
The Geometer's Sketchpad™  Resources 
General Information & Tutorials
Resources for grades K12, multiplegrades spanned  NEW content, 20110309
Grade 2
Grade 4
Grade 5
Grade 6
Grade 7
Grade 8

General Information & Tutorials 
Description 
Two Tours 
These two tours introduce users to the most common functions of Geometer's Sketchpad.
Lesson Plans for use with these tours:

Basic skills Miniposters 
Miniposters for your classroom or lab, any grade. (Thought for the day: print off 6 of each in color, then laminate them individually; store these in a hanging file in the computer lab, so they can be referenced by any users.) 
Keyboard Shortcuts 
A single page of commonlyused keyboard shortcuts; see the GSP user manual for the whole series. 
Making MultiPage GSP Files 
A onepage document describing how to build multipage GSP documents (i.e. saved as one file); also, how to change order and/or page names in multipage documents. 
Measuring Angles & Segments 
A short tutorial detailing how to measure angles and segments with Sketchpad. (gsp file) 
Polygons Quick Reference 
Two pages of "quick reminders" about measuring segments and angles, and using the calculator and tabulate functions. 
Setting Preferences in GSP 
A quick tutorial on how/where to set measurement and other display preferences in GSP version 4.xx. 
NEW  Transformational Geometry 
A onepage aidememoire featuring reminders about the most common tools and operations for transformational geometry (pdf) 
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Grades K12 
Description 
Applets from the Ontario Ministry of Education  NEW 
A large collection of premade "Sketchpad" sketches for grades 712 covering many topics that have proven (through experience and research) problematic for students. Some have accompanying videos and/or documentation. 
Sketchpad Activities for Young Learners: Grades 35 
This collection of activities for grades 35 offers examples of the ways in which Sketchpad can be used productively across the range of mathematical strands in the elementary curriculum. In addition to geometry activities, there are many activities that touch on various parts of the Measurement, Algebra, and Number & Operations strands. 
Sketches from PRISMNEO, Grades 7, 8, 9 Applied 
A collection of "Sketchpad" sketches, in all strands, most authored in the summer of 2005 by teachers from across Ontario. Many sketches have "Quick Time" movies and/or print documentation to show how the sketches work.  Links revised
Grade 7  Grade 8  Grade 9 
Sketches from PRISM, Grade 11 
A collection of "Sketchpad" sketches for Grade 11 authored in the summer of 2006 by teachers from across Ontario. Use the navigation matrix to select the topic.  Link revised 
Constructing versus sketching a parallelogram 
Demonstrate the advantages and disadvantages of sketching versus constructing; as well, investigate properties of parallelograms, by dragging corresponding vertices. The one parallelogram was sketched "by eyeball"; the other was constructed by first sketching two segments then using the construct menu to construct parallel lines. 
Ferris Wheel 
Directions for building a working Ferris Wheel: presumes experienced users; applies properties of translations. (Applications to grades 6 and 7) 
Fractions: Multiplication 
A sketch with virtual manipulatives to develop conceptual understanding about fraction multiplication. 
Mathfest: Resources for The Geometer's Sketchpad 
A single page linking out to current known sites hosting a panoply of resources for all ages and skill levels. (Duplicates some of the links elsewhere on this page; has additional sources.) Maintained by Ross Isenegger of the Near North DSB, North Bay, ON. 
Pentominoes 
A GSP sketch in which students manipulate pentominoes to complete several activities including solving a series of puzzles. 
Patterned Squares 
A sketch to supplement the NCTM journal article (Mathematics Teaching in the Middle School, vol 12, no 8).

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Grade 2 
Description 
The Quadrilateral Family 
Two Geometer's Sketchpad files to develop relationships and conenctions among the four most common quadrilaterals (for Grade 2, geometry, expectation 2m44 ): square, rectangle, rhombus, and parallelogram. Use "Quadrilaterals lite" as a teacherled demonstration (e.g., with digital projector) to develop conceptual understanding and connections; consider using "Quadrilaterals student" for pairs or small groups of students to use, e.g. at a center, for consolidation.

