6th Grade 6th 6 Weeks Numercial Fluency

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Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency Specification Sheet
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
6-1
6-2
6-3
Matrix
#
TEKS
#
TAKS
Obj #
223
501
223
501
223
6.5
6.9A
6.5
6.9A
6.5
2
5
2
5
2
Answers
1
2
C
B
1
2
C
A
1
2
A
There are 12 combinations of a pair of pants, a shirt, and a pair
of shoes as listed below.
501
6.9A
5
Navy, red, white
Navy, red, black
Navy, green, white
Navy, green, black
Navy, orange, white
Navy, orange, black
127
501
6.2B
6.9A
1
5
1
2
3
4
6-4
502
6.9B
5
5
6
127
501
6.2B
6.9A
1
5
1
2
3
4
6-5
502
6.9B
5
5
6
Austin ISD Secondary Mathematics Department
Khaki, red, white
Khaki, red, black
Khaki, green, white
Khaki, green, black
Khaki, orange, white
Khaki, orange, black
1, 2, 3, 4, 5, 6
All outcomes are equally likely as long as it is a fair (balanced)
number cube.
1
P(6) =
6
1 1 1 3
1
P(2)+P(4)+P(6)= + + = or
6 6 6 6
2
1 1 6 2 4 2
1 – P(3)-P(6) = 1 - - = - = or
6 6 6 6 6 3
P(10)=0
1, 2, 3, 4, 5, 6, 7, 8
All outcomes are equally likely since each section of the circular
spinner has equal area.
1
P(7)=
8
1 1 1 3
P(3)+P(4)+P(5)= + + =
8 8 8 8
1
1 1 1 1 4
P(1)+P(4)+P(6)+P(8)= + + + = or
8 8 8 8 8 2
P(12)=0
6th Six Weeks 2009-2010
Page 1 of 36
Grade 6 Mathematics
NF
Problem
Numerical Fluency Problems
Matrix
#
TEKS
#
TAKS
Obj #
127
220
501
6.2B
6.3C
6.9A
1
2
5
Answers
1
2
3
6-6
4
502
6.9B
5
5
6
127
220
501
6.2B
6.3C
6.9A
1
2
5
1
2
3
4
6-7
502
6.9B
5
5
6
6-8
6-9
6-10
6-11
6-12
6-13
117
502
117
502
110
117
502
6.1B
6.9B
6.1B
6.9B
6.1A
6.1B
6.9B
1
5
1
5
1
1
5
1
2
117
6.1B
1
220
6.3C
2
502
6.9B
5
501
6.9A
5
502
6.9B
5
127
6.2B
1
135
6.2D
1
Austin ISD Secondary Mathematics Department
Black ball, checkered ball, white ball
Not all outcomes are equally likely because there are a different
number of black, checkered, and white balls.
3
P(black)=
8
1 7
P(not white)=1- =
8 8
25 checkered balls because half of the balls are checkered.
5 50
3 5
P(not black)=1- = and =
so 50 balls can be expected
8 80
8 8
not to be black.
One, Two, Three, Four
Not all outcomes are equally likely because “One” on the spinner
has more area than the other outcomes.
1
P(Three)=
5
2
P(One)=
5
1
8
Since 
, it can be expected that “Three” can be landed on
5 40
the spinner for 8 of 40 spins.
2 20
Since 
, it can be expected the spinner was spun 50 times
5 50
if the spinner landed on “One” 20 times.
B
D
1
2
D
D
1
2
B
A
1
2
B
B
1
There are 9 possible pairs of outcomes as listed below.
