Properties of Equality

Match

Match the following Property of Equality with each one-step equation.

Properties of Equality are the set of mathematical rules that allow us to "undo" operations in order to isolate our variable.

• x-7=20

• 17+x=30

• x/2=32

• 2x=40

Addition Property of Equality

Subtraction Property of Equality

Multiplication Property of Equality

Division Property of Equality

• Addition Property of Equality

• Subtraction Property of Equality

• Multiplication Property of Equality

• Division Property of Equality

​8th Grade Expectation

1. ​Show all work

2. Label each step of work with the
   appropriate Property of Equality

1. ​Addition Property of Equality

2. Subtraction Property of Equality

3. Multiplication Property of Equality

4. Division Property of Equality

Properties of Equality

7th Grade Standard

7.EE.B.3 - Solve multi-step real-world and mathematical problems posed with positive and negative rational numbers presented in any form (whole numbers, fractions, and decimals.

Reverse PEMDAS

What does that mean?

Model it!

2x + 15 = 315

Any change?

How does the problem we solves on the previous page change if we restructure the problem to look like this?

315 = 2x + 15

"Slope-Intercept Form"

y = mx + b 315=2x + 15

This is the format you will be using in 8th grade.
Therefore, this is how we will set up our two-step equations, moving forward.

Use the graph to the right to write an equation in the form of y=kx, where k is the constant of proportionality.

​

Write an Equation

ONLY y=kx is proportional.

7th grade: y=kx
8th grade: y=mx + b

What changes happened from seventh grade to 8th grade in the equations above?

y is your y-coordinate
m is your rate of change (otherwise known as "slope")
x is your x-coordinate
b is your y-intercept

Non-Proportional Relationships
y=mx+b

Proportional Relationships
y=kx

7th Grade --> 8th Grade

y is your y-coordinate

​k is your constant of proportionality
x is your x-coordinate

Goal: For you to be able to fluently solve two-step equations. We will set our two-step equations we practice with like y=mx+b to get you practicing in the format you will be using in 8th grade.

Let's Practice

Showing work & correctly labeling.

You are going to practice solving and labeling two-step equations with rational numbers. We will work a couple out together so you understand my expectation. Then, for every four problems you have completed correctly -- you will raise your hand, I will come to you, I will check your four problems, and if you got all four problems correct, then you will get to come up to the board and put your initials on the board on a number. At the end, I will be using a random number generator to select 5 winners for candy.

#5 & #10

Quiz - 10 pts

Show me you know how to show your work and label.

Rewrite the following problems on your piece of paper, showing all work and labeling each step with SPOE, APOE, MPOE, and/or DPOE.

1. 18 = 0.25b + 2
2. -6 = n/2 - 10
3. -10 = 7m + (-10)
4. -5 = x/4 + (-6)
5. -7 = 9x - 7