Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency Specification Sheet
5th Six Weeks: 34 Days
Discuss Numerical Fluency Problems with your students by sharing multiple correct
strategies. This sharing will help students become flexible, efficient, and accurate with
numerical reasoning while learning the TEKS deeply.
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
5-1
412
6.8B
4
5-2
412
6.8B
4
5-3
412
6.8B
4
5-4
412
6.8B
4
5-5
412
6.8B
4
5-6
605
6.11A
6
127
6.2B
1
412
6.8B
4
127
412
6.2B
6.8B
1
4
5-7
5-8
127
6.2B
1
Answers
1
2
3
4
1
2
C
About 36
25.5 cm
36 cm
36 cm2
C
D
1
2
D
98 cm
C
Answers will vary depending on the size of the rectangle and
parallelogram. The answers given are when NF #113 is printed on 8”
by 10” paper.
1
1 12 inches
2
2 30.2 cm
1 A
2 .37 seconds
1
2
5-9
3
124
6.2A
1
4
Austin ISD Secondary Mathematics Department
cm2
1
4
1
3
4
1
5
2
1
5
4
4
5th Six Weeks 2009-2010
Page 1 of 38
Grade 6 Mathematics
NF
Problem
Matrix
#
TEKS
#
Numerical Fluency Problems
TAKS
Obj #
Answers
Note: The ruler has been scaled so be 6 inches on 8” by 10” paper.
7
The sum is 4 inches.
8
1
127
6.2B
3
4
1
1
3
4
2
1
4
1
2
5-10
2
5
8
4
5-11
5-12
124
6.2A
1
127
124
127
124
6.2B
6.2A
6.2B
6.2A
1
1
1
1
Austin ISD Secondary Mathematics Department
7
8
1
inches
4
4 inches
4
5th Six Weeks 2009-2010
Page 2 of 38
Grade 6 Mathematics
NF
Problem
Matrix
#
TEKS
#
Numerical Fluency Problems
TAKS
Obj #
Answers
1
127
6.2B
2
5-13
1
3
124
6.2A
4
5-14
113
6.1D
1
5-15
113
6.1D
1
5-16
511
6.10B
5
5-17
511
6.10B
5
1
2
3
1
2
B
208
6.4A
2
5-19
208
6.4A
2
2
3
1
2
3
1
5-20
215
6.4B
2
2
5-21
208
6.4A
2
5-22
208
6.4A
2
5-23
208
6.4A
2
Austin ISD Secondary Mathematics Department
3
4
3
4
4
8x9=2x2x2x3x3
2 and 3
23 x 32
B
D
2
D
1
5-18
1
2
3
4
3
1
2
3
1
2
3
1
2
3
Answers will vary. Examples: The father’s age is always greater
than Anna’s age. The father is always 25 years older than Anna.
3 + 25; 6 + 25; 10 + 25; 15 + 25
D
Answers will vary. Examples: The number of Mexican pesos is
always greater than the number of US dollars. The number of
Mexican pesos is 9 times the number of US dollars.
9 x 4; 9 x 7; 9 x 9; 9 x 20
C
Answers will vary. The height and base measurements are
almost always smaller numbers than the corresponding area
measurement. The product of the height and base divided by 2
equals the area of the triangle.
10  1 10  2 10  4 10  8
;
;
;
2
2
2
2
D
1, 3, 5, 10
16 16; 48 16; 80 16; 160 16
A
Answers will vary. The value of the term in the sequence is
always greater than the position number. The value of the term in
the sequence is almost 4 times the position number.
4 x 1 – 1; 4 x 2 – 1; 4 x 3 – 1; 4 x 4 – 1; 4 x 5 – 1
C
500, 1000, 2000, 3000, 3500, 10000, 36000, 1000k
B
A
5th Six Weeks 2009-2010
Page 3 of 38
Grade 6 Mathematics
NF
Problem
5-24
5-25
Numerical Fluency Problems
Matrix
#
TEKS
#
TAKS
Obj #
208
6,4A
2
223
6.5
2
418
6.8D
4
208
6,4A
2
223
6.5
2
418
6.8D
4
Answers
n
8
1
1, 2, 3, 5, 8,
2
3
D
B
1
2
3
24, 48, 72, 168, 720, 24d
B
D
2 dozen cupcakes is the same as 24 cupcakes so there will be
enough for each student to get one cupcake.
5-26
412
6.8B
4
Since 1 gallon = 4 quarts, 2 gallons = 8 quarts.
Since 1 quart = 2 pints, 8 quarts = 16 pints.
There is only enough orange juice for 16 students to get one pint
each.
It would take 8 more pints, or 4 quarts, or 1 more gallon to have
enough orange juice for each student to get 1 pint.
However, if the serving size were decreased to 1 cup of orange juice
each, there would be enough since 16 pints = 32 cups.
5-27
412
6.8B
4
5-28
418
6.8D
4
5-29
418
6.8D
4
511
6.10B
5
217
6.3B
2
5-30
5-31
5-32
217
511
6.3B
6.10B
2
5
Austin ISD Secondary Mathematics Department
1. 40 inches
2. the area will increase by 4 square tiles
1.
2.
3.
4.
5.
1.
2.
72
2
112
8
3 hours and 15 minutes
27.5 T
Since 2 pints = 1 quart and 4 quarts = 1 gallon, then 1 gallon
= 8 pints. To get the number of pints from the number of
gallons, just multiply by 8.
Since 1 pint = 2 cups and 1 cup = 8 ounces, then 1 pint = 16
ounces. To get the number of ounces from the number of
pints, just multiply by 16.
1. 43 mnutes
2. 9
1. 85%
2. $14.40
MEAN
MEDIAN
MODE
Part Time:
71
68.5
65
Full Time:
102
72
65
5th Six Weeks 2009-2010
Page 4 of 38
Grade 6 Mathematics
NF
Problem
5-33
Matrix
#
127
TEKS
#
6.2B
Numerical Fluency Problems
TAKS
Obj #
1
Austin ISD Secondary Mathematics Department
Answers
1. 2 and 1/4 hours
2. 15.8 cm.
5th Six Weeks 2009-2010
Page 5 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-1
Note: The shape below is not drawn to scale.
1
Approximate the area of the shape below.
2
What is the perimeter of the shape below?
4.25 cm
8.5 cm
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 6 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-2
