My students finished up their second big arithmetic unit in math last week (on the addition and subtraction of greater numbers–that is, numbers in the 10,000s or larger), and so we have started a mini unit on geometry. This is one of the aspects of our math curriculum that I rather like. Instead of teaching geometry as one big unit at the end of the year, I teach mini units between arithmetic units, providing a break between some of the more abstract concepts of mathematics that fourth graders have to master.
The geometric unit of study this week is triangles. Initially, one might this this is really simple. I mean, come on, we’re talking about triangles here. Three sides, three angles, badabing, badaboom, we’re done, right?
Well, not quite.
We are explore all sorts of fun facts about triangles. Triangles can be classified according to their angles (right, acute, or obtuse), or by the congruency of their sides and angles (equilateral, isosceles, or scalene). The first method of classification does not necessarily exclude a triangle from being classified under the second method. For example, a right triangle may also be an isosceles triangle or a scalene triangle, but it can’t be an equilateral triangle.
We are also examining how any parallelogram can be divided into two congruent triangles. This is going to be important to understand when we start exploring how to find the area of a triangle. (In our first geometry unit, we determined that the area of a parallelogram can be found by multiplying the base by the height. Today we determined that a triangle is, essentially, half of a parallelogram. So the way to find the area of a triangle is the same as finding the area of a parallelogram, but with the additional step of dividing in half!
Triangles are also very useful in design, particularly when it comes to engineering. If I can find an engineer, perhaps who has specialised in structural engineering, who has the time and the desire to visit, I may see if I can have someone come in and talk with my class about why triangles are so often used in engineering. This would be a good transition into our science unit on force and motion that we will be starting after the winter break!