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Topic: Simplifying Algebraic Expressions with Subtracted Expressions
Replies: 67   Last Post: Nov 25, 2013 12:57 PM

 Messages: [ Previous | Next ]
 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.

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 per-item 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

Date Subject Author
11/11/13 MVTutor
11/11/13 Robert Hansen
11/12/13 Bishop, Wayne
11/12/13 MVTutor
11/13/13 Jonathan Crabtree
11/13/13 Bishop, Wayne
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Louis Talman
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/14/13 Robert Hansen
11/16/13 Bishop, Wayne
11/16/13 Robert Hansen
11/14/13 Joe Niederberger
11/14/13 Robert Hansen
11/16/13 Bishop, Wayne
11/14/13 Pam
11/15/13 Robert Hansen
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/15/13 Joe Niederberger
11/15/13 Joe Niederberger
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/16/13 Bishop, Wayne
11/16/13 Robert Hansen
11/17/13 Bishop, Wayne
11/17/13 Robert Hansen
11/17/13 Bishop, Wayne
11/15/13 Joe Niederberger
11/15/13 Robert Hansen
11/15/13 Pam
11/15/13 Robert Hansen
11/15/13 Pam
11/16/13 Robert Hansen
11/16/13 Robert Hansen
11/16/13 Joe Niederberger
11/16/13 Robert Hansen
11/18/13 Louis Talman
11/21/13 Robert Hansen
11/21/13 Louis Talman
11/16/13 Pam
11/16/13 Robert Hansen
11/16/13 Pam
11/16/13 Robert Hansen
11/18/13 GS Chandy
11/17/13 GS Chandy
11/17/13 Pam
11/17/13 Robert Hansen
11/17/13 Pam
11/17/13 Robert Hansen
11/17/13 Pam
11/18/13 Robert Hansen
11/18/13 Robert Hansen
11/18/13 Pam
11/18/13 Robert Hansen
11/25/13 Bishop, Wayne
11/25/13 Robert Hansen
11/22/13 Joe Niederberger
11/25/13 Bishop, Wayne
11/23/13 GS Chandy
11/24/13 Robert Hansen
11/25/13 Bishop, Wayne