Download 6th Grade Math Benchmark

Name: ________________________ Class: ___________________ Date: __________
ID: A
6th Grade Math Benchmark
Multiple Choice
Identify the choice that best completes the statement or answers the question.
____
1. CC6.RP.1
Use the table to write the ratio of soccer balls to the total number of balls in the store.
Type of Ball
Number of Balls
Baseballs
61
Softballs
10
Footballs
80
Soccer balls
33
a.
b.
____
184:33
184:80
c.
d.
33:80
33:184
2. CC6.G.2
Which is the volume a rectangular prism that has a length
a.
cubic feet
b.
cubic feet
c.
cubic feet
d.
cubic feet
feet, width
feet, and height
feet?
____
3. CC6.NS.5
The highest temperature recorded in the town of Westgate this summer was 100°F. Last winter, the lowest
temperature recorded was –1°F. Find the difference between these extremes.
a. –101°F
c. –99°F
b. 101°F
d. 99°F
____
4. CC6.N6.1
3
7
How many 8 -foot pieces of wood can you cut from a board that is 1 8 feet long?
a.
45
64
b.
3 pieces of wood
pieces of wood
c.
1
5
d.
5 pieces of wood
1
pieces of wood
Name: ________________________
ID: A
____
5. CC6.RP.1
A recipe calls for 1 batch of cookies calls for 2/3 of a cup of cooking oil. How many cups of cooking oil
would be required for 4 batches of cookies
a. 1/6
c. 2 2/3
b. 2
d. 4 2/3
____
6. CC6.RP.3
Manuel just bought a new television for $629.00. He made a down payment of $57.00 and will pay monthly
payments of $26.00 until it is paid off. How many months will Manuel be paying? (Assume that Manuel pays
no interest.)
a. 21 months
c. 27 months
b. 22 months
d. 25 months
____
7. CC6.EE.8
Write an inequality for the situation.
There are at least 38 women in the house.
a. number of women  38
b. number of women  38
c.
d.
number of women  38
number of women  38
____
8. CC6.EE.6
A bag of hot dog buns contains 8 buns, and a package of hot dogs contains 10 hot dogs. How many packages
of each are needed so that each of the 40 campers has hot dogs and buns with none left over?
a. 5 bags of buns, 4 packages of hot dogs
c. 2 bags of buns, 2 packages of hot dogs
b. 8 bags of buns, 10 packages of hot dogs d. 4 bags of buns, 5 packages of hot dogs
____
9. Chase got 80% of the questions on a test correct. If
there were 20 problems on the test, how many
problems did Chase miss?
a.
b.
4
12
c.
d.
8
16
____ 10. CC6.RP.3d
1
1
cans of chicken broth to make soup. Each can contained 7 ounces of broth. What was the
2
2
total number of ounces of chicken broth that Amy used?
Amy used 2
a.
b.
10 ounces
1
14 ounces
4
c.
d.
2
18 ounces
3
18 ounces
4
Name: ________________________
ID: A
____ 11. CC5.NF.6
Look at the expression below.
Which expression has a value of 24?
a.
6+2x3
b.
2x3+6x2
c.
4 (2 + 4)
d.
3 (7 + 3)
____ 12. Fencing is sold for $1.00 per foot at the garden store. Shawn needs 24 feet of fence for his dog’s yard. How
much will the fence cost?
a. $9.00
c. $25.50
b. $24.00
d. $36.00
____ 13. CC6.NS.2
Benjamin paid a total of $36.12 for12 goldfish. How much did each gold fish cost?
a.
$10.66
b.
$3.01
c.
$2.16
d.
$14.92
____ 14. CC6.NS.3
Boxes that are 12 inches tall are being stacked next to boxes that are 18 inches tall. What is the shortest
height at which the two stacks will be the same height?
a.
b.
72 inches
12 inches
c.
d.
