1. C. A. Warm Up 9/8/14 Write the question:
How many feet per second is 80 miles per hour?
Harold and Kumar are digging up treasure. Harold can dig the treasure up in 4 hours and Kumar can dig it up in 5 hours. How long will it take for them to dig it up together?
What is the sum of the coefficients in the following expression: 5x + y + 3z
The perimeter of a rectangle is 40 inches. The length is 4 more than twice the width. What is the width of the rectangle?

2. REI.1: Explain each step in solving a simple equation
Sept. 8th, 2014
REI.1: Explain each step in solving a simple equation

3. The Properties of Operations Here a, b, and c stand for arbitrary numbers in a given number system.
Name of the Property
Using a, b, and c
Example
Associative Property of addition
 (a + b) + c = a + (b + c)
 (1 + 2) + 3 = 1 + (2 + 3)
Commutative Property of addition
a + b = b + a 
1 + 2 = 2 + 1 
Additive Identity Property
a + 0 = 0 + a = a 
2 + 0 = = 2
Additive Inverse
 a + (-a) = (-a) + a = 0
2 + (-2) = (-2) + 2 = 0 

4. Associative Property of multiplication (a × b) × c = a × (b × c)
Name of Property
Using a, b, and c
Example
Associative Property of multiplication
 (a × b) × c = a × (b × c)
(2 × 3) × 4 = 2 × (3 × 4)
Commutative Property of multiplication
a × b = b × a 
(2 × 3) = (3 × 2)
Multiplicative Identity Property
 a × 1 = 1 × a = a
2 × 1 = 1 × 2 = 2
Multiplicative Inverse
a ≠ 0,
a × 1/a = 1/a × a = 1
2 × ½ = ½ × 2 = 1
Distributive Property of multiplication over addition
 a × (b + c) = a × b + a × c
2 × (1 + 3) = 2 × × 3

5. Examples:
Identify which property each of the following is:
7 + 3 = 3 + 7
7 × 1 = 7
(3 + 4) + 5 = 3 + (4 + 5)
3 × 1/3 = 1
1 + (-1) = 0
(5 × 6) × 7 = 5 × (6 × 7)
7 × 4 = 4 × 7
2 (4 + 5) = 2 × × 5
8 + 0 = 8

6. The Properties of Operations Here a, b, and c stand for arbitrary numbers in a given number system.
Name of the Property
Using a, b, and c
Example
Reflexive Property of equality
 a = a
 3 = 3
Symmetric Property of equality
If a = b, then b = a 
If y = 3, then 3 = y
Transitive Property of equality
 If a = b and b = c, then a = c
If y = 3 and y = x – 7, then 3 = x – 7
Addition Property of equality
If a = b, then a + c = b + c 
If y = 3, then y + 2 = 3 + 2
Subtraction Property of equality
If a = b, then a – c = b – c
If y = 3, then y – 4 = 3 – 4
Multiplication Property of equality
 If a = b, then a × c = b × c
If y = 3, then y × 5 = 3 × 5
Division Property of equality
If a = b and c ≠ 0, then a ÷ c = b ÷ c 
If y = 3, then 𝑦 2 = 3 2  
Substitution Property of equality
 If a = b, then b may be substituted for a in any expression containing a.
If y = 3 and 5 = 2y + 4, then
5 = 2(3) + 4

7. If x = 5 and y = 3x + 4, then y = 3(5) + 4
Examples:
Identify which property each of the following is:
x = x
If x = 5 and x = y + 3, then 5 = y + 3
If x = 5, then 2 × x = 2 × 5
If x = 5, then 5 = x
If x = 5, then x + 3 = 5 + 3
If x = 5, then x – 4 = 5 – 4
If x = 5, then x/2 = 5/2
If x = 5 and y = 3x + 4, then y = 3(5) + 4  

8. Equation to be solved
Written Step (including property used)
2(3x + 5) = 22
Distributive Property
6x + 10 = 22
Subtraction Property: Subtract 10 from both sides
6x = 12
Combined like terms
Division Property: Divide each term on both sides by 6
x = 2
Simplify both sides

9. Complete the REI.1 Assignment Worksheet
9/8/14