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) Warm-up exercises on number sense including place value, operations with large numbers, and distances in miles and inches. 3) A lesson on absolute value including its definition as the distance from zero and illustrations of evaluating it for positive and negative numbers. 4) Additional absolute value problems to work through.

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+

5. -3 + (-5) + 6 + 9 + 2 + (-4) =
Integers: Simplify
5 + (-4) + (-6) + 8 + (-3) + 3 =
7
3
-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”
Absolute Value can also be defined as:
 if a >0, then |a| = a
 if a < 0, then |-a| = a

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

12. • If a number is positive (or zero), the absolute value
function does nothing to it: |4| = 4
• If a number is negative, the absolute value function
makes it positive: |-4| = 4
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

13. • 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 tomorrow
 Khan Due by Sun. eve.