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Standard 4 (Geometry) in Grades 6-8

Standard 4 (Geometry) in Grades 6-8. Eddie Keel Haywood High School keelmath@bellsouth.net http://keelmath.wordpress.com/. Objectives. Examine all SPIs in the Geometry standard for grades 6-8 Complete one classroom activity for each grade Examine key web sites

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Standard 4 (Geometry) in Grades 6-8

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  1. Standard 4 (Geometry) in Grades 6-8 Eddie Keel Haywood High School keelmath@bellsouth.net http://keelmath.wordpress.com/

  2. Objectives • Examine all SPIs in the Geometry standard for grades 6-8 • Complete one classroom activity for each grade • Examine key web sites • Examine other resources

  3. Grade 6 Standard 4 • SPI 0606.4.1 Identify, define or describe geometric shapes given a visual representation or a written description of its properties. • SPI 0606.4.2 Find a missing angle measure in problems involving interior/exterior angles and/or their sums. • SPI 0606.4.3 Solve problems using the Triangle Inequality Theorem. • SPI 0606.4.4 Calculate with circumferences and areas of circles.

  4. Grade 6 Standard 4 • SPI 0606.4.5 Determine the surface area and volume of prisms, pyramids and cylinders. • SPI 0606.4.6 Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa.

  5. Area and Circumference • http://illuminations.nctm.org/activitydetail.aspx?id=116 • http://illuminations.nctm.org/LessonDetail.aspx?ID=L573

  6. Triangle Inequality Theorem • http://teachers.henrico.k12.va.us/math/igo/03TrianglesPolygons/3_3.html • http://www.keymath.com/x3323.xml • http://www.deltastate.edu/docs/math/lp3lclark.pdf • http://schoolwires.henry.k12.ga.us/437520715143758627/lib/437520715143758627/unit3skillsworksheettriangleinequality.pdf

  7. Angles • GEOGEBRA! • http://www.geogebra.org/en/wiki/index.php/Angles

  8. Volume • 0606.4.18 Use manipulatives to discover the volume of a cone is one-third the volume of the related cylinder (the heights and base areas are equal). • SPI 0606.4.6 Given the volume of a cone/pyramid, find the volume of the related cylinder/prism or vice versa. • Use a manipulative to attack this check and SPI

  9. Volume Activity • http://www.ncpublicschools.org/docs/curriculum/mathematics/middlegrades/grade08/goal03/objective3.01/3.01-tasks/3.01-volumerelationships.pdf

  10. Grade 7—Standard 4 • SPI 0706.4.1 Solve contextual problems involving similar triangles. • SPI 0706.4.2 Use SSS, SAS, and AA to determine if two triangles are similar. • SPI 0706.4.3 Apply scale factor to solve problems involving area and volume.

  11. Similar Triangles • Shadow Problem/Mirror Problem • http://www.learner.org/courses/learningmath/geometry/session8/part_b/measuring.html • Using Geoboards • http://www.edu.gov.on.ca/eng/studentsuccess/lms/files/tips4rm/gr10Unit1.pdf • Java Applets • http://members.shaw.ca/ron.blond/SimilarTriangles.APPLET/index.html • http://www.cut-the-knot.org/Curriculum/Geometry/SimilarTriangles.shtml

  12. Scale Factor • S=1 • Perimeter of one square (one face of the cube) • Surface Area of the Cube • Volume of the Cube • Repeat for S=2 • Repeat for s=3 • Do you see a pattern? • P=4s • SA=6s2 V=s3

  13. Scale Factor • WE can use CUBES to really see this pattern! • Make a cube with s=1 using cubes • Make a cube with s = 2 • S=3 • http://illuminations.nctm.org/LessonDetail.aspx?ID=L260 • http://www.worsleyschool.net/science/files/scalefactor/factors.html • http://www2.whidbey.net/ohmsmath/webwork/story/mf_story_scalefact.htm

  14. Grade 8-Standard 4 • SPI 0806.4.1 Use the Pythagorean Theorem to solve contextual problems. • SPI 0806.4.2 Apply the Pythagorean theorem to find distances between points in the coordinate plane to measure lengths and analyze polygons and polyhedra. • SPI 0806.4.3 Find measures of the angles formed by parallel lines cut by a transversal. • SPI 0806.4.4 Convert between and within the U.S. Customary System and the metric system. • SPI 0806.4.5 Identify the intersection of two or more geometric figures in the plane.

  15. Pythagorean Theorem • http://www.shodor.org/interactivate/activities/PythagoreanExplorer/ • http://www.keypress.com/documents/ALookInside/DiscoveringGeometry/DG_TE_Ch09.pdf • http://www.pbs.org/teachers/mathline/concepts/historyandmathematics/activity1.shtm

  16. Graph Paper Activity • http://www.regentsprep.org/Regents/math/ALGEBRA/AT1/TActive.htm

  17. Tangrams • http://www.math.wichita.edu/history/activities/geometry-act.html#pyth-tan

  18. Parallel Lines: Trick

  19. Parallel Lines • http://www.mathsisfun.com/geometry/parallel-lines.html • http://www.geogebra.org/en/wiki/index.php/Angles • http://www.keymath.com/x3314.xml

  20. Additional Resources • http://www.stemresources.com/ • http://www.pbs.org/teachers/stem/ • http://www.tnelc.org/math.php

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