QUADRILATERALS (Double Feature Weekly Work)

For the past couple of classes we've been talking about quadrilaterals. There are 11 different main types of quadrilaterals we discussed in class, as shown below.

For SBG #2 question #7, it said to divide up a Geoboard into four or more different types of quadrilaterals. I not only took this as a challenge to fit as many quadrilaterals as possible on the Geoboard, I challenged myself to represent as many different shapes as possible. These were some of my attempts to fit as many different quadrilaterals onto one Geoboard as possible.

In the end, this was the division I was the most confident in. It is divided up into 9 separate quadrilaterals, which is the most I could fit on one without repeating any of the shapes. 

Here we have 13 found quadrilaterals, as identified with numbers. At first it only appears to have 9, but a second glance shows there are more quadrilaterals on the Geoboard. This involves combining some of the smaller quadrilaterals to form larger ones.  

The quadrilaterals represented are:

In the original 9: 
1. irregular trapezoid
2. regular trapezoid
3. parallelogram
4. general quadrilateral (convex)
5. general concave
6. rectangle
7. kite
8. chevron
9. right trapezoid

The others:
10. right trapezoid
11. general quadrilateral
12. right trapezoid
13. square

This is similar to the old chess board trick. Someone will ask, "How many squares are on a chess board?" And a person will generally count them up, counting 64 total. But they forget to count all of the combinations of squares that make larger squares! I found a website on this, giving ideas of how to use this principle in the classroom. Looks like it could be useful! Here is the website. 
http://www.teachingideas.co.uk/maths/chess.htm

Reflection: This activity had me thinking about quadrilaterals for a longer time than I wanted to. Trying to divide up the Geoboards into as many quadrilaterals as possible, without repeating any, was frustrating. There were many more trials and errors than what was even shown on the two worksheets. Lots of erasing lines and redrawing them, I wasn't going to settle for there being spaces left over or just putting in a big shape where smaller ones could fit! Over all I enjoyed this. It was fun to explore the different combinations and figure out which shapes fit together best, whether it was smarter to put the points toward the middle or the corners, etc. I learned a lot about quadrilaterals and I don't think it will be easy for me to forget the different types ever again! Also I realized how much teaching potential there was for this. Lots of lesson plan possibilities to be centered around quadrilaterals.

Want more quadrilateral fun? These links are worth trying out. They were linked to the course page. Similar resources could be helpful in a classroom someday as extensions for the students to try at home...on whatever technology we've created by then. (It'll be a few years before I'm actually a teacher. Who knows!)
http://www.sheppardsoftware.com/mathgames/geometry/shapeshoot/QuadShapesShoot.htm
http://www.visualmathlearning.com/Games/shapeology.html

Also, because I spent to much extra time on this, it was the weekly work for both 7 and 8. I would also like for this one to be considered for the SBG grade...because the question came straight from it!