Name:_________________________________________________________Date:_____/_____/__________
Quiz
Day
Matching (USE YOUR NOTES!):
2n
A.
6 times the sum of 2 and a number
2) _____ 2n – 6
B.
6 times 2, plus a number
3) _____ 6(2) + n
C.
6 less than the product of 2 and a number
4) _____ 6 – 2n
D.
6 less the product of 2 and a number
5) _____ n² + 6
E.
double a number, increased by 6
6) _____ 6(2 + n)
F.
a number squared, increased by 6
7) _____ 2n + 6
G.
the quotient of twice a number and 6
1) _____
6
Fill in the blanks (USE YOUR NOTES!):
Sequence
(What comes next?)
1)
-3, 0, 3, 6, ___
2)
1, 4, 16, 64, ___
3)
18, 10, 2, -6, ___
Rule
Common
+ Difference OR
x Ratio ÷
(4)
500, 100, 20, 4, ___
5)
1, -4, 16, -64, ___
)
𝟏
(-
)
+ Arithmetic OR
x Geometric ÷
Variable
Expression
PROPERTY
PREVIEW
Today
We will:
1. Finish Properties Foldable (add
Distributive and Zero
Properties)
2. Review the following properties:
IDENTITY
INVERSE
COMMUTATIVE
Associative
Distributive
Zero Property
DistributiveProperty:
Outside # gets multiplied to
everything inside parenthesis!
+
=
+
EVERYONE wants a
piece of the cupcake!
EXAMPLES
a(b+c)=a(b)+a(c)
2(3+5)=2(3)+2(5)
-3(x – 2) = -3(x) + -3(-2)
Zero Property of
MULTIPLICATION:
A # TIMES zero is ALWAYS ZERO!!
EXAMPLES
a(0) = 0
0 = (5x)0
1
( xyz)(0) = 0
2
DON’T confuse this property with
the Inverse of Addition. We have
2 properties that equal zero!!
Today’s Lesson:
What:
properties
Why:
To identify and apply the commutative,
associative, distributive, identity, inverse,
and zero properties.
Identity Property:
EXAMPLES:
a + 0 = a OR 5 + 0 = 5
a • 1 = a OR 5 • 1 = 5
Just remember you can
secure your identity if
you:
_______ZERO
ADD
OR
__________
MULTIPLY by ONE
Your Turn: Apply the Identity Property by
finishing the below examples:
1)
4
4 + 0 = _____
2)
x + ____
0 = x
3)
8
8 • 1 = _____
4)
1 = -5x
-5x • _____
Inverse Property:
This is like a
zero pair!
EXAMPLES:
-a + a = 0
𝑎
𝑏
▪
OR
-5 + 5 = 0
𝑏
=1
𝑎
1
5
▪
5
=1
1
Your Turn: Apply the Inverse Property by
finishing the below examples:
1)
2)
0
-8 + 8 = _____
2y + -2y
_____ = 0
3)
4)
3
1
•
1
3
1
= _____
𝒙
𝒚
𝒚
•
= 1
𝒙
Commutative Property:
+
=
EXAMPLES:
a+b=b+a
a•b=b•a
Works for
both Addition
and
Multiplication
+
OR 5 + 3 = 3 + 5
5•3=3•5
Your Turn: Apply the Commutative
Property by finishing the below examples:
1)
6+7=
7+6
4)
6•8=
8•6
2)
4+3+2=
3+2+4
5)
3x y =
3yx
3)
-5+(x + 2) =
(x + 2) + -5
6)
-2(a +b) =
(a + b)(-2)
Associative Property:
+
+
=
Works for
both Addition
and
Multiplication
+
+
EXAMPLES:
a + (b + c) = (a + b) + c OR 3 + (5 + 4) = (3 + 5) + 4
a • (b • c) = (a • b) • c
3 • (5 • 4) = (3 • 5) • 4
Your Turn: Apply the Associative Property
by finishing the below examples:
1)
4 + (7 + 3) =
2)
(3 + y) + 2x =
(4 + 7) + 3
3 + (y + 2x)
3)
(xy)z =
x(yz)
4)
3(-2 • 5) =
(3 • -2 ) 5
Distributive Property:
+
=
+
EXAMPLES:
a (b + c) = a(b) + a(c) OR 3(5 + 4) = 3(5) + 3(4)
Your Turn: Apply the Distributive Property
by finishing the below examples:
1)
4 (2 + 3) =
4(2) + 4(3)
2)
2(x + y) =
2(x) + 2(y)
3)
(-5x + 1) 8 =
4)
x(9 + 3) =
8(-5x) + 8(1)
9x + 3x
Zero Property of Multiplication:
If you have 5 empty plates, how
much food do you have?
