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Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Dear Incoming Grade 8 Students,
To better prepare for Grade 8 mathematics entry process, summer work is assigned to ensure an
easier transition into your next math course. The expectation is that all students bring the
completed assignment to their first math class in the Fall 2013. If you need help completing the
problems, you have a couple of options:
•
•
Visit links to examples, explanations, and instructional videos provided in the packet
Use the copy of the textbooks available at the Duxbury Free Library.
A TI-83(plus)/84(plus) graphing calculator will be necessary to
complete the calculator section. All Grade 8 mathematics courses
will use of this type of calculator. Therefore, it is essential that
every student obtain one.
Please keep in mind that non-calculator problems need to be
completed without the use of any type of calculator.
All answers must be justified by showing all work.
What Problems do I have to do?
Please allow enough time over the summer to complete the following sections of the packet.
Your Class Next Year
Course #
Complete These Sections
Pre Algebra
282
A
Honors Algebra
281
B
D
Accelerated Algebra 1
280
B
C
D
Grade 7 Topics Mastered Prior to Grade 8:
Ratios and Proportional Relationships
• Analyze proportional relationships and use them to solve real-world and mathematical problems.
Percents
• Solve percent problems using both the percent proportions and percent equation and the use them to solve real
world problems.
The Number System
• Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational
numbers.
Geometry
• Draw, construct and describe geometrical figures and describe the relationships between them.
• Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.
Statistics and Probability
• Use random sampling to draw inferences about a population.
• Draw informal comparative inferences about two populations.
• Investigate chance processes and develop, use, and evaluate probability models.
Checklist
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department I finished the sections listed for my class by showing all work
I have a graphing calculator
I circled the problems that I didn’t understand or couldn’t correct on my own.
My name, last year’s class, and last year’s teacher are filled out on the next page
I filled out this checklist
Name__________________________________
Class I took last year (circle) 270
271 NEW
Teacher I had last year _____________________
SECTION A
•
•
I.
NON-CALCULATOR : M282 Students
Show all work to justify your answers.
Circle any problems that you don’t understand.
The Number System
Operations with Rational Numbers- Completely simplify each numerical expression.
1) 11[( 25 – 8.7 ) –14] =
2) -12.6 – 3.2 – ( -20.75) =
3)
Adding negative numbers
4) (-51.2) (1.06) (0.5) =
5)
6)
Rational and Irrational Numbers
1) Identify all sets to which the following number belongs: 4.22
Rational, Irrational, Whole, Integer
2) Which point on the number line shows
45 ?
Division of fractions
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 3) Which of the following shows the rational numbers in order from least to greatest?
4) Which of the following show the fractions
2 3 1 1
5
in order from greatest to least?
, , , ,and
5 8 3 2
12
5) Which number belongs to the set of rational numbers and the set of integers?
6)
7)
Applications with Rational Numbers
1) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to
get to the same meeting. How many more miles did the business partner drive than Hector?
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 2) The gas tank of Ty’s truck holds 19.8 gallons. When the tank is empty, Ty fills it with gas that
costs $3.65 per gallon. How much will it cost to fill the tank?
3) To simulate space travel, NASA’s Lewis Research Center in Cleveland uses a 430-foot shaft. The
free fall of an object in the shaft takes 5 seconds to travel the 430 feet.
(a) Write an integer to represent the change in the height of the object.
(b) On average, how far does the object travel each second?
4) A scuba diver is 120 feet below the water’s surface. She then ascends 83 feet. What is her
current depth? Write an addition equation and then find the answer.
5) Monica reads 7
pages per minute?
1
pages of a mystery book in 9 minutes. What is her average reading rate in
2
6) Angela painted 3/8 of a room. Todd painted 2/5 of the same room. What part of the room has
been painted?
7) A high school Family and Consumer Science class has 12
taco shells. There are 3
1
cups of flour with which to make soft
2
3
cups flour per shell. How many soft taco shells can they make?
4
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Terminating and Repeating Decimals- Write each rational number as a decimal. Identify if it is
terminating or repeating.
1
35
5
8) −12
9)
10) 2
3
8
6
II.
Ratios and Proportional Reasoning: Percents, Ratios, Proportions
1) The table shows the eye colors of the students in Mr. Lee’s
class. Use the percent proportion to find the percent of students
with blue eyes.