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Grade 4 
Description 
Area Schmarea 
An activity designed to have students discover the formula for calculating the area of a rectangle; addresses grade 4 measurement expectation 4m50, "determine, through investigation, the relationship between the side lengths of a rectangle and its perimeter and area" 
Ghost Paths 
Students move two ghost characters (Doug and Linda) around the screen to explore geometric concepts. Students discover connections between the ghosts' constructed paths by comparing them and looking for similarities and differences. Vocabulary introduced: line segment, line, ray, circle, radius, hexagon, and octagon. A sketch authored by Judy Dussiaume, from the Key Press website. Addresses grade 4 geometry expectation 4m7, "communicate mathematical thinking orally, visually, and in writing, using everyday language,..., and observing basic mathematical conventions." 
Investigating the Properties of Quadrilaterals

Two activities to address grade 4 geometry expectation 4m58, "identify quadrilaterals and threedimensional figures and classify them by their geometric properties,...", as well as 4m62.
The two activities are designed to be used one after the other, and to introduce students to Geometer's Sketchpad. Both are .gsp files that should be saved before using. 
Lines of Symmetry 
A short sketch allowing students to view various lines of symmetry, then practice making them on a printout from the sketch. Addresses grade 4 geometry expectation 4m61, "draw the lines of symmetry of twodimensional shapes, through investigation using a variety of tools... and strategies." 
Mirrors and Reflection 
Activity from the GSP manual, "Geometry Activities for Middle School"  an excellent introduction to transformations, addressing grade 4 geometry expectation 4m72, "identify, perform, and describe reflections using a variety of tools (e.g.,... technology)" 
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Grade 5 
Description 
Angle Guesser 
A twopage activity in which students are asked to guess angle sizes, then sketch angles of given measures. Excellent practice to enrich grade 5 geometry expectation 5m51, "identify and classify acute, right, obtuse, and straight angles"

A Cute Sketch 
A tutorial about the principal types of angles. Reviews terminology, labelling, and benchmark angles as well as addressing grade 5 geometry expectation 5m51, "identify and classify acute, right, obtuse, and straight angles" 
Exploring Translations 
Activity from the GSP manual, "Geometry Activities for Middle School"  an excellent introduction to transformations, addressing grade 5 geometry expectation 5m59, "identify, perform, and describe translations" 
Investigating the Properties of Quadrilaterals

Two activities to address grade 4 geometry expectation 4m58, "identify quadrilaterals and threedimensional figures and classify them by their geometric properties,...", as well as 4m62.
The two activities are designed to be used one after the other, and to introduce students to Geometer's Sketchpad. Both are .gsp files that should be saved before using. 
Mirror Face 
Explicit instructions for making a face using reflection properties; addresses grade 5 geometry expectation 5m60, "create and analyze designs by translating and/or reflecting a shape, or shapes, using a variety of tools..." 
Mirrors and Reflection
Properties of Reflections 
Activities from the GSP manuals, these are excellent introductions to reflections, addressing grade 5 geometry expectation 5m60, "create and analyse designs by translating and/or reflecting a shape, or shapes, using a variety of tools..."
(Note: "Mirrors" is the quicker of the two activities to complete, but "Properties" is more thorough.) 
Perimeter and Area 
An activity designed to have students make discoveries about perimeter and area; addresses grade 5 measurement expectation 5m36, "estimate and measure the perimeter and area of regular and irregular polygons, using a variety of tools (e.g., ..., dynamic geometry software) and strategies." 
Polygons Sort 
A tutorial designed to have students learn the properties of common polygons; addresses grade 5 geometry expectation 5m49, "distinguish among polygons, regular polygons, and other twodimensional shapes."

Rotation Symmetry 
A tutorial about rotation symmetry, in which students explore through directed examples; addresses grade 5 geometry expectation 5m49, "distinguish among polygons, regular polygons, and other twodimensional shapes." 
Triangle Town 
A tutorial about the types of triangles, including some problemsolving activities that apply knowledge about triangle properties. Addresses grade 5 geometry expectation 5m53, "identify triangles (i.e., acute, right, obtuse, scalene, isosceles, equilateral), and classify them according to angle and side properties" 
Vecten 
Directions for students to investigate grade 5 measurement expectation 5m40, "create...twodimensional shapes with the same perimeter or the same area." An activity for experienced users of GSP. 
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Grade 6 
Description 
Angle Guesser 
A twopage activity in which students are asked to guess angle sizes, then sketch angles of given measures. Excellent enrichment to enhance grade 6 geometry expectation 6m48, "measure and construct angles up to 180° using a protractor, and classify them as acute, right, obtuse, or straight angles;" this should be used for enrichment of the topic.

