Download Summer math – entering seventh grade 2016

Dear Sixth Grade Parents and Guardians,
For middle school students, summer is all about getting rest, exploring new places and enjoying
time with family and friends. At the same time, students need to feed their curiosity with books,
games and other challenging activities. Reading is the most important part of a long summer
vacation, and strength in reading comprehension is closely related to success in math. We
encourage all students to read over the summer because becoming a ferocious reader often is a
great way to become successful in anything, including math.
The provided packet is simply a suggestion for summer practice. It is not designed as a required
assignment. Each student will be given a letter from his or her teacher outlining the topics to
make a priority to review over the summer. Answer keys have been provided to all worksheets.
Teachers will not collect this work in September, but if your child would like feedback about the
work, he or she can turn it to the teacher in September.
It is also important to make math relevant to a student's daily life. Although we provide you with a
packet in case you wish to follow a more structured work plan in math during summer months, we
strongly recommend you try to make math a part of daily activities, instead of just going through
worksheets. Either on a long road trip or a flight, exploring a new city or hiking a mountain, take
the opportunity to communicate with your child through mathematics. You can be very creative
with these simple “facts” of daily life, and they can add a lot of fun to cultural and natural
expeditions. When students connect the concepts they are studying in their math class to real life
experiences, it is incredibly valuable to their long-term development as mathematicians.
In other words, trying to make use of fractions, ratios and proportions, percent, and unit
conversion, all of which are constantly used when traveling, is a great way to “do” math in
summer. We are sure that with your child’s curiosity and creative answers, you would enjoy math
in a totally different way as well.
Have a great summer!
Ms. Ferrick, Ms. Simpson and Ms. Yoo
Summer
Math Packet
Factors
And
Exponents
Name :
Score :
Teacher :
Date :
Find the Greatest Common Factor for each number pair.
1)
8 , 30
2)
60 , 15
3)
12 , 20
4)
15 , 40
5)
24 , 30
6)
10 , 15
7)
3 , 8
8)
8 , 20
9 ) 120 , 24
10 ) 120 , 24
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Find the Greatest Common Factor for each number pair.
1)
8 , 30
2
2)
60 , 15
15
3)
12 , 20
4
4)
15 , 40
5
5)
24 , 30
6
6)
10 , 15
5
7)
3 , 8
1
8)
8 , 20
4
9 ) 120 , 24
24
10 ) 120 , 24
24
Math-Aids.Com
Name____________________________ Date _______
Greatest Common Factor
Using a Gradual Method
Many students can not look at a pair of numbers and immediately find the greatest common factor. Using the following
method, students can find the GCF by first finding any common factor (other than 1) to start with.
24, 42
Example:
What is the
GCF of 24
and 42?
Common factors
of 24 and 42. You
must multiply all
common factors
you used at the
end to find the
GCF!
2
24, 42
2
24, 42
12, 21
1) What number can fit into the two numbers given?
2) Because both numbers are even we can start with two.
3) Because 2 goes into 24 12 times, write 12 under 24. Because 2
goes into 42 21 times, write 21 under 42.
4) Can any factor evenly fit into the two new numbers you have? YES!
Three can fit into 12 and 21 so make another bracket and divide. Write the
results at the bottom(4 and 7)
5) The resulting numbers, 4 and 7 share no more common factors
besides one. If that is true than you must stop. Multiply all of the numbers
you wrote on the left side. 2 x 3 = 6 The G.C.F. = 6
3 12, 21
4, 7
G.C.F.= 6
1)
14, 64
2)
36, 93
3)
24, 72
4)
16, 48
5)
25, 125
6)
44, 99
7)
42 , 75
8)
32, 68
9)
40, 120
10)
13)
45, 60
14)
17)
26, 46
18)
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15, 60
40, 48
24, 140
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11)
13, 39
12)
27, 132
15)
55, 150
16)
24, 84
36, 54
20)
62, 100
19)
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CCSS 6.NS.4
Name____________________________ Date _______
Greatest Common Factor
Using a Gradual Method
Many students can not look at a pair of numbers and immediately find the greatest common factor. Using the following
method, students can find the GCF by first finding any common factor (other than 1) to start with.
24, 42
Example:
What is the
GCF of 24
and 42?
Common factors
of 24 and 42. You
must multiply all
common factors
you used at the
end to find the
GCF!
14, 64
1)
2
24, 42
2
24, 42
12, 21
3 12, 21
4, 7
G.C.F.= 6
2)
GCF = 2
5)
25, 125
40, 120
6)
45, 60
10)
26, 46
14)
40, 48
GCF = 8
18)
GCF = 2
ID# 0239
15, 60
24, 140
GCF = 4
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4)
GCF = 24
7)
42 , 75
11)
13, 39
8)
55, 150
12)
36, 54
GCF = 18
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27, 132
GCF = 3
16)
GCF = 5
19)
32, 68
GCF = 4
GCF = 13
15)
16, 48
GCF = 16
GCF = 3
GCF = 15
GCF = 15
17)
44, 99
24, 72
3)
GCF = 11
GCF = 40
13)
36, 93
GCF = 3
GCF = 25
9)
1) What number can fit into the two numbers given?
2) Because both numbers are even we can start with two.
3) Because 2 goes into 24 12 times, write 12 under 24. Because 2
goes into 42 21 times, write 21 under 42.
4) Can any factor evenly fit into the two new numbers you have? YES!
Three can fit into 12 and 21 so make another bracket and divide. Write the
results at the bottom(4 and 7)
5) The resulting numbers, 4 and 7 share no more common factors
besides one. If that is true than you must stop. Multiply all of the numbers
you wrote on the left side. 2 x 3 = 6 The G.C.F. = 6
24, 84
GCF =12
20)
62, 100
GCF =2
CCSS 6.NS.4
Name :
Score :
Teacher :
Date :
Find the Least Common Multiple for each number pair.
1)
3 , 2
2)
3 , 40
3)
8 , 24
4)
60 , 2
5)
12 , 8
6)
40 , 15
7)
30 , 8
8)
10 , 40
9)
20 , 2
10 )
60 , 24
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Find the Least Common Multiple for each number pair.
1)
3 , 2
6
2)
3 , 40
120
3)
8 , 24
24
4)
60 , 2
60
5)
12 , 8
24
6)
40 , 15
120
7)
30 , 8
120
8)
10 , 40
40
9)
20 , 2
20
10 )
60 , 24
120
Math-Aids.Com
Name________________________________ Date ______
COMMON FACTOR
STORY PROBLEMS
Directions: Use common factors to answer each question. Show your work and CIRCLE your answer!
1) Harry has 16 chocolate chip cookies and 24 peanut butter cookies. Harry wants create at least 2 bags
of cookies so there are some chocolate chip and some peanut butter cookies in each bag. He also wants to
make sure that all the bags he creates have the same contents as every other bag. How many ways can
he bag the cookies so every bag is identical in contents to each other. There should be no cookies left-over.
2) In problem number one, what is the largest amount of cookies that Harry could place in each bag?
3) In Gym class, there are 12 boys and 18 girls. The gym teacher wants to divide groups into just boys
and just girls. How many people could the teacher place in each group so that all groups have
the same number of people in them and still keep boy and girl only groups?
4) Marietta had 24 red licorice twists and 30 black licorice twists. How many ways could she bag them
so that the two kinds are in separate bags, yet all bags would have the same number of twists in them?
5) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles up into even
numbered groups. How many marbles could he place in each group so there would be the same number
in the red groups as well as the blue groups?
ID# 0238
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CCSS 6.NS.4
Name________________________________ Date ______
COMMON FACTOR
STORY PROBLEMS
Directions: Use common factors to answer each question. Show your work and CIRCLE your answer!
1) Harry has 16 chocolate chip cookies and 24 peanut butter cookies. Harry wants create at least 2 bags
of cookies so there are some chocolate chip and some peanut butter cookies in each bag. He also wants to
make sure that all the bags he creates have the same contents as every other bag. How many ways can
he bag the cookies so every bag is identical in contents to each other. There should be no cookies left-over.