36 inches
18 inches
____ 15. CC5.NS.4
In some juice drinks, only a portion is made up of real fruit juice. A juice carton advertises that it is 78% real
fruit juice. Express 78% as a fraction in simplest form.
39
50
a. 50
c. 39
b.
0.78
d.
3
39
100
Name: ________________________
ID: A
____ 16. CC6.RP.3c
An architect constructs a model of a building that will be 120 feet tall. If every 2 inches on the model
represents 5 feet on the building, which proportion will determine how tall the architect’s model will be?
a.
b.
5
2

120 x
x
2

120 5
c.
d.
5
2

x 120
2 120

5
x
____ 17. CC6.RP6.RPd
What are the coordinates of point R?
a.
b.
(3,5)
(3,5)
c.
d.
(5,3)
(5,3)
____ 18. On the stock market, four companies had stock price changes of 8 , 0.25,  8 , and 1.5 points. List these
5
numbers in order from least to greatest.
5
1
a. 8 , 0.25,  8 , 1.5
b.
0.25,  8 , 8 , 1.5
1
5
____ 19. CC6.NS.6c
Treya practices typing
a.
b.
1
8
c.
1.5, 8 ,  8 , 0.25
d.
 8 , 0.25, 8 , 1.5
5
1
hour each day. How many hours does Treya practice typing in 3 days?
7
8
2 hours
1
8
3 hours
5b
b5
1
5
c.
1
24
d.
3
8
c.
d.
b 5
b6
hour
hour
____ 20. Write (b)(b)(b)(b)(b) in exponential form.
a.
b.
1
4
Name: ________________________
ID: A
____ 21. CC6.EE.1
Evaluate the expression for the given value of the variable.
8y + 4 for y = 7
a. 91
c. 7y + 4
b. 19
d. 60
____ 22. CC6.EE.2
The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell x
muffins at $0.35 apiece and y bags of carrot sticks at $0.15 apiece, the total number of dollars raised will be
T  0.35x  0.15y . How many dollars will they raise if they sell 210 muffins and 120 bags of carrot sticks?
a. $73.50
c. T  210x  120y dollars
b. $330.50
d. $91.50
____ 23. CC6.EE.2c
If x = 3 and y = 5, what does 3(4y – 2x) equal?
a.
b.
17
42
____ 24. Solve 5h + 15 – 3h = 32. Check your answer.
a. h = 16
b.
1
h = 23 2
c.
d.
66
78
c.
h = 82
d.
h = 28
1
1
____ 25. CC6.EE.4
Erin spent $15.30 on ingredients for cookies she’s making for the school bake sale. How many cookies must
she sell at $0.35 apiece to make a profit?
a. At least 44 cookies
c. At most 5 cookies
b. At least 6 cookies
d. At most 41 cookies
____ 26. A snail is trying to get to the other side of a park. At what rate is the snail traveling?
a.
b.
1
foot per minute
2
1 foot per minute
c.
d.
5
1
feet per minute
2
2 feet per minute
1
Name: ________________________
ID: A
____ 27. Derek wants to survey students at his middle school. He plans to conduct his survey during each lunch
period. Which of the following questions is most likely to be an appropriate question for his sample?
a.
Which candidate for state school
superintendent do you support?
c.
Why do boys play more sports than girls
do?
b.
Which is your least favorite item served
in the lunch room?
d.
Do you like to go to the dentist?
____ 28. A study was conducted to determine the effectiveness of a speed limit sign. The speeds of cars at the 65 mph
sign were:
60 70 65 70 85 74 58 71 88 65
Which box-and-whisker plot correctly displays the information?
a.
c.
b.
d.
____ 29. A shipping company fills cartons with boxes that are cubes. They pack 65 boxes of goods in a case. What are
the possible dimensions for the case?
a. 1  1  5
c. 1  1  13 and 1  5  325
b. 1  1  13 and 1  5 5
d. 1  1  65 and 1  5  13
Short Answer
30. Yuan’s class has collected 143 cans in a food drive. The class plans to sort the cans into n bags, with an equal
number of cans in each bag. Write an expression to show how many cans will be in each bag.
