Module A
Grade 8 M/J Pre-Algebra
Rational Numbers & Percents
MA.7.A.1.1 Proportion Problems (high)
Example: The Key Club purchased 85 posters for $323.00. At this rate, how much would 110 posters
cost?
85
$323
110
x
x= $418.00
Answer: The 110 posters will cost $418.00.
1.
The Math Club purchases 85 posters for $323.00. At this rate, how much would 110 posters cost?
2. A test of a hybrid vehicle resulted in 4,400 miles driven using 88 gallons of gas. Find how many gallons of gas this
vehicle will need to travel 1,150 miles?
3. In the recent year, the population of Delaware was 783,600. Its land area is 1,953 square miles. North Carolina’s
population that year was 8,049,313. Its land area is 48,710 square miles. Which state had a greater number of
people per square mile? By how much? Round to the nearest whole number.
MA.7.A.3.1 Operations on Integers(moderate)
Example: With the drain open, a pool loses water at a rate of 8 gallons per minute. At that rate, how
long will it take to drain 486 gallons of water?
486gal
8gal / min
1.
60.75 The pool will take 60.75 minutes to drain.
A stock cost $46 on Wednesday. The price changed -$3 on Thursday and +$5 on Friday. What was the stock
worth at the end of the day on Friday?
2. With the drain open, a pool loses water at a rate of 8 gallons per minute. At that rate, how long will it take to
drain 486 gallons of water?
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MA.8.A.6.4 Operations on Real Numbers (high)
Example: The Banners need to borrow $100,000 to purchase a home. The Credit Union is offering a 30year mortgage loan at 4.25%. Assuming simple interest, what is total simple interest? I=prt
I=100,000(.0425)(30)
I=$127,500
Example: The cost of an electronic device was reduced from $499 to $399. What was the percent of
decrease?
100
499
499 – 399= 100
200%
1. A plumber has a pipe that is 64
an additional 1
2.
7
5
inches long. The plumber cuts 2 inches off the end of the pipe, then cuts off
8
8
3
inches. How long is the remaining pipe?
8
At Coast Line High School, about
3
of the students are in the band, 0.31 play at least one sport, and 13% are in
16
the drama club.
a.
Write
3
and 0.31 as a percent.
16
b. Of the three activities, which type is most popular among the students at Cost Line High School? How do you
know? Explain and justify your answer.
3.
The Waters need to borrow $100,000 to purchase a home. The credit union is offering a 30-year mortgage loan at
5.25% while the community bank has a 25-year mortgage loan at 6.125% interest. Assuming simple interest, which
loan will result in less total interest? How much less?
3
3
inches long for storing CDs. Each CD is inch wide. How many CDs will fit on one shelf, if
4
8
7
the shelf is extended 1 inches?
8
4. Madison has a shelf 7
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5. In 2009, the average purchase price of a new compact automobile was $19,000. One year later the compact
automobile that was purchased new in 2009 typically was worth $12,500. By what percent did the automobile
depreciate during the first year of ownership?
6. A soup recipe calls for 5
1
1
ounces of tomato juice per serving. You have 45 ounces of tomato juice. How
2
10
many servings of soup can you make?
7. A carpenter estimates that it will take one person 54 hours to complete a job. He plans to have three people work
on the job for two days. How many hours each day will the workers need to work to complete the job?
8. Jackie and Jillian had lunch together. Their check came to $36. They also gave the server $7.20 for a tip. What
percent of the check is the tip?
9. Myra is baking chocolate cupcakes. Each batch of 20 cupcakes requires
1
3
cup of cocoa. If Myra has 3 cups of
4
4
cocoa, how many full batches of cupcakes will she be able to make and how much cocoa will she have left over?
10. About 17% of kids will attend an overnight scout camp,
11
will attend a day camp, and 0.58 will attend no
50
summer camp at all. Which group of kids is the greatest? How do you know?
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Module B
Grade 8 M/J Pre-Algebra
Expressions and Functions
MA.8.A.1.1 (high)
Example:
Melvin belongs to a music club that charges a monthly fee of $6, plus $0.05 per song that he
downloads. Write a function to represent the amount money M(s) he would pay in one month
to download s songs. What is the cost if he downloads 35 songs?
