Geometers Sketchpad 4

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Geometers Sketchpad 4

• Using GSP4 Effectively at the Intermediate and
  Senior Levels
• Dan MacKinnon OCDSB/OCRI

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How do we use GSP?
Conjecturing Interacting Measuring Sk
etching Drawing
Far more than a drawingtool, GSP allows
studentsto discover and explore significant
mathematical concepts
increasing mathematical power
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Drawing
Selection Tool

• GSP has many elements of a typical drawing
  program
• The drawing options aresubject to the
  classicalruler and compassrestrictions

Point Tool
Compass Tool
Straight Edge Tool
Text Tool
Custom Tools
Hands On 1 Drawing
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From Drawing to Sketching

• Sketching is not drawing, but drawing and
  constructing
• In many ways creating a sketch is like writing a
  computer program
• a sketch must describe not just the visual form
  of the figure also but its logical form

Hands On 2 Drawing vs. Sketching
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Constructing

• The rules of GSP construction are the same as
  ruler and compass construction
• Think What is the minimal input I need to draw
  the shape I want
• Do Select objects that provide the input and use
  the Construct menu

Hands On 3 Exploring Construction
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Measuring

• For any selected object, there are different
  things that you can measure
• Select the item you want to measure and use the
  Measure menu
• You can use the Calculate menu item to work with
  your measurements

Hands On 4 Measuring
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Interacting

• Constructed objects maintain their geometric
  relationships when the drawn objects are moved
• You can explore what relationships exist for
  whole families of geometric figures
• Keep track of measurements using tables

Hands On 5 Interacting
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Conjecturing

• By sketching, measuring, interacting and
  recording their observations students can
• make conjectures about geometric relationships
• see concrete examples of abstract ideas

Hands On 6 Conjecturing
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Applied Sketching

• Student investigations
• students sketch the complete
• teacher provides scaffolding
• As a productivity tool
• use to create handouts, tests, etc.
• Classroom demonstrations
• Creating mathematical documents
• by teacher for students
• by students

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Student Investigations

• Some investigations should have the students go
  through all the stages
• create the sketch, measure, tabulate,
  investigate, conjecture
• Sometimes creating the sketch is not as
  important as investigating

Hands On 7 Investigating
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As a Productivity Tool

• Sketches in GSP can be easily copied and pasted
  into tests, handouts, etc.
• Example uses
• create x-y axis for graphing problems
• tests on solving triangles

Hands On 8 Productivity
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Demonstrations

• GSP can be used in front of the class to provide
  a visual demonstration

Hands On 9 Demonstrations
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Mathematical Documents

• GSP4 allows you to create documents that combine
  text, images, animation, mathematics, and
  interactive content
• can provide a learning environment
• an opportunity for students to produce an
  artifact that demonstrates their understanding

Hands On 10 Documents
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Version 3 to 4

• Easier to construct points on objects and
  intersections
• No scripting - has been replaced by more powerful
  construction options
• More intuitive animation
• Selection tool is sticky by default
• Better text editing

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Advanced Topics

• Animations
• Iterations
• Transformations
• Loci
• Document Options