1. September 11th, 2014 Day 20 xx
7-1 Learning Target – Today I will be able to compare and order integers to determine absolute value
Bellringer
Lesson
Exit Slip
Homework – pg. 64 #s 3-15, 64-68

2. September 11th, 2014 Day 20 xx
7-2 & 7-3 Learning Target – Today I will be able to compare and order integers to determine absolute value
Bellringer
Lesson
Exit Slip
Homework – pg. 64 #s 3-15

3. Bellringer - Inequalities
4 ___ 5
6 ___ 6
-5 ___ 5
-1 ___ -2
-10 ___ -11

4. Vocabulary
opposite
integer
absolute value

5. The opposite of a number is the same
distance from 0 on a number line as the
original number, but on the other side
of 0. Zero is its own opposite.
–4 and 4 are opposites –4 4 • •
–5–4–3–2–1 0
Negative integers
Positive integers
0 is neither positive
nor negative

6. The integers are the set of whole numbers and their opposites
The integers are the set of whole numbers and their opposites. By using integers, you can express elevations above, below, and at sea level. Sea level has an elevation of 0 feet.
The whole numbers are the counting numbers and zero: 0, 1, 2, 3,
Remember!

7. Graph the integer -7 and its opposite on a number line.
Additional Example 1: Graphing Integers and Their Opposites on a Number Line
Graph the integer -7 and its opposite on a number line.
7 units units
–7–6–5–4–3–2–1 0
The opposite of –7 is 7.

8. You can compare and order integers by graphing them on a number line
You can compare and order integers by graphing them on a number line. Integers increase in value as you move to the right along a number line. They decrease in value as you move to the left.

9. Additional Example 2A: Comparing Integers Using a Number Line
Compare the integers. Use < or >.
>
–7–6–5–4–3–2–1 0
4 is farther to the right than -4, so 4 > -4.
The symbol < means “is less than,” and the symbol > means “is greater than.”
Remember!

10. Additional Example 2B: Comparing Integers Using a Number Line
Compare the integers. Use < or >.
>
-9 is farther to the right than -15, so -15 < -9.

11. Additional Example 3: Ordering Integers Using a Number Line.
Use a number line to order the integers from least to greatest.
–3, 6, –5, 2, 0, –8
–8 –7–6 –5–4 –3 –2 –1 0
The numbers in order from least to greatest are –8, –5, –3, 0, 2, and 6.

12. A number’s absolute value is its distance from 0 on a number line
A number’s absolute value is its distance from 0 on a number line. Since distance can never be negative, absolute values are never negative. They are always positive or zero.

13. Additional Example 4A: Finding Absolute Value
Use a number line to find each absolute value.
|8|
8 units
–8 –7–6–5–4 –3–2 –1 0
8 is 8 units from 0, so |8| = 8.

14. Additional Example 4B: Finding Absolute Value
Use a number line to find each absolute value.
|–12|
12 units
–12 –11 –10 –9 –8 –7 –6 –5 –4 –3 –2 –
–12 is 12 units from 0, so |–12| = 12.

15. Exit Slip
SOLVE
|27| ___ |-30|

16. September 11th, 2014 Day 20 xx
8-1 Learning Target – Today I will solve multi-step equations with integers
Bellringer
Lesson
Exit Slip
Homework – None

17. Bellringer Solve. 1. 3x = 102 2. = 15 3. z – 100 = 21 x = 34
= 15
3. z – 100 = 21
w = 98.6
x = 34 y 15
y = 225
z = 121
w = 19.5

19. Additional Example 1A: Solving By Subtraction
Solve each question. Check each answer.
–6 + x = –7
–6 + x = –7
Add 6 to both sides to
isolate the variable.
x = –1
Check
–6 + x = –7
–6 + (–1) = –7 ?
Substitute –1 for x.
–7 = –7 ? 
True.

20. Additional Example 1C: Solving By Addition
Solve each equation. Check each answer.
y – 9 = –40
y – 9 = –40
Add 9 to both sides.
y = –31
Check
y – 9 = –40
–31 – 9 = –40 ?
Substitute –31 for y.
–40 = –40 ? 
True.

21. Additional Example 2A: Solving By Multiplication
Solve each equation. Check each answer. b –5
= 6 b –5
= 6 b –5
(–5)
= (–5)6
Multiply both sides by –5.
b = –30

22. Additional Example 2B: Solving By Division
Solve each equation. Check each answer.
–400 = 8y
–400 = 8y
–400 = 8y
Divide both sides by 8.
–50 = y

23. To solve a multi-step equation, you may have to simplify the equation first by combining like terms or by using the Distributive Property.

