This is the ultimate and penultimate guide to teaching the area of a triangle. If you're teaching your students the formula base x height ÷ 2 and handing them a bunch of problems where you show the base and height and have them do the rest, well, you're just wasting your time, and miseducating your students. Smooth move, Ferguson...
Here's are three essential things you should be teaching your students about finding the area of a triangle, some or all of which you are not teaching:
1) Every triangle can be dissected using a single straight cut and re-assembled as a parallelogram.
2) A rectangle is a type of parallelogram, as are squares and rhombi. The "tilted rectangle" actually has a specific name, which is called a.....
3) A triangle does not have a "base." In fact, any side can be a "base," and a "height" can be drawn from the bottom to the top.
4) Students should have practice dissecting triangles so that they understand that the formula can be b x h ÷ 2, b/2 x h and h/2 x b. If they don't know this, you didn't do a very good job.
5) Since any side of the triangle can be the base, then your students should get practice identifying bases and drawing in heights, and then measuring and calculating the area.
6) If you are giving your students problems where the base and height are already labeled, then you're doing a pretty cruddy job. Any practice sheet that identifies the bases and heights and shows them drawn in, is a truly cruddy sheet. Even if you don't buy this activity, PLEASE MAKE YOUR STUDENTS IDENTIFY BASES AND DRAW IN THE HEIGHTS!
Okay, enough of all that, just get your act together and check this out: there are lots of different triangles for your kids to cut out and dissect, as well as a few challenges, including drawing as many triangles as you can with an area of 8 square units. There's lots of other advice as well, but you get the point.....