Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency Specification Sheet
4th Six Weeks: 32 Days
Discuss Numerical Fluency Problems with your students by sharing their 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 #
Answers
3.75
4-1
220
6.3C
2
Number of Limes
2
4
8
16
24
28
30
Cost
$0.25
$0.50
$1.00
$2.00
$3.00
$3.50
$3.75
Number of Hours
4
8
12
16
2
1
19
Wages
$21
$42
$63
$84
$10.50
$5.25
$99.75
99.75
4-2
220
6.3C
2
D
4-3
220
6.3C
2
4-4
4-5
4-6
4-7
4-8
518
518
507
518
135
6.10D
6.10D
6.10C
6.10D
6.2D
5
5
5
5
1
4-9
135
6.2D
1
4-10
4-11
135
135
6.2D
6.2D
1
1
Austin ISD Secondary Mathematics Department
Meters of Tomatoes
2
6
42
Meters of Corn
3
9
63
C
D
B
D
B
About 17% of the class did not own any pets at all.
6
1 1
1 1
1
 ;
is half of a ;  33%; of 33% is about 17% .
36 6 6
3 3
2
B
C
4th Six Weeks 2009-2010
Page 1 of 36
Grade 6 Mathematics
NF
Problem
4-12
Matrix
#
TEKS
#
Numerical Fluency Problems
TAKS
Obj #
412
6.8B
4
605
6.11A
6
607
6.11C
6
Answers
1
2
3
15 m2
16 m
Answers will vary. Not all tiles or rails need to be used. Here are
two possibilities using all 36 tiles, but not necessarily all 26 rails.
Answers will vary. Not all tiles or rails need to be used. Here are two
possibilities using all 36 tiles.
412
6.8B
4
605
6.11A
6
607
6.11C
6
4-14
412
6.8B
4
4-15
412
133
605
6.8B
6.2C
6.11A
4
1
6
4-13
4-16
412
6.8B
4
4-17
217
6.3B
2
4-18
217
6.3B
2
4-19
218
6.3A
2
Austin ISD Secondary Mathematics Department
1 42 m2
2 34 m
$3380
33 x $60 + 28 x $50 = $1980 + $1400 = $3380
Because decimals are involved, students can count partial areas or
perimeters and then add them together for their final results.
1 36.125 cm2
2 25.5 cm
1 37.5%
2 36%
1
3 33 %
2
4 55%
1 C
2 D
1 C
2 A
4th Six Weeks 2009-2010
Page 2 of 36
Grade 6 Mathematics
NF
Problem
Matrix
#
TEKS
#
Numerical Fluency Problems
TAKS
Obj #
Answers
24
Number of
Pages
6
12
18
24
Number of
Minutes
45
90
135
180
Number
of Hours
0.75
1.5
2.25
3
4-20
220
6.3C
2
4-21
310
6.6B
3
D
4-22
310
6.6B
3
4-23
310
6.6B
3
4-24
310
6.6B
3
4-25
308
6.6A
3
4-26
310
6.6B
3
4-27
310
6.6B
3
308
6.6A
3
409
6.8C
4
308
6.6A
3
409
6.8C
4
308
6.6A
3
409
6.8C
4
308
6.6A
3
310
6.6B
3
58
180 – 53 – 69 = 58
A 69
180 – 42 = 138; 138  2 = 69
142
360 – (53 + 87 + 78) = 360 – 218 = 142
1 They are congruent.
2 They are congruent.
3 360
4 45
5 135 (360 – 2  45 = 270; 270  2 = 135)
6 45
7 135
45
180 – 90 = 90; 90  2 = 45
C 68
360 – 2(90) = 180; 180 – 112 = 68
1 The vertex
2 Obtuse
3 Outer scale
4 Between 120 and 130
5 125
1 The vertex
2 Acute
3 Inner scale
4 20 and 30
5 28
1. Obtuse
2. 130
3. Acute
4. 40
5. Right
6.
90
1 Acute
2 At 20 and 80
3 By subtracting 20 from 80
4 60
5 They are congruent.
6 60
409
6.8C
4
4-28
4-29
4-30
4-31
Austin ISD Secondary Mathematics Department
100
180 – 35 – 45 = 100
4th Six Weeks 2009-2010
Page 3 of 36
Grade 6 Mathematics
NF
Problem
Numerical Fluency Problems
Matrix
#
TEKS
#
TAKS
Obj #
308
6.6A
3
1
2
3
409
6.8C
4
4
4-32
Austin ISD Secondary Mathematics Department
Answers
40
180; the sum of the 3 angles of any triangle is 180.
70; the angles opposite the 2 congruent sides in an isosceles
triangle are congruent so 180 – 40 = 140; 140  2 = 70.
