Shape

A Professional Development Resource for K-12 Mathematics Teachers

Note: Geometers Sketchpad files used in these activities are available here

1 Chapter One: Triangle Recipes

�1.1 Necessary Conditions

�1.1.1 Challenge: Three sides � Three Angles

�1.1.2 Directed Activity: Segment Lengths

�1.1.3 Directed Activity: Angle Sums

�1.1.4 Directed Activity: Construct an Equilateral Triangle Using Straightedge-and-Compass

�1.1.5 Concepts and Connections

�1.1.6 Exercises

�1.2 Triangle Recipes

�1.2.1 Challenge: Spaghetti Triangles

�1.2.2 Directed Activity: Construct an equilateral triangle using the Geometers Sketchpad

�1.2.3 Directed Activity: Construct an equilateral using paper folding

�1.2.4 Directed Activity: Side-Side-Side

�1.2.5 Directed Activity: Side-Angle-Side

�1.2.6 Directed Activity: Duplicate a segment of unknown length

�1.2.7 Concepts and Connections

�1.2.8 Exercises

�1.3 More Triangle Recipes

�1.3.1 Challenge: More Spaghetti Triangles

�1.3.2 Directed Activity: Angle-Side-Angle

�1.3.3 Directed Activity: Angle-Angle-Side

�1.3.4 Directed Activity: Angle-Angle-Angle

�1.3.5 Directed Activity: Side-Side-Angle

�1.3.6 Concepts and Connections

�1.3.7 Exercises

�1.4 Concept Cards

�1.5 Summary

�

�2 Chapter Two: Properties of Triangles

�2.1 Area of Triangles

�2.1.1 Directed Activity: Perimeter vs. Area

�2.1.2 Directed Activity: Lattice Triangles

�2.1.3 Directed Activity: Area Formulas

�2.1.4 Concepts and Connections

�2.1.5 Exercises

�2.2 Sides, Angles, and Interior Lines & Points

�2.2.1 Directed Activity: Pythagorean Theorem

�2.2.2 Directed Activity: Pythagorean Triples

�2.2.3 Directed Activity: Angle bisectors

�2.2.4 Directed Activity: Perpendicular lines

�2.2.5 Directed Activity: Parallel lines

�2.2.6 Directed Activity: The Water Treatment Plant

�2.2.7 Directed Activity: The School Bus Garage

�2.2.8 Directed Activity: Balance point

�2.2.9 Concepts and Connections

�2.2.10 Exercises

�2.3 Classification & Hierarchical Relationships

�2.3.1 Directed Activity: Sorting by Attributes

�2.3.2 Concepts and Connections

�2.3.3 Exercise

�2.4 Summary

�3 Chapter Three: Properties of Polygons and Circles

�3.1 Naming, Describing, and Constructing Polygons

�3.1.1 Directed Activity: Names and Attributes of N-gons

�3.1.2 Directed Activity: Constructing a Square

�3.1.3 Directed Activity: Constructing a Parallelogram

�3.1.4 Concepts and Connections

�3.1.5 Exercises

�3.2 Perimeter and Area of Polygons

�3.2.1 Challenge: The Meaning of Area

�3.2.2 Directed Activity: Lattice Polygons

�3.2.3 Directed Activity: Perimeter vs. Area of Rectangles

�3.2.4 Directed Activity: Perimeter vs. Area of Parallelograms

�3.2.5 Directed Activity: Perimeter vs. Area of Pentagons

�3.2.6 Directed Activity: Inside a Parallelogram

�3.2.7 Directed Activity: Area of a Trapezoid

�3.2.8 Directed Activity: Perimeter vs. Area of Regular Pentagons

�3.2.9 Concepts and Connections

�3.2.10 Exercises

�3.3 Circumference and Area of Circles

�3.3.1 Challenge: Measuring the Circumference of the Earth

�3.3.2 Directed Activity: The Area of a Circle

�3.3.3 Concepts and Connections

�3.3.4 Exercises

�3.4 Chapter Three: Summary

�3.5 Chapter Three: Appendix

�4 Chapter Four: Symmetry and Transformation Geometry

�4.1 Symmetry

�4.1.1 Challenge: Seeing and Describing Geometric Patterns

�4.1.2 Directed Activity: Line Symmetry

�4.1.3 Directed Activity: Point of Symmetry

�4.1.4 Concepts and Connections

�4.2 Linear Transformations

�4.2.1 Directed Activity: Translations

�4.2.2 Directed Activity: Reflections

�4.2.3 Directed Activity: Rotations

�4.2.4 Directed Activity: Dilations

�4.2.5 Directed Activity: Problem-Solving

�4.2.6 Concepts and Connections

�4.2.7 Exercises

�4.3 Applications of Symmetry in Art and Design

�4.3.1 Directed Activity: Tilings

�4.3.2 Directed Activity: Friezes

�4.3.3 Directed Activity: Tessellations

�4.3.4 Directed Activity: Wallpapers

�4.3.5 Concepts and Connections

�4.3.6 Exercises

�4.4 Chapter Four: Summary

�

�5 Chapter Five: Coordinate Geometry

�5.1 Points, Segments, and Lines

�5.1.1 Directed Activity: Plotting Points

�5.1.2 Directed Activity: Segment Length

�5.1.3 Directed Activity: Segment Midpoint

�5.1.4 Directed Activity: Slope

�5.1.5 Concepts and Connections

�5.1.6 Exercises

�5.2 Area

�5.2.1 Directed Activity: Triangles and Trapezoids

�5.2.2 Directed Activity: More Triangles

�5.2.3 Directed Activity: Polygon Area

�5.2.4 Concepts and Connections

�5.2.5 Exercises

�5.3 Transformation Geometry

�5.3.1 Directed Activity: Translation

�5.3.2 Directed Activity: Reflection

�5.3.3 Concepts and Connections

�5.3.4 Exercises

�5.4 Chapter Five: Summary

�5.5 Chapter Five: Appendix

�6 Chapter Six: 3-D Geometry and Spatial Visualization

�6.1 Visualizing 3-Dimensional Objects

�6.1.1 Challenge: What Can You Build With 36 Cubes?

�6.1.2 Directed Activity: Sketching Isometric Views

�6.1.3 Directed Activity: Sketching Front-Top-Side Views

�6.1.4 Directed Activity: The Concept of Dimensionality

�6.1.5 Directed Activity: Five Platonic Solids

�6.1.6 Directed Activity: Geometric Solids and Euler's Formula

�6.1.7 Directed Activity: Slicing Platonic Solids

�6.1.8 Concepts and Connections

�6.1.9 Exercises

�6.2 Surface Area and Volume

�6.2.1 Challenge: Folding the Circle

�6.2.2 Directed Activity: The Concept of Volume

�6.2.3 Directed Activity: The Concept of Surface Area

�6.2.4 Directed Activity: The Volume of an Open Top Box

�6.2.5 Directed Activity: The Surface Area of an Open Top Box

�6.2.6 Concepts and Connections

�6.2.7 Exercises

�6.3 Drawing 3-Dimensional Objects

�6.3.1 Challenge: Hidden Points and Lines

�6.3.2 Directed Activity: 1-Point Perspective of a Tiled Floor

�6.3.3 Directed Activity: 2-Point Perspective of a Box

�6.3.4 Directed Activity: 2-Point Perspective of a House

�6.3.5 Concepts and Connections

�6.3.6 Exercises

�6.4 Chapter Six: Appendix

�

logo