Two Column Algebraic Proofs

Algebraic Proofs Intro Lesson

What is a proof?

What is an algebraic proof?

• We use algebraic proof all the time when we solve for x.

• Proofs are fun and have patterns.

• With proofs WE NAME EVERYTHING!!!!

• We name every step when solving for x.

Algebraic Properties of Equality

We do these all the time when solving for x, now we name it! Are you ready?

Algebraic Properties of Equality

We use the word Equality when there is an = sign.

Multiple Choice

What property of equality is used to solve y - 3 = 6?

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

What property of equality is used to solve y + 3 = 6?

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

$$What\ property\ of\ equality\ is\ used\ to\ solve\ \frac{y}{3}=2$$  

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

$$What\ property\ of\ equality\ is\ used\ to\ solve\ 3y=12$$  

• Addition POE

• Subtraction POE

• Multiplication POE

• Division POE

Multiple Choice

$$What\ property\ is\ used\ to\ simplify\ 2\left(a\ +3\right)$$  

• Distributive Property

• Subtraction POE

• Multiplication POE

• Division POE

What does a proof look like?

There is always a given and a prove.

The first line is always the given.

The last line is always the prove.

The reasons are the properties of equality.

Solving Proofs

What would go in line 1 of the reasons?

Solving Proofs

What would go in line 2 of the reasons?

Solving Proofs

What would go in line 3 of the reasons?

Multiple Choice

What goes in line 1 of the reasons?

• Given

• Addition POE

• Distributive Property

Multiple Choice

What goes in line 2 of the reasons?

• Subtraction POE

• Addition POE

• Distributive Property

Multiple Choice

What goes in line 3 of the reasons?

• Subtraction POE

• Addition POE

• Distributive Property

Multiple Choice

What goes in line 4 of the reasons?

• Subtraction POE

• Division POE

• Distributive Property

Special Property

Symmetric Property of Equality.

In math, we don't like 6 = x, we like

x = 6

Multiple Choice

What goes in line 5 of the reasons?

• Symmetric POE

• Division POE

• Distributive Property

Poll

Exit Ticket:

What do we put in the reasons part of proofs

• Algebraic Properties of Equality

• The answers

• Words