Investigation 1: A Triangle and Its Median Offspring

• Construct and label a triangle, using Sketchpad. Also construct and label the 3 medians in this triangle.
• Construct a second triangle, using the medians you constructed in #1 as its 3 sides.
  • Put a point A anywhere on your sketch.
  • Select this point A and one median of your triangle. Construct a circle using center and radius.
  • Put a point B on the circle and connect the center with this point using your segment tool. This is one side of your offspring triangle. Hide the circle
  • To make the second side, select point A again and a second median and construct a circle by center and radius. Then select point B and the third median and construct a circle by center and radius.
  • These two circles will intersect. Make a point at the intersection and complete the triangle.
• Estimate how the areas of these two triangles compare. Check your estimate, using Sketchpad measurement tools.
• How does your answer to the last question change if you start with a different triangle? Check by dragging the original triangle into different shapes. Write a report summarizing your findings, using words, pictures, and numbers.

Investigation 2: A Triangle and a Different Offspring Triangle

• What other line segments could you have possibly used in this investigation instead of medians? Brainstorm some ideas.
• Investigate one of the ideas you brain stormed. Write a report on your findings using words, pictures and numbers.

Investigation 3: A Square and Its Median Offspring

• The first investigation didn't have to be about triangles and medians. Carry out an investigation, like the first one, only this time start with a square. Write a report summarizing your findings, using words, pictures and numbers.

Investigation 4: A Quadrilateral and an Offspring Quadrilateral

• Predict the result you will get if you start with a different kind of quadrilateral ( rectangle, parallelogram, kite, rhombus, or general quadrilateral .) Conduct an investigation to test your prediction. Write a short report summarizing your findings.

• formulate conjectures and generalizations about geometric relationships involving two-dimensional figures, through investigations facilitated by dynamic geometry software, where appropriate.

Teacher Notes

• Investigation #1 is the 'trial run' investigation, an opportunity to work up approaches, techniques etc before students tackle one or more of the remaining investigations.
• Consider helping the students share the results of their brainstorming with others.

• skillfully uses The Geometer's Sketchpad tools to make necessary constructions and measurements
• report, accurate, clear, and comprehensive making sophisticated use of words, diagrams and numbers
• makes insightful conjectures
• initiates and successfully conducts original investigations in Investigations #2 and #4

• proficiently uses The Geometer's Sketchpad tools to make necessary constructions and measurements
• complete and accurate report, making effective use of words, diagrams, and numbers
• makes at least one appropriate conjecture
• needs minimal assistance to initiate and successfully conduct own investigation in Investigations #2 and #4

• needs some assistance to effectively use The Geometer's Sketchpad tools to make necessary constructions and measurements
• limited success making conjectures
• accurate incomplete report, using words, diagrams, and numbers
• needs some assistance to initiate/conduct own investigation in Investigations #2 and #4

• needs assistance to effectively use The Geometer's Sketchpad tools to make necessary constructions and measurements
• needs assistance to make an appropriate conjecture
• needs assistance to make adequate report using words, diagrams, and numbers
• has difficulty initiating investigation in Investigations #2 and #4

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