Incoming 6th Grade Standard Summer Packet
Kids’ Information Page
We’re so proud of you for taking the time to work on math over the summer!
Here are some helpful hints for success:
 Find a quiet work space where you can get organized and stay focused.
 Pay close attention to the examples and vocabulary.
 It’s ok to struggle, it allows you to self-monitor what you do and do not know.
 If you don’t know how to do something, make note of it on the answer sheet, so
you know to ask questions when you come back to school.
 Remember to persevere (Mathematical Practice #1)! Don’t just give up after one
attempt.
 Complete all of the problems in the packet.
 Calculators may ONLY be used when you see this symbol:
 Remember to do a little work each week. DO NOT wait until the week before
school starts to complete your packet!
 The packet should be returned to your math teacher during the first week of
school.
Have fun & we’ll see you in August!
Have fun & we’ll see you in August!
1
Incoming 6th Grade Standard Summer Packet
Objective: Solve problems involving whole number multiplication and division.
Ex:
5467 x 48
Ex: 8558 ÷ 22
1) 241 x 31
2) 3109 x 26
3) 638 ÷11
4) 7,800 ÷ 24
5) A machine pasted labels on 8316 soup 6) Sam is practicing running the 440 yd
cans in 27 minutes. How many cans did
sprint for track. Throughout the week he
the machine label each minute?
runs this distance 12 times. What is the
total distance he ran?
2
Incoming 6th Grade Standard Summer Packet
Objective: Find the area and perimeter of rectangles
Area formula: A = L x W
Perimeter formula: P = 2 (L + W) or P=2L + 2W
Ex:
A=LxW
A= 10 x 4
A= 40 sq ft
4feet
P = 2 (L+W)
P= 2 (10 + 4)
P= 28 ft
10 feet
7) Find the area of the rectangle below.
13 cm
8) Find the perimeter of the rectangle
below.
5m
12m
8 cm
9) Jess is planting a large vegetable
garden that is 7 feet long and 15 feet
wide. What is the area of her garden?
10) If Jess wants to put a fence around
the garden she planted in #9, how many
feet of fencing must she put up?
11) Juan measures in his backyard and
finds that the area of the yard is 176
square feet. The length of the yard is 11
feet. What is the width?
12) Mrs. Jones put up a border around
the perimeter of her bulletin board. The
total perimeter measures to 20 feet. If the
width of the bulletin board is 4 feet, what
is the length?
3
Incoming 6th Grade Standard Summer Packet
Objective: Understand place value of decimals. Given a number, identify the
digit in a specific place value. Round given decimals to a specified place value.
Ex: 156.4237
What number is in the tenths place?
156.4237 - the 4 is in the tenths place
Ex: Round 0.576 to the nearest hundredth
In 0.576, the 7 is in the hundredths place
0.576 - the 6 tells us to round the 7 up
so the solution is 0.58
13) In the number 752.1093
14) In the number 3489.276
What number is in the thousandths place? What number is in the tens place?
15) In the number 254.7631
16) Round 5.673 to the nearest tenth
What number is in the hundredths place?
17) Round 0.0437 to the nearest
hundredth
18) Round 7.943 to the nearest whole
number
4
Incoming 6th Grade Standard Summer Packet
Objective: Compare and order decimals
Ex: Fill in the blank with >, < or =
0.678 ______ 0.687
Ex: Put the following decimals in
order from least to greatest
0.625, 0.656, 0.612, 0.652
Compare the decimals beginning with the tenths place. If those digits are the same,
move on to the hundredths place. Find the number with the larger digit in that place.
0.678 < 0.687
19) Complete the statement with >, < or =
6.203 ______ 6.312
21) Complete the statement with >, < or =
9.5 ________ 9.05
23) Put the following decimals in order
from least to greatest
2.94, 2.90, 2.93, 2.99, 2.97
0.612, 0.625, 0.652, 0.656
20) Complete the statement with >, < or =
0.4 ________0.47
22) Complete the statement with >, < or =
5.6 ____________5.6000
24) Put the following decimals in order
from least to greatest
7.398, 7.03, 7.31, 7.3
5
Incoming 6th Grade Standard Summer Packet
Objective: Add and subtract decimals
To add or subtract decimals, line up the decimal points. Fill in empty places with zeros.
