Polygons and their OffspringGary Flewelling and Nathalie Sinclair |

## 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.
## Overall Expectation (Gr 9 Academic/Applied Geometry)- 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.
## Assessment of PerformanceLevel 4
- 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
Level 3
- 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
Level 2
- 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
Level 1
- 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
## Sample Student ResponseLevel 3 (Investigation #1) |