2 16 , 24
8
12
8 16 , 24
2 3
4 16 , 24
There are 3 ways to bag the
cookies. Harry can bag the
cookies the following ways:
2 bags
4 bags
8 bags
8 CC 12 PB in each bag.
4 CC 6 PB in each bag.
2 CC 3 PB in each bag.
4 6
2) In problem number one, what is the largest amount of cookies that Harry could place in each bag?
The largest number of cookies that
Harry can bag is 20. Out of the 20 , 8 of
the cookies would be chocolate chip
and 12 would be peanut butter.
3) In Gym class, there are 12 boys and 18 girls. The gym teacher wants to divide groups into just boys
and just girls. How many people could the teacher place in each group so that all groups have
the same number of people in them and still keep boy and girl only groups?
6 12 , 18
2
3
The gym teacher can create groups of 6. The boys
can make 2 groups of 6. The girls can create 3
groups of 6.
4) Marietta had 24 red licorice twists and 30 black licorice twists. How many ways could she bag them
so that the two kinds are in separate bags, yet all bags would have the same number of twists in them?
6 24 , 30
4
5
Marietta can bag 6 of each kind in every bag.
Red licorice = four bags of 6 = 24
Black licorice = five bags of 6 = 30
5) Malik has 28 red marbles and he has 35 blue marbles. Malik wants to divide the marbles up into even
numbered groups. How many marbles could he place in each group so there would be the same number
in the red groups as well as the blue groups?
7 28 , 35
4
5
Malik can make groups of seven marbles for both colors.
Malik can make 4 bags of 7 red marbles.
Malik can also make 5 bags of 7 blue marbles,.
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CCSS 6.NS.4
Name_________________________________ Date_______
Assessment
Exponents, GCF, LCM, Prime Factorization, Order Of Operations
5
1) Write 3 in expanded form. ___________________________
2) Write 8 x 8 x 8 x 8 in exponential form._____________________
Evaluate the following. Circle the correct choice.
3) 3
4
4) 8
a) 12
b) 24
c) 81
d) 108
2
5) 8 + 7 x 3 - 6 =
6)
a) 23
b) 25
c) 30
d) 35
a) 56
b) 64
c) 81
d) 100
2
(12 - 6) + 2 x 4 =
a) 12
b) 20
c) 24
d) 44
Use the order of operations to solve the following. Circle the correct choice.
2
2
2
7) 4 + 3 - 3 =
8)
5+4÷2x3=
a) 19
b) 22
c) 55
d) 60
a) 29
b) 32
c) 53
d) 60
9)
(9 + 6) x 5 ÷ 5 =
a) 5
b) 8
c) 10
d) 15
Use a < , > or = to compare the following values.
10)
ID# 0021
5
0
1
1
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11)
5
2
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2
4
12) 5
3
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12
2
13)
CCSS 6.EE.1
3
3
5
6.EE.2
6.NS.4
2
14) A carpenter wants to use screws to attach two boards together for strength. He
takes the first board and drills holes every 16 inches. He asks his friend to drill
holes in the other board, but his friend accidentally drills every 6 inches instead
of 16 to match the other board. How many inches will it be before two holes
will match up?
a) 20 in.
b) 32 in.
c) 48 in.
d) 80 in.
15) A radio station was giving away free movie passes for every 6th caller and a free
DVD for every 8th caller for the first 50 callers. How many people out the first 50
callers would win movie passes and a free DVD?
a) 2 callers
b) 6 callers
c) 8 callers
d) 14 callers
16) A carpenter made a flower box that was 2 feet wide by 12 feet in length to make
an area of 24 square feet. Including the dimensions of 2 x 12, how many total ways
can the carpenter create a flower box that would make an area of 24 square feet?
a) 2 ways
b) 3 ways
c) 4 ways
d) 5 ways
ID# 0021
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CCSS 6.EE.1
6.EE.2
6.NS.4
The following are prime factorizations of different numbers. Find what numbers they are
prime factorizations of.
17) 2 • 5²
19) 2²• 3 ²
18) 3 • 5 • 7
20) What is the greatest common factor of 60 and 72?
21) List all the factors of 36.
22) What is the least common multiple of 20 and 25?
Solve the following.
23) k = 27 - 5 x 4 + 2
24) d = 5 x (12 + 7) - 8
25) s = (5 - 3)² x 3 +2
Place a P next to the number if it is prime and a C if it is composite.
26) 13 ____
27) 9 ___
28) 30 ____
29) 31_____
30) 17______
Do a prime factorization of the following numbers.
31)
ID# 0021
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32)
28
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81
CCSS 6.EE.1
6.EE.2
6.NS.4
Name_________________________________ Date_______
Assessment
Exponents, GCF, LCM, Prime Factorization, Order Of Operations
5
3x3x3x3x3
1) Write 3 in expanded form. ___________________________
4
8
2) Write 8 x 8 x 8 x 8 in exponential form._____________________
Evaluate the following. Circle the correct choice.
3) 3
4
4) 8
a) 12
b) 24
c) 81
d) 108
2
5) 8 + 7 x 3 - 6 =
6)
a) 23
b) 25
c) 30
d) 35
a) 56
b) 64
c) 81
d) 100
2
(12 - 6) + 2 x 4 =
a) 12
b) 20
c) 24
d) 44
Use the order of operations to solve the following. Circle the correct choice.
2
2
7) 4 + 3 - 3 =
8)
a) 19
b) 22
c) 55
d) 60
a) 29
b) 32
c) 53
d) 60
2
5+4÷2x3=
9)
(9 + 6) x 5 ÷ 5 =
a) 5
b) 8
c) 10
d) 15
Use a < , > or = to compare the following values.
10)
ID# 0021
5
0
=
1
1
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11)
5
2
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> 2
4
12) 5
3
>
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12
2
13)
CCSS 6.EE.1
3
3
> 5
6.EE.2
2
6.NS.4
14) A carpenter wants to use screws to attach two boards together for strength. He
takes the first board and drills holes every 16 inches. He asks his friend to drill
holes in the other board, but his friend accidentally drills every 6 inches instead
of 16 to match the other board. How many inches will it be before two holes
will match up?
a) 20 in.
b) 32 in.
c) 48 in.
d) 80 in.
Strategy: Use least common multiple to solve.
Board one - 16 , 32 , 48 .
Board two - 6, 12, 18, 24, 30, 36, 42,. 48
It would be 48 inches before a hole would match up on each board.
15) A radio station was giving away free movie passes for every 6th caller and a free
DVD for every 8th caller for the first 50 callers. How many people out the first 50
callers would win movie passes and a free DVD?
a) 2 callers
b) 6 callers
c) 8 callers
d) 14 callers
Strategy - Use lcm to solve.
Every 6th caller out of the first 50 get a Movie Pass.
The 6th, 12 th, 18th, 24 th, 30th, 36 th, 42nd, and the 48 th caller would get movie passes.
Every 8th caller will get a DVD.
The 8th, 16 th, 16th, 24 th, 32nd, 40nd, and the 48 th caller will receive a DVD.
The 24th and 48th person will be considered every 6th and every 8th caller. So
two people will receive a movie pass and a DVD!
16) A carpenter made a flower box that was 2 feet wide by 12 feet in length to make
an area of 24 square feet. Including the dimensions of 2 x 12, how many total ways
can the carpenter create a flower box that would make an area of 24 square feet?
a) 2 ways
b) 3 ways
c) 4 ways
d) 5 ways
ID# 0021
Strategy - Find all the factor pairs that will produce 24.
1 x 24
2 x 12
3 x 8 and 4 x 6 .
There are 4 different ways to make 24!
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CCSS 6.EE.1
6.EE.2
6.NS.4
The following are prime factorizations of different numbers. Find what numbers they are
prime factorizations of.
17) 2 • 5²
2x5x5
10 x 5
50
19) 2²• 3 ²
18) 3 • 5 • 7
3x5x7
15 x 7
105
2x2x3x3
4x9
36
20) What is the greatest common factor of 60 and 72?
12 is the GCF of 60 and 72.
21) List all the factors of 36.