1
What is the perimeter of the shape below?
2
What is the area of the shape below?
3 cm
4 cm
4 cm
5 cm
6 cm
10 cm
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 7 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-3
1
2
The length of each side of a new square washcloth is
13 inches. What is the area of the washcloth?
A
26 in2
B
52 in2
C
169 in2
D
196 in2
The perimeter of a rectangular gym floor is 200 feet.
The width of the gym is 45 feet. What is the length of
the gym?
A
155 ft
B
245 ft
C
110 ft
D
55 ft
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 8 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-4
The Smith family put a rectangular patio in their
rectangular backyard as shown below. They planted
grass in the rest of their backyard. What is the area of the
backyard that is planted with grass?
50 feet
12 feet
25 feet
9 feet
A
1358 ft2
B
1250 ft2
C
1142 ft2
D
192 ft2
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 9 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-5
1
Jorge cut a triangle out of construction paper for a
geometry project.
31 cm
25 cm
42 cm
What is the perimeter of the triangle in centimeters?
Record your answer and
fill in the bubbles below your
answer. Be sure to use the
correct place value.
2
Nancy made a piece of jewelry using wire as shown below.
4 cm
4 cm
4 cm
How much wire did Nancy need to complete her piece of
jewelry?
A
12 cm
B
72 cm
C
48 cm
D
40 cm
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 10 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-6
The Baker family tiled their kitchen floor using
square tiles. Each box of tiles contained 24 square
tiles. The rectangular kitchen measures 14 feet by
22 feet. What piece of information is needed in
order to find the number of boxes of tile the Baker
family needs to purchase?
A
Area of the kitchen
B
Perimeter of the box
C
Perimeter of the kitchen
D
Area of each square tile
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 11 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-7
1
Use a ruler to measure the sides of the
1
rectangle to the nearest of an inch. Then find
4
the perimeter of the rectangle.
2
Use a ruler to measure the sides of the
parallelogram to the nearest 0.1 of a centimeter.
Then find the perimeter of the parallelogram.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 12 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-8
1
2
A rectangular window has a length of 118.6
centimeters. Its width is 34.9 centimeters less than
its length. What is the width of the window?
A
83.7 cm
B
84.3 cm
C
153.5 cm
D
307 cm
Jody is preparing for a 100-meter race at an
upcoming track meet. Her first practice time was
21.83 seconds. Her second practice time was 22.2
seconds. How many seconds faster was her first
practice time?
Record your answer and
fill in the bubbles below your
answer. Be sure to use the
correct place value.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 13 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-9
Find the sums of the problems given below. You
may use the number line to verify your answers.
0
1)
1
2
3
4
5
6
1
3
3
2
4
1 3
2) 2 
2 4
1 1
3
3) 1   3
4 2
4
3 3
3
4) 2   1
4 4
4
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 14 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-10
3 1
5
Use the ruler to find the sum of 1   2 .
4 2
8
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 15 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-11
3
1
Use the ruler to find the difference of 5  1 .
4 2
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 16 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-12
To find the distance around the figure below, David
measured each section of the figure using a string.
He found the 3 measures as given below.
5
in
8
5
in
8
3
2 in
4
Use the ruler to find the
5 5
3
sum of   2 .
8 8
4
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 17 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-13
Find the differences in the problems given below.
You may use the number line to verify your
answers.
0
1
2
3
4
5
6
1 3
1) 1 
4 4
1
3
2) 4  3
2
4
1
1
3) 5  2
4
2
4)
6 1
1
4
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 18 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-14
1
Complete the factor tree below to find the prime
factorization of 72.
72
2
The prime factors of 72 are _______________.
3
The prime factorization of 72 written using
exponents is______________________.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 19 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-15
1
2
Find the prime factorization of 120.
A
