Are you confused by terms that educators use? The ASCD Lexicon of Learning might be what you need.
CT4ME has identified resources related to each benchmark of the Ohio Mathematics Academic Content Standards that students should have mastered by the end of the grades 8-10 program.
Identify the benchmark (A-I) for review in Geometry and Spatial Sense. Below the benchmark, you will find Web resources for reviewing the concept and practice problems.
Students should be able to review on their own using these resources. If you are not an Ohio educator, these resources can still benefit your test prep efforts, as benchmarks in other states are similarly stated.
Download the Test Prep Strand Booklet
Geometry and Spatial Sense (pdf) This test prep booklet (about 200 KB) is designed to help you monitor your progress toward mastery of each benchmark in this strand. You can print the entire booklet, or just those pages for benchmarks you need to work on. Write notes in the booklet next to each resource you use in your review.
If
needed, download
Adobe Acrobat Reader, free software for viewing and printing PDF files.
You
might need to download Java, a
free plug-in from Sun Microsystems to interact with virtual manipulatives on
this page.
Other
strand resources:
[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ] [ Mathematical Processes ]
NOTE: As general resources for all Geometry and Spatial Sense benchmarks, students might consult the following:
Geometry from Oswego City School District (NY) Regents Exam Prep Center. Each sub-section includes lessons and interactive practice exercises. Sections address geometric relationships, constructions, locus, formal and informal proofs, transformations, and coordinate geometry.
Math Open Reference is a free geometry textbook for high school learners by John Page. There are topics in plane geometry, coordinate geometry, and solid geometry (e.g., cylinders, cubes). Its focus is on using interactive materials and animations to develop concepts. Students can manipulate numerous interactive applets with at least one accompanying nearly every concept that is presented.
A. Formally define geometric figures.
Learner.org: Glossary of key geometry terms
Math.com: Geometry basics. Figures are defined with lessons, examples, workout quizzes, and unit quizzes
Mathwords.com: interactive math dictionary with words, terms, formulas, pictures, diagrams, tables, and examples
Explore Learning Gizmos (Virtual Manipulatives): Quadrilaterals and other Polygons.
Geometry 3-D Shapes is one of the Interactives from Annenberg Media's Learner.org. Learn about three-dimensional shapes, calculate surface area and volume, and discover some of the mathematical properties of shapes. Use the tutorials and take the interactive test.
B. Describe and apply the properties of similar and congruent figures; and justify conjectures involving similarity and congruence.
Edmonton Public Schools (CA), Jim Reed, Math 9: Similar and Congruent Triangles
AlgebraLab.org: Lesson and fill in the blank practice problems, including word problems. Be sure to show the related AlgebraLab documents for additional practice problems on each topic.
Mathleague.com: Describe similar and congruent figures
Math.com: Congruent and similar figures including lesson and workout problems
Utah State University, National Library of Virtual Manipulatives: investigate methods for determining congruent triangles. Explore SSS, SAS, ASA, SSA. Note SSA does not guarantee congruent triangles.
Play videos at YouTube.com:
Similar Triangles illustrates the definition. Example is used to solve a problem of two triangles formed from by two parallel lines cut by two intersecting lines. This was posted from Nutshellmath.com
Proving Triangles Congruent explores 5 methods to show congruence: SSS, SAS, ASA, AAS, and HL in right triangles. This shows use of the two-column proof method: Statement/Reason. This was posted from Nutshellmath.com
C. Recognize and apply angle relationships in situations involving intersecting lines, perpendicular lines and parallel lines.
AlgebraLab.org: Lesson and fill in the blank practice problems. Be sure to show the related AlgebraLab documents for additional practice problems on each topic
Math.com: Angles and Intersecting Lines including lesson and workout problems
AmbleWeb, Virtual Manipulative: 20 Virtual Protractor Angle Activities -- investigate sum of interior and exterior angles in polygons, supplementary angles, angles created by parallel lines and a transversal, vertical angles, and so on.
Shodor Interactivate, Virtual Manipulative: Angles formed by parallel lines and one or two transversals
W. Fendt's Sum of Angles in a Triangle, Virtual Manipulative
D. Use coordinate geometry to represent and examine the properties of geometric figures.
Glencoe Online Study Tools, Geometry 2004, multiple choice practice:
Holt, Rinehart, Winston, Geometry, section 5.7 homework help: Proofs in Coordinate Geometry determine when to use distance, slope, or midpoint formula.
Math Warehouse: Using the coordinate plane in proofs is an interactive demonstrating how to do coordinate proofs. Do the proofs (perpendicular segments, trapezoid is not isosceles, and rectangle) and see the answers.