Red, red
Blue, red
Yellow, red
Red, yellow
Blue, yellow
Yellow, yellow
Red, blue
Blue, blue
Yellow, blue
3 1

9 3
2
P(match)=
1
Estimate: a little more than 6; Exact: 6
2
3
20
Estimate: a little less than 6; Exact: 5.62
6th Six Weeks 2009-2010
Page 2 of 36
Grade 6 Mathematics
Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
6-14
133
6.2C
1
127
135
502
418
127
135
127
6.2B
6.2D
6.9B
6.8D
6.2B
6.2D
6.2B
1
1
5
4
1
1
1
605
6.11A
6
127
6.2B
1
605
6.11A
6
127
6.2B
1
605
6.11A
6
127
6.2B
1
605
6.11A
6
131
605
L
6.11A
6
610
6.12A
6
131
605
610
112A
117
133
223
L
6.11A
6.12A
6.1F
6.1B
6.2C
6.5
6
6
1
1
1
2
6-15
6-16
6-17
6-18
6-19
6-20
6-21
6-22
6-23
6-24
6-25
1
$919
1
2
Estimate: a little more than 8; Exact: 8.18
Estimate: a little less than 4; Exact: 3.95
1
2
3/5
222
1
2
Estimate: about 18.25: Exact: 18.5
Estimate: about 14.5: Exact: 14.62
1
2
1
2
1
2
1
2
1
6-26
606
6.11B
6
6-27
133
220
127
6.2C
6.3C
6.2B
1
2
1
6-28
Answers
Austin ISD Secondary Mathematics Department
2
1
2
1
of the cabbages
3
5
3
hours or 3 hours 25 minutes
12
1
2 inches
2
5
of Clyde’s allowance
8
5
4 pounds of apples
8
4
of the cookies in the cookie jar
9
0.52 meters or 52 cm
$4.50
1155 miles
3
9 yards of blue string
5
1
of the pizza
8
12 boys
1. 120
2. 4.375
1. 5 hours
2. C
Who
Student
Teacher
Parent
Seat position
1, 4, 7, 10, 13, 16, 19
2, 5, 8, 11, 14, 17, 20
3, 6, 9, 12, 15, 18, 21
H
1. 500
2. x = 45.51
6th Six Weeks 2009-2010
Page 3 of 36
Grade 6 Mathematics
NF
Problem
Matrix
#
TEKS
#
Numerical Fluency Problems
TAKS
Obj #
6-29
117
6.1B
1
6-30
122
6.2E
1
127
502
218
220
6.2B
6.9B
6.3A
6.3C
1
5
2
2
6-31
6-32
Austin ISD Secondary Mathematics Department
Answers
1.
2.
3.
4.
1.
2.
3.
4.
1.
2.
0.6 repeating
0.875
3.20
2.5625
59
59
5
5
12
75% or 0.75
1. 5:2
2. 4
6th Six Weeks 2009-2010
Page 4 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-1
1
2
Jasmine bought 3 CDs that were originally priced at $12.98
each. Each CD was on sale for $4.50 off the original price.
Which equation can be used to find t, the total price of the 3
CDs?
A
t = 12.98 – 4.50
B
t = 3(12.98) – 4.50
C
t = 3(12.98) – 3(4.50)
D
t = 3(4.50) – 3(12.98)
Daniel takes one sandwich and one piece of fruit to school
for lunch. He has a choice of a ham or turkey sandwich.
His choices for fruit are an apple, a pear, or an orange.
Which table lists all possible combinations for Daniel’s
lunch?
A
B
Fruit
Apple
Apple
Pear
Pear
Sandwich
Ham
Ham
C
Ham
Turkey
Turkey
Turkey
Fruit
Apple
Apple
Apple
Orange
Orange
Orange
Fruit
Apple
Apple
Pear
Pear
Orange
Orange
Sandwich
Ham
Ham
Ham
Turkey
Turkey
Turkey
Fruit
Apple
Apple
Orange
Orange
Pear
Pear
Sandwich
Ham
Turkey
Ham
Turkey
Sandwich
Ham
Turkey
Ham
Turkey
Ham
Turkey
Austin ISD Secondary Mathematics Department
D
6th Six Weeks 2009-2010
Page 5 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-2
1
2
Doris and 3 friends ordered an extra large pizza for $13.25, 4
large drinks for $1.50 each, and one order of chicken wings
for $5.75. If they split these costs evenly, which equation
can be used to find a, the amount in dollars and cents each
person should pay, not including tax or tip?