Angle Properties of Triangles and Quadrilaterals 
This gsp file shows the angle relationships in both triangles and quadrilaterals, using some neat animation effects. Addresses grade 6 geometry expectation 6m46, "sort and classify quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools (e.g., geoboard, dynamic geometry software) and strategies (e.g., using charts, using Venn diagrams)" 
Areas of Parallelograms and Triangles 
This gsp file shows the relationships between the areas of parallelograms and triangles, with rectangles, and leads students to understanding the formulae. Addresses grade 6 measurement expectation 6m38, "solve problems involving the estimation and calculation of the areas of triangles and the areas of parallelograms." 
Constructing a Triangle Given the Area 
Students use Geometer's Sketchpad to discover they can easily construct a triangle with a given area, then investigate whether noncongruent triangles can have equal areas. This is a problemsolving activity arising from grade 6 measurement expectation 6m35, “construct a rectangle, a square, a triangle, and a parallelogram, using a variety of tools (e.g., concrete materials, geoboard, dynamic geometry software, grid paper), given the area and/or perimeter.” 
Coordinate Graphing 
An activity to address grade 6 geometry expectation 6m52, "explain how a coordinate system represents location, and plot points in the first quadrant of a Cartesian coordinate plane;." 
Coordinate Graphing: Lulu 
An activity where students solve a pair of problems, moving "Lulu" from point to point on the grid. One problem is impossible; the other can be solved by moving point locations. Good practice in routeplanning and gridpoint identification. 
Drawing a 3D SnapCube Object 
Stepbystep explicit directions for students to draw all views of a 3D figure constructed from "snap cubes"; addresses grade 6 geometry expectation 6m51, "sketch, using a variety of tools (e.g., isometric dot paper, dynamic geometry software), isometric perspectives and different views (i.e., top, side, front) of threedimensional figures built with interlocking cubes. 
Drawings to Objects

How to Make a 3D Snap Cube Object from Diagrams
A tutorial for students to use to learn how the various views in diagrams relate to the actual object; their learning is applied by building several objects then making diagrams for others to try. Addresses grade 6 geometry expectation 6m50, "build threedimensional models using connecting cubes, given ... different views (i.e., top, side, front) of the structure." 
Exploring Rotations 
An activity from the GSP manual, this is an excellent introduction to rotations, and addresses grade 6 geometry expectation 6m53, "identify, perform, and describe, through investigation using a variety of tools (e.g., grid paper, tissue paper, protractor, computer technology), rotations of 180º and clockwise and counterclockwise rotations of 90°, with the centre of rotation inside or outside the shape." 
Ferris Wheel 
Directions for building a working Ferris Wheel: presumes experienced users; applies properties of translations. 
Kaleidoscope 
Activity from the GSP manual, this is an excellent application of rotations, addressing grade 6 geometry expectation 6m54, "create and analyse designs made by reflecting, translating, and/or rotating a shape, or shapes, by 90º or 180º," although this activity is not limited to these particular angles. Best used as an enrichment application. 
Rotation Symmetry 
A tutorial about rotation symmetry, in which students explore through directed examples; addresses grade 6 geometry expectation 6m47, "sort polygons according to the number of lines of symmetry and the order of rotational symmetry, through investigation using a variety of tools (e.g., tracing paper, dynamic geometry software, Mira)." 
Solar System 
Make a simple solar system model with GSP by animating points on concentric circles. 
Tessellations 
Activities in tessellations, to address grade 6 geometry expectations 6m54, "explore tiling patterns that cover a plane"; and 6m54, "create and analyse designs made by reflecting, translating, and/or rotating a shape, or shapes, by 90º or 180º," although these activities are not limited to these particular angles. These activities should be considered enrichment/extension activities by teachers.
 Practising Tessellations  a gsp file with builtin directions to learn the steps of creating tessellations with GSP
 Tessellations by Translation  a stepbystep series of directions to make a tiled pattern (by Bill Lundy; revised 20041101)
 Rotation Tessellations  a stepbystep series of directions to make a tessellation whose elements have been rotated rather than translated (by Bill Lundy; revised 20041101)