2) The bill for the Morgan family at a restaurant was $62.14. Mr. Morgan would like to leave their
server a 20% tip. How much of a tip will the server receive?
3) In a community of 3200 homes, 72% of the households participate in the community recycling
program. How many households is this?
4) Last year there were 43 science projects submitted by students at a science fair. This year
there are 52 science projects. To the nearest tenth, what is the percent of change in the number
of science projects submitted?
5) The table shows the prices of different sized jars of peanut butter. Which of the jars has the
least unit price?
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department III. Expressions and Equations
Properties
1) Name the property shown by each statement.
(a) 42 + 36 = 36 + 42
(b) 16 + 0 = 16
________________________________
________________________________________
(c) (19 • 15) • 2 = 19 • (15 • 2) _____________________________
(d) 33 • 0 = 0 _______________________________
(e) (7 + 9) + 6 = 7 + (9 + 6) ________________________________
(f) 25 • 1 = 25 ________________________________
2) Which expression can be written as 7(c + d)? Explain your reasoning.
A. 7c • 7d
B. (7 + c) • (7 + d)
C. 7c + 7d
D. (7 + c) + (7 + d)
distributive property
Evaluate and Simplify Expressions
3) Evaluate each expression if x = -3, y = 4 and z = 2 (Note: the bars are absolute values)
(a) 10 – | x |
(b) | z | +19
(c) 2y - | x |
4) Simplify using exponents: a•a•a•b•a•b•b•a•b•a =
Translate into Algebraic Expressions, Equations or Inequalities
5) Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression
in simplest form that represents the total number of free throws made by both players.
6) The product of a number and -6.5 is -58.5. Write and solve an equation to find the number.
7) The quotient of a number and 6 is -14. Write and solve an equation to find the number.
8) What value of d makes the equation
1 4
= d true? (Solve the equation)
20 5
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 9) Solve each equation and graph the solution on the number line.
IV.
Geometry
Scale Drawings
1) Suppose a model of a dragonfly has a wing length of 4 cm. If the length of the insect’s actual
wing is 6 cm, what is the scale of the model?
2) Rebecca used a scale of 1 inch = 2 feet to construct a scale model of a kitchen. The kitchen
countertop in the model has a length of 8 inches. What is the actual length of the countertop?
Geometric Formulas: Circles, 3-D figures
1) A circular pool has a circumference of 40 meters. How long is the rope going across the pool?
2) Find the area of the circle:
3)
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Angles
4) In the figure, line a is parallel to b, and q and r are transversals. Classify the relationship
between the following angles:
(a) <2 and <3
(b) <13 and <15
V.
Statistics and Probability
1) Find the mean, median and mode of the set of data:
2) A bag contains 7 pink, 2 white, and 6 blue marbles. One marble is selected without looking.
Find P(blue). Describe if this is impossible, unlikely, equally likely, likely or certain.
3) What is the probability of tossing a penny and landing on heads three times in a row?
4) The spinner is spun twice. What is the probability that it will land on 8 after the first spin and
on an odd number after the second spin?
VI.
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department The Coordinate Plane
1) Write the ordered pair that names each point.
A=
B=
C=
D=
E=
F=
b) Which point(s) on the coordinate plane above are located in
a) Quadrant IV?
b) Quadrant II?
c) Quadrant I?
d) Quadrant III?
2) The table represents a relation.
a) Graph it.
b) Select the equation that represents the relation.
IF YOU ARE A COURSE 282 STUDENT,
YOU ARE DONE WITH YOUR SUMMER PACKET
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department SECTION B
•
•
I.
NON-CALCULATOR: M280 and M281 Students
Show all work to justify your answers.
Circle any problems that you don’t understand.
The Number System
Operations with Rational Numbers- Completely simplify each numerical expression.
1) 11[( 25 – 8.7 ) –14] =
2) -12.6 – 3.2 – ( -20.75) =
3)
Adding negative numbers
4) (-51.2) (1.06) (0.5) =
5)
6)
Division of fractions
7) 20 – (-1.34 +
1
)=
2
10)
8) 2 25 + 3 16 − π
5[2(8 – 5) + 1.5 – 2.5]
9) 12 + 68 •
11)
1
– 2 • 42 =
2
5(32 + 2) – 2(62 – 52)
Applications of Rational Numbers
1) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to
get to the same meeting. How many more miles did the business partner drive than Hector?
