Timberstone  Junior High Summer Packet for incoming 5th graders.

Welcome to Timerstone!

This summer work includes a variety  of skills that are important  in 6th grade math. Please take some time this summer to complete the packet. We will collect the  packet the second week of school and go over all of the answers.

When completing the packet, you may use any resources available to help you with your work. Ask a parent or older sibling, review your skills using educational websites like Khan Academy or Math Playground. You can even review with your friends!  We would like to see all of your work, so if needed, use extra notebook paper and staple it to the back of your packet. You can even check your work with a calculator as long as we see your handwritten
work.

If you have any questions, you can contact Mrs. Kasee via email @
jkasee@sylvaniaschools.orQ.

We hope you have a great summer and look forward to a great school year!

Happy Calculating!

Mrs. Gust Mrs. Kasee Mrs. Turnbell

Summer Packet- 5'h into 6'h grade	Name  	

1
---------

Addition
Find the sum of the two numbers in each problem.
Show all work. 	Example:

1	1

4 	4	8

+ 	1  8 	8

6 	3	6

1.	652
+ 345

2.	203
+  525

3. 	726
+ 268

Decimal Addition:
Remember to line up the decimals before adding. Bring the decimal straight down in your answer.

4. 	7.75
+ 1.46

5.	51.4 + 2.86 	6.	.1274 + 8.25

Subtroction
Find the  difference between the two numbers in each problem.  Show all work.

Example:

3  13

7 	A'	J
2 	1 	8

5 	2 	5

7. 	8.
407
-  198

7,007
-2,426

9..

3,414
-1.218

Decimal Subtraction:
Remember to line up the decimals before subtracting. Bring the decimal straight down in your answer.

10. 	11.	12.

338.38
-   149.27

80.401 - 44.23 	75.89-9.4

54	2
Multiplication	Example:	x16

324

Find the product of the two numbers in each
problem. Show all work.
+540
864

13.	14. 	15.
65 	42 	84
 	X	4 	.L.§	X    39

Decimal Multiplication:
Multiply as you would with whole numbers. Count the decimal places in each factor. The product
(answer) has the same number of decimal places.

16.	17.	18.

.13
X  70

5.1
X 	2

.108
X    2.5

Division
Find the quotient in each problem.  Ifthere is a remainder, state  the remainders as R=_. Show all work.  Feel free to use a separate sheet of
paper.

19.	20, 	21.

7)591	12)264 	43)2815

3
Decimal Division:
If the divisor (outside number) is a decimal, you must move the decimal point (using multiplication)
to the right until it becomes a whole number. Then, move the decimal in the dividend (inside

number) the same number of times. Divide to find your answer (quotient). Then, move the decimal straight up from the dividend to the quotient.
Remember, no remainders.

quotient divisor  ) dividend

22.

23. 	24.

.5 )7.45	.12 )12.24

Rounding
Underline the given place value. Look to the right.  If this digit is
5 or greater, increase the underlined digit by 1. Ifthe digit to
the right is less than 5, keep the underlined digit the same.

Round to the nearest...

hundredth

0.547 	0.55

Round to the nearest....

25. 	tenth
0.3479

26.  hundredth
0.7553

27. whole number
3.268

28.	ten	29.	thousandth	30.	hundred	
	162.21		0.0036		990.54	

Compare the decimals.

Compare using <, >, or =
1.2  01.20	1.2 =  1.20

31.	0.205   0 0.21 	32. 1.03  0 0.03 	33. 	0.04 0 0.050

34. 	0.1 0 0.1000 	35.  0.52  0 0.500 	36. 	0.41 0 0.405

Prime Number:  A whole  number greater than 1 that  has only two factors, 1 and itself. Examples: 2, 3, 5, 7, 11, 13, 17, and 19 are all prime numbers.

Composite   Number:  A whole number greater than 1 that has more than two factors. Example: 8 is a composite number since its factors are 1, 2, 4, 8.

Determine  if the following numbers are prime or composite.  If  the numbers are composite, please list all of the factors.

37. 	27:  	----------------------

38. 	39:  	--------	----

39.	43;  	

-------	--

40. 	49: 	--	----	--------------

Exponents
A  way to show repeated multiplication by the same factor is to use an exponent.  In this example:  23 = 2 x 2 x 2 = 8. The small raised  three is the exponent. It tells how
many times the number  2, called  the base,  is multiplied  by itself.

Solve the following expressions by writing the expanded notation (repeated multiplication) and find the value.

41.	42. 	43.

44. 	eight squared 	45. 	five cubed

Greatest  Common factor
The greatest  factor that two or more numbers have in common  (GCF).
1.   List all the factors of four in order
2.  List all the factors of twenty in order
3.  List the common factors
4.  Write the greatest  common factor

finding  Common Factors:
4:1,2,4
20: 1,  2,  4,  5, 10,  20
Common Factors: 1,  2, 4 	GCF=  4

List all the factors for  each number. Circle the  common factors.

46. 	18:  	_

30:	----	----------	-------= -----------

Common Factors:  ---	-	Greatest Common Factor: 	---

47. 	60:  	== ------ ------ --------------

45: -----------------------------------------------

Common Factors: --------	Greatest Common Factor:  	_

48. 	23:  	-----------

29: -----------------------------------------------
Common Factors:  --------	Greatest Common Factor:  	_

49. 	56:  	------------------

72:--- ------"-- -- --------------- -- -----

Common Factors: --------	Greatest Common Factor:  	_

Least Common Multiple
The smallest nonzero multiple that two or more numbers have in common.

