Mathematical Reflections #1

1) What are the common properties of all polygons?
      It has to be a closed shape, the shape is formed by straight lines, and none of the lines are overlapping.  For example here are some shapes that are organised in groups of polygons, and none polygons:

Polygons                   |                Not Polygons

2a) What does the size in degrees tell you about an angle?
          It tells us if an angle is obtuse, or acute.  If the angle measures less than 90 degrees it is an acute angle, but if it measures less than 90 degrees it is a obtuse angle.  Here are two angles.  One that is obtuse, and one that is acute:

The left angle is an acute and the right is an obtuse, I drew a 90 degree
line so you can see that it is greater or less than 90 degrees.

2b) What are some common benchmark angles?
         Some of the common benchmark angles are 45, 90, 135, 180, 225, 270, 315, and 360 degrees.  Knowing these benchmarks makes estimating angles really easily.  For example here is a picture of an "estimation of an angle:

3a) What strategies have you learned that can be used to estimate angle sizes?
         I learned that you can use benchmarks.  Throughout this part of the unit I've used benchmarks,  I really don't have any other special technique but if it is possible I sometimes draw a really light cross with the middle on the vertex of the angle to see what benchmarks it already passed.  On 2b you can see how I estimated 2 angles using benchmarks, here is my other way drawing a cross:

As you can see it is not a perfect cross, but is helps you visualize
the size of the angle. 

3b) What strategies have you learned that can be used to work out the size of an angle from given information i.e. no numbers given, words only.
      You can use benchmarks, but if you want to be more accurate you can use a protractor or a angle ruler.  If you want to use an angle ruler or a protractor it is always good to draw a dot on the vertex because then you can align it really well with the hole in the protractor.  For an angle ruler you have to move the angle ruler until the lines are aligned with the ruler.  Benchmarks is already shown above, but here is a picture of how to find an angle with a protractor:

http://www.open.edu/openlearnworks/pluginfile.php/65400/mod_page/content/1/MU120_B_I103i.jpg
This angle has only letters and the protractor is measuring it.  As you can see it is 40 degrees

3c) What strategies have you learned that can be used to measure and or draw accurate angles with math tools?
      I learned that for a protractor it is always important to draw a little dot in the vertex so you can place the protractor really accurately.  For an angle ruler (and this also goes to all of the math tools)  you can never do things rushed.  You always have to take your time, if not your angle or shape will not be accurate.  Lastly for a ruler you need to never move when you are drawing a line.  In this project I had to restart some drawings because of a crooked line.  For example here are some pictures of these tricks:

http://a.files.bbci.co.uk/bam/live/content/z4xv9j6/large
As you can see this angle has a dot in its vertex which makes it easier to measure the angle. 

1. 

   In the left you can se that I moved the ruler and did a crooked line,
    but on the right because I didn't move I did a perfect straight line.