Y= 0.50x + 6
y=0.50(35) + 6
y=$23.50
It will cost $23.50 to down load 35 songs.
1. After 1 hour, a cyclist had ridden 12 miles. If she then continued riding at an average rate of 8 miles per
hour, how long did it take her to ride 60 miles?
2. Donald belongs to a music club that charges a monthly fee of $6, plus $0.50 per song that he downloads.
Write a function to represent the amount of money M(s) he would pay in one month to download s
songs. What is the cost if he downloads 35 songs?
3. Arthur is saving money to buy a new computer for $1100. He already had $350 and plans to save $30 a
week. Write a function that represents the amount Arthur has saved after x weeks. Graph the function
to determine the number of weeks it will take Arthur to save enough money to buy the computer.
MA.8.A.1.2(moderate)
Example: A cake recipe requires 3 cups of flour for 15 servings. How much flour is required to
make a cake that serves 32?
3cups
15servings
xcups
32servings
96 = 15x
6.4 = x The cake recipe would require 6.4 cups of flour for 32 servings.
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1. Wheelchair ramps for access to public buildings are allowed a maximum of one inch of vertical increase
for every one foot of horizontal distance. Would a ramp that is 10 feet long and 8 inches tall meet this
guideline? Explain your reasoning.
2. For working 3 hours, Martha earns $30.60. For working 5 hours, she earns $51. For working 6 hours, she
earns $61.20. What is the slope of the line?
What does the slope of the line represent?
3. A cake recipe requires 2
1
2
cups of flour for 15 servings. How much flour is required to make a cake
that serves 32?
4.
The number of centimeters in a measure varies directly with the number of inches. Find the measure of
an object in centimeters if it is 50 inches long.
Inches, x
6
9
12
15
Centimeters, y
15.24
22.86
30.48
38.10
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Module C
Grade 8 M/J Pre-Algebra
Linear Functions and Systems of Equations
MA.8.A.1.3(High)
Example:
A company has motorcycles(two wheels) and ATVs(four wheels) in stock. The store has a total of 35
vehicles, that together, have 120 wheels.
Write a system of equations that represents the situation.
Solve the system of equations. Interpret the solution.
4 x 2(35 x ) 120
X + y = 35
4x + 2y = 120
4x 70 2x 120
2x 50
x 25
There are 25 ATVs(four wheels) and 10 motorcycles(two wheels).
1.
Northeast Florida Motorsports has motorcycles(two wheels) and ATVs(four wheels) in stock. The store has a total
of 35 vehicles, that, together, have 120 wheels.
Write a system of equations that represents the situation.
Solve the system of equations. Interpret the solution.
2. Image Crafts gives scrapbooking lessons x for $15 per hour plus a $12 supply charge. Scrapbooks Hobby gives
lessons for $20 per hour with no additional charges. Write and solve a system of equations to find the total cost y
for each craft store. Interpret the solution.
3. Ms. Virginia is having the basketball team’s names put on the back of their jerseys. Super Letters Company
charges $70 plus $4 per jersey. Average Letter Company charges a flat rate of $130.
a. There are 15 players on the basketball team. Which company offers the better deal?
b. For what number of jerseys is the cost the same for both companies?
c. Does the company you chose for part a always offer a better deal? Explain
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MA.8.A.1.5(moderate)
Example:
1. Exam The table below shows how much Martha pays to rent DVDs.
Number
of DVDs
Cost ($)
2
5
4
10
6
15
8
20
Write an expression that can be used to find the total cost of renting any number of DVDs.
Answer:
5
n
2
2. The table below shows how much Martha pays to rent DVDs.
Number
of DVDs
Cost ($)
2
5
4
10
6
15
8
20
Write an expression that can be used to find the total cost of renting any number of DVDs.
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Module C
Grade 8 M/J Pre-Algebra
Linear Functions and Systems of Equations
3. The cost to rent a jet ski from a marina is $25 plus $5 per hour.
a. Write an expression to find the total cost for any number of hours.
b. Copy and complete the table to show how much it will cost for 2,3,4, or 5 hours.
Hours
Total Cost ($)
4.
2
?
3
?
4
?
5
?
Write an expression that can be used to find the nth term of the sequence shown.