A
a = 13.25 + 1.50 + 5.75  4
B
a = 13.25 + 4  1.50 + (5.75  4)
C
a = (13.25 + 4  1.50 + 5.75)  4
D
a = (13.25 + 3  1.50 + 5.75)  3
A penny and a nickel are tossed. Which tree diagram shows
all the possible outcomes?
Penny
Heads
Tails
Nickel
Heads Tails
Heads Tails
Penny
Heads
Tails
Nickel
Heads
Tails
Penny
Heads
Tails
Nickel
Tails
Heads
Penny
Heads
Tails
Nickel
Heads Tails
Heads
A
B
C
D
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 6 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-3
1
2
If the cost of renting a bicycle is a basic fee of $8 plus
an additional $2 per hour for each hour the bicycle is
rented, which equation can be used to find c, the cost
in dollars of the rental for h hours?
A
c = 2h + 8
B
c = 8h + 2
C
c = 2(h + 8)
D
c = 8(h + 2)
The table below shows the colors of all of Juan’s
pants, shirts, and shoes.
Pants
Navy
Khaki
Shirts
Red
Green
Orange
Shoes
White
Black
If Juan wears one pair of pants, one shirt and one
pair of shoes, what are all the possible combinations
of clothing he can wear?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 7 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-4
A normal six-sided number cube as shown below is
tossed.
1
What are all the possible outcomes?
2
Are all outcomes equally likely? Be prepared to
explain your reasoning.
3
What is the probability that a 6 will be rolled?
4
What is the probability that an even number will be
rolled?
5
What is the probability that a multiple of 3 will NOT be
rolled?
6
What is the probability that a 10 will be rolled?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 8 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-5
The spinner shown below is spun once.
1
2
8
3
4
7
6
5
1
What are all the possible outcomes?
2
Are all outcomes equally likely? Be prepared to
explain your reasoning.
3
What is the probability that a 7 will be spun?
4
What is the probability that a number greater than 2
but less than 6 will be spun?
5
What is the probability that a prime number will NOT
be spun?
6
What is the probability that a 12 will be spun?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 9 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-6
One ball is randomly drawn from the container shown
below.
1
What are all the possible outcomes?
2
Are all outcomes equally likely? Be prepared to
explain your reasoning.
3
What is the probability of drawing a black ball?
4
What is the probability of NOT drawing a white ball?
5
If one ball was randomly drawn from the container 50
times, how many would you expect to be checkered
balls?
6
If one ball was randomly drawn from the container 80
times, how many would you expect NOT to be black
balls?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 10 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-7
The spinner shown below is spun once.
1
What are all the possible outcomes?
2
Are all outcomes equally likely? Be prepared to
explain your reasoning.
3
What is the probability that the spinner will land on
“Three”?
4
What is the probability that the spinner will land on
“One”?
5
If the spinner was spun 40 times, how many times
would you expect the spinner to land on “Three”?
6
If the spinner landed on “One” 20 times, how many
times would you expect the spinner to have been
spun?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 11 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-8
Use the following information to answer problems 1 and 2 below.
In a mathematics game, students created the following
vocabulary word with their cards.
P
1
2
R
O
P
O
R
T
I
O
N
If one of the cards from the word “PROPORTION” was
selected at random, what is the probability the card showed
a vowel?
A
3
10
B
2
5
C
1
10
D
3
5
If one of the cards from the word “PROPORTION” was
selected at random, what is the probability the card did NOT
show a P?
A
20%
B
40%
C
60%
D
80%
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 12 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-9
Use the following information to answer problems 1 and 2 below.
Brianna has a bag with 10 blue marbles, 4 green marbles, 8
purple marbles, and 2 red marbles.
1
2
If Brianna draws one marble at random from the bag, what is
the probability the marble will be purple?
A
8.24%
B
2
66 %
3
C
25%
D
1
33 %
3
If Brianna wants the probability of picking a blue marble to
1
be , what could she do?
2
A
Remove 1 green, 1 purple, and 1 red marble
B
Add 2 blue marbles
C
Add 2 green, 2 purple, and 2 red marbles
D
Add 4 blue marbles
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 13 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-10
Use the following information to answer problems 1 and 2 below.
Each box pictured below holds the number of marbles stated
below the box. In each box, half of the marbles are black. Also,
in each box, there is only one red marble.