24. Additional Example 1A: Solving Equations That Contain Like Terms
Solve.
8x x – 2 = 37
11x + 4 = 37 Combine like terms.
– 4 – 4 Subtract 4 from both sides.
11x = 33 33 11
11x =
x = 3

25. Additional Example 1A Continued
Check
8x x – 2 = 37
8(3) (3) – 2 = 37 ?
Substitute 3 for x.
– 2 = 37 ?
37 = 37 ? 

26. Additional Example 1B: Solving Equations That Contain Like Terms
Solve.
4(x – 6) + 7 = 11
4(x – 6) + 7 = 11 Distributive Property
4(x) – 4(6) + 7 = 11
Simplify by multiplying:
4(x) = 4x and 4(6) = 24.
4x – = 11
4x – 17 = 11
Add 17 to both sides.
4x = 28
Divide both sides by 4. 4
x = 7

27. September 11th, 2014 Day 20 xx
8-3 Learning Target – Today I will solve one-step equations with integers
Bellringer
Lesson
Exit Slip
Homework – pg. 86 #s ODD ONLY

28. Inverse Property of Addition
Words
Numbers
Algebra
The sum of a number and its opposite, or additive inverse, is 0.
3 + (–3) = 0
a + (–a ) = 0

29. Warm Up
Use mental math to find each solution.
y = 15
2. x ÷ 9 = 9
3. 6x = 24
4. x – 12 = 30
y = 8
x = 81
x = 4
x = 42

30. Additional Example 1A: Solving By Subtraction
Solve each question. Check each answer.
–6 + x = –7
–6 + x = –7
Add 6 to both sides to
isolate the variable.
x = –1
Check
–6 + x = –7
–6 + (–1) = –7 ?
Substitute –1 for x.
–7 = –7 ? 
True.

31. Additional Example 1C: Solving By Addition
Solve each equation. Check each answer.
y – 9 = –40
y – 9 = –40
Add 9 to both sides.
y = –31
Check
y – 9 = –40
–31 – 9 = –40 ?
Substitute –31 for y.
–40 = –40 ? 
True.

32. Additional Example 2A: Solving By Multiplication
Solve each equation. Check each answer. b –5
= 6 b –5
= 6 b –5
(–5)
= (–5)6
Multiply both sides by –5.
b = –30

33. Additional Example 2A Continued
Check b –5
= 6
–30 ?
= 6
Substitute –30 for b.
– 5
True.
6 = 6  b –5
= 6.

34. Additional Example 2B: Solving By Division
Solve each equation. Check each answer.
–400 = 8y
–400 = 8y
–400 = 8y
Divide both sides by 8.
–50 = y

35. Additional Example 2B: Solving By Division
Check
–400 = 8y
Substitute –50 for y. ?
–400 = 8(–50)
True.
–400 = –400 

36. September 11th, 2014 Day 20 xx
8-2 Learning Target – Today I will translate words into numbers, variables and operations
Lesson
Homework – pg. 77 #s 1-20 EVEN ONLY & 47

37. Algebraic Expressions
Operation
Verbal Expressions
Algebraic Expressions
• add 3 to a number
• a number plus 3 +
• the sum of a number and 3
n + 3
• 3 more than a number
• a number increased by 3
• subtract 12 from a number
• a number minus 12
• the difference of a number
and 12 -
x – 12
• 12 less than a number
• a number decreased by 12
• take away 12 from a number
• a number less than 12

38. Algebraic Expressions
Operation
Verbal Expressions
Algebraic Expressions
• 2 times a number
• 2 multiplied by a number
2m or 2 • m +
• the product of 2 and a
number
• 6 divided into a number ÷ a 6
÷ 6 or
• a number divided by 6
• the quotient of a number
and 6

39. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions
Write each phrase as an algebraic expression.
A. the quotient of a number and 4
quotient means “divide” n 4
B. w increased by 5
increased by means “add”
w + 5

40. Additional Example 1: Translating Verbal Expressions into Algebraic Expressions
Write each phrase as an algebraic expression.
C. the difference of 3 times a number and 7
the difference of 3 times a number and 7
3 • x – 7
3x – 7
D. the quotient of 4 and a number, increased by 10
the quotient of 4 and a number, increased by 10 4 n
+ 10

41. When solving real-world problems, you may need to determine the action to know which operation to use.
Action
Operation
Put parts together
Add
Put equal parts together
Multiply
Find how much more
Subtract
Separate into equal parts
Divide

42. Additional Example 2B: Translating Real-World Problems into Algebraic Expressions
On a history test Maritza scored 50 points on the essay. Besides the essay, each short-answer question was worth 2 points. Write an expression for her total points if she answered q short-answer questions correctly.
The total points include 2 points for each short-answer question.
Multiply to put equal parts together. 2q
In addition to the points for short-answer questions, the total points included 50 points on the essay.
Add to put the parts together: q

43. Check It Out: Example 2A
Julie Ann works on an assembly line building computers. She can assemble 8 units an hour. Write an expression for the number of units she can produce in h hours.
You need to put equal parts together. This involves multiplication.
8 units/h · h hours = h

44. Lesson Quiz for Student Response Systems
1. Which of the following is an algebraic expression that represents the phrase ‘15 less than a number’?
A. x – 15
B. x + 15
C. 15 – x
D. 15x

45. Lesson Quiz for Student Response Systems
2. Which of the following is an algebraic expression that represents the phrase ‘the product of a number and 36’?
A. 36x C.
B D. x + 36 36 x x 36

46. Lesson Quiz for Student Response Systems
3. Which of the following is an algebraic expression that represents the phrase ‘5 times the sum of y and 17’?
A. 5(y + 17)
B. y + 17
C. 5y + 17
D. 5(y – 17)

47. Lesson Quiz for Student Response Systems
4. Which of the following is an algebraic expression that represents the phrase ‘9 less than the product of a number and 7’?
A. 7x + 9
B. 7x – 9
C. 9x + 7
D. 9x – 7

48. Lesson Quiz for Student Response Systems
5. A painter charges $675 for labor and $30 per gallon of paint. Identify an algebraic expression that represents the total cost of painting, if the painter used x gallons of paint.
A x
B. 675x
C x
D. 30x