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 2) The gas tank of Ty’s truck holds 19.8 gallons. When the tank is empty, Ty fills it with gas that
costs $3.65 per gallon. How much will it cost to fill the tank?
3) To simulate space travel, NASA’s Lewis Research Center in Cleveland uses a 430-foot shaft. The
free fall of an object in the shaft takes 5 seconds to travel the 430 feet.
(a) Write an integer to represent the change in the height of the object.
(b) On average, how far does the object travel each second?
4) A scuba diver is 120 feet below the water’s surface. She then ascends 83 feet. What is her
current depth? Write an addition equation and then find the answer.
5) Monica reads 7
1
pages of a mystery book in 9 minutes. What is her average reading rate in
2
pages per minute?
6) Angela painted 3/8 of a room. Todd painted 2/5 of the same room. What part of the room has
been painted?
7) A high school Family and Consumer Science class has 12
taco shells. There are 3
1
cups of flour with which to make soft
2
3
cups flour per shell. How many soft taco shells can they make?
4
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Terminating and Repeating Decimals- Show that each decimal is a rational number by changing
it to a mixed number or fraction.
1) −12
1
3
4) 0.6666…
II.
2)
35
8
___
5) 1. 27
3) 2
5
6
6) 0.030303…..
Ratios and Proportional Reasoning: Discount/Tax/Tip
1) Isabella is shopping for clothes at a department store. Before tax, her bill is $95.
(a) She has a coupon to receive an additional 25% off her total purchase. What is the total cost of
her items before tax?
(b) After she receives the discount, how much will her total bill be if there is a 7.95% sales tax?
2) Marcus borrowed $4000 to buy a car. If his monthly payments are $184.17 for 2 years, what is
the simple interest rate for the loan?
3) The table shows the heart rates of different animals.
(a) What is the ratio of a cat’s mass to its heart rate? Express the
ratio as a fraction in simplest form.
(b) Order the animals from greatest mass to heart rate ratio to least
mass to heart rate ratio.
(c) Which animal had the greatest ratio? Explain your reasoning.
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 4) Determine whether the number of legs are proportional to the number of spiders. If the
relationship is proportional, identify the constant of proportionality. Explain your reasoning.
III.
Expressions and Equations
Properties
1) Name the property shown by each statement.
(a) 42 + 36 = 36 + 42
(b) 16 + 0 = 16
________________________________
________________________________________
(c) (19 • 15) • 2 = 19 • (15 • 2) _____________________________
(d) 33 • 0 = 0 _______________________________
(e) (7 + 9) + 6 = 7 + (9 + 6) ________________________________
(f) 25 • 1 = 25 ________________________________
2) Which expression can be written as 7(c + d)? Explain your reasoning.
A. 7c • 7d
B. (7 + c) • (7 + d)
C. 7c + 7d
D. (7 + c) + (7 + d)
distributive property
3) Admission to a science museum is d dollars and a ticket for the 3D movie is t dollars. Which
expression represents the total cost of admission and a movie for p people? Explain your
reasoning.
A. dtp
B. p(d + t)
C. p + (dt)
D. d(p + t)
Evaluate and Simplify Expressions
1) Evaluate each expression if x = -3, y = 4, and z = 2
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department (a) 10 – | x |
(b) | z | +19
(c) 2y - | x |
(d) 3y + 3z + | x |
(e) | 4yz | – 3 | x |
(f) 2(z + y) – | x |
Translate into Algebraic Expressions, Equations
1) Karen made 5 less than 4 times the number of free throws that Kimi made. Write an expression
in simplest form that represents the total number of free throws made by both players.
2) The quotient of a number and 6 is -14. Write and solve an equation to find the number.
3) April has saved $144 to buy a new car. If m is the monthly payment for one year, the
expression $12m + $144 represents the total cost of the car.
a) Find the monthly payment by using the most efficient method if the total cost of the car is
$5,088.
Geometry:
Scale Drawings
1) The blueprint of a skateboard ramp shows that its length is 11.4 inches. If the scale of the
blueprint is 1 inch = 6 feet, what is the length of the actual skateboard ramp?
Geometric Formulas
2) Find the area of the circle:
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 3) A ferris wheel has a circumference of 226 meters. What is the radius of the ferris wheel?
4) A hockey rink is shown below. If the shaded region is called the
neutral zone, find the area of the neutral zone.
Angles
5) In the figure, line a is parallel to b, and q and r are transversals.
Classify the relationship between the following angles:
(a) <2
<3
and
(b) <13 and <15
V.
Statistics and Probability
1) Find the mean, median and mode of the set of data.
2) A bag contains 7 pink, 2 white, and 6 blue marbles. One marble is selected without looking.
Find P(blue). Describe if this is impossible, unlikely, equally likely, likely or certain.
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 3) The average wait times for 10 different rides at an amusement park are 65, 21, 17, 52, 25, 17,
11, 22, 60, and 44 minutes. Would the park advertise the mean or median to show that the wait
time for its rides are short? Explain.
4) Each number on the dart board has an equal amount of the circle’s section.
If a dart is thrown, find each of the probabilities of it landing on each:
(a) P(odd)
(b) P(prime)
(c) P(greater than 20)
IF YOU ARE A COURSE 281 STUDENT,
SECTION C
•
•
YOU ARE DONE WITH YOUR SUMMER PACKET
NON-CALCULATOR: M280 Students
Show all work to justify your answers.
Circle any problems that you don’t understand.
Ratios and Proportional Reasoning
1) The line graph shows Alicia’s and Jermaine’s average rates in a race.
(a) Express each person’s speed as a unit rate.
(b) How long would it take Alicia and Jermaine each to run 1 mile?
(Hint: 1 mile = 5280 feet)
(c) Suppose Max runs at a rate of 5 feet per second. Predict where the line representing his speed
would be graphed. Explain.
2) A cell phone store displayed the phone at the right on a poster. The length of the
phone on the poster is 3 feet 4 inches. Write a ratio comparing the length of the
actual cell phone to the length of the cell phone on the poster as a fraction in simplest
form.
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 1
pounds of meat is $7.20. Find the constant of proportionality. Then write an
2
equation relating cost to pounds. How much will 4 pounds cost?
3) The cost for 2
4) The number of students on a school trip is proportional to the number of teachers as shown on
the graph.
(a) Find and interpret the constant of proportionality.
(b) Explain what the points (0, 0), (1, 25) and (4, 100) represent.
5) A bushel of apples will make approximately 3 gallons of apple cider.
The table shows the relationship between the number of bushels of
apples and the number of gallons of apple cider.
(a) Given b, the number of bushels needed, write an equation that can
be used to find g, the number of gallons of apple cider.
(b) How many bushels are needed to make 54 gallons of cider?
III.
Expressions and Equations
Properties
1) Insert grouping symbols in the expression so the value of the expression is 14. Show calculations
to obtain the 14.
9 + 39 + 22 ÷ 11 – 9 + 3
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Evaluate and Simplify Expressions
2) Evaluate each at the variable value given.
Translate into Algebraic Expressions, Equations or Inequalities
3) Dean made a collage on a square sheet of poster board. The perimeter of the collage is (20x +
12) centimeters. What is the length of one side of the collage?
4) Kurt and four friends are eating in the food court at South Center Mall. They will divide the bill
equally among the five of them. Two friends order hamburgers and two order pizza. All of them
order soda. Kurt has only $3.75 with him. What can Kurt order so that each will pay only $3.75?
V.
Statistics and Probability
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 1) The ages of the players on a volleyball team are 29, 25, 26, 31, 28, 23, 21, and 25. Suppose a
new player joins the team. What must the age be of the new player to have a mean age of 27?
Explain your reasoning.
2) A school committee consists of 4 girls and 6 boys. How many girls need to be added so that the
probability of selecting a girl at random is 70%?
SECTION D
•
•
I.
NON-CALCULATOR: M280 and M281 Students
Show all work to justify your answers.
Circle any problems that you don’t understand.
The Coordinate Plane
1) Write the ordered pair that names each point.
A=
B=
C=
D=
E=
F=
b) Which point(s) on the coordinate plane above are located in Quadrant IV?