10 Marbles
1
2
100 Marbles
1000 Marbles
If one marble is selected at random from the middle-sized
box, what is the probability that the marble will NOT be
black or red?
A
48%
B
49%
C
50%
D
51%
Which box would give you the greatest chance of picking a
red marble?
A
The box with the 10 marbles
B
The box with the 100 marbles
C
The box with the 1000 marbles
D
All three boxes have the same chance of picking a red
marble
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 14 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-11
Use the following information to answer problems 1 and 2 below.
At Mendez Middle School, in a survey of 100 students about their
favorite pizza topping, 25 students chose pineapple.
1
2
According to the results of the survey, if a student is picked
at random from Mendez Middle School, what is the chance
that the student prefers pineapple as a pizza topping?
A
1 out of 5
B
1 out of 4
C
1 out of 2
D
1 out of 6
Which proportion can be used to predict s, the number of
students who like pineapple as a favorite topping, if 220
Mendez Middle School students are asked about their
favorite topping?
A
25 220

100
s
B
1
s

4 220
C
25 100

220
s
D
1 220

4
s
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 15 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-12
Use the following information to answer problems 1 and 2 below.
Two bags each contain one red, one yellow, and one blue block
as shown below.
1
If a pair of blocks, one block from each bag, is randomly
selected, what are all the possible outcomes of the pairs of
blocks that can be selected?
2
If a pair of blocks, one block from each bag, is randomly
selected, what is the probability that the pair of blocks will
have matching colors?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 16 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-13
First, state an estimated answer for each problem.
Then find the exact answer. Write each answer in
lowest terms.
1
2
1
9 3
5
4
Estimated Answer: _________________
Exact Answer: _____________________
Don’t
Forget to
Estimate!!!
2
14  8.38
Estimated Answer: _________________
Exact Answer: _____________________
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 17 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-14
1. Alex earns $16 dollars per hour for his work at a
factory. He works 32 hours per week and gets paid every
2 weeks. If the factory takes $105 out of each check for
taxes how much money will Alex be paid? Be prepared to
explain your reasoning.
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 18 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-15
First, state an estimated answer for each problem.
Then find the exact answer. Write each answer in
lowest terms.
1
1
3  4.68
2
Estimated Answer: _________________
Exact Answer: _____________________
Don’t
Forget to
Estimate!!!
2
5.7  1
3
4
Estimated Answer: _________________
Exact Answer: _____________________
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 19 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-16
1. The National Weather Service states that there is a 60%
chance of a thunderstorm. What is this probability written
as fraction is simplest form?
2. The movie Gone with the Wind is 3 hours and 42
minutes long. How many minutes is this?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 20 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-17
First, state an estimated answer for each problem.
Then find the exact answer. Write each answer in
lowest terms.
1
1 19
2
7 
9
4 12
3
Estimated Answer: _________________
Exact Answer: _____________________
Don’t
Forget to
Estimate!!!
2
4 13
14.12  1 
5 10
Estimated Answer: _________________
Exact Answer: _____________________
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 21 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-18
Write each answer in lowest terms.
1
of the cabbages
2
planted this spring on the community farm. If Mrs. Florio
1
picked of the cabbages, what fraction of the cabbages did
6
Mrs. Lee pick?
1
Mrs. Florio and Mrs. Lee together picked
2
Jill studied math for 2
2
3
hours and Spanish for 1 hours.
3
4
What was her total study time for math and Spanish?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 22 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-19
Write each answer in lowest terms.
5
inches on one side.
6
What is the perimeter of this triangle?
1
An equilateral triangle measures
2
Clyde expected to spend
3
of his allowance on candy but
4
1
of his allowance on candy. What
8
fraction of his allowance did Clyde save?
actually spent only
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 23 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-20
Use the following information to answer problems 1 and 2 below.
Write each answer in lowest terms.
Mr. and Mrs. Garcia are preparing food for a family reunion.
3
3
pounds of apples to bake pies and 5
8
4
pounds of apples to make applesauce. How many more
pounds of apples does he use for the pies than for the
applesauce?
