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Algebraic Proof Lesson

Description: 

The students will get their first introduction to proofs. Since we are dealing with algebraic proofs, this is the first time students will be challenged to justify every step of solving an equation. They must start to think WHY along with HOW. This is a great introduction to geometric proofs because although the statement-reasons format stay the same, students will start to enter the abstract world and prove things that seem foreign to them. Instead of scaring them away, lets start with solving algebra equations that they are comfortable with!

Learning Targets: 
Students will be able to solve a multi-step equation
Students will be able to give justification for each step of an algebraic proof
Students will be able to use properties of equality and congruence to complete an algebraic proof
Link: 
Video for extra help
https://www.youtube.com/watch
AttachmentSize
PDF icon 2-5 Algebraic Proof DO-NOW.pdf115.89 KB
PDF icon 2-5 Algebraic Proof EXIT TICKET.pdf201.19 KB
PDF icon 2-5 Algebraic Proof NOTES KEY.PDF155.17 KB
PDF icon 2-5 Algebraic Proof NOTES.PDF75.26 KB
PDF icon 2-5 Algebraic Proof WORKSHEET.pdf340.95 KB
Author: 
davesarkipato
Content Area: 
Mathematics
Geometry
Language: 
English
Resource Type: 
Lesson
Licensing: 
Creative Commons Licence
Grade: 
9
10
Common Core Math
Common Core Math: 
CCSS.MATH.CONTENT.HSA.REI.1
Tags: 
Algebraic Proof
Addition Property of Equality
Subtraction Property of Equality
Multiplication Property of Equality
Division Property of Equality
Reflexive Property of Equality
Symmetric Property of Equality
Transitive Property of Equality
Substitution Property of Equality

How are the standards/objectives assessed?

Practice Worksheet

Exit Ticket

Student prerequisite skills and knowledge

Students will need to have a knowledge of how to solve a multi-step equation. This will include using the distributive property, variable on both sides, and the combination of like-terms.

How is the concept or procedure explained or demonstrated?

Solving equations should be a review for students, but we are introducing how to justify your steps. This idea will be used for geometric proofs the rest of the year. Students will be writing 2-column proofs where each step must have a correct justification and this is the first step in the process towards that.

What concepts or procedures are being explained or demonstrated in this lesson object?

On the surface, students will need to solve multi-step equations. However, this lesson pushes them to think deeper because they need to provide justification for each of their actions. They need to think "why/how am I allowed to move that variable to the other side?" Kick-starting the thought process is crucial as we move into geometric proofs and including more abstract concepts.

What was your experience, both successes and challenges, using this lesson object with your students?

Successes - most students excelled in solving the equations. I heard many comments like "these proofs aren't very hard" or "I don't mind doing proofs" (if they only knew what was coming!). Challenges - getting students to justify EVERY step of the proof was difficult. They would say things like "I already know how to do this" and "why do I have to justify if I know what I'm doing". Keep preaching that it is a thought process and they will need to use that process for the remainder of the year. The proofs will get much harder and if you practice now you will be ahead in the long run.