The numbers listed are factors of 36 because
36 is evenly divisible by each one.
1, 2, 3, 4, 6, 9, 12, 18, 36
22) What is the least common multiple of 20 and 25?
20 - 40 - 60 - 80 - 100
25 - 50 - 75 - 100
100 is the LCM of 20 and 25
Solve the following.
23) k = 27 - 5 x 4 + 2
k = 27 - 20 + 2
k=7+2
k=9
25) s = (5 - 3)² x 3 +2
s = (2) x 3 + 2
s=4x3+2
s = 12 + 2
s = 14
24) d = 5 x (12 + 7) - 8
d = 5 x 19 - 8
d = 95 - 8
d = 87
Place a P next to the number if it is prime and a C if it is composite.
P
26) 13 ____
C
27) 9 ___
C
28) 30 ____
P
29) 31_____
P
30) 17______
Do a prime factorization of the following numbers.
31)
4
2
32)
28
x
x
2
7
x
9
7
3
²
2•7
ID# 0021
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x
x 3x3x 3
3
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9
4
CCSS 6.EE.1
6.EE.2
6.NS.4
Fractions
and
Decimals
Name__________________________________ Date_________
Percentage Practice
Write the following decimals as a percent.
1) 0.24
6) 0.99
11) 0.045
16) 3.24
2) 0.08
7) 0.6
12) 0.098
17) 4.02
3) 0.12
8) 0.09
13) 0.015
18) 9.23
4) 0.8
9) 0.19
14) 0.432
19) 7.343
5) 0.03
10) 0.37
15) 0.3
20) 1.5
Directions: Express as a fraction, decimal and percent what part of each object below is shaded.
21)
22)
Fraction
23)
Fraction
Decimal
Decimal
Percentage
Percentage
24)
Fraction
Fraction
Decimal
Decimal
Percentage
Percentage
25) Explain how you can tell which of the four objects above is more than 60% shaded
using mental math!!
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
________________________________________________________________________
ID# 0269
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CCSS 6.RP.3
Draw a line matching the value on the left
with its equivalent value on the right.
The pie chart below represents the favorite pets
of 40 students in Mr. Smith’s class. Answer the
following questions using the pie chart below.
Favorite Pets
0.0825
26) 0.03
25%
35%
Cats
75%
27) 4.23
3
8
28) 8.25%
29)
1
8
0.6
30) 60%
3%
31) 0.375
423%
32)
9
12
0.125
33) If 100 % of
is
and 50% of
is
Draw picture here.
34) Tony answered 28 out of 35 questions
correctly on his test. What percent did
Tony answer correctly?
copyright
20%
Reptiles
20%
Rodents
35) What fraction of Mr. Smith’s class said their
favorite pet was a rodent? Express answers
in lowest terms.
36) What fraction of Mr. Smith’s class said their
favorite pet is either a cat or a dog? Express
answer in lowest terms.
37) There are 40 students in Mr. Smith’s class.
How many must of said that they like reptiles
as pets?
what is 25% of
ID# 0269
Dogs
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Directions: Using the choices given in the answer
bank, write the only value which would complete
the list from the greatest to the smallest value.
Not all choices will be used.
BANK
38) 45% _____ 0.3
7%
39)
0.8 _____ 65%
40)
25% _____
1
5
41)
0.09 ______ 5%
42)
0.2 ______ 0.1
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0.22
2
5
0.7
90%
15%
0.28
0.04
CCSS 6.RP.3
Name__________________________________ Date_________
Percentage Practice
Write the following decimals as a percent.
1) 0.24
24%
6) 0.99
99%
11) 0.045
4.5%
16) 3.24
324%
2) 0.08
8%
7) 0.6
60%
12) 0.098
9.8%
17) 4.02
402%
3) 0.12
12%
8) 0.09
24%
13) 0.015
24%
18) 9.23
24%
4) 0.8
24%
9) 0.19
19%
14) 0.432
43.2%
19) 7.343
734.3%
5) 0.03
3%
10) 0.37
37%
15) 0.3
30%
20) 1.5
150%
Directions: Express as a fraction, decimal and percent what part of each object below is shaded.
Express each fraction in lowest terms.
21)
23)
Fraction
3
4
Fraction
2
5
Decimal
0.75
Decimal
0.4
Percentage
75%
Percentage 40%
22)
1
2
Fraction
24)
0.5
Decimal
Percentage
3
5
Fraction
0.6
Decimal
50%
Percentage
60%
25) Explain how you can tell which of the four objects above is more than 60% shaded
using mental math!!
You
can tell that the object in problem 21 is more than 60% shaded. 60% is a little more than half. It is easy to
________________________________________________________________________
________________________________________________________________________
see
that the figure in problem 21 is shaded significantly more than half.
________________________________________________________________________
________________________________________________________________________
ID# 0269
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CCSS 6.RP.3
Draw a line matching the value on the left
with its equivalent value on the right.
The pie chart below represents the favorite pets
of 40 students in Mr. Smith’s class. Answer the
following questions using the pie chart below.
Favorite Pets
0.0825
26) 0.03
25%
35%
Cats
75%
27) 4.23
3
8
28) 8.25%
29)
1
8
0.6
30) 60%
3%
31) 0.375
423%
32)
9
12
0.125
20%
Reptiles
20%
Rodents
35) What fraction of Mr. Smith’s class said their
favorite pet was a rodent? Express answers
in lowest terms.
1
5
of the class chose rodents as their favorite pet.
36) What fraction of Mr. Smith’s class said their
favorite pet is either a cat or a dog? Express
answer in lowest terms.
3
5
33) If 100 % of
Dogs
of the class chose dogs or cats as their favorite pet.
37) There are 40 students in Mr. Smith’s class.
How many must of said that they like reptiles
as pets?
is
20% of 40 students is the same as 0.2 x 40
is
and 50% of
8 students said they like reptiles as their favorite pet.
what is 25% of
Draw picture here.
34) Tony answered 28 out of 35 questions
correctly on his test. What percent did
Tony answer correctly?
28
4
=
35
5
ID# 0269
= 80%
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Maisonet Math 2012
Directions: Using the choices given in the answer
bank, write the only value which would complete
the list from the greatest to the smallest value.
Not all choices will be used.
2
BANK
5 0.3
38) 45% _____
39)
0.7 65%
0.8 _____
40)
0.22
25% _____
1
5
41)
7% 5%
0.09 ______
42)
15% 0.1
0.2 ______
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7%
0.22
2
5
0.7
90%
15%
0.28
0.04
CCSS 6.RP.3
Name____________________________________ Date_______
Problem Solving
Decimals, Fractions and Percents
1)
Henry had $24.12. His friend Greg had onehalf as much as Henry. Another friend Kasey
had one-fourth of what Henry has. How much
money do the three friends have altogether?
2)
Dionte, George and Tayvion were growing plants
for science class. Dionte’s plant grew to a height
of 24 cm. George’s plant grew to a height 75% the
height of Dionte’s. Tayvion’s plant grew twice as
tall as Dionte’s plant. What is the total height of all
three plants?
3)
In 2009, a local restaurant posted annual
earnings of $400,000. Because of a slow local
economy, the same restaurant in 2010 posted
earnings that were 80% of what they were in
2009. How much did the restaurant earn in
2010?
4)
Kyla decided to go on a diet to lose a few pounds.
Kyla lost 10% of her body weight after three
months of dieting. If Kyla lost 15 pounds, how
much did she weigh at the beginning of her diet?
5)
The theoretical probability of rolling a number
cube and landing on an even number is onehalf. However, when James rolled a number
cube 24 times, he landed on an even number
one-third of the time. How many times did
James land on an even number?
6)
Tyler has 80 jellybeans. His younger brother
has 60% the amount Tyler has. How many
jellybeans does Tyler and his brother have
altogether?
7)
In a town called Littleton, it rained 4.5 inches
during the month of May. In June it rained
three times the amount that it did in May. In
July it rained one-third of the amount that it
rained in May. What is the rainfall total of May,
June and July?