70; the angles opposite the 2 congruent sides in an isosceles
triangle are congruent so 180 – 40 = 140; 140  2 = 70.
4th Six Weeks 2009-2010
Page 4 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-1
Limes are 8 for $1.00 at the local grocery store. How
many dollars will 30 limes cost at this same rate?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 5 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-2
William works four hours after school at a local sandwich
shop and earns $21. At this rate, how many dollars does
William earn for 19 hours of work at the sandwich shop?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 6 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-3
Justin is planting a large garden to have vegetables to
sell at a local farmer’s market. Justin plants 2 square
meters of tomatoes for every 3 square meters of corn he
plants. If Justin plants 42 square meters of tomatoes,
how many square meters of corn does he plant?
A
47 m2
B
126 m2
C
28 m2
D
63 m2
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 7 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-4
In a recent survey, 6th and 7th graders were asked what
their favorite snack was. The table below contains the
results of the survey.
Preference
Popcorn
Dots
Soda
6th Graders
75
25
200
7th Graders
160
125
115
What part of the 7th graders prefers the most popular
snack for their grade level?
A
3
5
B
160%
C
0.4
D
2
66 %
3
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 8 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-5
Ms. Copeland asked her students how they spent their
time over the holidays. The results are shown in the
graph below.
Over the Hoidays
12
10
8
6
4
2
0
Watching Movies
Shopping at the Mall
Out of Town
What percent of the students surveyed went out of town
over the holidays?
A
25%
B
7%
C
32%
D
28%
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 9 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-6
At Dripping Springs Middle School, the student
population consists of 150 sixth graders, 250 seventh
graders, and 100 eighth graders. Which circle graph best
represents this information?
A
C
8th
8th
6th
6th
7th
7th
D
B
8th
8th
6th
7th
7th
Austin ISD Secondary Mathematics Department
6th
4th Six Weeks 2009-2010
Page 10 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-7
A surveyed was conducted among young adults about
what type of vehicles they like to drive. The results of the
survey indicated that 20% liked trucks, 35% liked SUV’s,
10% liked passenger cars, and 35% liked sports cars.
Which circle graph best represents this information?
A
C
Pass enge r
Cars
Pass enge r
Cars
Sports
Cars
Sports
Cars
Trucks
Trucks
SUVs
SUVs
Pass enge r
Cars
B
Sports
Cars
Trucks
Pass enge r
Cars
D
Sports
Cars
Trucks
SUVs
SUVs
Austin ISD Secondary Mathematics Department
4th Six Weeks 2009-2010
Page 11 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-8
Each of the 148 sixth graders on a recent camping
trip went on a 3.9-mile hike. About how many
miles did the sixth graders hike altogether?
A
150 miles
B
600 miles
C
400 miles
D
40 miles
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 12 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-9
A class investigated how many pets each student in
class owned. There were a number of students who did
not own any pets at all. The class data is represented
below.
Pets in Students’ Families
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
x
0
1
2
3
4
x
x
5
6
x
7
8
9
x
10
11
12
13
Number of Pets
Estimate the percent of the class that did not own any
pets at all.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 13 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-10
The following polygon shows the shape of a plot of land.
86 m
80 m
55 m
40 m
105 m
What is the approximate perimeter of the land?
A
500 m
B
400 m
C
300 m
D
200 m
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 14 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-11
The Young Runners’ Club was preparing for a foot race
along the streets of Austin. About 31 cases with bottles
of water were placed along the route for the runners.
There were 48 bottles of water in each case. About how
many bottles of water were placed along the route of the
race?
A
80
B
1250
C
1500
D
1600
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 15 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-12
Bumper cars are a popular ride at carnivals. Bumper cars
ride around on a floor made of smooth square tiles. To
take apart and put together easily, as carnivals travel
from city to city, each square tile measures 1 meter by 1
meter. Bumper rails each 1-meter long surround the
floor.
1
How many square meters of floor are shown in the
picture?
2
How many meters of bumper rails are shown in the
picture?
3
A carnival has 36 square meters of tile for their
bumper car floor. They have 26 meters of bumper
rails (not all bumper rails have to be used). Sketch at
least 2 possible floor plans for this bumper car ride.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 16 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-13
A carnival has 36 square meters of tile for their
bumper car floor. They have lots of bumper rails
sections. Sketch at least two possible floor plans
for this bumper-car ride.
(For this problem, sketch floor plans that are
different than what you sketched in Numerical
Fluency 4-12.)
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 17 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-14
The number of 1-meter by 1-meter square tiles needed to
cover a bumper-car floor is the area.
The number of 1-meter rail sections needed to surround a
bumper-car floor is the perimeter.