2345
B
23  3  5
C
24  3  5
D
2  2  15
Which is the prime factorization of 420?
A
24  3  5
B
2  32  5  7
C
2  3  52  7
D
22  3  5  7
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 20 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-16
The table below shows the low temperatures in Denver
for one week.
Low Temperatures
Sunday
24F
Monday
32F
Tuesday
28F
Wednesday
20F
Thursday
18F
Friday
30F
Saturday
?
The lowest temperature for the week occurred on
Saturday. If the range of low temperatures for the week
was 21F, what was the low temperature on Saturday?
A
39F
B
11F
C
9F
D
14F
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 21 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-17
An electronics store kept track of their sales of DVD
players from 1999 to 2008. The table below shows the
number of DVD players sold each year.
DVD Players Sold
Number of DVD
Year
Players Sold
1999
154
2000
325
2001
410
2002
388
2003
380
2004
420
2005
345
2006
355
2007
225
2008
128
What is the median of the number of DVD players sold?
A
400
B
335
C
313
D
350
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 22 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-18
1
In the table of data below, how do Anna’s age and her
father’s age compare?
Anna’s age, a
3
6
10
15
2
Complete the process column to show how to use
Anna’s age to obtain her father’s age.
Anna’s age, a
3
6
10
15
3
Father’s Age, f
28
31
35
40
Process
Father’s Age, f
28
31
35
40
Using the tables of data above, which expression
represents the father’s age in terms of Anna’s age?
A
f + 25
B
a – 28
C
f – 28
D
a + 25
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 23 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-19
1
In the table of data below, how do the number of US
dollars and the number of Mexican pesos compare?
US Dollars, d
4
7
9
20
2
Complete the process column to show how to use
the number of US dollars to obtain the number of
Mexican pesos.
US Dollars, d
4
7
9
20
3
Mexican pesos, p
36
63
81
180
Process
Mexican pesos, p
36
63
81
180
Using the tables of data above, which expression
represents the number of Mexican pesos in terms of
the number of US dollars?
A
9p
B
d+9
C
9d
D
9
p
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 24 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-20
1
In the table of data below, how do the height and
base of a triangle compare to the area of the triangle?
Height (units)
10
10
10
10
2
Area (square units)
5
10
20
45
Complete the process column to show how the
height and base of a triangle can be used to obtain its
area.
Height (units)
10
10
10
10
10
3
Base (units)
1
2
4
9
Base (units)
1
2
4
9
n
Process
Area (square units)
5
10
20
45
?
Using the tables of data above, which expression can
be used to find the area of a triangle that has a height
of 10 units and a base of n units?
A
10n
B
n
2
C
n+8
D
10n
2
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 25 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-21
1
Use the TAKS Mathematics Chart to complete the
table below.
Measurement Conversions
Number of Ounces, x
Number of Pounds, y
16
48
80
160
2
Complete the process column to show how the
number of ounces can be used to obtain the number
of pounds. Enter the data in the last column also.
Measurement Conversions
Number of Ounces, x
Process
Number of Pounds, y
16
48
80
160
3
Using the tables of data above, which expression
represents the number of pounds in terms of the
number of ounces?
A
x  16
B
16x
C
x8
D
8x
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 26 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-22
1
In the table below, how do the two columns of
numbers compare?
Position, n
1
2
3
4
5
2
Complete the process column to show how to use
the position number, n, to obtain the value of the
term in the sequence of numbers in the last column.
Position, n
1
2
3
4
5
n
3
Value of Term
3
7
11
15
19
Process
Value of Term
3
7
11
15
19
?
Using the tables of data above, what rule can be used
to find the value of a term in the sequence of
numbers in the last column?
A
3n
B
n+5
C
4n - 1
D
n+4
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 27 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-23
Use the TAKS Mathematics Chart to help you complete the following problems.
1
Complete the following table.
Number of
Kilometers, k
Number of
Meters, m
2
1
2
3
3.5
10
36
k
Which equation can be used to determine m, the number of
meters for k kilometers?
A
B
C
D
3
0.5
m = 1000 + k
m = 1000k
1000
m=
k
k
m=
1000
Lance rode in an endurance bicycle race that was 236
kilometers long. Which proportion could be used to find m,
the number of meters in this race?
A
1
236

