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9/11/2019 4 Comments

Key Skill: Congruence Statements vs. Equations

Students blend congruence statements with equations incorrectly in lines of Geometry Proof. Explicitly teach the distinction with this free skill download.
When students start out with any confusion at all with converting between congruence statements and equations, they struggle through each next step all the way through proofs.  Take time to tackle this key skill before moving on.

As a geometry teacher, this pet peeve that would pop up over and over again: I'd be grading and see students mixing up their usage of congruent and equal in lines of a proof.  Since I make kids write out separate lines for each step, including converting from a statement of congruence over to an equation with the measures, missing this was really messing up their scores, along with driving me crazy.  Every class, with no exception, would continually mix these up for weeks on end.
 
Eventually, I discovered that it was worth taking time to explicitly teach this skill.  We took a while to practice converting between the two types of statements.  I explained how when you describe figures you use the term congruent, and when you are describing numbers you use the term equal. 
 
We had to bother to take time showing how to switch back and forth between a statement like "length AB = length BC" while saying aloud "The DISTANCE between A and B is a NUMBER!" and a statement showing "SEGMENT AB being CONGRUENT to SEGMENT BC."  Talk these through out loud before assuming that students can see the distinction.  Practice converting back and forth before you allow them to actually use these statements in a Geometry proof. 

​Trust me, it is worth the time.
 
Otherwise, you’ll see hybrids such as <2 = <5 over and over again, which leads students to stumble between steps in their proofs.
 
It helps to display a Reminders poster, like the one below in the room. 
download congruent vs. equal skill poster for geometry
​Then, after practicing a few examples, we work on determining if a statement uses congruent or equal correctly with statements like the ones below.  
 
Lastly, I’d pull up the answer key, and we would discuss why each statement was either correct or incorrect.

Here is a PDF dowload version for you if you'd like to use them too.
Equations in Geometry Proofs
equal vs. congruent in geometry proof lines
This really comes into play in examples like the following proof:
key skills for teaching geometry proofs
Students MUST convert from the congruent notation in the first line into an equation in order to use substitution later on in the proof.  Segment addition postulate does not blend with congruent statements.  It only works with statements of equality, since addition is required.  To work in an equation format, which is necessary in many proofs, students need to be able to smoothly switch from congruence statements into equations and vice versa.

Hopefully these short little downloads and this tip will help you prioritize this skill and take 15 minutes now to save yourself many future headaches and give your students a boost to help them through proofs.  What's your own pet peeve when grading proofs?

Do you teach Geometry proofs?  Subscribe to get more free materials in your inbox:

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4 Comments
Masey DeMoss
10/25/2019 02:46:01 pm

Hey Brigid! I am doing a master's thesis project on doodle notes vs standard note-taking and need some information on research behind doodle notes etc. I am an avid doodle notes user, but do you know where I can get some more information on research in this area? Or possibly of someone I can contact to talk to about this? Thanks! :)

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Math Giraffe link
10/26/2019 12:40:08 pm

Hi Masey,
Yes, we have a lot collected over on the blog at doodlenoteclub.com but the home page and go-to resource would be doodlenotes.org where you can see the basics, download a presentation explaining the concept, and access the Doodle Note Handbook. There are also links to research here on the Math Giraffe blog as well. Thanks so much and have a great weekend! Good luck with the masters!
-Brigid

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Toni Ray
1/10/2020 12:01:59 pm

I have been trying to figure out how to get in touch with ANYONE about my Doodle Notes "one time" subscription as I am no longer able to access the "lifetime" supply of Doodle Note Templates/ resources promised with this one-time fee of $120. I have tried resetting my password to see if it is my login information and that doesn't seem to be the issue as I am able to login, but then when I click on a resource or template tab it says that I must "login" to access this!? When I click on "Join Group" it says that I am already a member of this group when I enter my email address.... I would like a refund or for this issue to be fixed immediately as I have not had access to these resources since last spring.

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Math Giraffe link
1/11/2020 10:56:22 am

Hi Toni Ray,
We can help you with your login. :) Just email mathgiraffe.bd@gmail.com so we have your email address, and we will help you with accessing everything, or give you a refund if you prefer - no problem. Sorry for the inconvenience. We're happy to help you figure out what may be going on and giving you trouble, and we apologize for the difficulty. Thanks so much,
-Brigid

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