ST. MARK Catholic School
9972 Vale Road
Telephone 703 281-9103
Vienna, Virginia 22181-4005
Fax 703 766-3430
Mathematics Summer Work
Rising 6th Grade
Dear Rising 6th Grade Students,
Sixth grade math is an important year of math. All of the basics of number sense and
computation are mastered during this year of math to provide the foundation for more
advanced algebra and geometry. The purpose of this packet is to review your 5th grade
concepts to better prepare you for your 6th grade year of mathematics.
To complete the problems in this math packet, you may not use a calculator. Please use a
pencil for your work, and please neatly show your work beside each problem that requires
computation. I always want to see your work, so please do not erase it! I have separated
out the concepts based on:
Number Sense (Place value, comparing decimals and fractions)
Computation (Decimals and fractions)
Data Analysis
Geometry and Measurement
This packet is due the first week of school. It will be your first grade of 6th grade math.
It is recommended that you spread the work for this packet across the summer to keep
your math skills fresh.
I am really looking forward to getting to know you better next year. I know we will have
a great school year together. Thank you in advance for your hard work on this!
1
Student Name:________________________________
1. What do you like best about math?
2. What do you like least about math?
3. What is easiest for you in math?
4. What topic has been hardest for you in math in the past?
5. Let me know anything else you would like to share with me about math. (If there is
nothing else, that is fine, too!)
Thanks for sharing. I want to get to know you better to help you be the best you can be this
year.
Websites:
- www.mathisfun.com
- www.coolmath4kids.com
- www.aaamath.com (choose Grade 6)
- www.aplusmath.com
- http://www.weeklyreader.com/kids/games/multiply.asp
- www.mathstories.com
- http://www.escapefromknab.com
- http://mathforum.org/students
- www.khanacademy.org
- www.ixl.com
Have an ipod touch? Consider buying some “math apps” like Sudoku, 2048, NineGaps,
Multiplication Fact Time Tests, or Epic Math. It feels like a game, but it will keep your brain
working and get you ready for middle school.
2
Number Sense - Decimals
Rounding Decimals
Hint: Underline the place value indicated. Look one place value to the right of this number. Five or above, give
it a shove. Four or below, let it go.
1) Round 5.4515 to the nearest tenth ______________
2) Round 6.7746 to the nearest hundredth ______________
3) Round 34.5555 to the nearest thousandth ______________
4) Round 123.8531 to the nearest hundredth ______________
5) Round 123.8531 to the nearest one ______________
Compare values of two decimals using <, >, or =.
Hint: Before you compare two decimals, make sure they both go to the same place value.
6)
1.451 ______ 1.423
7)
8)
0.03 ______ 0.004
9)
10) 0.206______0.211
1.4 _______ 1.400
6.111 _______ 6.3
11) 34.34 ______ 34.34000
Order the decimals from least to greatest.
Hint: Again, it is easiest if you re-write the decimals so that they all have the same number of place values. I
often re-write them in a column to compare them easier.
12) 0.265; 0.243; 0.251
13) 0.02; 0.002; 0.2; 0.022
14)
15) 341.5; 342.0; 341.45
2.65; 2.6; 2.623; 2
3
Number Sense – Fractions
Convert Between Decimals and Fractions
Convert the fraction or mixed number into its decimal equivalent.
Hint: Turn it into an improper fraction. Divide the numerator by the denominator.
1) 1
2
= ________
5
2)
2
5
= _________
6
3)
2
= _________
3
Convert the decimal into a fraction or mixed number in lowest form.
Hint: Say the formal name of the decimal. Write that as a fraction. Simplify.
4) 3.75 = _________
5) 0.625 = ________
6) 32.4 = ________
Order the Fractions from Least to Greatest
Hint: Either turn them all into decimals and compare them. Or, you can find a common denominator and
compare the numerators.
7)
3 5 7
, ,
4 6 8
8)
1 1 1
, ,
2 4 3
9)
2 1 5
,
,
3 10 6
1
3
10) 6.35; 6 ; 6.31; 6
3
10
Need more practice with fractions or decimals? Go to www.mathisfun.com and choose “Numbers”. There is a
tutorial as well as practice and games.
4
Computation - Decimals
Adding, Subtracting, Multiplying, and Dividing with Decimals
Hint: When you add or subtract decimals, you must line up the decimal points. When you multiply, you do not
need to line up the decimal points. You just multiply as if they were whole numbers and then add up the total
number of decimal places. When you divide with decimals, you must turn your divisor into a whole number.
Then, you move the decimal place of the dividend the same number of places.
Remember, show your work right on this page and circle your final answer, please! (If you would like to use
graph or lined paper,that is fine as well. Please make sure you staple it onto this sheet so that I can see it.)
1) 2.345 + 1.5
2) 14 – 0.55
3) 3.1 + 0.0076
4) 33.1 – 7
5) 0.289 + 73.9
6) 4.7 – 0.92
7) 6 x 0.07
8) 0.08 x 0.007
9) 56  0.07
10) 3096 ÷ 0.3
11) 4.56 x 1.203
12)
2.96 ÷ 8
Computation – Fractions
5
Adding, Subtracting, Multiplying, and Dividing with Fractions
Hint: When you add or subtract fractions, you need to re-write the fractions with a common denominator.
When you multiply or divide, you must always first turn your mixed numbers into an improper fraction. When
you divide, you “keep switch flip”…..or keep the first fraction, switch the sign, and flip the second fraction.
Remember, show your work right on this page and circle your final answer, please! (If you would like to use
graph or lined paper, that is fine as well. Please make sure you staple it onto this sheet so that I can see it.)
