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06/12/09

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Inquiry-Based Lessons in Geometry

This collection of inquiry-based lessons in geometry is a work in progress.  They provide a resource for geometry teachers interested on the use of dynamic geometry software (DGS) and the inquiry-based (IB) approach in their classrooms. To the best of our knowledge, the lessons are original work; materials used from other sources are cited within the lessons. 

DGS used include Cabri, Geometer Sketchpad, and the TI-Nspire calculator from Texas Instruments; these lessons can be easily changed to be used with other technologies.  Lessons using the TI-Nspire are listed separately, other lessons may list technology used within the title of the lesson.

 The lessons are been developed under the guidance of Dr. Antonio R. Quesada by students of the course “Concepts of Geometry” and by participant teachers in the summer workshops “Using Dynamic Geometry Software in the Geometry and/or Algebra Classroom” and “Selected Topics in Secondary Mathematics for HS Teachers Grades 8-12, Parts I and II (Project AMP: 2008-2009) offered at The University of Akron.

 An link to lesson contributors is at the bottom of this page.

 Users of these lessons are encouraged to submit corrections and/or suggestions on how to improve them.  Readers are encouraged to submit additional lessons on missing topics using the same format.  An editorial committee will review any lesson submitted prior to being accepted or rejected.  Once a lesson is accepted, the author(s) will be acknowledged in the index.

The following institutions have provided initial support for the development of lessons or for the workshops: the Ohio Department of Education Mathematics Initiative Grant, The Ohio Department of Education, The University of Akron Graduate School Tuition Scholarships and TI price reduction equipment grants, the Board of Regents Title II Program, The Knight Foundation (with the Summit Education Initiative as a fiscal agent), and The University of Akron.

TI-Nspire

High School Level

Perpendicular Bisectors of a Triangle

Middle School Level

Pythagorean Theorems and Special Right Triangles

High School and Middle School Level

Development and Application of the Distance Formula - 2D and 3D 
 

Other Geometry IB Lessons (specific technology indicated when used)

High School Level

1.1ConstructingPerpendiculars
1.2ConstructingTriangles
1.3ConstructingParallelLines
1.4DividingALineSegmentIntoNCongruentParts
10.1Pick'sTheorem
10.2Euler'sTheorem
10.3PedalTriangle
10.4NapoleonTriangle
10.5Menelaus'Theorem
10.6Ceva'sTheorem
10.7SpecialLines
11.2SecantLineApproxToTangent
12.1FiniteGeometryExample
2.1.2Incenter
2.1.4Orthocenter
2.2.1CorrespondingSidesandAnglesofSimilarTriangles
2.2.2SASSimilarityTheorem
2.2.4SimilarityTrianglesOnTheCoordinatePlane
3.11ExploringHingeTheorem
3.12TriangleInequalityTheoremsInvestigation
3.2.5SSALab
3.2.6Area&PerimeterInSimilarPolygons
3.2Interior&ExteriorAngles
3.3.1IsoscelesTriangles
3.4MidsegmentofTriangles
3.5HeronFormula
3.6ExploringHarmonicConjugates
3.7ExploringTrigoRatios
3.8RightTriangles(45-45,30-60)
3.9The Minimal Distance Point from the Vertices of a Triangle
4.4CricumscribedPolygon
5.1CircleConjectures
5.2TheDiameter&Pi
5.3.1AreaofTrianglesWithSameHeight&Base
7.3CompoundLocus
7.5ConicSectionsandLocii
8.1TriangleswithcollinearCircumcenters
9.2CompositionOfReflections
9.3TransformationsandMatrices
Area of Triangle and incenters
Exterior Angle Thm
Inscribed Angles
Inscribed Right Triangles
Median of a trapezoid
Secant and Secant Segments
Side Splitter Theorem
Triangle Side Lengths and Angle Measures
Variation on Koch fractal

Similar Triangles, Ratios and Proportions

Circle Investigation - Part 1

Abstract

Lesson Lab 1 Circle Investigation

Transformations

Summary

Exploring Pi

Transformations LP

Parallel Lines and Associated Angles

Parallel Lines Worksheet

Parallel Lines Quiz

Circles

Circles Lab

Abstract

 

Toothpick Geometry

High School and Middle School Level

2.1.1 Investigating a Point on an Angle Bisector
2.1.3 Finding the Center of Mass of a Triangle
3.1.2 Quadrilaterals within Quadrilaterals
3.1.5.4 Trapezoids
3.1.5.5 Kite
4.3 Tessellations
4.5 AreaofPolygons
6.3 Inscribed quads and parallelogram
Arc Measurement
Conjecture for Intersecting Circles
Dragon Curve Fractal
Dream Home Floor Plan
Exploring Angle Pairs
Exploring Secants Lesson two
Exploring the Properties of Rectangular Prisms 2
Finding the Area of a Parallelogram with Translations
Fractal Tree
Geometric Mean
Koch Snowflake Fractal Lesson and Lab
Orthographic Drawings
Parallels and Perpendiculars
Products of Chords
Pythag-lab
Pythagorean Triples Shortened
Sierpinski Triangle Fractal
The Trappings of Trapezoids
Trig Ratios
Properties of Parallelograms (TI-84)
Right Triangles and Trigonometry (Geo. Sketchpad) 
 

Middle School Level

2.1ExploringParallelLinesandRelatedAngles
3.1.1DiagonalsofSpecialQuadrilaterals
3.1.4PropertiesofParallelograms
4.1GeoboardDiscovery
9.1Transformations

Community Geometry

Exploring Similarity

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This site was last updated 06/12/09