Grade 6 practice – Coordinate Plane
1. John and Jacob are going hiking. Below is the map they are using. They start out at
John’s house located at (-3.6, -2.6). They hike six units north and 4 units east. What are
the coordinates of their new location?
2. The absolute value of the coordinate are (5, 8). What are the coordinates if they were
located in quadrant IV?
3. What is the absolute value if the coordinates shown on the graph?
4. Give Kristy directions to get from point C to point A.
5. Using the graph in number 4, what is the absolute value of point D’s coordinates?
Grade 6 practice – Whole Number Exponents
1. Evaluate: 73
2. Rewrite H3 without using exponents.
3. Write the expression using exponents: 2 ∙ 2 ∙ 2 ∙ x ∙ x
4. Simplify: 62 ∙ 63
5. Simplify: -3x4 ∙ 2x
Grade 6 practice – Expressions involving variables
1. When the expression 3(x + 6) is evaluated the result is 33. What is the value of x?
2. Evaluate the expression for x = 9: 8x – 38 + 2x
3. Which number is acting as a coefficient in this expression? 420 + 88x – 290
4. Evaluate the following for b = -3: (5b – 3b) + 2b
5. Translate the following expression: “eight less than double a number”
Grade 6 practice – Writing equivalent expressions
1. Write an equivalent expression to: -xy + (-xw)
2. Simplify x + x + x + x + x – y + y – y + w
3. Simplify 9x +11 - 2(x + 8)
4. What is the greatest common factor for 14a and 42?
5. Why is 6(m – 3) equivalent to 6m – 18? Be specific.
Grade 6 practice – Equations and Inequalities
1. From the list below, which of the values used for x could make 750 – x < 362?
390 388 477 201 450 -388 -477 261
2. How many positive whole number solutions (values for x) does this inequality have?
X ≤ 18
3. Write the number sentence that the following words describe: eight is equal to the
difference of 11 and m
4. Write the number sentence that the following words describe: the product of seven
and x decreased by three is less than or equal to 9
5. A batting cage offers 9 pitches for a quarter. Tamara was $1.50. Write and expression
that could be used to calculate how many pitches Tamara could get for her money.
Grade 6 practice – Modeling with expressions
1. Juan had 121 baseball cards. Jessie had x less than ½ the amount that Juan had. Write
an expression to show how many baseball cards Jessie had.
2. Jimmy had y dollars to spend. He spent $3.45 on candy, found a five dollar bill, bought
a shirt for $12.00. Write a simplified expression to show how much money he has left.
3. Jill had 67 boxes of cookies. She gave away x boxes of cookies, then got back triple what
she gave away. Write a simplified expression to show how many boxes of cookies she
has now.
4. Jorge buys a shirt every time he visits a college. He has visit 18 colleges, each of the
twice. Write and equation to show how many shirts Jorge now has.
5. Janice collects dolls. She had 291 dolls in her collection. Janice acquired x more doll.
She then bought twice that amount at a store sale. She now has 413 dolls in her
collection. Write an equation that could be used to show how many dolls she added to
her collection.
Grade 6 practice – Solving one step equations
1. Solve for x: 100x = 1 (Express you answer as a decimal)
2. Solve for n: n + 86 = 123
3. Solve for w:
𝑤
14
= 28
4. What is the value of m? -7m = 56
5. Solve for n: 428 – n = 120
Grade 6 practice – Representing Inequalities
1. Kevin is a lawyer. He is working on x number of cases. His case load is doubles and
then 5 more are added. He now has more than 35 cases. Write and inequality to
represent this situation.
2. Mindy has magazine subscriptions. She subscribes to at least 6 magazines. Write an
inequality to show how many magazines Mindy receives each month.
3. Stephanie has at least 3 favorite foods. How many favorite foods does she have?
4. The quotient of a number and 2 decreased by 92 is less than 300. Write an inequality to
represent this situation.
5. How would y ≤ be represented on a number line? Explain in words. Be specific.
Grade 6 practice – Quantitative relationships
1. Kristine wants to buy bulk candy that cost $.79 per pound. She wants to buy x pounds
of candy and need to know how much money (m) she needs. Write and equation that
could be used to figure out how much money Kristine needs.
2. Rolando collects baseball cards. He buys them in packs with 30 cards in each pack.
Rolando bought x baseball cards. Write and equation to figure out how many (p) packs
he purchased.
3. Hen A lays 4 times as many eggs as Hen B. Write an equation to represent this scenario.
4. Lenny is a florist. He is putting together 7 arrangements for a party. Each arrangement
will have 6 roses in it. The roses cost $3 each. Write an equation to find the total cost
of the flowers. Find the total cost.
5.
Camryn works at Publix and earns $9.55 per hour. Her hours vary each week. Write an
equation that represents the amount of money (m) Camryn earns per week.
Grade 6 practice – Nets
1. Identify the solid given its net. Be specific.
2. Identify the solid given its net. Be specific.
3. Identify the solid given its net. Be specific.
4. Identify the number of faces, edges and vertices in a rectangular pyramid.
5. Find the surface are of a rectangular prism if L= 15m, W= 5m, and H=5m.
Grade 6 practice – Area
1. What is the area of the shaded portion of the figure below?
2. In the figure below, the larger circle has a diameter of 24 and the smaller circle has a
diameter of 12. Find the area of the shaded portion. Use 3.14 for π and round to the
nearest hundredth.
3. Katie says the area of her shape is 36 cm2. Which of the following shapes could be
Katie’s shape?
A.
B.
C.
D.
E.
4. Mrs. Dudley’s office is shaped like a L. She has decided to lay hard wood flooring in her
office. Using the diagram below, what is the area of Mrs. Dudley’s office?
5. Find the area of the shape below. Show your work and explain your reasoning.
Grade 6 practice – Surface Area and Volume
1. A cube has a volume of 1,000 cm3. What is it surface area?
2. Carla is wrapping a box with contact paper. She needs 52 square feet of contact paper
to cover the box. Find the length of the missing side in the Carla’s diagram below.
3. Jennifer caught a game winning home run baseball at the World Series. Her dad made
a display case in the shape of a square pyramid pictured below. How many square
inches of plexiglass did Jennifer’s dad use.
4. A gross of pens is sold in a box
10
12
ft. by
6
12
ft. by
3
ft. Draw the right rectangular prism.
12
Find the volume in cubic feet.
5. John is making a crate to ship an antique bowl to a customer. His boss told him that the
crate is a cube with a total surface area of 96 square inches. What are the lengths of the
sides of the cube? What is the volume of the cube?
Grade 6 practice – Coordinate geometry
1. Jane is drawing a parallelogram. Three of the vertices are (4, -6), (3, 0), and (-4, 0).
What are the coordinates of the fourth vertex?
Use the drawing to answer questions 2-4.
2. Tonya left her house went to the arcade. Then met Jennifer at the donut shop. Before
returning home, where would Tonya need to stop before going home for her travels to
be in the shape of a trapezoid?
3. What is the distance between Eddie’s house and the Arcade?
4. Eddie went to the Arcade, then to Tonya’s. If he then reversed his route to go home,
how far did he travel in all?
5. Graph the points (0,0), (5,0), (6,2), (5,5), (0,5). Name the figure and describe the angles.
Grade 6 practice – Statistical questions
1. Choose all of the question that are statistical questions.
A.
B.
C.
D.
E.
F.
What is the quantity of each type of video game in the game store?
How many different games are in the game store?
How many games were purchased in one week?
How many lunches did the students eat?
How many students ate each type of lunch entrée?
How many students surveyed would buy each color of back pack?
2.
What statistical question could be asked to generate the data?
A.
B.
C.
D.
At lunch, what fruit do some students like to eat?
At lunch, which fruit is preferred?
At lunch, which fruit does each student prefer to eat?