All answers must be in simplest form and may not be improper fractions.
1)
7 1
+
8 2
2)
7 1
8 2
4)
7 1
÷
8 2
3)
7 1
x
8 2
5)
3
3
4
+2
4
5
6)
3
7)
3
3
4
x2
4
5
8)
3
3
4
-2
4
5
3
4
2
4
5
Need more practice? Go to www.mathisfun.org, and choose numbers and then fractions. We
will have a “Fraction Friday” quiz every Friday because fractions are the foundation of your
future math classes. You will be very confident with your fractions by the end of 6th grade.
No worries!
Data Analysis
Ashley had the following test scores in math last quarter:
6
8
9
10
7 9
1 3 3 6
0
Measures of central tendency:
Hint: To calculate the mean, you add up the numbers and divide by the number of numbers. To calculate the
median, you line up the numbers from least to greatest and find the middle value. To find the mode, you find
the number that occurs the most. To find the range, you subtract the smallest number from the biggest
number.
Mean:__________
Median:_________
Mode:__________
Range:__________
Using the table below, decide what type of graph would best represent the data, and sketch
the graph to the right of the table. For full credit, you must give your graph a title and label
the axis!
Stock Price of Apple in 2011
Month
Price
Jan
$540
Feb
$554
March
$592
April
$584
May
$596
Start thinking about stocks that you would like to invest in with $1000 of “St. Mark Money”.
We do a group stock project every year in 6th grade math!
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Geometry and Measurement
Circle the best unit of measure for each.
Length of a pencil
Distance from home to park
Running a race
Weight of a train
Weight of a soccer player
Weight of a textbook
Weight of a pencil
Capacity of a can of soup
Capacity of a swimming pool
Inches
Inches
Millimeter
Ounces
Ounces
Milligrams
Milligrams
Milliliters
Milliliters
Feet
Feet
Centimeter
Pounds
Pounds
Grams
Grams
Liters
Liters
Yards
Yards
Meter
Tons
Tons
Kilograms
Kilograms
Kiloliters
Kiloliters
Mile
Mile
Kilometer
State whether each scenario would be measured in perimeter, area, or volume
Hint: Perimeter is the distance around a 2-dimensional figure. Area is the square units within a 2-dimensional
figure. Volume is the cubic units within a 3-dimensional figure – how much something holds.
Filling a swimming pool
Fence around a garden
Carpet in a room
Cover that goes over a swimming pool
Filling a glass full of juice
Putting molding around the ceiling of a room
Perimeter
Perimeter
Perimeter
Perimeter
Perimeter
Perimeter
Area
Area
Area
Area
Area
Area
Volume
Volume
Volume
Volume
Volume
Volume
Geometry Concepts
Hint: Always write out the formula for perimeter or area first, and then solve. Always include the appropriate
unit of measure in your answer.
1.
Find the perimeter and area of a rectangle whose length is 45cm and width is 15cm.
____________________
____________________
2. Find the area of a triangle whose height is 6in and base is 4in.
____________________
3. Find the circumference and area of a circle whose radius is 7ft.
____________________
____________________
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Challenge Material
This part is optional, but not extra credit. This is the fun stuff! The mandatory part of this
packet is the “basics”. It covers the basic skills you need going into 6th grade math. With
this optional material on the next two pages, I’d like to see your problem solving skills. Again,
please show all of your work. (And I don’t expect any Algebra….just pictures!) Go for it!
1.
Going Marbles
There are 100 marbles in five bags. If the first and second bags contain between them 52 marbles, the
second and third bags together contain 43 marbles, the third and fourth together contain 34 marbles,
and the fourth and fifth together contain 30 marbles, how many marbles are in each bag?
a.
b.
c.
d.
e.
Bag 1:
Bag 2:
Bag 3:
Bag 4:
Bag 5:
____________
____________
____________
____________
____________
2. Days on Other Planets
On any planet, one day is the time it takes for the planet to rotate once about its axis. For example, an
Earth day takes 24 hours. The time it takes a planet to go once around the sun is called a year. On
Earth, one year takes about 365 days. The following table gives each planet's day and year in terms of
Earth hours, days, and years.
Questions:
Suppose you arrived on Mercury on your 13th birthday. How old in Earth years would you be after
100 Mercury days?
______________________
Suppose you arrived on Saturn on your 13th birthday. How old in Earth years would you be after
100 Saturn days?
______________________
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3. The World's Largest Popcorn Ball
Constructed in June, 2004, the then-World's Largest Popcorn Ball weighed 3100 pounds
and was 7 feet tall. It was made of 910 pounds of popcorn, 1500 pounds of sugar, and 690
pounds of corn syrup.
One box of microwave popcorn typically contains three bags that each holds 3.5 ounces of
popcorn. How many boxes of microwave popcorn would it take to make that giant popcorn ball?
______________________
4. Pumpkin Carving for Charity
Instead of going Trick-or-Treating on Halloween this year, six friends decided to use their time to
carve pumpkins for a local charity event. The artistically carved pumpkins were auctioned at the event
and much to everyone's surprise they raised $180 for the charity!



The final bid on Selena's pumpkin was $10 more than the final bid on Ty's pumpkin.
Ty's, Niko's, and Corrine's pumpkins each earned the same amount.
Araceli's and Forrest's pumpkins each brought in the same amount of money as Selena's.
What were the final bids on the individual pumpkins carved by the six friends?
Ty:___________________
Selena:________________
Niko:_________________
Corrine:_______________
Araceli:_______________
Forrest:_______________
Source of challenge problems: Drexel University Problems of the Week, http://mathforum.org/pows/,
Retrieved April 22, 2013.
mjt 4/15
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