Name:___________________________________________________________________Date:_____/_____/__________
1. How many terms are in the following algebraic expression? _____
x – 8xyz + 6 + yz
2. Fill-in-the-chart:
Algebraic Expression
Coefficient(s)
Variable(s)
Constant(s)
-3 + a – 9b
3. Evaluate when m = -8 and n = -5 :
a)
n² + (2n)²
b)
c)
- 4²
d)
mn
11 – m
4. Matching (USE YOUR NOTES!):
5
A.
5 less than twice a number
2) _____ 2n – 5
B.
5 less the product of 2 and a number
3) _____ 5∙2 + n
C.
the quotient of 5 and 2 times a number
4) _____ 5 – 2n
D.
5 minus a number squared
5) _____ 5(2 + n)
E.
the product of 5 and 2, plus a number
6) _____ 5 - n²
F.
5 times the sum of 2 and a number
1) _____
2𝑛
NAME:_______________________________________________________________________________ DATE: _____/_____/__________
Math-7 classwork
PROPERTY
PREVIEW
Today
We will:
1. Continue Properties Foldable
2. Practice the Following Properties:
IDENTITY
INVERSE
COMMUTATIVE
Associative
REVIEW
Identity Property:
The answer STAYS the SAME!
EXAMPLES
Additive Identity
3+0=3
0+
1
3
=
1
3
Multiplicative Identity
1
4
▪1=
1
4
1 ▪ -8 = -8
Just remember you can
secure your identity if you:
ZERO
Add ______
OR
Multiply by ONE
_____
REVIEW
Inverse Property:
All about the OPPOSITE!
EXAMPLES
Additive Inverse
1
2
- +
1
2
=0
10 + (-10) = 0
This is like a
zero pair!
Multiplicative Inverse
𝟏𝟎
𝟓𝟎
𝟓𝟎
▪
𝟏𝟎
𝟏
3▪
𝟑
=
500
500
3
3
=1
= =1
REVIEW
Commutative
Property:
+
=
+
EXAMPLES
Commutative
of Addition
Commutative
of Multiplication
2+9=9+2
2▪9 = 9▪2
(3▪y)+7 = 7+(3▪y) (3▪y)+7 = (y▪3)+7
The order of
the ADDITION
changed
The order of the
MULTIPLICATION
changed
Associative
Property:
+
+
=
+
+
EXAMPLES
Associative
of Addition
Associative
of Multiplication
a+(b+c)=(a+b)+c
a ▪ (b ▪ c) = (a ▪ b) ▪ c
(3+4)+5=3+(4+5) (3 ▪ 4) ▪ 5 = 3 ▪ (4 ▪ 5)
Works for Addition
and Multiplication
Name:_________________________________________________________________Date:_____/_____/__________
FILL IN THE BLANK
Identity Property ► The answer stays the ___________
same.
Inverse Property ► All about the ___________________
opposite.
Commutative Property ► _______________
changes
ORDER
Associative Property ► _______________
GROUPING changes
You can use your foldable too!
Identify the properties using the following answer bank:
Associative of Addition; Associative of Multiplication
Commutative of Addition; Commutative of Multiplication;
Identity of Addition; Identity of Multiplication;
Inverse of Addition; Inverse of Multiplication;
1.
31.7 + (-31.7) = 0
Inverse of A.
___________________________________
5.
(3+ 8)+ 2 = 3 + (8 + 2)
___________________________________
Associative of A.
2.
abc = cba
___________________________________
Commutative of M.
6.
1 • -75 = -75
___________________________________
Identity of M.
3.
0+¾=¾
___________________________________
Identity of A.
7.
3/
8
4.
5(4 • 6) = (5•4) •6
___________________________________
Associative of M.
8.
7 + 5x = 5x + 7
___________________________________
Commutative of A.
• 8 3 =1
___________________________________
Inverse of M.
Today’s Lesson:
What:
sequences
Why:
To identify the common difference or ratio
in a sequence and determine whether or
not the sequence is arithmetic, geometric,
or neither.
vocabulary:
• Arithmetic Sequence— goes from one term to
the next term by always adding or
_________________________
the same value. We
subtracting
difference
call this the common __________________________.