Add or subtract. Bring down the decimal.
Ex: 16.573 + 4.21
16.573
+04.210
20.783
line up decimal points, add a zero in empty places
25) 15.76 + 9.4
26) 240.007 + 38.19
27) 0.42 – 0.361
28) 12 – 8.62
29) Antone went to the grocery store and bought a pound of apples for $1.98, chicken
tenders for $3.87 and a 6-pack of soda for $2.99. He paid with a $20. How much
change did he get back?
6
Incoming 6th Grade Standard Summer Packet
Objective: Multiply and divide decimals
Examples: Multiply 3.4 ● 1.2
3.4
X 1.2
3.4 (1 decimal place)
X
1.2 (1 decimal place)
6 8  multiply 34 by 2 (ignore the decimal point)
4.08
2 total decimal places
+ 3 4 0  multiply 34 by 10 (the 1 is in the tens place)
4 0 8  add 68 and 340
Count the number of decimal places in the original problem.
Since there are 2 total decimal places, the answer should also have 2 decimal places.
Answer 4.08
Example: Divide 45.9  3
15.3
3 45.9
Place decimal directly above the
decimal point in the dividend
3
15
Divide as with whole numbers
- 15
9
-9
If there is a decimal in the divisor, first move the decimal to the right until the number is a whole number. Move the decimal
in the dividend the same number of places. Then move the decimal up and divide.
30) 5.6 x 0.8
31) 12.4 x 0.09
32) 56.43 ÷ 3
33) 32.985 ÷ 0.5
7
Incoming 6th Grade Standard Summer Packet
Objective: Identify the factors or multiples of a given number. Find the greatest common
factor or least common multiple of a pair of numbers.
Factor: The factors of a number are any whole numbers that divide evenly into the number. A
number is divisible by each of its factors.
Multiple: The product of a number and any whole number
Greatest Common Factor (GCF): The largest common factor or two or more numbers
Least Common Multiple (LCM): The smallest number that two numbers have in common as a
multiple
Ex: The factors of 15 are 1, 3, 5, 15 The factors of 45 are 1, 3, 5, 9, 15, 45
The GCF of 15 and 45 is 15
Ex: Multiples of 10 include 10, 20, 30, 40, 50…. Multiples of 25 include 25, 50, 75….
The LCM of 10 and 25 is 50
34) List all of the factors of 42
35) List all of the factors of 36
36) List the first five multiples of 15
37) List the first five multiples of 20
38) What is the greatest common factor of 39) What is the least common multiple of
27 and 45? Find the solution by listing the 14 and 21? Find the solution by listing the
factors.
first 5 multiples of each number.
8
Incoming 6th Grade Standard Summer Packet
Objective: If given a mixed number, be able to turn it into an improper fraction. If given an
improper fraction, turn it into a mixed number in simplest form.
Improper fraction: a fraction whose numerator is greater than its denominator
Mixed number: a whole number and proper fraction
Ex: Change
16
3
7
Ex: Change 6 8 to an improper fraction
to a mixed number
9
40) Write the improper fraction as a
4
mixed number.
2
42) Write the mixed number 2 as an
3
improper fraction.
41) Write the improper fraction
mixed number.
15
8
as a
1
43) Write the mixed number 3 as an
7
improper fraction.
9
Incoming 6th Grade Standard Summer Packet
Objective: Simplify a given fraction. Find equivalent fractions or determine if two fractions
are equivalent
Which of the fractions below are equivalent?
𝟐
𝟑
, 𝟖,
𝟔
𝟔
𝟏𝟖
,
𝟓
Answer:
𝟏𝟐
𝟐
𝟔
and
𝟔
𝟏𝟖
are equivalent because both simplify to
44) Circle the fractions that are equivalent.
𝟏
𝟑
45) Circle the fractions that are equivalent.
1
5
2
4
2
6
18
14
3
18
9
12
5
12
40
35
.
46) Write three fractions that are equivalent to
6
48) Write the fraction 9 in simplest form.
4
6
47) Write the fraction
10
24
in simplest form
8
49) Write the fraction 28 in simplest form.
