Geometer’s Sketchpad 4

1. Geometer’s Sketchpad 4 Using GSP4 Effectively at the Intermediate and Senior Levels Dan MacKinnon OCDSB/OCRI

2. How do we use GSP? Conjecturing Interacting Measuring Sketching Drawing Far more than a drawingtool, GSP allows studentsto discover and explore significant mathematical concepts increasing mathematical power

3. Drawing Selection Tool • GSP has many elements of a typical drawing program • The drawing options aresubject to the classical“ruler and compass”restrictions Point Tool Compass Tool Straight Edge Tool Text Tool Custom Tools Hands On 1: Drawing

4. 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

5. 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

6. 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

7. 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

8. 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

9. 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

10. 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

11. 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

12. Demonstrations • GSP can be used in front of the class to provide a visual demonstration Hands On 9: Demonstrations

13. 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

14. 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

15. Advanced Topics • Animations • Iterations • Transformations • Loci • Document Options