From: Nancy <nstrom@cvsd.org>
To: Teacher2Teacher Public Discussion
Date: 2003020420:30:10
Subject: Use manipulatives (cups and objects)

	
I have taught students this method because many find solving equations
too abstract to 'see' what is happening. It takes some prep time to
set up. Use 10 pairs of paper cups,pennies, and other easy-to-find
objects (Q-tips, plastic spoons, washers, bolts, paper clips, etc.)
This works great for equations involving only positive numbers - where
I start them. For negative numbers, I use something different.

1.  Mark 2 cups on the outside with the same number (1 - 10)and the 
equation that represents its contents. Pennies stand for constants and
the objects represent variables. For example, if you are trying to
teach them to solve 3B + 1 = 2B + 5, put 3 Bolts + 1 penny in one cup
and write 3B + 1 on the outside. In the other cup put 2 bolts and 5
pennies.

2.  The student knows that the goal is to get one bolt (variable) in
one of the cups and only pennies (constants) in the other. To keep it
balanced, you have to remove the same amount of items from each cup.
The students usually dump the contents out into two piles and begin
taking away the same from each pile. I have them write down what they
are doing with the equation as they are doing it. 

3.  After replacing the contents correctly back into their cups, they
take another pair of cups and repeat until 6-7 are done. By the time
this is over, they really have a grasp on equations.

4.  For negative numbers, I draw a little scale with objects on them
where negative numbers are represented with "balloons" making that
side lighter than the other. It is still a visual way for students to
picture what is happening.

Hope this helps!  
 

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