Position
1
3
5
Term
8
14
7
20
26
MA.8.A.1.6(moderate)
1. Judy has $300 in a safe. Each month, she adds another $12 to the safe Miguel opens a savings account with a
$250 deposit and earn 10% interest each month on the total amount of money in the bank.
a. Make a table showing the money they have each saved after 7 months.
b. Graph each person’s savings on the same coordinate plane.
c. Explain why one function is linear and other is not.
2. The table shows the measures of the sides of several rectangles. Are the widths of the rectangles a linear function
of the lengths? Explain.
Length(in.)
1
4
8
10
Width(in.)
3.
64
16
8
6.4
Tickets to the school dance cost $6 per student. Are the ticket sales a linear function of the number of tickets
sold? Explain.
Number of
1
2
3
4
tickets sold
Tickets Sales
$6
$12
$18
$24
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Module D
Grade 8 M/J Pre-Algebra
Equations and Inequalities
MA.8.A.4.2(moderate)
Example:
Hippos weight up to 5,300 pounds. Write and solve an equality that described how much weight a
young hippo is likely to gain if its current weight is 2,200 pounds.
2,200 x
5,300
x
3100
The young Hippos is likely to gain 3,100 pounds to reach a weight of 5,300.
1. An F1 tornado has wind speeds that are at least 73 miles per hour. An F2 tornado has wind speeds that are at least
113 miles per hour. Write and solve an inequality to determine how much the winds of an F1 tornado need to
increase to become at least an F2 tornado.
2. Hippos weight up to 5,300 pounds. Write and solve an equality that describes how much weight a young hippo is
likely to gain if its current weight is 2,200 pounds.
3. Mya has $95 to go clothes shopping. She spent $30 on a new shirt. Write an inequality that represents how much
money she has left to spend on clothes.
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4. Nathan saved $355 from his pay and joined a golf club. He paid a $150 membership fee and also pays $15 for each
round of golf he plays.
Nathan used the following inequality to determine the number of round of golf he could play.
150 + 15 r < 355
What is the maximum number of rounds of golf Nathan can play?
A gym charges $5 each time you go, or you can buy a yearly membership for $190. Write and solve an inequality
to find how many time a person should use the gym so that a yearly membership is less expensive than paying
each time. Interpret the solution.
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Module E
Grade 8 M/J Pre-Algebra
Operations on Real Numbers
MA.8.A.6.1
6
Example: The average width of a strand of a spider web is 7.0 x 10 meters. What is the length
expressed in standard notation?
The average length of a spider web is 0.000007.
1.
The average width of a strand of a spider web is 7.0 x 10 6 meter. What is the length expressed in standard
notation?
2. Arrange these numbers in increasing order.
a. 216,000,000, 2.2 x 103 , 3.1 x 107 , 310,000
b. -4.56 x 10 3 , 4.56 x 102 , -4.56 x 102 , 4.56 x 10
3.
A high school basketball court has an area of 2
court?
3
2
3 5 2 7 square feet. What is the area of a high school basketball
4. In one week, a small library checked out 2.3 x 104 books. This is
1
4
the total number of books in the library. How
many books does the library have all together?
MA.8.A.6.2
1.
In Little League, the bases are squares with sides of 14 inches the expression
(s 2
s 2 ) represents the distance
across a square of side length s. Estimate the distance across a base to the nearest inch.
2. Mark is buying the grass seed advertised below. Estimate the side length of the largest square Mark could see if he
purchases 5 bags.
Grass Seeds
2 pounds
Covers 1,000 sq. ft
3. How much greater is the perimeter of a square with area 250 square meters than a square with area 125 square
meters?
4. In the sequence 4, 12, _, 108, 324, the missing number can be found by simplifying ab
Where a and b are the numbers on either side of the missing number. Find the missing number.
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MA.8.6.4
Example:
A quilter made 256 small squares for a large quilt. If the quilt is shaped like a square, how many small
squares will she use on each side?
The quilter should use 16 small squares on each side, since the quilt is shaped like a square.
1. A quilter made 256 small squares for a large quilt. If the quilt is shaped like a square, how many small squares will
she use on each side?
2. The area of a square vegetable garden is 360 square meters. To the nearest hundredth meter, what is the
perimeter of the garden?
3. What is the length of a side of a square whose area is 225 m 2 ?
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