6
ID: A
6th Grade Math Benchmark
Answer Section
MULTIPLE CHOICE
1. ANS: D
soccer balls to the total number of balls in the store
33:184
Feedback
A
B
C
D
Check the order of the ratio.
Check the type of the ball.
The ratio should compare a part to the whole, not a part to a part.
Correct!
PTS: 1
DIF: Average
REF: Page 352
OBJ: 7-1.1 Writing Ratios
NAT: 8.1.4.b
STA: M6A1
TOP: 7-1 Ratios and Rates
KEY: ratio
2. ANS: C
PTS: 1
STA: M5M3.d. |
3. ANS: B
Subtract the lowest temperature from the highest temperature.
Feedback
A
B
C
D
Subtract the lowest temperature from the highest temperature.
Correct!
Check the signs.
Check the signs.
PTS: 1
DIF: Average
REF: Page 89
OBJ: 2-3.4 Application
NAT: 8.1.3.g
TOP: 2-3 Subtracting Integers
KEY: integers | subtraction
4. ANS: D
Write any mixed numbers as improper fractions. Then, multiply by the reciprocal. If necessary, simplify.
7
3
15
8
1 8  8 = 8  3 = 55
You can cut 5 pieces of wood.
Feedback
A
B
C
D
Perform the correct operation.
Divide the length of the board by the length of the piece of wood.
Dividing by a fraction is equivalent to multiplying by its reciprocal.
Correct!
PTS: 1
DIF: Average
REF: Page 201
OBJ: 3-11.3 Application
NAT: 8.1.3.g
TOP: 3-11 Dividing Fractions and Mixed Numbers
KEY: division | fraction | mixed number
1
ID: A
5. ANS: C
To subtract an integer, add its opposite.
Feedback
A
B
C
D
Correct!
Add the opposite of the second number.
To subtract an integer, add its opposite.
To subtract an integer, add its opposite.
PTS: 1
DIF: Average
REF: Page 89
OBJ: 2-3.2 Subtracting Integers by Adding the Opposite
NAT: 8.1.3.a
TOP: 2-3 Subtracting Integers
KEY: integers | subtraction
6. ANS: B
Set up an equation.
total price = down payment + monthly payment • number of payments
Solve the equation for the number of payments.
Feedback
A
B
C
D
Use inverse operations to solve.
Correct!
Set up an equation and solve.
Set up an equation and solve.
PTS: 1
DIF: Average
REF: Page 679
OBJ: 12-1.3 Application
NAT: 8.5.4.c
TOP: 12-1 Solving Two-Step Equations
KEY: addition | division | multiplication | solving | subtraction | two-step equations
7. ANS: D
Symbol
Meaning
Word Phrases
less than
Fewer than, below

>
greater than
More than, above
less than or equal to
At most, no more than

greater than or equal to
At least, no less than

Feedback
A
B
C
D
Look for keywords in the situation.
Look for keywords in the situation.
Look for keywords in the situation.
Correct!
PTS: 1
NAT: 8.5.4.c
DIF: Basic
REF: Page 692
TOP: 12-4 Inequalities
2
OBJ: 12-4.1 Writing Inequalities
KEY: inequality
ID: A
8. ANS: A
Find the least common multiple of the number of buns and the number of hot dogs. The LCM is the smallest
multiple of each that divides evenly into the number of campers.
Feedback
Correct!
Find the least common multiple of the number of buns and the number of hot dogs.
Use a model to find the LCM.
You have reversed the numbers.
A
B
C
D
9.
10.
11.
12.
13.
14.
15.
