Unit 1: Algebraic Reasoning
Grade 7 Math Common Assessment
Find the value of
.
Order the numbers
to greatest.
Multiply
from least
Which expression does NOT simplify to 81?
a.
c.
b.
d.
Victor wants to display leaf specimens for a
science fair. Victor has 51 leaves, which is 30
fewer than the total needed. Will the science
display have a total of 21 leaves, 91 leaves, 82
leaves, or 81 leaves?
.
Simplify the expression 45 + 16  2  4 – 6.
Simplify the expression
.
In an online media store, downloaded songs cost
$3 each and books cost $9 each. Taji paid $7 in
sales tax when he purchased 15 songs and 3
books. Write and evaluate an expression to show
how much Taji spent on everything, including
sales tax.
Evaluate n + 13 for n = 24.
Evaluate 7y – 2 for y = 9.
Write the phrase as an algebraic expression.
the product of 3 and a number
Which problem situation best matches the
equation
?
a. The mechanic’s bill to repair Mr. Wong’s car
was $294. The mechanic charges $35 an hour
for labor, and the parts that were used cost
$469. How many hours did the mechanic
work on the car?
b. The mechanic’s bill to repair Mr. Wong’s car
was $294. The mechanic charges $469 an
hour for labor, and the parts that were used
cost $35. How many hours did the mechanic
work on the car?
c. The mechanic’s bill to repair Mr. Wong’s car
was $469. The mechanic charges $35 an hour
for labor, and the parts that were used cost
$294. How many hours did the mechanic
work on the car?
d. The mechanic’s bill to repair Mr. Wong’s car
was $469. The mechanic charges $294 an
hour for labor, and the parts that were used
cost $35. How many hours did the mechanic
work on the car?
It takes 78 days to create a custom motorcycle.
Write an algebraic expression to describe the
number of days it takes to create n custom
motorcycles. How many days will it take to
create 6 custom motorcycles?
Hector and Selma play baseball. Selma has 13
trophies. Hector has 5 more trophies than Selma
has. Write an equation showing this, using h as
the number of trophies Hector has.
a.
c.
b.
d.
Which operation should be performed first to
simplify the expression
?
Solve the equation
answer.
. Check your
Stephanie makes cocoa mix to sell at the winter fair.
She makes 230 cups of one flavor of cocoa mix and
180 cups of another flavor. To package the cocoa
mix, Stephanie needs to purchase containers that hold
2 cups each. The containers are sold in boxes of 50.
Which would be the correct order for Stephanie to do
the following steps to find the number of boxes of
containers she needs to buy?
Step R: Divide the total number of cups of cocoa mix
by 2.
Step S: Find the sum of the numbers of cups of the
two different types of cocoa mix.
Step T: Divide the number of containers needed by
50 to find the number of boxes of containers to buy.
a. R, S, T
b. S, R, T
c. T, R, S
d. R, T, S
Write the rules for adding integers.
Write the rules for subtracting integers.
Write the rules for multiplying integers.
Write the rules for dividing integers.
Write the rules for adding fractions.
Write the rules for subtracting fractions.
Solve the equation 9s = 36. Check your answer.
Write the rules for multiplying fractions.
Riding your bike is good exercise. If your goal is
to ride your bike a total of 140 laps around the
block over the next 20 days, how many laps
must you ride each day?
Segal’s father wants to install a new swimming
pool. It will cost $13 per square foot. If Segal
wants a 325 square foot swimming pool, how
much will it cost?
A square playground has an area of 81 ft2. What
is the approximate length of each side (square
root) of the playground? Round your answer to
the nearest foot.
Short Answer
Draw a model for 52.
Write the rules for dividing fractions.
Write the rules for adding decimals.
Write the rules for subtracting decimals.
Write the rules for multiplying decimals.
Write the rules for dividing decimals
Unit 2: Rational Numbers
Kristi had $7.00 when she went to the store.
When she got back, she had $2.39. How
much did she spend?
On one day, the temperature at dawn in
1
Chattanooga, Tennessee is 21 4 °C. During
2
the day, it warms up 6 7 °C. What is the new
temperature?
Write the decimal 1.71 as a mixed number
in simplest form.
Write
as a mixed number.
Write
as a decimal.
3
Write 2 4 as an improper fraction.
Divide. Express your answer in simplest
form.
3
13
÷ 14
10
1
One day, a plant is 3 6 cm tall. Three weeks
1
later, it is 3 5 cm tall. How much did the
plant grow in three weeks?
7
How many 8 -foot pieces of wood can you
Mr. Romito is a bus driver. He drove the
Maple Hills Senior Citizen Group on a 2day motor trip through upstate New York.
On the first day, he drove 433.4 miles. On
the second day, he drove 347.9 miles. How
many more miles did he drive the first day
than the second day?
Write the decimal 0.51 as a fraction in
simplest form.
1
cut from a board that is 6 8 feet long?
Multiply. Express your answer in simplest
form.
2
5
37 • 8
Compare the decimals 0.22 __?_ 0.79. Write
< or >.
Divide. Estimate to check whether your
answer is reasonable.
33.208  4
In 2001, bus fare on the Metropolitan Bus
3
Line was $2.88. In 1975, the fare was 8 the
fare in 2001. What was the fare in 1975?
Compare the fractions
. Write < or >.
During a review game, Mr. Pai’s class
correctly answered 68 questions on the first
try. If there were 73 questions in the game,
at what rate were questions answered
correctly on the first try? Express your
answer as a decimal. Round to the nearest
hundredth.
