Pam
Posts:
1,507
Registered:
12/6/04


Re: Simplifying Algebraic Expressions with Subtracted Expressions
Posted:
Nov 17, 2013 12:19 PM


> You are so > enamored by this manipulative that you don't see its > serious limitations. Hopefully some of this > discussion will wear off on both of us. > > Bob Hansen
One can hope. Bar diagrams are so much more than a manipulative. They represent variables in much the same way as letters do, but allow for a visual solution before students know how to manipulate variable equations. Earlier Lou posed this problem:
"A sundae with a cherry costs six dollars. The sundae alone costs five dollars more than the cherry. What does the cherry cost?"
Using bar diagrams, we come to a quick and easy solution. Draw a bar, label it "sundae", divide it arbitrarily in two sections, label one section "cherry" and the other "$5". Draw an identical bar (or you could add onto the first) but add a cherry to your sundae by adding a section the size of the original cherry. Label the entire bar $6. By now the student may see the solution: 2 cherries equal the difference of $1.
In much the same way that we "translate" a story problem into an algebraic equation, we use the bar diagram to translate a story problem into a visual solution that is accessible to a younger child.
And in this case, the bar diagram is a more direct solution than the algebraic solution would be. Not only a good tool in the toolbox, but one that promotes reasoning that would allow that problem to be solved mentally.
But that was too easy. How about this one from Purple Math? http://www.purplemath.com/modules/systprob2.htm
A landscaping company placed two orders with a nursery. The first order was for 13 bushes and 4 trees, and totalled $487. The second order was for 6 bushes and 2 trees, and totalled $232. The bills do not list the peritem price. What were the costs of one bush and of one tree?
Draw a bar divided in two sections, label one section "6 bushes" and the other "2 trees", bracket it all with a label $232. Relating this to the first order, I draw a second bar consisting of two copies of my first bar, to total 12 bushes and 4 trees, then add another section for the remaining bush. Bracket each of the copies and label $232, thus $464 total, and it is easy to see that one bush is $23. Bracket the 6 bushes of the first bar and label $138, 2 trees thus equal $94, or $47/tree.
See? Simply algebra but without having to know how to do algebraic manipulations with variable letters.
Pam