• Geometric Sequence— goes from one term to
the next term by always multiplying or
______________________
by the same value. We
dividing
call this the common _________________.
ratio
Sequence
Rule
Common
Difference
OR
Common
Ratio
1)
2)
3)
27
-5, 3, 11, 19, ___
“plus
eight”
80
5, 10, 20, 40, ___
“times
two”
-8 “minus
16, 10, 4, -2, ___
six”
4)
80, 20, 5,
𝟓
𝟒
___
Difference:
8
Arithmetic
or
Geometric
?
Arithmetic
Ratio: Geometric
2
16
1, 2, 4, 7, 11, ___
-6
“divide Ratio:
𝟏
by four”
NA
Expression
n+8
2n
Difference:
Arithmetic
n-6
Geometric
𝒏
𝟒
Neither
NA
𝟒
5)
Variable
NA
Sequence
6)
𝟏
𝟗
,
𝟑
,
𝟗
9
1, 3, ___
Rule
Common
Difference
OR
Ratio
“times
three”
Arithmetic
or
Geometric
?
Variable
Expression
Ratio:
Geometric
3
3n
7)
4
1, 1, 2, 2, 3, 3, ___
NA
NA
Neither
NA
NA
NA
Neither
NA
10) Bonus:
1,1, 2, 3, 5, 8, 13, 21
__
1)
A. 3, 9, 27 . . .
Which of the following
sequences is an arithmetic B. 1, 3, 6, 10, 15 . . .
sequence?
C. 52, 49, 46, 43 . . .
2)
What would be the 5th term A. 125
of the following geometric B. 625
sequence?
C. 30
1, 5, 25 . . .
3)
Which of the following
sequences is a geometric
sequence?
A. 27, CV
9, 3, 1 . . .
B. 1, 2, 6, 24. . .
C. 2, 4, 6, 8 . . .
4)
What is the common
difference in the following
arithmetic sequence?
10, 6, 2, -2 . . .
A. 4
B. -4
C. ¼
5)
What is the common ratio in
the following geometric
sequence?
A. -2
B.
2
C.
½
1, -2, 4, -8, 16 . . .
6)
A. 4n
Which variable expression
describes the relationship
B. -4n
between any two consecutive
C. ¼ n
terms in the following
sequence?
-1, 4, -16, 64 . . .
7)
Which variable expression
describes the relationship
between any two
consecutive terms in the
following sequence?
A. n – 8
B. 8n
C.
n+8
-12, -4, 4, 12, 20 . . .
8)
What is the common ratio in A. 2
the following geometric
B. ½
sequence?
88, 44, 22, 11, 11/2
C. - ½
...
END OF LESSON
The next slides are student copies of the notes for this
lesson. These notes were handed out in class and
filled-in as the lesson progressed.
NOTE: The last slide(s) in any lesson slideshow
(entitled “Practice Work”) represent the homework
assigned for that day.
NAME:
Math-7 NOTES
DATE: ______/_______/_______
What: sequences
Why: To identify the common difference or ratio in a sequence and determine
whether or not the sequence is arithmetic, geometric, or neither.
Arithmetic Sequence— goes from one term to the next term by always
adding or _____________________ the same value.
We call this the common __________________________.
Geometric Sequence— goes from one term to the next term by always
multiplying or __________________ by the same
value. We call this the common _________________.
Sequence
(What comes next?)
1)
-5, 3, 11, 19, ___
2)
5, 10, 20, 40, ___
3)
16, 10, 4, -2, ___
4)
80, 20, 5, ___
5) 1, 2, 4, 7, 11, ___
6)
1
3
9
9
,
, 1, 3, ___
7) 1, 1, 2, 2, 3, 3, ___
BONUS:
1, 1, 2, 3, 5, 8, 13, ___
Rule
Common
+ Difference OR
x Ratio ÷
+ Arithmetic or
x Geometric ÷
Variable
Expression
Multiple Choice:
1) Which of the following
sequences is an arithmetic sequence?