PTS: 1
DIF: Average
REF: Page 228
OBJ: 5-1.1 Application
NAT: 8.1.5.b
STA: M6N1.c
TOP: 5-1 Least Common Multiple
KEY: LCM | least common multiple
ANS: A
PTS: 1
ANS: D
PTS: 1
STA: M6N1. e. Multiply and divide fractions and mixed numbers.
ANS: C
PTS: 1
STA: M5N2.a. |
ANS: B
PTS: 1
ANS: B
PTS: 1
STA: M5N3.c. |
ANS: C
PTS: 1
STA: M6N1. c. Determine the greatest common factor (GCF) and the least common multiple (LCM) for a
set of numbers.
ANS: A
78%
78
= 100
Write the percent as a fraction with a denominator of 100.
=
39
50
Write the fraction in simplest form.
Feedback
A
B
C
D
Correct!
The answer should be a fraction, not a decimal.
First, write the percent as a fraction with a denominator of 100. Then, write the fraction
in simplest form.
First, write the percent as a fraction with a denominator of 100. Then, write the fraction
in simplest form.
PTS:
NAT:
16. ANS:
17. ANS:
1
8.1.1.e
C
A
DIF:
STA:
PTS:
PTS:
Average
M6N1.g
1
1
REF:
TOP:
STA:
STA:
3
Page 382
OBJ: 7-7.3 Application
7-7 Percents KEY: percent | fraction
M6G1. d. Interpret and sketch simple scale drawings.
M7A3. a. Plot points on a coordinate plane.
ID: A
18. ANS: B
Rewrite each fraction as a decimal to compare.
5
 0.625
8
 8  0.125
1
The correct order is 0.25  0.125  0.625  1.5.
So, in order from least to greatest:
1 5
0.25,  8 , 8 , 1.5
Or locate the numbers on a number line and read them from left to right.
Feedback
A
B
C
D
The negative numbers are less than the positive numbers. Write the fractions as
decimals to compare.
Correct!
Order the numbers from least to greatest, not greatest to least.
Write the fractions as decimals to compare.
PTS: 1
NAT: 8.1.1.i
19. ANS: D
Multiply.
1
1 3
3
(3)  8  8
8
DIF: Average
REF: Page 69
OBJ: 2-2.3 Application
TOP: 2-2 Comparing and Ordering Rational Numbers
Treya practices typing
3
8
hour in 3 days.
Feedback
A
B
C
D
When multiplying a fraction by a whole number, multiply the whole number by just the
numerator and keep the same denominator.
Multiply to put equal parts together.
Multiply the fraction and the whole number.
Correct!
PTS: 1
NAT: 8.1.3.g
DIF: Average
REF: Page 77
TOP: 2-4 Multiplying Rational Numbers
4
OBJ: 2-4.4 Application
ID: A
20. ANS: B
Identify how many times (b) is a factor.
(b)(b)(b)(b)(b) = b 5
Feedback
A
B
C
D
Check that you are not using the base as the exponent.
Correct!
Check the sign on the exponent.
The exponent tells the number of times the base is used as a factor.
PTS: 1
DIF: Basic
REF: Page 162
NAT: 8.5.3.c
TOP: 4-1 Exponents
21. ANS: D
Example:
Evaluate 10n – 5 for n = 2.
10(2) – 5
20 – 5
15
OBJ: 4-1.1 Writing Exponents
KEY: exponent | write
Substitute 2 for n.
Multiply.
Subtract.
Feedback
A
B
C
D
Did you multiply? Remember that the variable does not represent the ones place of a
greater number.
Did you add instead of multiplying?
Did you replace the variable with the number given and then multiply?
Correct!
PTS: 1
DIF: Basic
REF: Page 6
OBJ: 1-1.1 Evaluating Algebraic Expressions with One Variable
NAT: 8.5.2.a
TOP: 1-1 Variables and Expressions
KEY: algebraic expression | variable
5
ID: A
22. ANS: D
Example:
The students in the astronomy club are selling snacks to raise money for a planetarium field trip. If they sell y
muffins at 20 cents apiece and z bags of carrot sticks at 15 cents apiece, the total number of dollars raised will
be T  0.20y .015z. How many dollars will they raise if they sell 100 muffins and 230 bags of carrot sticks?
