The document discusses topics covered in a math class the previous week, including order of operations with negative numbers, integer addition and subtraction, and comparing absolute values. It notes that students spent over 10 hours finishing these topics, completing them at the "11th hour". Doing something at the "11th hour" means completing or dealing with something just before a deadline. The document also provides examples of integer operations and rules for determining the sign of products and quotients of integers based on the number of negative factors.

1. November 2, 2015
Today:

2. Topics for Week Ending
Sunday, November 8th.
Order of Operations with
Negative Numbers
Integer Addition
& Subtraction
Comparing Absolute
Values

3. Two charts from this past week
Thank you
Yesterday alone, students spent 625 minutes (10.4 hrs.),
finishing up (at the 11th hour) their topics.
Question:
What does it mean when something is done at the 11th hour?

4. 1)
𝒙−𝟓
𝟑
+
𝒙+𝟕
𝟓
-
𝒙+𝟒
𝟏𝟎
=
𝟒𝒙
𝟏𝟓
A) 1 B)
−𝟏
𝟒
C)
−𝟒
𝟓
D)
𝟑
𝟒
E) None
33%
33%
2) Find three consecutive odd numbers so that the
sum of the two smallest numbers is 17 more than the
largest number. The largest of the numbers is:
A) 13 B) 17 C) 23 D) 25 E) 33

5. 30%
3. A triangular lot has 135 yards of fencing around the
perimeter. The longest side of the lot is
5 yards more than twice the length of the shortest side.
The other side is 10 yards longer than the shortest side. What
is the length of longest side?
A) 65 B) 30 C) 40 D) 75 E) 15
x + 2x + 5 + x+ 10 = 135

6. 30%
10(r + 3) = 7r 10r + 30 = 7r
30 = -3r
30 = -3r
-3 -3
r = -10
A.
𝟖
𝟐𝟓𝟎
B.
𝟑𝟔
𝟏𝟎𝟎
C.
𝟗
𝟐𝟓𝟎
D.
𝟑𝟔
𝟏𝟎𝟎
E.
𝟑𝟔
𝟏𝟎𝟎𝟎
9) 0.036
From Part I of the
Final Exam
28%

7. 8. In a wooden crate, there are 56 apples & oranges. There
are 6 more oranges than apples. How many oranges are
there?
A) 50 B) 31 C) 36 D) 34 E) 27
27%
27%
10. 4(2x – 2) = -8(x – 4)
A) 2
𝟏
𝟐
B) 2 C) -2 D)
𝟑
𝟒
E) No Solution
x + x + 6 = 56

8. 24%
The most missed question: V. 2, # 9
A) -1 B) 3 C) 17 D) -24 E) -7

9. Integers &
Order of Operations
Definition: An integer is a whole number (not part of a fraction),
that is either positive, negative, or zero.
The sum of an integer and its opposite always equals zero.
Every integer, except zero, has an opposite.

10.  Adding a negative number, 8 + (- 4) =
Is the same as subtracting a
positive number.
8 – 4 =(+ )
In both cases, the
signs are different,
and subtraction is
the operation
 Addition can be used on any and all subtraction problems,
6 – 9 = - 9+ + 6
 And subtraction on any and all addition problems.
-2 + (-2) = -2 - 2+

11. Rewrite using the opposite operation and solve. All results
should be the same as the original equation.
If the signs are different, (-, +) or (+, -) subtract.
Subtracting a positive
is just subtracting
Increasing by a negative amount
is just subtracting
If the signs are the same, (+, +) or (-, -) add. (+ )
The sign of the first integer
does not change. It is our
‘starting point’
Think: starting point, direction,
amount

12. The sign of the first number never changes. It is the starting
point, and must remain so.
The last number is the distance from the first number.
It is the signs between the numbers that determine the
direction of the move.
There are various methods used to remember integer
addition & subtraction rules. Pick a method and stick to it
every time.
Summary:

13. Multiplying & Dividing Integers:
Simply count the number of negative signs:
a. If the number of negative signs is even, the product is
positive.
b. If the number of negative signs is odd, the product is
negative.
Class Work 2.1
a. be sure to put your name
b. Add to your tracker; I will let you know the due date tomorrow
CLASS WORK 2.1