# Dynamic geometry software

Use GeoGebra to make constructions that fit the criteria below.

## Constructions

Choose one of the following subproblems, which must be unique from your fellow group members:

• Three of the four vertices should be able to be manipulated. Be sure a parallelogram is maintained when the figure is distorted.
• For each edge, construct a square extending out from each side of the parallelogram.
• Label the center of each square with four points, $$A, B, C, D$$, in clockwise order.
• Construct quadrilateral $$ABCD$$. Use display properties (color, thickness, etc.) to make the quadrilateral stand out.
• Provide a reasonable conjecture about quadrilateral $$ABCD$$.

• Each vertex should be able to be manipulated. Be sure a generic quadrilateral is maintained when the figure is distorted.
• For each edge, construct a square containing that edge that is outside the quadrilateral.
• Locate the center of each square. Label four points, $$A, B, C, D$$, in clockwise order.
• Construct $$\overline{AC}$$ and $$\overline{BD}$$. Use display properties (color, thickness, etc.) to make the segments stand out.
• Provide a reasonable conjecture about $$\overline{AC}$$ and $$\overline{BD}$$.

• Each vertex should be able to be manipulated. Be sure a generic triangle is maintained when the figure is distorted.
• For each edge, construct an equilateral triangle. These triangles should all go outward.
• Label centroids of these equilateral triangles, $$A, B, C$$, in clockwise order.
• Construct $$\triangle ABC$$. Use display properties (color, thickness, etc.) to make the construction stand out.
• Provide a reasonable conjecture about $$\triangle ABC$$.

• Each vertex should be able to be manipulated. Be sure a generic triangle is maintained when the figure is distorted.
• Trisect each angle of the triangle.
• Extend the trisections until they meet at three points: $$A, B, C$$.
• Construct $$\triangle ABC$$. Use display properties (color, thickness, etc.) to make the construction stand out.
• Provide a reasonable conjecture about $$\triangle ABC$$.

• Each vertex should be able to be manipulated. Be sure a generic quadrilateral is maintained when the figure is distorted.
• Construct midpoints for each edge. Label these midpoint $$A, B, C, D$$ in clockwise order.
• Construct quadrilateral $$ABCD$$. Use display properties (color, thickness, etc.) to make the segments stand out.
• Provide a reasonable conjecture about quadrilateral $$ABCD$$.

Create a sketch to help solve the crossed ladders problem.

The sketch should …

• Have clear directions to the student.
• Allow a student to manipulate the sketch to find the answer.

### Challenge (+1 TP)

Create an easy way for students to change the lengths of the ladders.

## Fractions

Create a visual representation of a fraction that students can manipulate. Also create a handout with directions to create the representation.

1. Create a visual representation of a fraction that students can manipulate.
• Emphasis on visual. Consider the part-whole model of fractions and remember the parts need to be the same size.
• Emphasis on interactive. The student should be able to change fractions and clearly see what is happening.
• Include directions on the GeoGebra activity.
• Numerator range: 0 to 10.
• Denominator range: 1 to 10.
• Deal with fractions > 1. (don't allow it or clearly show it)
2. Create a set of step-by-step instructions that could be used to recreate your visual representation.

### Challenge (+2 TP)

Create an interactive, visual model to aid students' understanding of fraction addition, $$\frac{a}{b} + \frac{c}{d} = \frac{ad + bc}{bd}$$.

May reduce denominators to maximum of 5. May also "fix" the construction to certain coordinate points in order to simplify the creation process.

## Discussion questions

(Note: You cannot pick my favourites that I gave above. Sorry.)

## SUBMISSION

1. Publish the assignment to your EduBlog by: