This document contains notes from a math class that covered the following topics: 1) First quarter grades being posted, class work being due, and a review of order of operations and integers. 2) A warm-up on number sense including simplifying expressions and solving equations. 3) A beginning lesson on absolute value, defining it as the distance from zero and that it makes all values positive. 4) Examples of evaluating absolute value expressions and order of operations within absolute value. Class work and Khan Academy assignments were assigned.

1. Today
 First Qtr. Grades Posted @ v6math
 Class Work 2.1 Due Now
 Review Order of Operations/Integers
 Begin Absolute Value

2. Warm-Up: Number Sense
Large & Small Numbers
1. What number comes after a trillion? A Quadrillion
2. How many billions in a trillion?
Write your answer in numbers and words:
3. How far (in miles)is a one-way trip from the Earth to
the Sun?
1000
20,420,060,000 miles
Twenty billion, four-
hundred twenty million,
sixty-thousand miles.
(‘and’ is not a number)
4. Each time a comma is
added to a number, we have
multiplied by what number?
1,000

3. Write your answer in numbers and words:
4. In inches, what is the average width of a human hair?
0.007 inch Seven -Thousandths of an inch
A thousand hairs lined up is how long?
Write your answer in numbers and words:
5. In seconds, how long does it take a hummingbird to flap its
wings one time?
7 inches
0.12 seconds Twelve-Hundredths of a second
6. How many times can it flap it’s wings in 1.2 seconds?
10 times
Warm-Up: Number Sense

4. Simplify
10 – 2 -3 + 36 ÷ 4 • 9 86
Simplify the expression.
5x2 + 2x - 1+
-44 135
-45

5. -3 + (-5) + 6 + 9 + 2 + (-4) =
Integers: Simplify
5
-5(1 – 5x) + 5( -8x -2) = -4x -8x
Solve the equation.
0.5(x – 12) = .4

6. Absolute Value:
 What is the elevation of the diver from sea level?
 How many feet did the diver travel to
get there?
 Is it possible for this diver to travel a
negative distance?
 It is this fact, that all distances must be
positive, that forms the basis for
absolute value.

7. Definition
 The absolute value of a number is its distance from zero.
 Since distances are always positive, the absolute Value of a
number is always positive.
 Even negative numbers have a positive distance to zero.
 The symbol |x| represents the absolute value of the
number x. It is read, ”The absolute value of x”

8. Absolute Value: |x|
• Absolute Value measures the distance a number is from zero.
The following are illustrations of what absolute value means
using the numbers -3 and 3:
Note: Any pair of opposite numbers has the same absolute value
since they are the same distance from 0 on a number line.

9. Notice that for any real number a, but
Be careful to notice that these two expressions are not
equal.
Absolute Value:

10. Absolute Value
What two points are 5 away from 0?
0 5-5 10-10
− 𝟓 = 𝟓
𝟓 = 𝟓

11. Find the value of the following: |5 + (-2)|
Did you get 7? Unfortunately, that's wrong.
The absolute value bars are also grouping symbols.
Simplify inside the absolute value first, then take the
absolute value.
The correct answer is:
Absolute Value: |x|
|5 + (-2)| = |3| = 3

12. • Simplify | 0 – 6 |
• | 4+ (– 6)|
• | 2 – 5 |
• | 0(–4) |
• | 2 + 3(–4) |
• –| –4 |
• –| (–2)2 |
Absolute Value: |x|
6
0
-4
-4
10
2
3
6-8 + 8-6 =
|(-2)(-3)(-2)|
 Class Work 2.2
 Khan Due by Sun. eve.

13. 5 + (-4) + (-6) + 8 + (-3) + 3 = 3

14. Absolute Value
The distance away from 0
𝒙 = 𝟏𝟎
0 5-5 10-10
10 10
𝒙 = −𝟏𝟎 𝒙 = 𝟏𝟎