8)
Ashley earned $480 by babysitting children in
her neighborhood during the summer. At the
end of summer, Ashley spent 20% of her
earnings and saved the rest. How much
money did Ashley save?
ID# 0135
copyright
Maisonet Math 2012
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CCSS 5.NF.4
6.RP.3
Name____________________________________ Date_______
Problem Solving
Decimals, Fractions and Percents
1)
Henry had $24.12. His friend Greg had onehalf as much as Henry. Another friend Kasey
had one-fourth of what Henry has. How much
money do the three friends have altogether?
$42.21
Dionte, George and Tayvion were growing plants
for science class. Dionte’s plant grew to a height
of 24 cm. George’s plant grew to a height 75% the
height of Dionte’s. Tayvion’s plant grew twice as
tall as Dionte’s plant. What is the total height of all
three plants?
Henry ---- 24.12 < – This amount was given.
Greg ----- 12.06 <---because 1/2 of 24.12 is 12.06
Kasey ----- 6.03 < --because 1/4 of 24.12 is 6.03
Dionte — 24 cm
George - 18 cm <--75% of 24 is 18.
Tayvion - 48 cm <---2 times 24 is 48
90 cm
42. 21
<-- total of the three friends.
In 2009, a local restaurant posted annual
earnings of $400,000. Because of a slow local
economy, the same restaurant in 2010 posted
earnings that were 80% of what they were in
2009. How much did the restaurant earn in
2010?
3)
2)
90 cm <---- total height of three plants
4)
$320,000
Kyla weighed 150 pounds at the beginning
of her diet. 10% of 150 pounds is 15 pounds.
To find 80% of $400,000, multiply
400,000 by 0.8.
0.8 is 80% written as a decimal.
5)
The theoretical probability of rolling a number
cube and landing on an even number is onehalf. However, when James rolled a number
cube 24 times, he landed on an even number
one-third of the time. How many times did
James land on an even number?
6)
In a town called Littleton, it rained 4.5 inches
during the month of May. In June it rained
three times the amount that it did in May. In
July it rained one-third of the amount that it
rained in May. What is the rainfall total of May,
June and July?
The total amount during the given three months
is 19.5 inches.
May - 4.5
June - 13.5
July - 1.5
<--- was given
<---- 3 times May
<--- 1/3 of may
copyright
60% of 80 is 48. You must add 48 and 80
to find out how many jellybeans Tyler and
his brother have altogether.
8)
Ashley earned $480 by babysitting children in
her neighborhood during the summer. At the
end of summer, Ashley spent 20% of her
earnings and saved the rest. How much
money did Ashley save?
Ashley saved $384 dollars.
if Ashley spent 20%, she must have saved 80%
80% of $480 is $384.
Multiply $480 by 0.8 to find 80% of $480.
19.5 inches
ID# 0135
Tyler has 80 jellybeans. His younger brother
has 60% the amount Tyler has. How many
jellybeans does Tyler and his brother have
altogether?
128 jellybeans
James landed on an even number 8 times out of 24.
8 out of 24 is equal to 1/3.
7)
Kyla decided to go on a diet to lose a few pounds.
Kyla lost 10% of her body weight after three
months of dieting. If Kyla lost 15 pounds, how
much did she weigh at the beginning of her diet?
Maisonet Math 2012
www.mrmaisonet.com
CCSS 5.NF.4
6.RP.3
Name :
Score :
Teacher :
Date :
x
78.42
100
x
99.43
100
x
23.93
10
x
49.72
100
x
59.94
1000
x
63.37
10
x
86.43
1000
x
97.87
1000
x
59.27
100
x
12.98
100
x
26.18
1000
x
39.53
10
x
15.85
1000
x
96.33
100
x
13.12
100
x
45.63
1000
x
91.55
10
x
25.67
1000
x
97.71
1000
x
27.57
10
x
40.69
100
x
90.24
10
x
19.29
10
x
25.95
100
x
47.69
10
Math-Aids.Com
Name :
Score :
Teacher :
Date :
x
78.42
100
7842.00
x
99.43
100
9943.00
x
23.93
10
239.30
x
49.72
100
4972.00
x
59.94
1000
59940.00
x
63.37
10
633.70
x
86.43
1000
86430.00
x
97.87
1000
97870.00
x
59.27
100
5927.00
x
12.98
100
1298.00
x
26.18
1000
26180.00
x
39.53
10
395.30
x
15.85
1000
15850.00
x
96.33
100
9633.00
x
13.12
100
1312.00
x
45.63
1000
45630.00
x
91.55
10
915.50
x
25.67
1000
25670.00
x
97.71
1000
97710.00
x
27.57
10
275.70
x
40.69
100
4069.00
x
90.24
10
902.40
x
19.29
10
192.90
x
25.95
100
2595.00
x
47.69
10
476.90
Math-Aids.Com
Percent
Name :
Score :
Teacher :
Date :
Percentage Calculations
Round your answer to two decimal points if required.
1 ) 30% x 85 = ___
6 ) 0.01 x 65 = ___
2 ) 35% x 70 = ___
7 ) 51 ÷ 97 = ___ %
3 ) 72 ÷ 0.45 = ___
8 ) 50 ÷ 65 = ___ %
4 ) 68 ÷ 0.46 = ___
9 ) 88 ÷ 76 % = ___
5 ) 0.5 x 70 = ___
10 ) 51 ÷ 11 % = ___
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Percentage Calculations
Round your answer to two decimal points if required.
1 ) 30% x 85 = 25.5
6 ) 0.01 x 65 = 0.65
2 ) 35% x 70 = 24.5
7 ) 51 ÷ 97 = 52.58 %
3 ) 72 ÷ 0.45 = 160
8 ) 50 ÷ 65 = 76.92 %
4 ) 68 ÷ 0.46 = 147.83
9 ) 88 ÷ 76 % = 115.79
5 ) 0.5 x 70 = 35
10 ) 51 ÷ 11 % = 463.64
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Converting Between Percents, Decimals, and Fractions
Convert Decimal to Percent
1.82 =
0.45 =
0.654 =
1.19 =
0.333 =
0.785 =
189 % =
59.8 % =
83 % =
14 % =
29 % =
19.6 % =
1.55 =
0.475 =
0.33 =
1.63 =
0.24 =
0.64 =
7
__
50
3
__
20
25
__
20
45
__
25
Convert Percent to Decimal
Convert Decimal to Fraction
Convert Fraction to Decimal
99
__
50
1
__
10
=
=
=
=
=
=
Convert Fraction to Percent
29
__
25
13
__
10
=
=
1
__
8
13
__
50
=
=
3
__
25
23
__
20
=
=
Convert Percent to Fraction
9%=
47.7 % =
69.9 % =
62 % =
138 % =
83.9 % =
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Converting Between Percents, Decimals, and Fractions
Convert Decimal to Percent
1.82 = 182 %
0.45 = 45 %
0.654 = 65.4 %
1.19 = 119 %
0.333 = 33.3 %
0.785 = 78.5 %
189 % = 1.89
59.8 % = 0.598
83 % = 0.83
14 % = 0.14
29 % = 0.29
19.6 % = 0.196
Convert Percent to Decimal
Convert Decimal to Fraction
1.55 =
155
___
1.63 =
163
___
100
=
31
___
20
100
0.475 =
475
___
1000
0.24 =
24
___
100
=
19
___
=
6
___
40
25
0.33 =
33
___
0.64 =
64
___
100
100
=
Convert Fraction to Decimal
99
__
50
1
__
10
7
__
50
3
__
20
= 1.98
= 0.1
25
__
20
45
__
25
= 0.14
= 0.15
= 1.25
= 1.8
Convert Fraction to Percent
29
__
25
13
__
10
1
__
8
13
__
50
= 116 %
= 130 %
3
__
25
23
__
20
= 12.5 %
= 26 %
= 12 %
= 115 %
Convert Percent to Fraction
9%=
9
___
62 % =
62
___
100
100
=
31
___
50
47.7 % =
477
___
1000
138 % =
138
___
100
=
69
___
50
69.9 % =
699
___
1000
83.9 % =
839
___
1000
Math-Aids.Com
16
___
25
Name :
Score :
Teacher :
Date :
Multiplying by Percents that are Powers of Ten
1 ) What is 10 percent of 15 ?