1
What is the area of the bumper-car floor plan shown
below?
2
What is the perimeter of the bumper-car floor plan
shown below?
(Each
represents a 1-meter by 1-meter square tile.)
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 18 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-15
The tiles used for the floor for bumper car rides cost $60
for each 1-meter by 1-meter square tile. The bumper rail
sections cost $50 for each 1 meter of length.
(Each
represents a 1-meter by 1-meter square tile.)
What is the cost in dollars for the total number of square
tiles and bumper rails needed for the following floor plan
of a bumper car ride?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 19 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-16
Note: The shape below is not drawn to scale.
1
What is 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
4th Six Weeks 2007-2008
Page 20 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-17
What percent represents the shaded area of each model
below?
1
3
2
4
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 21 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-18
1
2
Ramona answered 72% of the questions on a test
correctly. Which fraction is equivalent to 72%?
A
1
72
B
28
72
C
18
25
D
100
72
In basketball, Joshua typically makes 1.5 free throws
for every 4 free throws attempted. Which fraction
best describes this ratio of the number of free throws
made to the number of free throws attempted?
A
B
C
D
1.5
1
8
3
3
4
3
8
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 22 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-19
1
2
The ratio of DVD’s to videotapes owned by the
Fernandez family is 7: 3. Which of the following
shows the possible numbers of DVD’s and
videotapes the Fernandez family owns?
A
9 DVD’s and 21 video tapes
B
18 DVD’s and 42 video tapes
C
28 DVD’s and 12 video tapes
D
49 DVD’s and 24 video tapes
Jason has 48 colored pencils and 16 markers. What
is the ratio of the number of markers to number of
colored pencils?
A
1 to 3
B
4 to 9
C
6 to 2
D
3 to 1
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 23 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-20
Myrna can type 6 pages every 45 minutes. How many
pages can Myrna type in 3 hours if she types at the same
rate?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 24 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-21
A triangle has angles measuring 35 and 45. What is the
measure of the triangle’s third angle?
A
80
A
70
B
110
C
100
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 25 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-22
A triangle has angles measuring 53 and 69. What is the
measure of the triangle’s third angle?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 26 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-23
Triangle ABC is an isosceles triangle. If the measure of
C is 42, what is the measure of B?
A
69
B
42
C
142
D
139
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 27 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-24
Quadrilateral PQRS shows the shape of a plot of land.
P measures 53, Q measures 87, and R measures
78. What is the measure of S?
P
Q
S
R
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 28 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-25
Rhombus RSTP is shown below.
1
How are the side lengths of a rhombus related?
2
How are the opposite angles of a rhombus related?
3
What is the sum of the four angles of a rhombus?
4
What is the measure of R?
5
What is the measure of S?
6
What is the measure of T?
7
What is the measure of P?
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 29 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-26
What is the measure of 1, in degrees, in square WXYZ?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 30 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-27
The drawing below shows the shape of a flower garden.
The measure of D is 112.
A
B
D
C
What is the measure of A?
A
90
B
72
C
68
D
180
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 31 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-28
1
What part of H aligns with the center of the
protractor?
2
What type of angle is H?
3
Ray HK is lined up with 0 degrees on the protractor.
To find the measure of H, should the inner or outer
scale of the protractor be used?
4
Does Ray HJ of H cross the protractor between 50
and 60 or between 120 and 130? Explain your
reasoning.
5
What is the measure of H to the nearest degree?
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 32 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-29
1
What part of D aligns with the center of the
protractor?
2
What type of angle is D?
3
The horizontal ray is lined up with 0 on the
protractor. To find the measure of D, should the
inner or outer scale of the protractor be used?
4
Does the other ray of D cross the protractor
between 20 and 30 or between 150 and 160?
Explain your reasoning.
5
What is the measure of D to the nearest degree?
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 33 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-30
1
What type of angle is ABC?
2
What is the measure of ABC?
3
What type of angle is ABD?
4
What is the measure of ABD?
5
What type of angle is DBC?
6
What is the measure of DBC?
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 34 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-31
A parallelogram is shown below on a protractor.
1
What type of angle is X?
2
What are the two locations where the rays of X
cross the inner scale of the protractor?
3
How can you determine the measure of X?
4
What is the measure of X?
5
How are the opposite angles in a parallelogram
related?
6
What is the measure of W?
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 35 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 4-32
Triangle STB below is an isosceles triangle.
1
What is the measure of S?
2
What is the sum of the measures of S, T, and B?
Explain how you know.
3
Without measuring, what is the measure of T?
Explain how you know.
4
Without measuring, what is the measure of B?
Explain how you know.
Austin ISD Secondary Mathematics Department
4th Six Weeks 2007-2008
Page 36 of 36