A.
B.
C.
3, 9, 27 . . .
1, 3, 6, 10, 15 . . .
52, 49, 46, 43 . . .
2) What would be the 5th term of the
following geometric sequence?
1, 5, 25 . . .
A.
B.
C.
125
625
30
3)
A.
B.
C.
27, 9, 3, 1 . . .
1, 2, 6, 24. . .
2, 4, 6, 8 . . .
4) What is the common difference in the
following arithmetic sequence?
10, 6, 2, -2 . . .
A.
B.
C.
4
-4
¼
5) What is the common ratio in the following
geometric sequence?
1, -2, 4, -8, 16 . . .
A.
B.
C.
-2
2
½
6) Which variable expression describes the
relationship between any two consecutive
terms in the following sequence?
-1, 4, -16, 64 . . .
A.
B.
C.
4n
-4n
¼n
7) Which variable expression describes the
relationship between any two consecutive
terms in the following sequence?
-12, -4, 4, 12, 20 . . .
A.
B.
C.
n–8
8n
n+8
8) What is the common ratio in the following
A.
B.
C.
2
½
22
Which of the following
sequences is a geometric sequence?
geometric sequence?
88, 44, 22, 11, 11/2
...
NAME:__________________________________________________________________________________DATE: _____/_____/__________
Math- 7 Homework
For the following sequences, identify what comes next and write the variable expression:
1)
30
6, 12, 18, 24,… _____
Variable Expression:
4)
n +6
62, 58, 54, 50…_____
2) 1, 4, 16, 64, … _____
Variable Expression: ____________________
5) 0.2, 0.4, 0.8, 1.6,…_____
Variable Expression: ____________________
Variable Expression: ____________________
7) 0, 16, 32, 48, 64…._____
8) 1.2, 2.3, 3.4, 4.5, ….____
Variable Expression: ____________________
Variable Expression: ____________________
10) 128, 32, 8, 2, …._____
Variable Expression: ____________________
11)
2 , -6, 18, -54,…_____
Variable Expression: ____________________
3)
72, 36, 18, 9,…_____
Variable Expression: ____________________
6)
1, 3, 9, 27,…_____
Variable Expression: ____________________
9)
33, 37, 41, 45…._____
Variable Expression: ____________________
12)
58, 50, 42, 34 …______
Variable Expression: ____________________
13.
What is the 8th term in the following sequence?
3, 9, 27, 81, 243, 729 . . .
14.
What is the 6th term of the geometric sequence shown?
80, 40, 20 . . .
15.
What is the common difference of the arithmetic sequence shown?
-5, -1, 3, 7 . . .
16.
What is the common ratio of the geometric sequence shown?
729, 243, 81, 27, 9 . . .
17.
Write a variable expression that can be used represent the relationship between two
consecutive terms of the following sequence:
8, 12, 16, 20 . . .
18.
What is the missing tem in this sequence?
1, 5, 25, ____, 625, ….
continued . . .
Match each sequence with the variable expression that describes the relationship
between the consecutive terms of the sequence.
1. ____
2, 4, 6, 8, 10, …
A. n + 10
2. ____
1, 3, 9, 27, 71
B.
1/
3. ____
45, 41, 37, 32, 29, ….
C.
0.2n
4. ____
11, 21, 31, 41, 51, ….
D. n + 5
5. ____
10, 5, 2.5, 1.25, 0.625, ….
E.
n+2
6. ____
11, 3, -5, -13, -21, ….
F.
0.5n
7. ____
100, 20, 4, 0.8, 0.16,…..
G. n + (-2)
8. ____
7, 10.5, 15.75, 23.625, 35.4375, …..
H . n + (-4)
9. ____
36, 12, 4, 1.333, ….
I.
1.5n
10. ____
-3, -6, -12, -24, -48,
J.
3n
11. ____
-80, -75, -70, -65, -60, ….
K.
n + (-8)
12. ____
1, -1, -3, -5, ….
L.
2n
3
n
13. Which of the above problems are arithmetic sequences? _________________________
14. Which of the above problems are geometric sequences? _________________________