1.   List the first 6 multiples of 4
2.  List the first 6 multiples of 6
3.  List the common multiples
4.  Write  the least common multiple.

Finding  Common Multiples:
4: 4, 8,  12,  16,  20,  24
6: 6, 12,  18, 24,  30,  36
Least Common Multiple= 12

50. 	8: 	--	------------ ---------------

12: ------------	--------------------------

Common Multiples: -- -------'Least Common Multiple:  	_

51.	7:  	

--------------------

11:-----------------------------------------------

Common Multiples:  	Least Common Multiple:  	_

52.	25: ------ -----------------------

10:  -------------------- ------ -------------

Common Multiples:  	Least Common Multiple:  	_

53.	24:  	

--------------

36: -----------------------------------------------

Common Multiples:  	Least  Common Multiple:  	_

···=

Area and Volume
The number of square units needed to cover a region is the area. (square units)
The amount of space inside a solid figure is the
volume of the figure. (cubic units)

54. 	Find the area of the figure below.

3 inches

6 inches

56. 	Find the volume of the figure below.

2cm
2cm/	7

r------- ------------ 7
Formulas
Area of a rectangle:
lxw
Volume of a rectangular  prism:
I X  wx h

55. Find the area of the figure below,

4 inches

4 inches

57.  Find the volume of the figure below.

5cm
f.'--/ ----(/

·.·.·

5 em

4 em

2cm

Comparing Fractions
Compare each pair of numbers. Write the correct comparison symbol ( <, >, = ) in each circle. Make sure you have common denominators before comparing numerators.

Example:

8

0

1 	-3
3 	4

4	9
12	12

58. 	59.
5

8

60.

0

0

0

61.	62.
3 	3 	5
7 	4	5	6

63.

Ordering Fractions

Order the following fractions from least to greatest.

64.					

65.		

3	
5	
4	
2	
7		
1	
4	
1	
6	
7	
8	8	8	8	8		5	5	10	10	10	

66.					67.		

1	
1	
I	
1	
1		
1	
5	
30	
3	
9	
2	4	6	3	5		2	16	64	8	32	

Order of Operations
Solve the following problems. Show your work. Be sure to follow the order of operations.

farenthesis
£xponents
Multiplication or Division: Which ever comes first from left to right.
Addition or ubtraction: Which ever comes first
from left to right.

Example:	8 - 4 + 2 + 2 =
8-2+2=
6+2=
8

68. 	15 X  8- 3: 	69. 	36 + 4 X   3 =

71.	(30 + 8) X   (6-1) =	72. 	(29 - 18) + 14 + 2 + 6 =

74. 	36-  5 (16 - 11) =	75.	25 + 18 + 6 - 1=

9

70.	(30 + 8) X   6 -1:

73.  64 + 8 X   2

76.	24 + 62 - 14 	=

10
Geometry-Who am I?
Use the following shapes  to answer the questions  below.

D !_ 	/0600

77.  I am a 2 dimensional shape that  has four sides.  I have four 90 degree angles. I have two sets of parallel lines. I also have two sides that are one length, and my other  two sides are a different length.

Who am!? 	.........; 	

78.  I am a 2 dimensional shape that  has three  acute angles.  All of my sides are the same length.  I have no parallel sides.

Who am I?	---	--

79. 	I am a 2 dimensional shape that  has four sides.  I have two obtuse angles and two acute angles.  I have two different sets of parallel sides.  I also have two sides that are one length, and my other  two sides are a different length.

Who ami?_ -- ----

80.  I am a 2 dimensional shape that  has 5 obtuse angles.  I do not have any sides that are parallel.

Who ami?  	_

81.  I am a 2 dimensional shape that  has four 90 degree angles.  I have four sides that are all the same length.  I have two different sets of parallel lines.

Who ami? --------

82.  I am a 2 dimensional shape.  My perimeter  is also known as a circumference.

Who ami? -- -----

11

Simply Fractions
Simplify the following fractions. If  the fractions are improper, change them to mixed numbers then simplify.

83. 	84.

14 	15
28 	55

86. 	87.

34 	17
48	4

Example:

85.

10+5= .f
25+5=	5

12
51

88.

80
25

Adding Fractions  and Mixed Numbers
Add the following fractions.  Make sure you have common denominators  before adding. Remember, you only add the numerator (top number) and you keep the denominator (bottom number) the same! Simplify your final answers.

Example:

1	1
-+-=
3 	5
l 	l
5	3	8
-+-=-
15   15 	15

89. 	90.
6	3
-+-=
10	I 0

23- + 12- =
8 	8

91.

=

I	5
-+-
9 6

92.

=

1	2
-+1-
12	3

Subtracting  Fractions
Subtract  the following fractions. Make sure you have common denominators before subtracting.  Remember, you only subtract  the numerator (top number) and you keep the denominator (bottom number) the same! Simplify your final answers.

Example:

12

-5 --1--
6	3

l	!

93. 	94.
5	3	8 	3

95.

96.
7 	2 	4	1

--- =
6 6

Multiplying Fractions

2--1- =
12 	12

----
10   4

3--- =
5	4

Multiply the following fractions. Multiply the numerators; then multiply the denominators. Simplify, if necessary.

Example:

3	5 	15	1
-X-:-·:-
5	9 	45	3

97. 	98.
3 	1
-X-:
4 	3

2 	5
-X-:
3 	8

99.

1 	2
-X-:
3 	5

100.

-7 x2=
8