Write the fraction
as a decimal. If
necessary, round your answer to the nearest
hundredth.
The average yearly rainfall in Lakeview is
24.5 inches. What is the total amount of
rainfall in inches in Lakeview in 7.5 years?
Graph the integer –9 and its opposite on a
number line.
a
c
. –10 –8 –6 –4 –2 0 .2 4–10 6–8 8–6 10–4 –2
b
.
–10 –8
–6
–4
–2
0
d
.2
4–10 6–8 8–6 10–4
–2
0
2
4
6
8
10
0
2
4
6
8
10
Compare –4 _?__ 4. Write < or >.
2
Two boxes are stacked. One is 2 3 feet tall;
6
the other is 2 7 feet tall. How high is the
stack?
a. >
c. =
b. <
Use a number line to order the integers
3, –7, 7, –9, 6, and 0 from least to greatest.
Gridded Response
Adam is planing to buy a new electric piano
that costs $2,245.00. In addition to $254.80
he has in his savings account, Adam
receives $255.50 for work he has done for
his father’s business and $250.50 from his
grandparents. How much more money does
Adam need in order to buy the electric
piano?
Use a number line to find the sum 2 + 3.
+3
2
–8
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
4
5
6
7
8
4
5
6
7
8
11.
Use a number line to find the
difference 6 – 9.
–9
Unit 3: Integers
Grade 7 Math Common Assessment
6
–8
Which list of numbers is in order from
greatest to least?
a.
c.
b.
d.
Which integer will meet the condition for x
in the diagram below?
a.
b. 7
c.
d.
5.
Find the absolute value. |6|
6.
Find the absolute value. |–7|
–7
–6
–5
–4
–3
–2
–1
0
1
2
3
Find the product 3(–5).
The four best scores from an amateur golf
tournament sponsored by a local golf club
are given in the table. Since the lowest score
wins, which golfer won the tournament?
Player
Score
Mr. Benitez
2
Mr. Hill
–3
Mr. Williams
–8
Mr. Hayashi
8
a. Mr. Hayashi
b. Mr. Benitez
c. Mr. Hill
d. Mr. Williams
Solve the equation
= –9. Check your
answer.
The table shows the change in four
companies’ stock prices at the end of a day’s
trading. Which company’s stock lost the
most?
Company
Change in Price
King
–5
Farley
1
Allendale
5
Tellers
–3
a. Farley
b. Tellers
This year, a construction company had
expenses of $500 million, which was $75
million more than the expenses from last
year. How much were last year’s expenses?
The model represents the equation x
8 = 2.
c. King
d. Allendale
Find the sum –37 + (–25).
Evaluate
for
–46 and
34.
The income from the Spanish Club’s bake
sale was $240. Expenses for the sale totaled
$40. Use integer addition to find the total
profit or loss from the bake sale.
Find the difference 10
What is the value of x?
The diagram below shows a scale and an
equation
(–25).
Find the product 6 • (–9).
Find the quotient –65
(–5).
A submarine started at the surface of the
water and was moving down at –15
kilometers per minute toward the ocean
floor. The submarine traveled at this rate for
48 minutes before coming to rest on the
ocean floor. What is the depth of the ocean
floor?
Solve the equation h – (–22) = 11. Check
your answer.
Which of the following is a way to find the
value of a?
a. Remove 1 from
c. Remove 1 from
each pan on the
eahc pan on the
scale. then divide
scale. Then
by 2.
multiply by 2.
b. Add 1 to each pan d. Add 1 to each pan
on the scale. then
on the scale. Then
divide by 2.
multiply by 2.
Ramón borrowed $88 from his sister Lydia
to buy a new bike. So far he has paid her
$18, $34, and $25. How much does he still
owe her? Show your work.
Which description shows the relationship
between a term and n, its position in the
sequence?
Unit 5
An athlete on the school football team can
run 20 yards in 2.9 seconds. During the last
foodball game, the athlete ran 64 yards for a
touchdown. If the athlete’s rate of speed
remained the same, about how long did it
take him to run for the touchdown?
Solve the proportion
a.
b.
Multiply n by
Subtract
from n
c.
d.
Add
to n
Divide n by
Which sequence follows the rule 8n 4,
where n represents the position of a term in
the sequence?
.
The Anderson family is preparing for a
family reunion. They think they will need 12
juice boxes for every 4 children who attend.
How many juice boxes will they need if they
are expecting 18 children?
Convert 512 oz to pounds.
a. 16, 12, 8, 4, 0,...
b. 8, 16, 24, 32,
40,...
c. 4, 16, 64, 216,
1,024,...
d. 4, 12, 20, 28, 36,...
Which rule can be used to find the value of
any term in the sequence below where n
represents the position of the term?
Convert 192 in. to feet.
Gary mailed a box that weighed 2 pounds 8
ounces. The postage cost $15.60. How much
was the postage in cents per ounce?
Cindy bought 3 pounds of candy for $2.16.
At this rate, how much would the candy
have cost if she had bought only 2 pounds?
A recipe that makes 18 cookies calls for
cup of sugar. How much sugar is needed to
make 2 dozen cookies using this recipe?
A model airplane is built to a scale of 1
in.:12 ft. If the model plane is 11 inches
long, find the length of the actual plane.
Lisa and Susan are driving to college
together. They look at a map to find out how
far they have to drive. On the map, Lisa
measures the distance to be 3.5 inches. How
many miles do they have to drive if the map
scale is 1 in. = 50 mi?
Emmanuel can run 100 meters in 20
seconds. If he competes in the 400-meter
race, about how many seconds will it take
him to run the race?