1000 m
B
1000 236

1
m
C
1
236

m 1000
D
m 236

1 1000
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 28 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-24
Use the TAKS Mathematics Chart to help you complete the following problems.
1
Complete the following table.
Number of Ounces, n
8
16
24
40
64
n
2
Which equation can be used to determine c, the number of
cups equivalent to n ounces?
A
B
C
D
3
Number of Cups, c
c=n+7
c = 8n
8
c=
n
n
c=
8
Rosa makes 128 ounces of juice for her family. Which
proportion could be used to find c, the number of cups in
the 128 ounces of juice?
A
1 128

8
c
B
1
c

8 128
C
1
c

128 8
D
1 128

c
8
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 29 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-25
Use the TAKS Mathematics Chart to help you complete the following problems.
1
Complete the following table.
Number of Days, d
1
2
3
7
30
d
2
Which equation can be used to determine h, the number of
hours equivalent to d days?
A
B
C
D
3
Number of Hours, h
h = d + 23
h = 24d
24
h=
d
d
h=
24
The months January and March always have 31 days each.
In 2005, February had 28 days. Which proportion could be
used to find h, the total number of hours in the first three
months of 2005?
A
B
C
D
1
24
1
24
1
24
1
24
59
h
h

59
h

90
90

h

Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 30 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-26
Use the TAKS Mathematics Chart to help you complete the following problems.
Lucio’s mother is bringing cupcakes and orange
juice for an after school celebration. She brought 2
dozen cupcakes and 2 gallons of orange juice. If
there are 24 students in the class, did she bring
enough to give each student 1 cupcake and 1 pint
of orange juice?
Be prepared to explain your reasoning.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 31 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-27
1. A photo is 4 inches X 6 inches long. To enlarge
the photo Tony doubles both the length and the
width. What is the perimeter of the enlarged
photo? Explain your reasoning.
2. If Jennifer enlarges a 3-inch X 4-inch photo so
that it is 12-inch X 16-inch, how will its area
change? Explain your reasoning.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 32 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-28
Convert:
1. 6 ft. =____ in.
2. 8qt. =____ gal.
3. 7lb. =____ oz.
4. 4qt. = ____ pt.
5. Tomas got into the pool to swim laps at 12:10
p.m. He got out of the pool at 3:25 p.m. How long
was he in the pool?
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 33 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-29
1. The world’s largest ice cream sundae weighs
about 55,000 pounds. How many tons does it
weigh? Explain your reasoning.
2. Explain how you would convert gallons to pints
and then to ounces.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 34 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-30
1. Carrie rode her bike 30 minutes on Monday, 45
minutes on Tuesday, 30 minutes on
Wednesday, 60 minutes on Thursday and 50
minutes on Friday. Find the mean amount of
time Carrie rode her bike in these 5 days.
2. Ryan has a collection of music boxes. Of the 36
boxes he owns, 25% of them have parts that
move when the music plays. How many of his
music boxes have moving parts.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 35 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-31
1. Mike’s baseball team won 17/20 of their games.
What percent of the games did Mike’s baseball
team win? Explain your reasoning.
2. Mia wants to buy a book that is 10% off the
marked price. If the marked price is $15.99,
about how much will the book cost with the
discount?
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 36 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-32
1. Jacinda saved $65, $82, $58, $74, $65, and $72
each month from her part-time job for six
months. The next month she worked full- time
and saved $287. Find the mean, median and the
mode of the amounts saved with and without
full- time work. Be prepared to explain your
reasoning.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 37 of 38
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 5-33
1. Mr. Gonzales spends 3 ½ hours a week working in
his yard. He spends 1 ¼ hours pulling weeds. He
spends the rest of the time mowing the yard. How
much time does he spend mowing the yard? Be
prepared to explain your reasoning.
2. Mischa has a piece of lumber that is 48.6 centimeters
long. How many centimeters does she need to cut
off if she wants the piece of lumber to measure 32.8
centimeters. Be prepared to explain your reasoning.
Austin ISD Secondary Mathematics Department
5th Six Weeks 2009-2010
Page 38 of 38