6 ) What is 10 percent of 12 ?
2 ) What is 10 percent of 87 ?
7 ) What is 1 percent of 13 ?
3 ) What is 1 percent of 38 ?
8 ) What is 100 percent of 60 ?
4 ) What is 100 percent of 84 ?
9 ) What is 100 percent of 48 ?
5 ) What is 100 percent of 92 ?
10 ) What is 10 percent of 15 ?
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Multiplying by Percents that are Powers of Ten
1 ) What is 10 percent of 15 ?
10% x 15 =
0.1 x 15 = 1.5
2 ) What is 10 percent of 87 ?
10% x 87 =
0.1 x 87 = 8.7
3 ) What is 1 percent of 38 ?
1% x 38 =
0.01 x 38 = 0.38
4 ) What is 100 percent of 84 ?
100% x 84 =
1 x 84 = 84
5 ) What is 100 percent of 92 ?
100% x 92 =
1 x 92 = 92
6 ) What is 10 percent of 12 ?
10% x 12 =
0.1 x 12 = 1.2
7 ) What is 1 percent of 13 ?
1% x 13 =
0.01 x 13 = 0.13
8 ) What is 100 percent of 60 ?
100% x 60 =
1 x 60 = 60
9 ) What is 100 percent of 48 ?
100% x 48 =
1 x 48 = 48
10 ) What is 10 percent of 15 ?
10% x 15 =
0.1 x 15 = 1.5
Math-Aids.Com
Rate
Name ____________________________________________ Date _______
Equivalent Rates vs. Unit Rates
Directions: Find the value to complete each equivalent rate and each unit rate.
1.
2.
Equivalent Rate:
Unit Rate:
6 months
3 books read
6 months
3 books read
=
=
12 months
=
4 cookies
$1.60
Unit Rate:
1 book read
3.
$1.60
Equivalent Rate:
=
4 cookies
20 cookies
1 cookie
4.
Equivalent Rate:
Unit Rate:
22,000 people
2 square miles
22,000 people
2 square miles
=
=
12 square miles
Equivalent Rate:
Unit Rate:
1 square mile
5.
3 miles
30 minutes
3 miles
30 minutes
=
=
9 miles
1 minute
6.
Equivalent Rate:
Unit Rate:
64 females
100 teachers
64 females
100 teachers
=
=
25 teachers
Equivalent Rate:
Unit Rate:
1 teacher
7.
24 candies
4 bags
24 candies
4 bags
=
=
54 candies
1 bag
8.
Equivalent Rate:
Unit Rate:
ID# 0531
$500
40 hours
$500
40 hours
copyright
=
=
30 hours
1 hour
Maisonet Math
Equivalent Rate:
Unit Rate:
1,520 miles
2 hours
1,520 miles
2 hours
www.mrmaisonet.com
=
=
6 hours
1 hour
CCSS 6.RP.A.2 6.RP.A.3
9.
10.
Equivalent Rate:
Unit Rate:
48 meters
6 seconds
48 meters
6 seconds
=
=
9 seconds
Equivalent Rate:
Unit Rate:
1 second
11.
24 problems
=
48 minutes
24 problems
=
48 minutes
240 minutes
1 minute
12.
Equivalent Rate:
Unit Rate:
79,200 people
3 square miles
79,200 people
3 square miles
=
=
15 square miles
Equivalent Rate:
Unit Rate:
1 square mile
13.
30,000,000 stars
3 cubic parsecs
30,000,000 stars
3 cubic parsecs
=
=
50,000,000 stars
1 cubic parsec
14.
Equivalent Rate:
Unit Rate:
36 millimeters
12 months
36 millimeters
12 months
=
=
3 months
Equivalent Rate:
Unit Rate:
1 month
15.
340 miles
5 hours
340 miles
5 hours
=
=
476 miles
1 hour
16.
Equivalent Rate:
Unit Rate:
112 km
8 hours
112 km
8 hours
=
=
56 km
Equivalent Rate:
Unit Rate:
1 hour
17.
$168
7 hours
$168
7 hours
=
=
35 hours
1 hour
18.
Equivalent Rate:
Unit Rate:
ID# 0531
105 liters
3 minutes
105 liters
3 minutes
copyright
=
=
70 liters
1 minute
Maisonet Math
Equivalent Rate:
Unit Rate:
1,750 sq. ft.
5 lbs. of seed
1,750 sq. ft.
5 lbs. of seed
www.mrmaisonet.com
=
=
10 lbs. of seed
1 lb. of seed
CCSS 6.RP.A.2 6.RP.A.3
Name ____________________________________________ Date _______
Equivalent Rates vs. Unit Rates
Directions: Find the value to complete each equivalent rate and each unit rate.
1.
2.
Equivalent Rate:
Unit Rate:
6 months
3 books read
6 months
3 books read
=
=
12 months
6 books read
2 months
=
4 cookies
$1.60
Unit Rate:
1 book read
3.
$1.60
Equivalent Rate:
=
4 cookies
$8.00
20 cookies
$0.40
1 cookie
4.
Equivalent Rate:
Unit Rate:
22,000 people
2 square miles
22,000 people
2 square miles
=
132,000 people
=
11,000 people
12 square miles
Equivalent Rate:
Unit Rate:
1 square mile
5.
3 miles
30 minutes
3 miles
30 minutes
=
9 miles
90 minutes
=
0.1 mile
=
54 candies
1 minute
6.
Equivalent Rate:
Unit Rate:
64 females
100 teachers
64 females
100 teachers
=
=
16 females
25 teachers
Equivalent Rate:
0.64 females
Unit Rate:
1 teacher
7.
24 candies
4 bags
24 candies
4 bags
=
9 bags
6 candies
1 bag
8.
Equivalent Rate:
Unit Rate:
ID# 0531
$500
40 hours
$500
40 hours
copyright
=
=
$375
30 hours
$12.50
1 hour
Maisonet Math
Equivalent Rate:
Unit Rate:
1,520 miles
2 hours
1,520 miles
2 hours
www.mrmaisonet.com
=
4,560 miles
=
760 miles
6 hours
1 hour
CCSS 6.RP.A.2 6.RP.A.3
9.
10.
Equivalent Rate:
Unit Rate:
48 meters
6 seconds
48 meters
6 seconds
=
12 meters
=
8 meters
9 seconds
Equivalent Rate:
Unit Rate:
1 second
11.
24 problems
48 minutes
24 problems
48 minutes
=
120 problems
=
0.5 problems
240 minutes
1 minute
12.
Equivalent Rate:
Unit Rate:
79,200 people
3 square miles
79,200 people
3 square miles
=
=
396,000 people
15 square miles
Equivalent Rate:
26,400 people
Unit Rate:
1 square mile
13.
30,000,000 stars
3 cubic parsecs
30,000,000 stars
3 cubic parsecs
=
50,000,000 stars
=
10,000,000 stars
5 cubic parsecs
1 cubic parsec
14.
Equivalent Rate:
Unit Rate:
36 millimeters
12 months
36 millimeters
12 months
=
9 millimeters
=
3 millimeters
3 months
Equivalent Rate:
Unit Rate:
1 month
15.
340 miles
5 hours
340 miles
5 hours
=
476 miles
=
68 miles
7 hours
1 hour
16.
Equivalent Rate:
Unit Rate:
112 km
8 hours
112 km
8 hours
=
=
56 km
4 hours
Equivalent Rate:
14 km
1 hour
17.
Unit Rate:
$168
7 hours
$168
7 hours
=
=
$840
35 hours
$24
1 hour
18.
Equivalent Rate:
Unit Rate:
ID# 0531
105 liters
3 minutes
105 liters
3 minutes
copyright
=
=
70 liters
2 minutes
35 liters
1 minute
Maisonet Math
Equivalent Rate:
Unit Rate:
1,750 sq. ft.
5 lbs. of seed
1,750 sq. ft.
