PENNSBURY SCHOOL DISTRICT

SUMMER MATH REFRESHER

For students entering

6th Grade

2020

Dear Student,

This packet is meant to provide you with a review of math skills from sixth grade. As you work through the following pages be sure to show all of your work. Please do not use a calculator, except where indicated with --------------------->

Do your best work and remember – THINK!!!!

The answer key is attached for you to check your answers once you have completed the packet (or as you work through it).

Thank you,

Middle School Math Department Staff

&

Dr. Gary McManus, Mathematics Supervisor

“It’s not what we do once in a while that shapes our lives. It’s what we do consistently.” Anthony Robbins—best selling author

Section 1: Whole Numbers

1) Write the place value of the underlined

digit in the number 523,411,396.

______________________________________

2) Write the place value of the underlined

digit in the number 523,411,396.

___________________________________

3) Write 41,005 in words.

___________________________________

___________________________________

___________________________________

4) Write one million, sixty-two thousand,

nine hundred five in standard form.

_______________________________________

5) Write two hundred sixty-one and four

hundredths in standard form.

_______________________________________

6) Use >, <, or = to compare:

106,218______ 106,403

7) Use >, <, or = to make the statement

true:

8) Order the numbers from least to

greatest:

2,706; 2,805; 2,766; 2,689

____________________________________

9) What is 5,674 rounded to the nearest

hundreds place?

_______________________________________

10) What is 384,216 rounded to the

nearest ten thousand?

____________________________________

11) Find the product of $3,045 and 72.

__________________________________

12) Find the difference of 2,051 and 988.

____________________________________

13) What is the quotient of 822 and 6?

____________________________________

14) Four thousand sixty-two plus nine

hundred eighteen

____________________________________

15) Six thousand eighty-one multiplied by

seventy-five

____________________________________

16)

____________________________________

17)

____________________________________

18) Find the quotient:

___________________________________

19) Jackson played a game with his friend.

The winner of each round got 15 points.

Jackson got 90 points in all. How many

rounds did Jackson win?

___________________________________

Section 2: Decimals

20) Write in order from least to greatest.

3.22, 3.5, and 3.134

____________________________________

21) Round the number below to the place

of the underlined digit.

96.672

___________________________________

22) Hanna gave her mother a gift. Hanna

spent $4.19 on a card, $23.50 on the

present, and $2.95 on the wrapping paper.

What is the best estimate of the total

amount of money Hanna spent on her

mother’s gift?

____________________________________

23) Tom is balancing 3 blocks on top of

each other to make a tower. The heights of

the blocks are 22.4 in., 41.2 in., and 21.9 in.

Estimate the height of Tom’s tower to the

nearest tens.

____________________________________

24) Paula is buying lunch. She buys an ice

tea for $1.15, a turkey sandwich for $3.52.

What is the total she pays for lunch?

___________________________________

25) Using your answer from #24, how much

change will Paula get if she pays with a $5

bill?

____________________________________

26)

___________________________________

Section 3: Fractions

27) What portion of the circle is shaded?

Express your answer as a fraction.

_________________________________

28) What portion of the rectangle is

shaded? Express your answer as a

simplified fraction.

____________________________________

29) Write the numbers in order from least

to greatest.

____________________________________

30) Write as a mixed number.

____________________________________

31) Write as an improper fraction.

____________________________________

32) What is the LCD (least common

denominator) for and ?

___________________________________

33)

34)

35)

Section 4: Number Theory and Patterns

36) List all the factors of 48.

____________________________________

37) Find the GCF (greatest common factor)

of 18 and 45.

___________________________________

38) List the first 5 multiples of 12.

___________________________________

39) Find the LCM (least common multiple)

of 8 and 12.

__________________________________

40) Find the LCM of 12, 15, and 30.

__________________________________

41) Which of the numbers is a prime

number and why?

19, 24, 33

__________________________________

__________________________________

42) Write the rule for the pattern:

5, 15, 25, 35, . . .

__________________________________

43) Write the rule for the pattern:

6, 25, 101, 405, 1621,. . .

__________________________________

Section 5: Algebra

44 – 45; Write each of the following

sentences using mathematical symbols.

44) Nineteen is greater than eleven.

____________________________________

45) One hundred divided by twenty-five.

____________________________________

46 – 47; Simplify.

46)

___________________________________

47)

__________________________________

Section 6: Geometry

48 – 60; Draw the geometric figures. Use a

straightedge or ruler.

48) A ray

49) A line

50) A line segment

51) A pair of parallel lines

52) A pair of intersecting lines

53) A pair of perpendicular lines

54) An acute angle

55) An obtuse angle

56) A right angle

57) A right triangle

58) A trapezoid

59) A rhombus

60) A cylinder

61) Barbara is decorating her pencil case,

which is in the shape of a rectangular prism.

She puts a sticker on each face of the pencil

case. How many stickers does Barbara use?

____________________________________

62) What solid figure can be made using

the net below?

____________________________________

63) How many lines of symmetry can be

drawn in the square below?

____________________________________

Use the following formulas for exercises

64-65.

64) Find the perimeter and area of a

rectangle with sides 5ft. and 8ft.

____________________________________

65) Find the perimeter and area of a square

with a length of 13 mm.

____________________________________

ANSWER KEY

1) Hundred-thousands

2) Ten-millions

3) Forty-one thousand, five

4) 1,062,905

5) 261.04

6) <

7) < , <

8) 2,689, 2,706, 2,766, 2,805

9) 5,700

10) 380,000

11) $219,240

12) 1,063

13) 137

14) 4,980

15) 456,075

16) 143

17) 568,708

18) 4170 r1

19) Jackson won 6 rounds

20) 3.134, 3.22, 3.5

21) 96.7

22) $31.00

23) 80 inches tall

24) $4.67

25) $0.33

26) 0.252

27)

28)

29) , ,

30)

31)

32) LCD = 8

33)

34)

35)

36) 1, 2, 3, 4, 6, 8, 12, 16, 24, 48

37) GCF = 9

38) 12, 24, 36, 48, 60

39) LCM = 24

40) LCM = 60

41) 19 is a prime number because it is

only divisible by itself and 1.

42) Add 10

43) Multiply by 4 and add 1

44) 19 > 11

45)

46) 60

47) 12

48)

49)

50)

51)

52)

53)

54) 55)

56)

57)

58)

59)

60)

61) 6 stickers

62) triangular pyramid

63) 4

64) P = 26 feet; A = 40 square feet

65) P = 52 millimeters; A = 169 square

millimeters