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Grade 7 
Description 
Area of a Parallelogram 
A gsp file to help you visualize how the area of a parallelogram can be calculated without learning a new formula. 
Angle Properties of Triangles and Quadrilaterals 
This gsp file shows the angle relationships in both triangles and quadrilaterals, using some neat animation effects. Addresses grade 7 geometry expectation 7m47, "sort and classify triangles and quadrilaterals by geometric properties related to symmetry, angles, and sides, through investigation using a variety of tools (e.g., dynamic geometry software) and strategies (e.g., using charts, using Venn diagrams);" 
Equation Balance 
A gsp file in which students manipulate virtual objects on a virtual balance in order to understand some basic principles about solving equations (i.e., "do the same thing to both sides"). Addresses grade 7 patterning & algebra expectation 7m59, "model reallife linear relationships graphically and algebraically, and solve simple algebraic equations using a variety of strategies, ..." 
Ferris Wheel 
Directions for building a working Ferris Wheel: presumes experienced users; applies properties of translations. 
Glide Reflect Tiling 
Observe and manipulate an example of a glide reflect tiling; use as a model to make your own. Addresses grade 7 geometry expectation 7m45 (overall), "describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, and apply transformations to create and analyse designs." 
Integers  Addition
Activity directions 
A gsp file to help you visualize adding integers with a number line; useful as a teaching tool using data projector or "net support", or as a personal manipulative. Use to address grade 7 number sense expectation 7m26, "add and subtract integers, using a variety of tools..." 
PRISM  NEO Sketches 
A collection of sketches, most authored in the summer of 2005, covering Measurement, Central Tendency, Equations, Integers, Ratios, and more. Most have an accompanying "Quick Time" movie and/or print documentation to accompany them. 
Properties of Reflections 
This activity, from the GSP manual, is an excellent introductions to reflections, addressing grade 7 geometry expectation 7m45 (overall), "describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, and apply transformations to create and analyse designs." 
Semicephalus! 
This activity is a quick introductions to reflections, addressing grade 7 geometry expectation 7m45 (overall), "describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, and apply transformations to create and analyse designs." 
Similarity and Congruency 
A GSP tutorial about similarity and congruency, showing the tests for, and properties of, similar or congruent shapes; addresses grade 7 geometry expectation 7m53, "distinguish between and compare similar shapes and congruent shapes, using a variety of tools (e.g., dynamic geometry software) and strategies..." 
Tessellations 
Activities in tessellations, to address grade 7 geometry expectation 7m45 (overall), "describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, and apply transformations to create and analyse designs."", and 7m57, "determine, through investigation using a variety of tools (e.g., pattern blocks, Polydrons, grid paper, tiling software, dynamic geometry software, concrete materials), polygons or combinations of polygons that tile a plane, and describe the transformation(s) involved."
 Practising Tessellations  a gsp file with builtin directions to learn the steps of creating tessellations with GSP
 Tessellations by Translation  a stepbystep series of directions to make a tiled pattern (by Bill Lundy; revised 20041101)
 Rotation Tessellations  a stepbystep series of directions to make a tessellation whose elements have been rotated rather than translated (by Bill Lundy; revised 20041101)
 Hexatessellation!  build upon a regular hexagon to make an Escherlike design

Transformations 
A tutorial that demonstrates various kinds of transformations, and has users analyse the properties of the various transformations; addresses grade 7 geometry expectation 7m57, "determine, through investigation using a variety of tools (e.g., pattern blocks, Polydrons, grid paper, tiling software, dynamic geometry software, concrete materials), polygons or combinations of polygons that tile a plane, and describe the transformation(s) involved." 
Trapezoids  Constructing, and Area 
A tutorial that (a) compares sketching with constructing, and (b) has students develop a method of determining the area of a trapezoid. 
Triangle Congruence 
Explore the different conditions needed to make triangles and establish congruence rules. 
Wintry Transformational Geometry 
Directions for making snowflakes and a "blizzard", most of the work being done by using reflections, rotations, and dilations; addresses grade 7 geometry expectation 7m45 (overall), "describe location in the four quadrants of a coordinate system, dilatate twodimensional shapes, and apply transformations to create and analyse designs."

