Geometry and Measurement: Analyzing two- and three-dimensional space and figures by using distance and angle.

These activities offer your eighth graders visual, interactive experiences with geometry. Through games as well as lessons and problems, they work with concepts of angle, parallel lines, the Pythagorean theorem, and solids.

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Angles http://www.shodor.org/interactivate/activities/angles/index.html

This Java applet enables students to investigate acute, obtuse, and right angles. The student decides to work with one or two transversals and a pair of parallel lines. Angle measure is given for one angle. The student answers a short series of questions about the size of other angles, identifying relationships such as vertical and adjacent angles and alternate interior and alternate exterior angles. MSP full record

Triangle Geometry: Angles http://www.utc.edu/~cpmawata/geom/geom.htm

This site directly addresses students as it leads them to explore angles and their measurement. Most important, it offers applets to introduce the Pythagorean theorem by collecting data from right triangles online and provides an animated picture proof of the theorem. MSP full record

Manipula math with Java : the sum of outer angles of a polygon http://www.ies.co.jp/math/java/geo/gaikaku/gaikaku.html

This interactive applet allows users to see a visual demonstration of how the sum of exterior angles of any polygon sums to 360 degrees. Students can draw a polygon of any number of sides and have the applet show the exterior angles. They then decrease the scale of the image, gradually shrinking the polygon, while the display of the exterior angles remains and shows how the angles merge together to cover the whole 360 degrees surrounding the polygon. MSP full record

Parallel Lines and Ratio http://www.ies.co.jp/math/java/geo/hiresen/hiresen.html

Three parallel lines are intersected by two straight lines. The classic problem is: If we know the ratio of the segments created by one of the straight lines, what can we know about the ratio of the segments along the other line? An applet allows students to clearly see the geometric reasoning involved. (From Manipula math with Java — MSP full record)

Area triangles http://illuminations.nctm.org/ActivityDetail.aspx?ID=106

This applet shows triangle ABC, with a line through B parallel to base AC. Students can change the shape of the triangle by moving B along the parallel line or by changing the length of base AC. What happens to the length of the base, the height, and the area of the triangle as students make these moves? Why? MSP full record

The Pythagorean Theorem http://www.arcytech.org/java/pythagoras/index.html

This site invites learners to discover for themselves “an important relationship between the three sides of a right triangle.” Five interactive, visual exercises require students to delve deeper into the mystery; each exercise is a hint that motivates and entices. The tutorial ends with information on Pythagoras of Samos and problems that rely on the theorem for their solutions. MSP full record

Understanding the Pythagorean Relationship Using Interactive Figures http://standards.nctm.org/document/eexamples/chap6/6.5/index.htm

The activity in this example presents a visual and dynamic demonstration of this relationship. The interactive figure gives students experience with transformations that preserve area but not shape. The final goal is to determine how the interactive figure demonstrates the Pythagorean theorem. (From Ohio resource center for mathematics, science, and reading — MSP full record)

Distance Formula http://www.explorelearning.com/index.cfm?method=cResource.dspDetail&ResourceID=64

Explore the distance formula as an application of the Pythagorean theorem. Learn to see any two points as the endpoints of the hypotenuse of a right triangle. Drag those points and examine changes to the triangle and the distance calculation.

Measuring by Shadows http://mathforum.org/library/drmath/view/55316.html

A student asks: How can I measure a tree using its shadow and mine? This letter from Dr. Math carefully explains the mathematics underlying this standard classroom exercise. MSP full record

Finding the Height of a Lamp Pole http://www.ohiorc.org/pm/math/richproblemmath.aspx?pmrid=31

Without using trigonometry, how can you find the height of a lamp pole or other tall object? Two methods, both depending on similar triangles, are outlined and illustrated. A rich problem. (From Ohio resource center for mathematics, science, and reading — MSP full record)

Polygon Capture http://illuminations.nctm.org/LessonDetail.aspx?id=L270

In this lesson, students classify polygons according to more than one property at a time. In the context of a game, students move from a simple description of shapes to an analysis of how properties are related. (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

Sorting Polygons http://illuminations.nctm.org/LessonDetail.aspx?id=L277

In this companion to the above game, students identify and classify polygons according to various attributes. They then sort the polygons in Venn diagrams according to these attributes. (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

Fire hydrant : what shape is at the very top of a fire hydrant? http://www.figurethis.org/challenges/c35/challenge.htm

This activity begins an exploration of geometric shapes by asking students why the five-sided (pentagonal) water control valve of a fire hydrant cannot be opened by a common household wrench. The activity explains how geometric shape contributes to the usefulness of many objects. A hint calls students' attention to the shape of a normal household wrench, which has two parallel sides. Answers to questions and links to resources are included. MSP full record

Diagonals to Quadrilaterals http://illuminations.nctm.org/LessonDetail.aspx?id=L655

Instead of considering the diagonals within a quadrilateral, this lesson provides a unique opportunity: Students start with the diagonals and deduce the type of quadrilateral that surrounds them. Using an applet, students explore characteristics of diagonals and the quadrilaterals that are associated with them. (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

Geometric Solids and Their Properties http://illuminations.nctm.org/LessonDetail.aspx?id=U112

A five-part lesson plan has students investigate several polyhedra through an applet. Students can revolve each shape, color each face, and mark each edge or vertex. They can even see the figure without the faces colored in — a skeletal view of the "bones" forming the shape. The lesson leads to Euler’s formula connecting the number of edges, vertices, and faces, and ends with creating nets to form polyhedra. An excellent introduction to three-dimensional figures! (From Illuminations, National Council of Teachers of Mathematics Vision for School Mathematics — MSP full record)

Slicing solids (grades 6-8) http://nlvm.usu.edu/en/nav/frames_asid_126_g_3_t_3.html?open=instructions

So what happens when a plane intersects a Platonic solid? This virtual manipulative opens two windows on the same screen: one showing exactly where the intersection occurred and the other showing the cross-section of the solid created in the collision. Students decide which solid to view, and where the plane will slice it. MSP full record

Studying Polyhedra http://mathforum.org/alejandre/applet.polyhedra.html

What is a polyhedron? This lesson defines the word. Students explore online the five regular polyhedra, called the Platonic solids, to find how many faces and vertices each has, and what polygons make up the faces. An excellent applet! From this page, click on Polyhedra in the Classroom. Here you have classroom activities to pursue with a computer. Developed by a teacher; the lessons use interactive applets and other activities to investigate polyhedra. (From The Math Forum — MSP full record)

NCTM. (2006). Curriculum Focal Points for Kindergarten Through Grade 8 Mathematics: A Quest for Coherence. Reston, VA: Author

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Copyright May 2008 — The Ohio State University. This material is based upon work supported by the National Science Foundation under Grant No. 0424671. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.

This work is licensed under a Creative Commons License.