Wednesday, April 2, 2014

Some Elementary Geometry

I mentioned in a previous post about our love of Sir Cumference books. We read the Dragon of Pi book when we celebrated pi day last month. Yesterday, we read Sir Cumference and the Great Knight of Angleland as we talked about types of angles and triangles. We also introduced the protractor. There is a Montessori protractor that is sized to match the metal insets/fraction circles but we do not have one yet. T had fun learning how to use the regular protractor. The book uses a medallion as a protractor so T was excited to get his own. This book actually came with a small very thin plastic protractor but as its a library book we couldn't keep it.

(please click on any of the following photos and they will get larger, some of them may be difficult to see fully if you don't enlarge them)

We started our discussion with types of triangles.  Montessori Print Shop has a wonderful FREE printable of the seven types of triangles 3 part cards. He measured the angles of the triangles and we talked about right, acute and obtuse angles. We also talked about what isosceles and scalene meant. He matched the cards to their name and then compared them to the control cards.

T located each of the seven types of triangles in our geometry cabinet. You can see from the tray that there are only six triangles on the triangle tray in the cabinet. The last triangle (obtuse angled scalene triangle) is located in the last tray of the cabinet with the "extras".

After matching the triangles from the Geo cabinet, he tried his hand at the blue triangle constructive triangles box. This box contains two obtuse isosceles, two equilateral, three right angled scalene and one obtuse angled scalene triangles.

Today we moved our focus to the angles. We talked about how right angles are always 90º, acute angles are always less than 90º and obtuse angles are always greater than 90º. T used these angle cards from Cultivating Dharma. There is a heading for each type of angle and five cards for each. He sorted them, measuring when he needed to.

There is a wonderful short lesson called The Story of Geometry. Don't worry, this isn't another Great Lesson. Its very short and simple. You don't really need any materials unless you would like to do the demonstration and then you only need some rope/string and a few weights/markers.
The Story of Geometry gives the history of Geometry going back to the Egyptians. The Egyptians had trouble with flooding moving their markers for their farms and they used rope to fix their problem. There is a wonderful free version of this story at Montessori Commons that we used. This site doesn't have any photos so I also used a post from Making Montessori Ours where they did this lesson.
The Egyptians learned that if they always used sides of 3:4:5 in their triangles they would always make a right angled triangle. In our example we used 6" segments so one side was 3x6=18", then 4x6=24" and finally 5x6=30.

Later Pythagoras figured out why this worked and named it the Pythagorean Theorem.
$a^2 + b^2 = c^2\!\,$

We used the 3:4:5 for this triangle using inches so there was 3", 4" and 5" sides to this triangle. It made a right angled scalene triangle as it should have. Then we made each side a square and determined its area. I could tell I was losing T by this point so we pulled out our trusty bead squares. He immediately understood what the square of 3, 4, and 5 were. Then we added the beads from the 3 square to the beads of the 4 square and it did, indeed, equal the beads of the 5 square. T understood it but he was less than excited about it. I got a few looks because I was excited that he was learning some more interesting math. I love math but he thinks its a bit boring. This is just a foundation though, he will tuck this info in the back of his mind and will be able to pull it out later and understand it more easily. For now, I think we i'll just stick with measuring angles because he finds that fun.