10
Incoming 6th Grade Standard Summer Packet
Objective: Convert between fractions and decimals.
𝟕
𝟏𝟑
Example: Write (a) 𝟐𝟎 and (b) 𝟑𝟑 as decimals.
15
50) Convert 20 to a decimal
4
Example: Write (a) 0.85 and (b) 4.375 as a
fraction orfraction or mixed number.
8
51) Convert 24 to a decimal
52) Convert 2 9 to a decimal
53) Convert 5.66 to a fraction in simplest form
54) Convert 0.125 to a fraction in simplest form
55) Convert 12.75 to a fraction in simplest form
11
Incoming 6th Grade Standard Summer Packet
Objective: Compare and order fractions and mixed numbers
Example
Compare the following fractions:
𝟕
𝟏𝟎
𝟑
and .
𝟒
56) Fill in the blank with >, <, or =
5
8
________
8
________
9
10
11
15
𝟐 𝟑 𝟏 𝟑
, , ,
𝟑 𝟖 𝟔 𝟒
57) Fill in the blank with >, <, or =
7
58) Fill in the blank with >, <, or =
6
Write the fractions in order from least to greatest:
________
4
5
59) Order the following fractions from least to
greatest
20
60) Order the following fractions from least to
greatest
61) Order the following fractions from least to
greatest
12
Incoming 6th Grade Standard Summer Packet
Objective: Add and subtract fractions and mixed numbers
3
64)
5
+
4
62)
5
6
−
8
4
9
1
66) 7 4 +
4 59
63)
65)
1
+
2
4
5
2
5
3
12
5 − 3
67)8
−4
3
10
13
Incoming 6th Grade Standard Summer Packet
Objective: Multiply fractions and mixed numbers
Multiply numerator by
numerator and denominator
by denominator.
Simplify if needed
68)
70)
72)
3
8
1
x
1
6
69)
x 15
71
2 39 x 1 45
73)
3
3
5
x
1
4
2
1
3
7
)4 x 5
8x3
5
6
14
Incoming 6th Grade Standard Summer Packet
ANSWER KEY
Answer
1)
7,471
2)
80,834
3)
58
4)
325
5)
6)
308 cans per
minute
5,280 yards
7)
104 sq. cm
8)
34 m.
9)
105 sq. ft
I got it on the
1st try!
I got it with
corrections.
I have no idea.
10) 44 ft.
11) 16 ft
12) 6 ft.
13) 9
14) 2
15) 6
16) 5.7
17) 0.04
18) 8
19) <
20) <
21) >
22) =
23) 7.03, 7.3, 7.31,
7.398
15
Incoming 6th Grade Standard Summer Packet
24) 2.90, 2.93, 2.94,
2.97, 2.99
I got it on the
1st try!
Answer
I got it with
corrections.
I have no idea.
25) 25.16
26) 278.197
27) 0.059
28) 3.38
29) $11.16
30) 4.48
31) 1.116
32) 18.81
33) 65.97
34) 1, 2, 3, 6, 7, 14,21,
42
35) 1, 2, 3, 4, 6, 9, 12,
18, 36
36) 15, 30, 45, 60, 75
37) 20, 40, 60, 80, 100
38) 9
39) 42
40) 2
41) 1
42)
43)
44)
45)
8
1
4
7
8
3
22
7
1
3
2
5
2
46) ,
and
and
8
,
4
12
14
35
12
3 12 18
and others
16
47)
48)
Incoming 6th Grade Standard Summer Packet
5
12
2
3
Answer
49)
2
I got it on the
1st try!
I got it with
corrections.
I have no idea.
7
50) 0.75
51) 0.33333….
52) 2.44444444..
33
53) 5
54)
1
50
8
55) 12
3
4
56) <
57) >
58) =
59)
60)
61)
5
,
9
1
,
,
3
12 4
9 5 3
,
,
, ,
,
4 32 16 8
2 5 7 3
5
62) 1
63) 1
64)
7
7
3
8 10 4
8
3
10
18
1
65) 2
4
66) 11
67) 3
68)
69)
1
29
36
7
10
16
3
20
70) 5
17
Incoming 6th Grade Standard Summer Packet
71) 24
72) 4
1
5
73) 30
2
3
18