5 lbs. of seed
www.mrmaisonet.com
=
=
3,500 sq. ft.
10 lbs. of seed
350 sq. ft.
1 lb. of seed
CCSS 6.RP.A.2 6.RP.A.3
Name ________________________________________ Date _________
Unit Rates
When The Amount Received Is A Fraction
Directions: Solve each of the following by finding a unit rate. Express each fraction in simplest form.
Write your answer in a complete sentence and as a ratio. Express the ratio as a unit rate.
1. If 5 friends equally share 4 cookies, how much
2. Twelve friends ordered 4 pizzas. If the pizzas
3. Eight prospectors looking for gold agreed that
4. Nine students needed rope for a class project.
5. Ten gardeners at a community garden equally
6. How much would each of 8 friends receive if
7. I t t o o k M e l a n i e 3 2 m i n u t e s t o r e a d
8. Twenty-seven guests shared three cakes. If both
of a cookie will each friend receive?
they would equally share any gold that they found.
If they collectively found 2 ounces of gold, how
much would each person get?
shared 6 cubic feet of soil. How much of a cubic
foot did each gardener receive?
64 pages. On average, how long did it take Melanie
to read each page?
9. Six individuals ran a 4-mile relay. Each runner
had to run an equal distance. How far did each
individual run?
ID# 0530
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Maisonet Math
are equally shared, how much pizza will each
friend receive?
The teacher gives the students 6 feet of
rope to equally share.
If each student
receives the same amount of rope, what
length will each student receive
they equally share 6 lbs. of ground beef?
cakes were completely eaten, how much did
each guest receive if each person ate the
same amount?
10. In a hot dog eating contest, Timothy ate 12
hot dogs in 6 minutes. On average, how long
did it take Timothy to eat each hot dog?
www.mrmaisonet.com
CCSS 6.RP.A.2
Name ________________________________________ Date _________
Unit Rates
When The Amount Received Is A Fraction
Directions: Solve each of the following by finding a unit rate. Express each fraction in simplest form.
Write your answer in a complete sentence and as a ratio. Express the ratio as a unit rate.
1. If 5 friends equally share 4 cookies, how much
of a cookie will each friend receive?
Each friend will receive
O of a cookie.
O cookie: 1 friend
are equally shared, how much pizza will each
friend receive?
Each friend would receive
# of a pizza.
# cookie: 1 friend
3. Eight prospectors looking for gold agreed that
they would equally share any gold that they found.
If they collectively found 2 ounces of gold, how
much would each person get?
Each person would receive
$ of an ounce.
$ ounce: 1 person
4. Nine students needed rope for a class project.
The teacher gives the students 6 feet of
rope to equally share.
If each student
receives the same amount of rope, what
length will each student receive
Each student would receive
L of a foot.
L foot: 1 student
5. Ten gardeners at a community garden equally
shared 6 cubic feet of soil. How much of a cubic
foot did each gardener receive?
Each gardener would receive
of a cubic foot.
N
6. How much would each of 8 friends receive if
they equally share 6 lbs. of ground beef?
Each friend would receive
N cubic foot: 1 gardener
P of a pizza.
P of a pizza: 1 friend
7. I t t o o k M e l a n i e 3 2 m i n u t e s t o r e a d
64 pages. On average, how long did it take Melanie
to read each page?
On average Melanie read one page in
of a minute.
@
@ page: 1 minute
8. Twenty-seven guests shared three cakes. If both
cakes were completely eaten, how much did
each guest receive if each person ate the
same amount?
Each guest would receive
( ) of! a cake.
( cake: 1 guest
9. Six individuals ran a 4-mile relay. Each runner
had to run an equal distance. How far did each
individual run?
Each runner would have to run
L of a mile.
L mile: 1 runner
ID# 0530
2. Twelve friends ordered 4 pizzas. If the pizzas
10. In a hot dog eating contest, Timothy ate 12
hot dogs in 6 minutes. On average, how long
did it take Timothy to eat each hot dog?
On average Timothy ate each
hot dog in of a minute.
@
@ minute: 1 hot dog
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Maisonet Math
www.mrmaisonet.com
CCSS 6.RP.A.2
Algebraic
Expressions
Name ___________________________________________ Date _____________
QUIZ
Identifying Parts Of An Expression
Algebraic Expressions And Word Phrases
1. Identify the coefficient in the expression 9x + 4.
a
4
b
x
a
12
b
m
c
+
d
9
c
-
d
10
3. Which of the following choices is an example of
an algebraic expression?
4. Identify the constant in the expression 12x + 8.
a
8-7
b
12y - 9
a
12
b
x
c
9 + 12
d
3(8 - 5)
c
8
d
+
5. How many terms are there in the expression
9x + 8y + 3?
6. How many terms are there in the expression
24m + 12n - 14 + 2t?
a
2 terms
b
3 terms
a
4 terms
b
5 terms
c
4 terms
d
5 terms
c
7 terms
d
10 terms
7. Which of the following algebraic expressions has
the same meaning as 9 less than 12 times a
a number n?
8. Select the word phrase below that has the same
meaning as 3(x + 8).
a
9 - 12n
b
12(n - 9)
a
3 times x increased
by 8
b
triple the difference
of x and 8
c
12 - 9n
d
12n - 9
c
triple the sum of
x and 8
d
3 times 8 increased
by x
9. What algebraic expression means 7 times
the difference of 15 and x?
10. Select the algebraic expression that means
8 more than x.
a
7(15 - x)
b
7 15 - x
a
8x
b
8+x
c
15 - x
d
15(7 - x)
c
8x + 8
d
x+8
7
11. In the expression 9m + 5, what two operations
are being used?
ID# 0438
2. Identify the variable in the expression 12m - 10.
12. Which of the following algebraic expressions
means the quotient of n and 8 increased by 3?
n
a
subtraction
and division
b
multiplication
and addition
a
3 +
c
addition and
subtraction
d
addition and
division
c
n
+ 3
8
copyright
Maisonet Math 2012
8
mrmaisonet.com
b
8
+3
n
d
3 +
8
n
CCSS
6.EE.2
Name ___________________________________________ Date _____________
QUIZ
Identifying Parts Of An Expression
Algebraic Expressions And Word Phrases
1. Identify the coefficient in the expression 9x + 4.
a
4
b
x
a
12
b
m
c
+
d
9
c
-
d
10
3. Which of the following choices is an example of
an algebraic expression?
4. Identify the constant in the expression 12x + 8.
a
8-7
b
12y - 9
a
12
b
x
c
9 + 12
d
3(8 - 5)
c
8
d
+
5. How many terms are there in the expression
9x + 8y + 3?
6. How many terms are there in the expression
24m + 12n - 14 + 2t?
a
2 terms
b
3 terms
a
4 terms
b
5 terms
c
4 terms
d
5 terms
c
7 terms
d
10 terms
7. Which of the following algebraic expressions has
the same meaning as 9 less than 12 times a
a number n?
8. Select the word phrase below that has the same
meaning as 3(x + 8).
a
9 - 12n
b
12(n - 9)
a
3 times x increased
by 8
b
triple the difference
of x and 8
c
12 - 9n
d
12n - 9
c
triple the sum of
x and 8
d
3 times 8 increased
by x
9. What algebraic expression means 7 times
the difference of 15 and x?
10. Select the algebraic expression that means
8 more than x.
a
7(15 - x)
b
7 15 - x
a
8x
b
8+x
c
15 - x
d
15(7 - x)
c
8x + 8
d
x+8
7
11. In the expression 9m + 5, what two operations
are being used?
ID# 0438
2. Identify the variable in the expression 12m - 10.
12. Which of the following algebraic expressions
means the quotient of n and 8 increased by 3?
n
a
subtraction
and division
b
multiplication
and addition
a
3 +
c
addition and
subtraction
d
addition and
division
c
n
+ 3
8
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b
8
+3
n
d
3 +
8
n
CCSS
6.EE.2
Name _______________________________ Date _________
QUIZ
Evaluating Expressions And Simplifying Expressions
1. Evaluate the following expression if x = 6.
2. Evaluate the following expression if y = 8.
9x  3  2x
a
c
40
45
6(12  y )  8
b 55
a
32
b
d 62
c
46
d 38
3. Select the expression that is equivalent
to 9(x - 6).