At lunch, which fruit is least liked by students?
Grade 6 practice – Bar Graphs
Use the above graph to answer the following questions.
The 6th Grade students at Fort King Middle School can choose to participate in one of the four music programs.
1.
Which group has the greatest number of 6th grade participants?
2.
How many 6th grade girls participate in a music activity at Fort King?
3.
How many more girls than boys in the 6th grade participate in Chorus?
4.
How many 6th grades are in Orchestra?
5.
How many 6th grade students participate in a music activity at Fort King?
Grade 6 practice – Circle Graphs
John’s Music Collection
John has download 500 songs of varying genres to his computer. The circle graph show the breakdown by
genre of his downloads.
1.
2.
3.
4.
5.
How many songs are downloaded in Pop and Rock genres?
How many songs are downloaded in R & B?
Which genre has the most songs?
About what percent of songs are downloaded in R & B, Country and other?
About how many more R & B songs than rock songs has John downloaded?
Grade 6 practice – Mean, Median, Mode and Range
1. A quarterback recorded the number of passes he had at each practice: 73, 14, 55, 37,
84. What is the mean of the number of passes per practice?
2. Jerry has 5 stamp collections. He wants to average 35 stamps per collection. If he has
62, 12, 28 and 44 stamps in 4 of his collections, how many stamps does he need to have
in his 5th collection to average 35?
3. Will is a dog breeder. He takes very good care of the puppies that he has and feeds them
as much food as they need. He keeps track of how much food he feeds the puppies over
a 10 day period. This is the data Will kept: {7, 9, 12, 7, 10, 8, 11, 9, 12, 10}. What is the
median number of pounds Will fed the puppies?
4. Teddy counts the number of marbles in 8 different bags. {28, 33, 31, 28, 29, 34, 35, 28}
What is the mode?
5. Carrie has to travel for her job. In one week, she traveled all 5 days. The shortest
distance she traveled was 71 miles. The range of miles she traveled was 98 miles. What
is the longest distance that Carrie traveled for her job that week?
Grade 6 practice – Graphs
1. The graph show the Science test results. How many students passed (passing grade is
61%)?
2. How many students scored 90 or below?
3. Below is a graph of a week of temperatures. Which two days had a temperature range
of 10 degrees?
4. What percentage of the days had a temperature 70° or higher?
5. Which of the following graphs best represents the values in this table?
Grade 6 practice - Ratio
Mr. Jones has 75 parrots and 125 song birds. Use this information for questions 1-3
1. What is the lowest ratio of the number of parrots to the total number of birds?
2. What is the lowest ratio of parrots to song birds.
3. Ms. Albritton has the same ratio of parrots to song birds. If she has 51 parrots, how
many song birds does she have?
4. Francie Frog laid 345 eggs in the spring. 23 of those eggs live to become adult frogs.
What is the lowest ratio of adult frogs to eggs?
5. The little league team called the Jets has 7 blonds, 5 brunettes, and 2 red heads. What
is the lowest ratio of redheads to the entire team?
Grade 6 practice – Ratio and Proportion
Cindy and Alex were people watching one spring day and decided to count the number of
people that walked by wearing orange. Out of 78 people that walked by 26 were wearing
orange.
1. What is the lowest ratio of the total number of people to the number of people wearing
orange?
2. What is the lowest ratio of the people who walked past that were NOT wearing orange
to the total number of people?
3. Sam was baking a cake and could not find his tablespoon measure. The recipe call for
1
3 tablespoons. How many teaspoons must Sam use in order to have the recipe turn
2
out all right?
4. The ratio of pears to apples in a fruit basket is 9 to 2. If there are 66 pears and apples in
the fruit basket, how many pears are there?
5. 5:6 = x: 72. Find the value of x.
Grade 6 practice – Division of Fractions and Decimals
1. Circle all the fractions below that would not result in a repeating decimal when
converted.
4
18
15
7
2
3
2
12
99
24
9
7
8
5
2. What is the quotient of 20 divided by one-fourth?
3. Perform the following operation: 3
2
3
1
÷2 .