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Grade 8 
Description 
Angle Properties of Parallel Lines and Transversals 
An activity to address grade 8 geometry expectation 8m47, "determine, through investigation using a variety of tools (e.g., dynamic geometry) and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle."

Angle Relationships 
An interactive gsp tutorial in which students investigate the relationships known as complementary, supplementary, and verticallyopposite angles. Addresses grade 8 geometry expectation 8m47, "determine, through investigation using a variety of tools (e.g., dynamic geometry) and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle." 
Area 
This large sketch by Judi Hanta reviews the calculation of area for quadrilaterals, triangles, and circles, in an engaging, interactive fashion that provides review when needed, and reinforcement for success. Addresses grade 8 measurement expectation 8m36, "solve problems involving the estimation and calculation of the circumference and the area of a circle"; also reviews topics from earlier years' learning. 
Circular Reasoning 
A gsp file in which students explore the relationship between radius and diameter, then apply their knowledge about π to calculate circumference. Addresses grade 8 measurement expectation 8m35, " determine, through investigation using a variety of tools (e.g., cans and string, dynamic geometry software) and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas [i.e., Circumference of a circle = [pi] x diameter; Area of a circle = [pi] x (radius)^2]." 
Equation Balance 
A gsp file in which students manipulate virtual objects on a virtual balance in order to understand some basic principles about solving equations (i.e., "do the same thing to both sides"). Addresses grade 8 patterning & algebra expectation 8m77, "identify, create, and solve simple algebraic equations." 
Exploring Angles Formed by Parallel Lines and a Transversal 
An excellent, succinct introduction to the patterns of equal angles created by a transversal; selected from the GSP user manual, addressing grade 8 geometry expectation 8m47, "determine, through investigation using a variety of tools (e.g., dynamic geometry) and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle."

Integers  Multiplication 
A virtual manipulative using the GSP Cartesian plane (integer axes) to illustrate the multiplication of integers. Addresses grade 8 number sense and numeration (operational sense) expectation 8m21, "represent the multiplication and division of integers, using a variety of tools..." 
Investigating the
Triangle Sum Conjecture 
Use the dynamic nature of GSP to explore the conjecture about the sum of a triangle's interior angles. These directions show how to explore the conjecture, as well as make a table of data to illustrate it. Addresses grade 8 geometry expectation 8m47, "determine, through investigation using a variety of tools (e.g., dynamic geometry) and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle." 
Parallel Lines and Transversals 
Use this GSP sketch to understand what parallel lines and transversals look like, and explore the various relationships of the angles created; addresses grade 8 geometry expectation 8m47. 
Parallel Lines and Triangles 
An activity to address grade 8 geometry expectation 8m47, "determine, through investigation using a variety of tools (e.g., dynamic geometry) and strategies, the angle relationships for intersecting lines and for parallel lines and transversals, and the sum of the angles of a triangle."

PRISM  NEO Sketches 
A collection of sketches, most authored in the summer of 2005, covering Measurement, Central Tendency, Equations, Integers, Ratios, and more. Most have an accompanying "Quick Time" movie and/or print documentation to accompany them. 
The Pythagorean Relationship 
An activity where students interactively work with the Pythagorean theorem to develop understanding of its principles. Addresses grade 8 geometry expectations 8m49, "idetermine the Pythagorean relationship, through investigation using a variety of tools (e.g., dynamic geometry software; paper and scissors; geoboard) and strategies" and 8m50, "solve problems involving right triangles geometrically, using the Pythagorean relationship."

Where's You Get That Pi? 
An activity to learn where "pi" comes from; addresses grade 8 measurement expectation 8m35, " determine, through investigation using a variety of tools (e.g., cans and string, dynamic geometry software) and strategies, the relationships for calculating the circumference and the area of a circle, and generalize to develop the formulas [i.e., Circumference of a circle = [pi] x diameter; Area of a circle = [pi] x (radius)^2]." 
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