1
Mr. Garcia uses 10
2
Mrs. Garcia baked cookies and placed them in a cookie jar.
2
of the cookies in the cookie jar have chocolate chips,
9
1
while of the cookies have oatmeal and raisins. What
3
fraction of the cookies in the cookie jar does not have
chocolate chips, oatmeal, or raisins?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 24 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-21
1
During track practice, Trent jumped 4.2 meters and Will
jumped 3.68 meters. How much further did Trent jump than
Will?
2
Clarissa went to a sandwich shop to buy her lunch. She
bought a turkey sandwich for $3.10, a bag of pretzels for
$0.88 and lemonade for $1.10. The tax was $0.42. How
much change did Clarissa received back from a $10 bill?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 25 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-22
1
An airplane flew at an average speed of 462 miles for 2
1
2
hours. How far did the plane fly?
2
Simone is going to make shoelaces in school colors for
2
everyone on her basketball team. She will use of a yard
5
of blue string for one shoelace. There are 12 players on the
basketball team. How many yards of blue string does
Simone need to buy?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 26 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-23
1
Armando found
3
4
of a pizza leftover in the
refrigerator. He ate
1
6
of the pizza in the
refrigerator. How much of the pizza did he eat?
2
There are 32 students in Mrs. Hall’s class.
3
8
of
the students are boys. How many boys are in
Mrs. Hall’s class?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 27 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-24
1. What is the least common multiple of 5, 6 and
8?
2. Write 4 3/8 as a decimal. Be prepared to explain
how you converted.
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 28 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-25
1. Michelle’ family is planning a trip from Dallas to
San Antonio. Dallas is about 272 miles from San
Antonio. If Brandon’s dad drives an average of
60 miles per hour, about how long will the trip
take?
2. Let d represent the number of dogs that Mark
walks in 1 day. Which expression shows the
number of dogs Mark walks in 7 days? Be
prepared to explain your reasoning.
A. 7+d
B. d-7
C. 7d
D. d/7
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 29 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-26
A parent group is planning an awards dinner for
students, teachers, and parents. The parent group
plans to seat the guests around a circular table that
has seating for 30. The guests will be seated in the
order of student, teacher, and parent, in a repeating
pattern. Will the 20th guest be a student, a teacher
or a parent?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 30 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-27
1. When Javier sits down today to read, he notices
that he is on page 20 of a 200 page book. He
decides to read 4 pages of this book every day until
he is finished. If this pattern continues, what page
of the book will Javier be on in 10 more days? Be
prepared to explain your reasoning.
F. 24
G. 44
H. 60
J. 130
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 31 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency #6-28
1. You are making gift baskets that each contain 6
bananas, 4 oranges, and 5 apples. If you need to
make 100 gift baskets, how many apples do you
need?
2. What is the solution to the equation?
97.56 + X = 143.07
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 32 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-29
Write each fraction or mixed number as a decimal.
Show your work and be prepared to explain your
strategies.
1. 2/3
2. 7/8
3. 3 1/5
4. 2 9/16
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 33 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency #6-30
Evaluate each expression and be prepared to
explain the Order of Operations.
1. 9 X 8 – 13
2. (9 X 8) - 13
3. 30 / 2 – 5 X 2
4. (30 / 2) - (5 X 2)
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 34 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-31
1. Paula will use 15 ft of ribbon to decorate gift
baskets for her friends. If each basket requires 1.2
feet of ribbon, how many baskets can she
decorate?
2. There is a 25% chance of snow on Friday. What is
the probability that it will NOT snow on Friday?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 35 of 36
Grade 6 Mathematics
Numerical Fluency Problems
Numerical Fluency 6-32
1. There were 18 teachers and 45 students
registered to participate in a 5K walk-a-thon. Which
ratio accurately compares the number of students
to the number of teachers?
A. 1 to 5
B. 5:2
C. 3 to 15
D. 18 to 45
2. Katie drives at an average rate of 60 miles per
hour. How many hours will it take her to drive 240
miles?
Austin ISD Secondary Mathematics Department
6th Six Weeks 2009-2010
Page 36 of 36
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