4. Simplify the following expression:
8 g  9m  5 g  4m
a
9x - 48
b
9x - 54
a
3g + 5m
b
3g + 13m
c
9x - 6
d
9x + 15
c
4g + 5m
d
2g + 4m
5. Simplify the following expression.
6. Evaluate the following expression. Let x = 7.
8(2m  3)  4m  10
2( x 2  1)
a
16m - 24
b
20m + 14
a
10
b
30
c
20m - 7
d
20m + 8
c
150
d
100
7. If m = 4, evaluate the following expression.
20m 
ID# 0442
26
8. Simplify the following expression.
12
m
9m  3m  9  12
a
83
b
84
a
12m + 21
b
12m - 21
c
85
d
86
c
12m + 9
d
12m + 3
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CCSS
6.EE.2
6.EE.3
6.EE.4
9. Simplify the following expression.
10. If y = 10, evaluate the following expression.
y2  5 3
9a  9b  7 a  4b  8
a
16a + 13b - 8
b
16a + 5b - 8
a
35
b
115
c
15a + 5b - 8
d
13ab
c
120
d
315
11. Mary purchased a plant that was 8 inches
tall. Mary’s plant grew at a rate of 3 inches
per month. If the expression below represents
the height of Mary’s plant, evaluate how tall
Mary’s plant will be in 9 months. Let m = months.
3m  8
12. Jarred has $45 in his savings account. Jarred
decided to mow lawns for the summer to increase
his savings. Jarred charges $20 per lawn. Evaluate
how much Jarred will have in his savings account if
he mows 30 lawns this summer and places all of his
earnings in his savings account. Use the expression
20g + 45 to solve. Let g = the number of lawns cut.
a
32 inches
b
24 inches
a
$600
b
$620
c
28 inches
d
35 inches
c
$632
d
$645
13. Simplify the following expression.
14. Evaluate the following expression if b = 32.
9b
12( x  5)
a
12x + 60
b
12x - 5
a
288
b
41
c
12x - 60
d
x - 60
c
272
d
312
15. Simplify the following expression.
16. Simplify the following expression.
4( x  2)
4k  5k  3k
ID# 0442
a
k
b
16k
a
288
b
4x + 8
c
2k
d
12k
c
272
d
312
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Maisonet Math 2012
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CCSS
6.EE.2
6.EE.3
6.EE.4
Name _______________________________ Date _________
QUIZ
Evaluating Expressions And Simplifying Expressions
1. Evaluate the following expression if x = 6.
2. Evaluate the following expression if y = 8.
9x  3  2x
a
c
40
45
6(12  y )  8
b 55
a
32
b
d 62
c
46
d 38
3. Select the expression that is equivalent
to 9(x - 6).
4. Simplify the following expression:
8 g  9m  5 g  4m
a
9x - 48
b
9x - 54
a
3g + 5m
b
3g + 13m
c
9x - 6
d
9x + 15
c
4g + 5m
d
2g + 4m
5. Simplify the following expression.
6. Evaluate the following expression. Let x = 7.
8(2m  3)  4m  10
2( x 2  1)
a
16m - 24
b
20m + 14
a
10
b
30
c
20m - 7
d
20m + 8
c
150
d
100
7. If m = 4, evaluate the following expression.
20m 
ID# 0442
26
8. Simplify the following expression.
12
m
9m  3m  9  12
a
83
b
84
a
12m + 21
b
12m - 21
c
85
d
86
c
12m + 9
d
12m + 3
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CCSS
6.EE.2
6.EE.3
6.EE.4
9. Simplify the following expression.
10. If y = 10, evaluate the following expression.
y2  5 3
9a  9b  7 a  4b  8
a
16a + 13b - 8
b
16a + 5b - 8
a
35
b
115
c
15a + 5b - 8
d
13ab
c
120
d
315
11. Mary purchased a plant that was 8 inches
tall. Mary’s plant grew at a rate of 3 inches
per month. If the expression below represents
the height of Mary’s plant, evaluate how tall
Mary’s plant will be in 9 months. Let m = months.
3m  8
12. Jarred has $45 in his savings account. Jarred
decided to mow lawns for the summer to increase
his savings. Jarred charges $20 per lawn. Evaluate
how much Jarred will have in his savings account if
he mows 30 lawns this summer and places all of his
earnings in his savings account. Use the expression
20g + 45 to solve. Let g = the number of lawns cut.
a
32 inches
b
24 inches
a
$600
b
$620
c
28 inches
d
35 inches
c
$632
d
$645
13. Simplify the following expression.
14. Evaluate the following expression if b = 32.
9b
12( x  5)
a
12x + 60
b
12x - 5
a
288
b
41
c
12x - 60
d
x - 60
c
272
d
312
15. Simplify the following expression.
16. Simplify the following expression.
4( x  2)
4k  5k  3k
ID# 0442
a
k
b
16k
a
288
b
4x + 8
c
2k
d
12k
c
272
d
312
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Maisonet Math 2012
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CCSS
6.EE.2
6.EE.3
6.EE.4
Name _________________________________ Date __________
Evaluating Expressions
Evaluate each of the following expressions. Let x = 9.
1. 3 x  4
2. x  4
3. 5( x  2)
4. 12 x
5. 3x  21
6. 2 x  3 x
7. x 3
8. 36
x
9. x(4  x)
2
11. x
9
10. 8 x  10
12. 20 x  70
Evaluate each of the following expressions. Let x = 7.
13. 8 x  23
14.
x  12
15. 5( x  3)
16. 9 x  15
17.
3x 2
18. ( x  2) 3
19. x 2  x
20.
x  2x
21. 8  ( x  1) 2
22. 6 x  2 x
23.
x3
24. 4( x 2  1)
ID# 0440
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CCSS
6.EE.2
Name _________________________________ Date __________
Evaluating Expressions
Evaluate each of the following expressions. Let x = 9.
2. x  4
1. 3 x  4
23
3. 5( x  2)
13
4. 12 x
5. 3x  21
108
35
6. 2 x  3 x
48
8. 36
x
7. x 3
729
45
9. x(4  x)
4
2
11. x
9
10. 8 x  10
82
117
12. 20 x  70
9
110
Evaluate each of the following expressions. Let x = 7.
13. 8 x  23
14.
33
15. 5( x  3)
19
16. 9 x  15
17.
48
3x 2
50
18. ( x  2) 3
147
19. x 2  x
20.
56
x  2x
125
21. 8  ( x  1) 2
21
22. 6 x  2 x
23.
56
ID# 0440
x  12
x3
72
24. 4( x 2  1)
343
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CCSS
6.EE.2
Coordinate
Geometry
Name :
Score :
Teacher :
Date :
Four Quadrant Ordered Pairs
YA
.
9
Z
8
.
.
7
X
W
6
5
4
3
.
<
-9
-8
-7
.
-6D -5
-4
-3
.
2
A
E
1
-2
-1
1
2
5
.
6
7O 8
. .
.
P
-3
.
-4
Q
.
>X
9
.
Y
I
B
-5
.
-6
M
H
4
-1
-2
.
3
.
T
-7
C
-8
-9
V
Tell what point is located at each ordered pair.
1 ) (-9,+6 ) _____
3 ) (-1,-5 ) _____
5 ) (+6,-7 ) _____
7 ) (+4,-3 ) _____
2 ) (+9,-3 ) _____
4 ) (+8,+6) _____
6 ) (-9,-8 ) _____
8 ) (+2,-3 ) _____
Write the ordered pair for each given point.
9)
B
_______
11)
O
_______
13)
Z
_______
15)
M
_______
10)
E
_______
12)
D
_______
14)
T
_______
16)
A
_______
Plot the following points on the coordinate grid.
17)
F (+8,+5)
19)
J (+7,-7 )
21)
U (-9,+5 )
23)
R (-6,-5 )
18)
K (+3,+7)
20)
N (+0,+9)
22)
G (-8,+8 )
24)
S (-3,-6 )
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Four Quadrant Ordered Pairs
.