3
4. When any non-zero number is divided by itself, what is the result?
5. What is the result when a fraction is multiplied by its reciprocal?
Grade 6 practice - Rate
1.
George drove from Newark to Atlantic City. He drove at a constant speed of 58 mph
for 284 miles. How long did it take George to drive 284 miles?
2. It took Mrs. Jones 15 minutes to drive from her house to her son’s school. If the school
was 4 miles away from her house what was her unit rate of speed?
3. If a gallon of ice tea costs $3.84. At this rate, how much does a cup of ice tea cost?
4. If James pay $62.90 to fill the 17-gallon gas tank on his truck and he can drive 330 miles
on one tank of gas, about how much does he pay per mile to drive his truck?
5. Sally has two jobs. For her first job she earns $7.55 an hour. For her second job she
earns $8.45 an hour. Last week she work her first job 10 hours and her second job 15
hours. What were her average earnings per hour?
Grade 6 practice – Percent and Measurement
1. Kristen incorrectly answered 8 out of 20 questions on a quiz. What percentage score
should she receive?
2. How many milligrams are there in 6 centigrams?
3. How many inches are there in 3 yards?
4. How many quarts are there in 11 gallons?
5. What is 75% of 96?
Grade 6 Practice – Division of whole numbers
1.
A team of 12 chess players got an award of $1800 for winning a tournament. If the captain is allowed to keep
$315, how much would each of the other players get if they split it equally?
2.
Janie earns $125 per week. She wants to buy a new computer system that costs $3,960. She saves $55 per
week. Write an expression that could be used to find out how many weeks it will take her to save enough
money for the computer system.
3. There are 49 rabbits and each has the same size litter of bunnies. Together, they have 343 bunnies. How many
are in each litter?
4. Elizabeth cut off 18 inches of her hair for “Locks of Love”. It took her 3 years to grow it back. How much did her
hair grow each month?
5. James wrote a reference book. It sold for $9.00 per copy. If a total of $78,687 was collected from the sale of the
book. How many copies were sold?
Grade 6 Practice – Operations with decimals
1.
Three friends went out to dinner together. Josie got a meal that cost $7.20. Kristy got a meal that cost $8.11
and Jenny got a mean that cost $5.54. If they split the bill evenly how much did each pay for dinner?
2. Chris went shopping for gifts for 3 friends. At the sporting goods store he found a jersey for $14.99, a hat for
$6.95, and a sign for $5.39. If he gave the clerk 2 $20 bills how much change should he get back?
3. When Jim and his father started on their road trip their odometer reading was 19,234 miles. Aft they reached
their destination the odometer reading was 21,099. If the fuel cost 16 cents a mile, how much money did they
spend on fuel to reach their destination?
4. Circle all the equivalent numbers:
3
8
5.
.37
1
2
36
96
37 %
37.5% 3.8
3.75%
Mrs. Florio wanted to purchase a certain book for the 18 students in her class. If the book cost $19.70 for a
hardback copy and $8.65 for a paperback copy, how much money would she save buying each student a
paperback copy?
Grade 6 practice – Representing negative numbers
1. On a number line, how far apart are -8 and 3?
2. On a number line, place the following set of numbers: {-3, -1, 5}.
3. Which numbers are NOT between -8 and -4?
0
-7
-3
7
5
-5
-1
1
4. What pair of numbers does -7.05 fall between?
-7 and -6 -5 and -3 -9 and -10 -7 and -8
5. Which set of numbers would be found to the left of 4 on the number line?
{-1, 4, 5} {1, -4, -5} {1, 4, -5} {1, 4, 5}
Grade 6 practice – Absolute Value
1. Evaluate the following: |8 – 22| + 6
2. Evaluate the following: 18 - |(20)(1/4) – 18|
3. Evaluate for M: |9 – 3M| = 3
4. What is the absolute value of -32?
5. Evaluate: -|23|