Teaching Area of Triangles

Date: 9/15/96 at 19:40:49
From: MS DAPHNE M BROWN
Subject: Area of a Triangle

I am teaching fifth grade math for the first time.  We have been 
studying geometry, specifically area, for the past week.  However, 
when I gave a Unit Assessment, all but one student got area of a 
triangle wrong. Where did I fail?  Can you help me learn a better 
way to teach area of a triangle?  Initially we used geoboards and 
found the area of rectangles and squares.  Then we proceeded to 
triangles.  I introduced the formula A=bh/2.  Help!

I look forward to your reply.  Thanks so much!

Date: 9/18/96 at 19:17:25
From: Doctor Jodi
Subject: Re: Area of a Triangle

Hi there! Don't worry that your students haven't grasped the material 
as quickly as you thought they would.  It doesn't mean that you've 
failed as a teacher, it just means that your students need more 
practice with the concepts.  

Find innovative ways to relate rectangles to triangles.  For example, 
you might start with a few rectangular sandwiches and show cutting 
each in half.  Compare triangular sandwich halves with the entire 
sandwich and with sandwiches cut in half in other ways.  You could 
also have students do similar activities with paper after 
demonstrating with a more memorable material.

Then you might want to move on to isosceles triangles, showing how you 
can divide the triangle with the perpendicular bisector into two 
congruent parts.  Then you can do similar experiments by cutting the 
triangles along the perpendicular bisector and fitting them into 
rectangles.  Discuss the relation between each smaller triangle, the 
entire triangle, and related rectangles.

Finally, use perpendiculars to divide scalene triangles into right 
triangles and relate them to TWO rectangles, rather than just one. 

You might also try searching the internet for lesson plans.  One good 
place to start is the Math Forum's Internet Mathematics Library at:

  http://mathforum.org/library/   

Best luck and let us know if we can help again!

-Doctor Jodi,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/