T  0.20y  0.15z
T  (0.20  100)  (0.15  230)
T  20.00  34.50
T  54.50
They will raise $54.50.
Substitute 100 for y and 230 for z.
Multiply.
Add.
Feedback
A
B
C
D
Did you substitute the correct value for each variable?
Did you add instead of multiplying?
Did you replace the variables with the numbers given and then multiply?
Correct!
PTS: 1
DIF: Basic
REF: Page 7
OBJ: 1-1.3 Application
NAT: 8.5.3.c
TOP: 1-1 Variables and Expressions
KEY: algebraic expression | variable
23. ANS: B
PTS: 1
STA: M7A1. b. Simplify and evaluate algebraic expressions, using commutative, associative, and
distributive properties as appropriate.
24. ANS: C
To solve this equation, combine like terms and then follow the order of operations in reverse. First, add or
subtract to isolate the term with the variable. Then, divide to isolate the variable.
Feedback
A
B
C
D
First, combine like terms. Then, add or subtract to isolate the term with the variable.
Finally, divide to isolate the variable.
Use inverse operations to solve.
Correct!
Combine like terms first.
PTS:
OBJ:
TOP:
KEY:
1
DIF: Average
REF: Page 682
12-2.1 Combing Like Terms to Solve Equations
NAT: 8.5.4.a
12-2 Solving Multi-Step Equations
addition | combine | division | like terms | multiplication | solving | subtraction | multi-step equations
6
ID: A
25. ANS: A
This problem can be translated into an inequality as follows. Since the cookies must be sold whole, the
number must be rounded up to the nearest whole cookie.
price per cookie • number sold >initial cost
Feedback
A
B
C
D
26.
27.
28.
29.
Correct!
Did you forget to combine the like terms?
Is your inequality set up correctly?
Did you round the amount sold correctly, since she cannot sell a fraction of a cookie?
PTS: 1
DIF: Average
REF: Page 605
OBJ: 11-5.3 Application
NAT: 8.5.4.a
TOP: 11-5 Solving Two-Step Inequalities
KEY: multi-step inequality | solving
ANS: C
PTS: 1
STA: M6A2. e. Graph proportional relationships in the form y = kx and describe characteristics of the
graphs.
ANS: B
PTS: 1
STA: M7D1. a. Formulate questions and collect data from a census of at least 30 objects and from samples
of varying sizes.
ANS: A
PTS: 1
STA: M7D1. f. Analyze data using appropriate graphs, including pictographs, histograms, bar graphs, line
graphs, circle graphs, and line plots introduced earlier, and using box and- whisker plots and scatter plots.
ANS: D
The possible dimensions are combinations of 3 factors of the number of boxes. The product of the three
factors, which is also the volume, is equal to the number of boxes that need to be shipped.
Feedback
A
B
C
D
The product of the dimensions is equivalent to the volume of the case.
The product of the dimensions is equivalent to the volume of the case.
The product of the dimensions is equivalent to the volume of the case.
Correct!
PTS: 1
DIF: Average
REF: Page 573
OBJ: 10-7.3 Problem-Solving Application
STA: M6M3.d
TOP: 10-7 Volume of Prisms
7
NAT: 8.2.1.j
KEY: volume | polygon | problem solving
ID: A
SHORT ANSWER
30. ANS:
143
n
To find how many cans will be in each bag, divide the number of cans by the number of bags.
143
n
PTS: 1
DIF: Average
NAT: 8.5.2.g
STA: M6P5.b
KEY: expression | algebraic expression
REF: Page 58
OBJ: 2-2.1 Application
TOP: 2-2 Translate Between Words and Math
8