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What the X?! How I teach basic linear equations.

5/11/2014

4 Comments

 
Picture
Source: http://www.zazzle.ca/satan_alphabet_in_math_tee_shirt-235801256845953337
At some point kids learned that algebra is hard, confusing, or some other description preceded usually by an expletive, and followed by a sigh.  As a lover of Math, I never understood that algebra was difficult, and it became stunningly obvious the first time I tried to teach basic equations that I was not "normal."  I stood in front of the board, and told my grade eights "Just do the opposite operation, that's it!  If you see adding just subtract."  It seemed so obvious to me.  No stress, just tell them.  We see it all the time. It just didn't work for my students, and it didn't work for me.  So I thought long and hard, and this is what I came up with.

Balancing Scales

With my mind on 3 acts so often, I wanted to boil down my problems to a simple question.  I began to ask my students "How many pennies are in that cup?"

Act 1 - Penny balance from Timon Piccini on Vimeo.

If you ask students how many pennies were in that first cup (assuming I divided the pennies equally), they will have the answer before the video is finished.
Picture
The thing that arose as the difficiency of this method, is that the problems became so easy in this case, that students couldn't see the connection between the algebra and the cups.  I worked for a while on a basic set of work that would bridge the gap between the visual and the abstract.  My process for my students went as follows:
  1. Student views visual and solves.
  2. Student develops visual from words and solves.
  3. Student views equation, develops visual (if necessary), and solve.

To see a copy of what this looks like just click on the link below.
one_step_equations_-_addition.docx
File Size: 590 kb
File Type: docx
Download File

I hummed and hawed about how to bridge two and three, but I found by the time students had finished step 2, they could complete step three without any hesitation.  It was fantastic! As soon as students get a bit stuck on the equation, I tell them, "Let's draw it on this lovely whiteboard."

To really hammer home the connection between them we play lots and lots of Algebranary!

Downfalls

There are a number of downfalls with this method, that I am still trying to work through, and I would love any critique that you can give.
  • When kids can do it in their head, they feel no need to draw anything; when the numbers are too large drawing is cumbersome, and inefficient (the necessary breaking of visual models to get to the abstract I guess).
  • Visually subtraction is impossible (very hard?) to show in a static image, so in my slides you will see I resort to number lines (I save the visual of that for last), since students will have a hard time drawing on their own.
  • Though students are able to UNDERSTAND the steps of solving equations, this set up does not create the desire FOR algebraic knowledge like some of the awesome projects we often see on the blogosphere.

It is not perfect, but this has all been incredibly valuable for student understanding the basics of solving linear equations.

Moving Further

I have always imagined this would also work great for inequalities (unbalanced scales and ask "What is the minimum number of pennies to do this?"). Dig through the slides, and the pictures, and the videos, take what you like, tell me where you would go, and hopefully enjoy.

The Goods

penny_equations_-_student_work.zip
File Size: 3610 kb
File Type: zip
Download File

penny_equations_-_mess_of_all_my_media.zip
File Size: 104463 kb
File Type: zip
Download File

I started to organize the video files, then I got lazy.  If you want to deal with the raw files however, you can download this mess of files. Otherwise see how I organized them in my PowerPoint.
linear_equations_with_pennies.pptx
File Size: 108444 kb
File Type: pptx
Download File

4 Comments
Isabelle
6/20/2014 11:08:03 pm

Wow! I'm very impressed! I will definitely try these activities with my students next year. But to you give me permission to translate these in french?

Thank you so much for this great resource.

Reply
Timon Piccini link
6/21/2014 01:28:42 am

Bien sûr!

Reply
Kaitlyn Rudy
7/20/2014 05:04:07 am

I am a student research assistant at Montana Tech of the University of Montana. Technology has created exciting ways to connect with others and form professional learning networks. As a part of an active member of a social media community made up of teachers, I wanted to contact you to ask you to participate in a study our research group is conducting.

Research shows that face-to-face professional networks provide much needed professional and personal support to teachers. You and the community you belong to are providing these types of support using social media. We are interested in learning more about your experiences using social media to connect with other teachers and your opinions about online professional networks.

The purpose of our study is to learn how professional learning networks created through social media are similar or different than face-to-face networks and what you feel are advantages of using social media to connect with other teachers. Our hope is that the results of this study will inform how professional networks for teachers are designed in the future. If you are interested in participating, please send an email to me at teacherblogPLN@gmail.com. I will send you a link to a short online survey and will set up time for a short skype interview.


If you have any questions you would like to ask about the study, please do not hesitate to contact me.

Sincerely,


Kaitlyn Rudy
Research Assistant
Department of Mathematical Sciences
Montana Tech of the University of Montana

Reply
Jessie
12/20/2016 08:52:41 am

Thank you so much!! I can't wait to introduce equations next semester!

Reply



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