Return to the Brainsarefun homepage
Go to the Brainsarefun index

 

SOLUTION KEYS
one effective tool

While useful in all areas of study, Solution Keys are especially useful in teaching math. Why most teachers have no experience using them is a mystery.

In all my years of teaching I have only met one teacher, Carol Gambill, who thoroughly understood the effectiveness of "solution keys."

Solution keys are not the same as "answer keys." A real solution key does not skip any of the steps required to reach the final answer. Solution keys never try to trick the student, or force the student to fill in missing gaps, or require the student to extrapolate. Solution keys provide the student with an ideal solution, every step spelled out.

When creating solution keys the teacher must sit down, and with pencil in hand, thoroughly write down every step required to solve the problem. What ends up on the page are the steps students are required to take to successfully solve the problem, with written comments under each step, or off to the side, adding explanation.

Let me see if I can create both a good and bad example.

Problem: Jerry and Jenny have $1.50 in cash. Jerry has twice as much as Jenny. How much does each have?

GOOD EXAMPLE

Solution:

X = Jenny

2X = Jerry


X+2X = $1.50


3X = $1.50

X = $1.50/3

X = $ 0.50

2X = $1.00

X = Jenny

Jenny has $.050

2X = Jerry

Jerry has $1.00

Commentary:

X is the unknown amount that Jenny has.

Since Jerry has twice as much as Jenny, 2X is the amount the Jerry has.

Added together, the total amount that Jerry and Jenny have equals $1.50.

1X + 2X = 3X
The total that 3X has equals $1.50

1X = $1.50 divided by 3

1X = $ 0.50

2X = $0.50 multiplied by 2, or $1.00

Jenny = 1X

Jenny has $. 0.50

Jerry = 2X (two times .50)

Jerry has $1.00

BAD EXAMPLE

 X = Jenny
2X = Jerry
3X = $1.50
X = .5
Jenny = .5
Jerry = $1
 


The reason that solution keys are ignored is that they require a lot of extra work on the part of the teacher. However, they are very effective when used with homework. Armed with solution keys, and problems that follow the solution keys step by step, students have a great deal of success. Little is more frustrating than the modern crop of textbooks that present no solution keys, and then a bunch of unrelated and dissimilar problems. The work is left to the teachers who really wants to consider themselves "good."

 

- end of article -


FOR MORE BRAINSAREFUN GO TO

- Other Resources / Ideas -

and

More fun with Brainsarefun Index

Return to top of page


COPYRIGHT NOTICE: SOLUTION KEYS © October, 2004 by Rory Donaldson. All rights reserved. In order to help reverse the tide of academic failure and optimize success, individuals may copy brainsarefun solutions for non-commercial use at no charge. Contents may not be sold or repackaged in any manner without the written permission of Rory Donaldson. Since all material is copyrighted, please ensure that this entire copyright notice and contact information continues to be attached to each article you download. Mr. Donaldson appreciates the feedback. Additional solutions may be viewed and downloaded at no charge by logging on to brainsarefun.com. Titles are being updated, edited and added regularly. To view most recently added titles you may click here.

Suggestions and comments encouraged, email: roryd@brainsarefun.com.

This document may be printed directly from your browser or cut into your word processor for additional formatting.

Brainsarefun.com is a
DONALDSON LEARNING PROJECT
Animos Servemus!
Save the brains!

Rory Donaldson
136 Mitchell Hill Road
Lyme, Connecticut 06371
860-526-9853


www.brainsarefun.com -- email: roryd@brainsarefun.com

Return to top of page