Answer: Zero! 5 • 0 = 0
Your Turn: Apply the Zero Property by
finishing the below examples:
1)
12 • 0 = ____
0
2)
-5x • ___
0 =0
3)
x(0) = _____
0
IXL HOmework
Seventh Grade – S.1 and S.2
https://www.ixl.com/signin/jlsms
EARN a Smart Score of 70 & work for at least 10 minutes!
DON’T FORGET TO LOG IN!
(You won’t receive credit for doing your homework if you are not logged in!)
TO LOG IN:
CLICK on the IXL button on the Simpson Home Page (left side)
Username: given to you by your teacher
(Usually your initial of first name, and full last name)
Password: math7
•
• CLICK on MATH
• CLICK on 7th GRADE
CLICK on the skill(s) assigned for homework
EARN a Smart Score of 70 on the assigned skill(s),
then you are done!
(Spend at least 10 minutes practicing.)
END OF LESSON
The next slides are student copies of the hand-outs.
NAME:_______________________________________________________________________________ DATE: _____/_____/__________
Math-7 guided classwork
Apply the Commutative Property by re-ordering the following expressions in order to
make them easier to evaluate MENTALLY (left to right). Give final answers as well.
1.
12 + 8 + 11 = 31
12 + 11 + 8 = _________________________________________________________________________
2.
(4)(4)(5)= ____________________________________________________________________________
3.
(12)(5)(2)= ___________________________________________________________________________
4.
35 + 13 + 5= ___________________________________________________________________________
Apply the Associative Property by re-grouping the following expressions in order to
make them easier to evaluate MENTALLY. Give final answers as well.
5.
9 + (1 + 17) =__________________________________________________________________________
6.
(3 + 19) + 11= ________________________________________________________________________
7.
5(2 ● 9) = ______________________________________________________________________________
Apply BOTH the Commutative and Associative Properties to re-order/ re-group the
following expressions in such a way that it is easier to evaluate MENTALLY. Give final
answers as well.
8.
4 + 22 + 6 + 8 = ______________________________________________________________________
9.
33 + 5 + 7 + 25 = _____________________________________________________________________
10. (3)(2)(5)(3) = _________________________________________________________________________
Apply the Distributive Property in order to make it easier to evaluate the following
expressions MENTALLY. Give final answers as well.
11. 2(5 + 12) =____________________________________________________________________________
12. 4(5 + 9) = _____________________________________________________________________________
13. 4(11 + 6) = ____________________________________________________________________________
Apply both the Inverse and Identity Properties in order to make it easier to evaluate
the following expressions MENTALLY. Give final answers as well.
14. 28 + (4 + -4) = _____________________________________________________________________
15. (-50 + 50) + -100 = ________________________________________________________________
16. (2/5 )(5/2)(-50) = _________________________________________________________________
Identify the properties used for EACH STEP in order to simplify the following
expressions:
17.
8 + 5 + (-8)
Step 1 = 8 + (-8) + 5
Step 2 = [ 8 + (-8) ] + 5
Step 3 = 0 + 5
Step 4 = 5
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
18.
7 + [3(3 + 11)] + 1
Step 1 = 7 + [9 + 33] + 1
_____________________________ Property
Step 2 = 1 + [9 + 33] + 7
_____________________________ Property of Addition
Step 3 = [ 1 + 9] + [ 33 + 7] _____________________________ Property of Addition
Step 4 = 10 + 40
Step 5 = 50
19.
[ (3/4 )(25)(4/3) ] + (-25)
Step 1 = [ (3/4 )(4/3)(25) ] + (-25) _____________________________ Property of Mult.
