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:
A. Start with a parallelogram…
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 \(ABCD\).
B. Start with a quadrilateral…
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 \( \overline{BD} \).
C. Start with a triangle…
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 \( \triangle ABC \).
D. Start with a triangle…
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 \( \triangle ABC \).
E. Start with a quadrilateral…
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 \( ABCD \).
Construction hints
Right-click on an object for more options (see "Object Properties")
The Regular Polygon tool might be helpful.
Create a custom tool for repetitive commands
Examples above my skill level: Area of circle , SSA example
Crossed ladders (revisited)
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.
Crossed ladder hints
Zoom in to have more precision with the Move Tool
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.
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)
Create a set of step-by-step instructions that could be used to recreate your visual representation.
Fraction hints
Sliders may be a useful way to change numerators and denominators.
Start with the denominators. Can you get a line to show correct segments based on a slider? (Hint: The correct answer is yes, yes you can.)
To make equally sized segments: Circle with center and radius.
To show or hide segments, first figure out how to shade just one segment. Then try "Object Properties > Advanced > Conditions to show object"
Logical operations: && (and), || (or), == (equal, e.g., round(f, 1) == 5 )
Some inspiration: Adding fractions , Visualize fractions , fractions collection
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
Provide a link to your favorite worksheet on GeoGebra materials . Why is it your favourite?
(Note: You cannot pick my favourites that I gave above. Sorry.)
SUBMISSION
Publish the assignment to your EduBlog by:
posting your solution
using LaTeX for all non-calculator mathematics notation
including any files that you created for the assignment
submitting the post's URL to Canvas
By submitting the assignment, you acknowledge that all work is your own.
Special note: Use "Menu > Share > Shared" to get a sharable link. This will require you to sign in via Google.
GeoGebra - Scoring guide 20 TP
Constructions
Crossed ladders (revisited)
Fractions
Instructions _____ provides all the steps needed to recreate the visual representation.
Discussion questions
CHALLENGES