to see how changing the length of the radius can affect the area and circumference. Students can also see how the diameter is affected by each of these. Students can also take a final challenge to find the arc and sector of the circle as well. The complete application needs a full subscription but you may only need to use it for five minutes to see how to find the area and circumefernce if the students don't already know.

Pros of Measuring Angles:

* Students learn by doing

* Students apply what they learned

* Students use real life tools (protractor)

Pros of Interactive Angles:

* Students can mark their progress

* Students answer problems similar to standardized tests

* Students learn about angles other than acute and obtuse

Pros of Circle Circumference and Area:

* Students discover how the area and perimeter are affected by the diameter and radius

* Students learn by doing

* Students make conjectures about what is happening

Pros of Circle Properties:

* Multiple Properites are presented

* Students make conjectures about what is happening

* Students build on what they learned about in Circle Circumference and Area Pros of Nets:

* Students create their own 3-D figures

* Students see the construction of the shapes

* Students can get a visual representation of the faces, vertices, and edges

Pros of Studying Polyhedra:

* Students can find the number of faces, vertices, and edges

* Students can visualize all sides of the polyhedra

* Students can compare and contrast five different polyhedra

Full transcriptSummary:

Students can interact with rectangular and triangular prisms by changing the length, width, and height using sliders and rotating the figure to see all the different faces. This ability to change the length, width, and height provides students both the surface area and volume of the 3-d shapes. Students can use these interactive features to predict both the formula for surface area and volume of these prisms.

Website: http://www.dynamicgeometry.com/

Summary:

Geometer Sketchpad gives students' a wealth of opportunities to create any geometric shape using a variety of drawing and measurement tools. The program provides a great opportunity for students to quickly adapt shapes to explore new problems and make conjectures about mathematical ideas. This program can be especially useful for proofs of the Pythagorean Theorem and informal proofs of congruence theorems such as SSS or SAS.

#4 - Geogebra Website: http://www.geogebra.org/cms/

Summary:

Geogebra is a free download with the ability to create graphs and math presentations for students. The graphing capabilities of this program allow students to create functions that they can see in front of them with greater visual abilities than a graphing calculator.

Geometry Applets and Applications! This presentation will show a set of applets and applications that can be implemented into a Geometry curriculum looking to use more technology. Each applet is aimed at either introducing students to a new concept, getting the students' to make an important conjecture, or is setup as an assessment of a unit. #6 - Complex Area Problems using Google Earth Website: http://realworldmath.org/Real_World_Math/Complex_Area_Problems.html

Summary:

Students can use Google Earth to predict the measurement of aerial snap shots of pieces of the Earth. Students will take their prior knowledge of composite area to find the area of irregular shapes formed by property lines or other formations. Students will explore various snap shots of local properties or fields to expand on their knowledge of composite area.

#2 - Measuring Angles Website: http://e-learningforkids.org/Courses/EN/M1108/index.html

Summary:

This geometry applet was created to help students' learn how to use a protractor. This applet saves teachers from having to teach students one on one by giving them a tutorial of how to read an angle and a protractor. Students will line up the protractor, choose whether the angle is obtuse or acute and provide the measurement for real world applications.

#1 - Measuring Distance Website: http://e-learningforkids.org/Courses/EN/M1106/index.html

Summary:

This applet allows students to use technology to explore how to set up and read a ruler. It provides students a tutorial of how to use both centimeters and inches to measure lines and eventually real world figures. After the tutorial, students will be able to apply their knowledge to a game set up by the applet. #19 - Google Sketchup Website: http://sketchup.google.com/

Summary:

This website allows students to download software to create 3-d models of the prisms and pyramids we discussed in class. Students can make an architectural design of any of the shapes we learned about in class. You can choose the shapes length, width, and height along with any aesthetic features to make the model come to life. Students can then present their models to their classmates.

#10 - Geoboard Website: http://nlvm.usu.edu/en/nav/frames_asid_279_g_4_t_3.html?open=activities&from=topic_t_3.html

Summary:

This applet is a virtual geoboard for students to create any 2-d polygon using a set of rubber bands. Besides letting the students create their own polygon of their choosing, the program also gives the students a set of directives in which to explore using the geoboard. For example, it may ask students to create multiple shapes with the same area or to find two different polygons with the same perimeter.

#15 - Tesselations Website: http://nlvm.usu.edu/en/nav/frames_asid_163_g_4_t_3.html?open=activities&from=topic_t_3.html

Summary:

Rather than having students create their own shapes for a tessellation, you can have students use any polygon to create a virtual tessellation that they can print out when complete. Students can use the applet as a way to quickly maneuver the shapes around without having to manually create multiple shapes or models. The applet allows students to save time in creating a geometric piece of art.

#12 - Congruent Triangles Website: http://nlvm.usu.edu/en/nav/frames_asid_165_g_1_t_3.html?open=instructions&from=topic_t_3.html

Summary:

In this applet, students are given the chance to create one of three congruence theorems. It also allows students to work with one non-congruence theorem. Students move the side lengths and angles to create two triangles that are either congruent or not. The applet also explains to students what it means if the triangle is created using SAS, SSS, AAS, SSA, etc.

#11 - Isosceles Triangle Website: http://www.amblesideprimary.com/ambleweb/sketchpad/isosco.htm

Summary:

This basic applet has the sole purpose of students making conjectures about an isosceles triangle. The program actually provides questions for the students to consider as they change the length of the legs and the length of the base of a triangle. Students are asked to measure both the angles and the sides of the triangles to make conjectures about the lengths of the sides and angles being equal.

#5 - Sine, Cosine, and Tangent of an Angle Website: http://www.walter-fendt.de/m14e/sincostan_e.htm

Summary:

The applet for Sine, Cosine, and Tangent of an angle shows students exactly how the unit circle can affect the graph of a trigonometric function. You can move a slider on the unit circle for one of the three trig functions and it will show how the point moves on a graph from 0 to 2 Pi. Students get a visual picture of the sine, cosine, and tangent wave as it moves across a period of 2 Pi.

#17 - Nets Website: http://www.mathsnet.net/geometry/solid/nets.html

Summary:

This applet allows students to see how different 3-D figures are created. Students can use a slider to demonstrate how the faces of the figure, in the form of a net, fold together to make the figure. It would be a good idea to have students predict how they think the faces would form together before you allow the students to move the sliders. After students have observed the figures provided, you can have students use these ideas to create their own nets.

#9 - Circle Properties Website: http://www.mathsnet.net/dynamic/car/circle01.html

Summary

This applet allows for six different properties of a circle to be explored. In each one, you can move the angle, the diameter, radius, etc. to change the circle. As the circle changes, so does the presented property of the circle. It does not tell the students what is changing but rather it implicitly asks the students to make conjectures about the changes that are occurring.

#20 - Interactive Shape Website: http://www.mathsnet.net/shape/index.html

Summary:

This is an application that advertises itself as an online course. In fact, it is a great tool for reviewing many geometric vocabulary and concepts. Students can choose the levels and the type of practice they want to complete. The student can also choose the level of problem that they want to complete (Unit 1, 2, etc). In each case, it gives feedback for the students to receive if the teacher is not around.

#13 - Triangle Explorer Website: http://www.shodor.org/interactivate/activities/TriangleExplorer/

Summary:

This applet is a simple check on finding the area of various triangles. The student can move the triangle to a different space on a coordinate plane. Using the horizontal and vertical distance, the student must predict the area, even though the sides of the triangle don’t perfectly match with the axes. The tool allows students to make their guess and then gives feedback on the correctness of their answer.

#18 - Studyging Polyhedra Website: http://mathforum.org/alejandre/applet.polyhedra.html

Summary:

This applet allows students to explore five different polyhedrons and see how the number of faces, edges, and vertices change. Students have questions to explore about the faces to see how the increase of faces changes the figure. Students can slow down the rotation of the figure to see more clearly the type and number of faces of each shape.

#3 - Interactive Angles Website: http://www.shodor.org/interactivate/activities/Angles/

Summary:

This is an applet that gives students an opportunity to indentify angle vocabulary and the measure of certain angles. Students can choose the difficulty level and can track their own progress on identifying the angles and the composition of the angles. There isn’t anything new to learn about the angles but it should reinforce a lot of the ideas that students have previously learned about angles.

#14 - Squaring the Triangle Website: http://www.shodor.org/interactivate/activities/SquaringTheTriangle/

Summary:

This is an interactive applet that leads to the proof of the Pythagorean Theorem. Students change how long side a and b are. As they change side a and b, the length of side c and the square on side c also change. Students should be able to make conjectures and test multiple examples of why we can take the squares on the legs of a right triangle and add them to make the area of the square on the hypotenuse.

#8 - Circle Circumference and Area Website: http://www.explorelearning.com/index.cfm?method=cResource.dspView&ResourceID=206

Summary:

This is a quick applet that allows students to see how changing the length of the radius can affect the area and circumference. Students can also see how the diameter is affected by each of these. Students can also take a final challenge to find the arc and sector of the circle as well. The complete application needs a full subscription but you may only need to use it for five minutes to see how to find the area and circumefernce if the students don't already know.

Pros of Measuring Angles:

* Students learn by doing

* Students apply what they learned

* Students use real life tools (protractor)

Pros of Interactive Angles:

* Students can mark their progress

* Students answer problems similar to standardized tests

* Students learn about angles other than acute and obtuse

Pros of Circle Circumference and Area:

* Students discover how the area and perimeter are affected by the diameter and radius

* Students learn by doing

* Students make conjectures about what is happening

Pros of Circle Properties:

* Multiple Properites are presented

* Students make conjectures about what is happening

* Students build on what they learned about in Circle Circumference and Area Pros of Nets:

* Students create their own 3-D figures

* Students see the construction of the shapes

* Students can get a visual representation of the faces, vertices, and edges

Pros of Studying Polyhedra:

* Students can find the number of faces, vertices, and edges

* Students can visualize all sides of the polyhedra

* Students can compare and contrast five different polyhedra