2) Suppose Javier’s school represents the origin on a coordinate plane. If Javier leaves school and bikes four miles et
and then two miles south to the recreation center, what is the location of the recreation center as an ordered pair?
3) The table represents a relation. Graph it and select the equation that represents the relation
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department II. Equation Solving
Solve each equation and graph its solution on the number line provided.
1. x – 4 = -2
4.
x
= −3
7
2. x + 7 = -3
5. 2d – 3 = 9
3. 3x = 70
6. 4(x – 2) = -4
7) Which operation should be performed first to solve the equation 2x + 4 = 8?
8) What value of d makes the equation
1 4
= d true? (Solve the equation)
20 5
9) A shipping company charges $3.50 plus $0.85 per pound to ship a package. Janet shipped a package and the total
charge was $8.60. Write and solve an equation to find the number of pounds she was charged for the package.
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 10) Tisa bought movie tickets for herself and two of her friends. She paid $8.50 for each ticket. If Tisa has $14.50
left, write and solve an equation to find how much money she had before she bought the movie tickets.
11) Write a proportion, an equation, and solve the following: A muffin recipe calls for 4 cups of sugar and yields 36
muffins. If Amelia only wants to make 24 muffins, how much sugar she will need?
12) The enrollment at a community college this year is 115% of last year’s enrollment. If there were 1240 students
enrolled at the college last year, write and solve an equation to find how many students are enrolled this year.
III.
Rational and Irrational Numbers
1) Identify all sets to which the following number belongs:
Rational, Irrational, Whole, Integer
2) Which point on the number line shows
4.22
45 ?
3) Which of the following shows the rational numbers in order from least to greatest?
4) Which of the following show the fractions
2 3 1 1
5
in order from greatest to least?
, , , ,and
5 8 3 2
12
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 5) Which number belongs to the set of rational numbers and the set of integers?
6)
7)
8) Constance wants to sew trim around the sleeves and collar of a gymnastics leotard. She needs a piece of trim that
is 12.25 inched long for the sleeves and a piece that is 19¾ inches long for the collar. She buys a 4-foot piece of trim.
How much trim will she have left once she finishes the leotard?
4
5
2
5
−
9) Simplify the following quotient:
10) Hector drove 185 miles to a business meeting. His business partner drove 5/4 of this distance to get to the same
meeting. How many more miles did the business partner drive than Hector?
11) Last year there were 43 science projects submitted by students at a science fair. This year there are 52 science
projects. To the nearest tenth, what is the percent of change in the number of science projects submitted?
12) The table shows the prices of different sized jars of peanut butter. Which of the jars has the least unit price?
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department Exponents
1) Simplify the following expression using exponent notation: a•a•a•b•a•b•b•a•b•a
2) Simplify the following exponent problems:
a) 2x•3x3 =
b) -3a2• -4a3=
d) -2x2=
e) (-2x)2=
c) (3x2y)3=
f) 2-3 =
(simplify w/o neg exponent)
IV. Scientific Notation
1) The distance from Earth to the Sun is 92,900,000 miles. What is this number in scientific notation?
2) The table shows the area in square miles of certain states. Which state has the greatest area?
3) The distance from the Sun to Earth is about 1.5 x 1011 meters. Suppose light travels at a speed of 3 x 108 meters per
second. About how long does it take light from the Sun to reach Earth? Compute and give your answer in Scientific
Notation.
IV
Geometry
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 1) 2) Find the volume of a soup can that has a height of 6 inches and a diameter of 5 inches.
Use 3.1 for π.
V
Statistics and Probability
1) What is the probability of tossing a penny and landing on heads three times in a row?
2) The spinner is spun twice. What is the probability that it will land on 8 after the first spin and on an odd number
after the second spin?
VI Rate of Change
1) Amy earns $7 per hour for babysitting. Which of the following statements is true about the relationship between
the number of hours Amy works and her earnings?
Incoming Grade 8 Summer Work Packet: Academic Year 2014 - 2015
DMS Mathematics Department 2) What is the rate of change of the relation in the table below? Is it proportional?
IF YOU ARE A COURSE 280 or 281 STUDENT,
YOU ARE DONE WITH YOUR SUMMER PACKET