YA
N
.
9
G
.
8
.
.
K
7
X
.
Z
.
.
W
6
U
F
5
4
3
.
<
-9
-8
-7
.
-6D -5
-4
-3
.
2
A
E
1
-2
-1
1
2
5
.
R
.
S
.
M
.
6
.
7O 8
. .
.
P
-3
H
4
-1
-2
.
3
-4
Q
>X
9
.
Y
I
B
-5
.
-6
..
T
-7
C J
-8
-9
V
Tell what point is located at each ordered pair.
X
Q
C
1 ) (-9,+6 ) _____
3 ) (-1,-5 ) _____
5 ) (+6,-7 ) _____
I
2 ) (+9,-3 ) _____
W
4 ) (+8,+6) _____
Write the ordered pair for each given point.
(+3,-5 )
(+7,-1 )
9)
B _______
11)
O _______
10)
E
(+1,+1)
_______
12)
D
(-6,-1 )
_______
H
6 ) (-9,-8 ) _____
Y
7 ) (+4,-3 ) _____
P
8 ) (+2,-3 ) _____
13)
Z
(+4,+8)
_______
15)
M
(-5,-7 )
_______
14)
T
(+1,-7 )
_______
16)
A
(-3,+1 )
_______
Plot the following points on the coordinate grid.
17)
F (+8,+5)
19)
J (+7,-7 )
21)
U (-9,+5 )
23)
R (-6,-5 )
18)
K (+3,+7)
20)
N (+0,+9)
22)
G (-8,+8 )
24)
S (-3,-6 )
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Four Quadrant Graphing Puzzle
YA
9
8
7
6
5
4
3
2
1
<
-9
-8
-7
-6
-5
-4
-3
-2
-1
1
2
3
4
5
6
7
8
9
>X
-1
-2
-3
-4
-5
-6
-7
-8
-9
V
Connect each sequence of points with a line.
(-5,9) , (1,9) , (1,8) , (-3.5,2) , (1,2) , (1,1) , (-5,1)
(-5,2) , (-.5,8) , (-5,8) , (-5,9) End of Sequence
What is the shape ?
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Four Quadrant Graphing Puzzle
.
.
.
. .
YA
9
8
7
6
5
4
. .
.
<
-9
-8
-7
-6
-5
-4
-3
.
.
3
2
1
-2
-1
1
2
3
4
5
6
7
8
9
>X
-1
-2
-3
-4
-5
-6
-7
-8
-9
V
Connect each sequence of points with a line.
(-5,9) , (1,9) , (1,8) , (-3.5,2) , (1,2) , (1,1) , (-5,1)
(-5,2) , (-.5,8) , (-5,8) , (-5,9) End of Sequence
What is the shape ?
The Letter Z
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Find the Slope of Each Line
Y^
5
1)
5
2)
4
.
Y^
4
.
3
2
3
2
1
< -5
-4
-3
-2
-1
1
1
2
3
4
-1
>
.
-2
-3
< -5
5X
-4
-3
-2
-1
-4
-5
-5
5
-4
-3
-2
.
3
2
1
1
1
2
3
4
>
< -5
5X
.
V
.
Y^
5
1
4
>
< -5
5X
-2
-5
V
Y^
5
-2
-1
1
Y^
5
1
-2
-3
>
< -5
5X
-4
-3
-2
-1
slope = ______
slope = ______
.
1
2
3
4
-1
-2
-4
-5
-5
V
>
5X
slope = ______
-3
-4
V
.
4
2
4
>
5X
V
1
3
4
-5
3
2
slope = ______
-4
8)
1
3
-3
2
-1
2
-2
3
-1
.
-2
.
4
-3
-3
-1
.
-4
-4
-4
slope = ______
-3
.
4
2
3
>
5X
5
1
2
4
Y^
3
1
3
V
2
-1
2
-5
3
-1
< -5
1
-4
6)
4
7)
-1
-3
.
.
-2
-2
-5
-2
-3
-1
-4
-3
-4
slope = ______
-3
-4
slope = ______
4
2
-2
< -5
.
5
4)
-1
5)
>
5X
Y^
3
-1
4
V
4
< -5
3
-3
-4
Y^
2
-2
slope = ______
V
3)
1
-1
.
Math-Aids.Com
Name :
Score :
Teacher :
Date :
Find the Slope of Each Line
Y^
5
1)
5
2)
4
.
Y^
4
.
3
2
3
2
1
< -5
-4
-3
-2
-1
1
1
2
3
4
-1
>
5X
.
-2
-3
< -5
- _12
slope = ______
-4
-3
-2
-1
-4
-5
-5
5
-4
-3
-2
.
3
2
1
1
1
2
3
4
>
< -5
5X
.
V
.
Y^
5
1
4
>
5X
-2
-3
-5
V
-3
Y^
5
-2
-3
-2
-1
1
V
Y^
5
1
-2
-3
>
< -5
5X
-4
-3
-2
-1
1
2
3
4
-1
- 10
slope = ______
-2
-3
-4
-4
-5
-5
V
.
4
2
4
.
1
_
5
slope = ______
-5
1
3
>
5X
-4
3
2
4
-3
8)
1
3
-2
2
-1
2
-1
3
-1
.
-4
.
4
-4
< -5
- _52
slope = ______
.
-4
.
1
_
5
slope = ______
4
2
3
>
5X
5
1
2
4
Y^
3
1
3
V
2
-1
2
-5
3
-1
< -5
1
-4
6)
4
7)
-1
-3
.
.
-2
-2
-5
-2
-3
-1
-4
-3
-4
10
slope = ______
-3
-4
4
2
-2
< -5
.
- _12
slope = ______
5
4)
-1
5)
>
5X
Y^
3
-1
4
V
4
< -5
3
-3
-4
Y^
2
-2
V
3)
1
-1
V
>
5X
10
- __
3
slope = ______
.
Math-Aids.Com
Slope-Intercept Form Worksheet- Name: _____________________
Review - Unit 3 lessons 5 & 6
1) Find the slope of the line through each pair of points.
Slope =
y 2 − y1
x 2 − x1
a. (8, -7) and (5, -3).
b. (-5, 9) and (5, 11).
c. (-8, -4) and (-4, -9).
2) For each graph: Write the equation of the line in SLOPE-INTERCEPT FORM
m = _______b =_______
m = ________b = ______
________________________ _________________________
m= _______ b =________
m = ________b=________
________________________ _______________________
m = ______b =______
_______________________
m = ______b =_______
________________________
3) In each linear equation, identify the slope (m) and the y-intercept (b)
2
5
19
a. y = 4x – 5
b. y = − x
c. y = x −
3
2
8
m = ______b =______
d. y = 11 +
2
x
3
m= _______b =_______
e. 2x + y = 8
m = _______b = ________
m=_________b = ________
m=_____b=_______
f. y – 4x = -2
m = _____b =________
4) Find the equation of the line in slope-intercept form (y = mx + b)
a. m = 2 and b = - 7
c. m = -5 and b = 0
b. b = 4 and m = -5
d. m = 4/5 and b = -2
5) Graph the line for each equation:
5a)
y=
3
x −3
4
Slope =
5b)
5
y = 4− x
3
Slope =
5c)
Y-Intercept =
Y-Intercept =
2x + y = −2
Slope =
Y-Intercept =
6. Sara rented a car for x amount of days. The linear equation below represents y, the total cost of Sara
renting a car.
y = 17x + 130
a. What is the slope of the line represented by this equation?
b. Explain what the slope tells you about renting a car.
c. What is the y-intercept of the line represented by this equation?
d. Explain what the y-intercept tells us about Sara’s rental.
e. If Sara rents a car for 9 days, how much will it cost her? Show how you got your answer.
17. The slope of a line is
3
and the line contains the points (5, 9) and (3, a). What is the value of a?
2
18. The slope of a line is -2 and the line contains the points (7 ,4) and (x, 12). What is the value of x?
KEY:
m = -1
b=3
y = -1x + 3