Coordinate Proofs. Mr. Vahn demonstrates how to set up the coordinate proof in general; then he shows how to prove that the medians to the legs of an isosceles triangle are congruent.
E. Draw and construct representations of two- and three-dimensional geometric objects using a variety of tools, such as straightedge, compass and technology.
MathsNet: Construction This is an interactive to learn to construct mathematical shapes out of points, lines and circles. Then you can change the diagrams yourself using the mouse and see the effect these changes have on the mathematical properties of the shapes.
Mathematics Open Reference: Visual demonstrations of how to do various Euclidean constructions with compass and straightedge. (highly recommended).
Oswego City School District (NY), Regents Prep, new Geometry section: Constructions
Virtual manipulative: Explore the net for a pyramid with rectangular base. You can modify the length, width, and height in this JAVA applet by Pavel Safronov (MSTE division at University of Illinois-Urbana-Champaign).
Virtual manipulative: Explore building "houses" with cubes, given the top, front, and right side views. This activity builds 3-D spatial abilities. This JAVA applet is from the Freudenthal Institute.
F. Represent and model transformations in a coordinate plane and describe the results.
Edmonton Public Schools (CA), Jim Reed, Math 9: Transformations (Translations, Rotations, Reflections, Dilations)
Glencoe Online Study Tools, Geometry Concepts and Applications 2004, multiple choice practice:
Utah State University, National Library of Virtual Manipulatives: show axes, create objects with pattern block pieces, then apply and explore the following:
Effect of two transformations (Translations, Reflections, or Rotations) in any order.
W. Fendt's Simple Geometric Transformations, Virtual Manipulative
Transformations: Review reflections and translations. This was posted from Nutshellmath.com
G. Prove or disprove conjectures and solve problems involving two- and three-dimensional objects represented within a coordinate system.
Glencoe Online Study Tools, Geometry Concepts and Applications 2004, multiple choice practice:
Utah State University, National Library of Virtual Manipulatives: Platonic Solids, Verify Vertices, Faces, Edges of five Solids
H. Establish the validity of conjectures about geometric objects, their properties and relationships by counter-example, inductive and deductive reasoning, and critiquing arguments made by others.
Glencoe Online Study Tools, Geometry Concepts and Applications 2004, multiple choice practice:
Utah State University, National Library of Virtual Manipulatives: walk through a visual proof of the Pythagorean theorem.
I. Use right triangle trigonometric relationships to determine lengths and angle measures
Are you wondering why a2 + b2 = c2 in the right triangle?
See an easy proof from the MacTutor History of Mathematics archive. Or, explore the virtual manipulative.
GCSE Maths Tutor no.5 the sine ratio: What is the sine ratio, plus an example.
GCSE Maths Tutor no.6 the cosine ratio: What is the cosine ratio, plus an example.
GCSE Maths Tutor no.7 the tangent ratio: What is the tangent ratio, plus an example.
GCSE Maths Tutor no.8 sine ratio problems: Three problems show use of sine ratio to find sides of a triangle using multiplication and division; then find an angle.
Glencoe Online Study Tools, Mathematics: Applications and Concepts, Course 3, multiple choice practice: Using the Pythagorean Theorem
Glencoe Online Study Tools, Geometry Concepts and Applications 2004, multiple choice practice:
AlgebraLab.org: Lesson and fill in the blank practice problems.
Pythagorean Theorem lesson and exercises
Mathguide.com: Pythagorean theorem quizmaster. The following are fill in and check answers, which are rounded to the nearest tenth. The formula is presented with the following:
Find the hypotenuse in a right triangle.
Find a leg in a right triangle.
Math.com: Right Triangle and Pythagorean Theorem including lesson and workout problems
Oswego City School District (NY), Regents Prep, new Algebra section:
Trigonometric Ratios finding sides, angles, and word problems.
Are you ready for the test?
Don't forget to review and complete the Six Steps for Success, including the full online practice tests.
Complete: Measurement and Geometry Strand Questions using California's High School Exit Examination (CAHSEE) released questions.
Ohio Mathematics Academic Content Standards. Available: http://www.ode.state.oh.us/GD/Templates/Pages/ODE/ODEPrimary.aspx?page=2&TopicID=1696&TopicRelationID=1704
See
other strand resources:
[ Number, Number Sense, and Operations ] [ Measurement ] [ Geometry and Spatial Sense ] [ Patterns, Functions, and Algebra ] [ Data Analysis and Probability ] [ Mathematical Processes ]
See
related pages: [ Standardized Test
Preparation and Tips for Success (first page)] [ OGT Introduction ]
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Send us your test prep resources and tips for success.
Contact Dr. Patricia Deubel: deubelp@neo.rr.com
Last revised 01/04/10
CT4ME Author: Dr. Patricia Deubel
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