Step 2 = [ 1(25)] + (-25)
_____________________________ Property of Mult.
Step 3 = [ 25] + (-25)
_____________________________ Property of Mult.
Step 4 = 0
_____________________________ Property of Add.
20.
3(7 + 8) + ( -5 + 5)
Step 1 = 21 + 24 + (-5 + 5)
Step 2 = 21 + 24 + 0
Step 3 = (21 + 24) + 0
Step 4 = 45 + 0
Step 5 = 45
_____________________________ Property
_____________________________ Property of Addition
_____________________________ Property of Addition
______________________________ Property of Addition
IXL: 7th Grade S.1 and S.2
NAME:_______________________________________________________________________________ DATE: _____/_____/__________
CLASSWORK (INDIVIDUAL PRACTICE)
Apply the Commutative Property by re-ordering the following expressions in order to
make them easier to evaluate MENTALLY (left to right). Give final answers as well.
1.
35 + 11 + 5 = _________________________________________________________________________
2.
(2)(13)(5)= ____________________________________________________________________________
3.
(8)(50)(2)= ___________________________________________________________________________
4.
98 + 13 + 2 + 7 = _____________________________________________________________________
Apply the Associative Property by re-grouping the following expressions in order to
make them easier to evaluate MENTALLY. Give final answers as well.
5.
(9 + 14) + 6 =__________________________________________________________________________
6.
3 + (117 + 47)= _______________________________________________________________________
7.
5(8 ● 2) = ______________________________________________________________________________
Apply BOTH the Commutative and Associative Properties to re-order/ re-group the
following expressions in such a way that it is easier to evaluate MENTALLY. Give final
answers as well.
8.
9 + 14 + 6 + 91 =______________________________________________________________________
9.
84 + 13 + 6 + 7 = _____________________________________________________________________
10. (5)(4)(2)(10) =________________________________________________________________________
Apply the Distributive Property in order to make it easier to evaluate the following
expressions MENTALLY. Give final answers as well.
11. 2(4 + 11) =____________________________________________________________________________
12. 4(2 + 12) = ____________________________________________________________________________
13. 20(2 + 5 )= ____________________________________________________________________________
Apply both the Inverse and Identity Properties in order to make it easier to evaluate
the following expressions MENTALLY. Give final answers as well.
14.
28 + -28 + 15 = _____________________________________________________________________
15.
(-5 + 5) + 27 = ______________________________________________________________________
16.
(5)(1/4 )(4/1) = _______________________________________________________________________
Identify the properties used for EACH STEP in order to simplify the following
expressions:
17.
18.
12 + 5 + (-12) + 25
Step 1 = 12 + (-12) + 5 + 25
Step 2 = [12 + (-12)]+[5 + 25]
Step 3 = 0 + 30
Step 4 = 30
𝟏
𝟐
𝟐
𝟏
[ ( )(9)( ) ] + (-9)
Step 1
Step 2
Step 3
Step 4
19.
20.
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
_____________________________ Property of Addition
𝟏
𝟐
= [ ( )( )(9) ] + (-9)
𝟐
𝟏
= [ 1(9)] + (-9)
= [ 9] + (-9 )
= 0
8 + [ 3(4 + 5) ] + 5
Step 1 = 8 + (12 + 15) + 5
Step 2 = ( 8 + 12) + (15 + 5)
Step 3 = 20 + 20
Step 4 = 40
2(6 + 9 ) + ( -30 + 30)
Step 1 = 12 + 18 + (-30 + 30)
Step 2 = 12 + 18 + 0
Step 3 = (12 + 18) + 0
Step 4 = 30 + 0
Step 5 = 30
_____________________________ Property of Mult.
_____________________________ Property of Mult.
_____________________________ Property of Mult.
_____________________________ Property of Add.
_____________________________ Property
_____________________________ Property of Addition
_____________________________ Property
_____________________________ Property of Addition
_____________________________ Property of Addition
______________________________ Property of Addition
NAME:_______________________________________________________________________________ DATE: _____/_____/__________
EXTRA PRACTICE