Austin Independent School District
Department of Curriculum and Instruction
Mathematics
Numerical Fluency
Algebra 1
Mathematics
1st Six-Weeks
2009-2010
Problems #1–1 through #1–25
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
1st Six Weeks’ Numerical Fluency Specifications
NF Problem
TEKS
TAKS
Problem Source
Obj
Answer
Problem #1–1
A.4A
2
Problem #1–2
A.4A
2
Problem #1–3
Problem #1–4
Problem #1–5
Problem #1–6
Problem #1–7
Problem #1–8
Problem #1–9
8.7D
A.2A
A.1E
A.2C
A.3B
A.3B
8.5B
6
Discovering Algebra page 184 #4 a
and b(modified)
TAKS Grade 9 2006 #39
1
TAKS Grad 9 2006 #22 mod.
1
TAKS 2004 Gr. 9 #46
2
TAKS 2003 Gr.9 #48
2
TAKS Exit Dec 2005 #56
2
TAKS IB March 2007 Obj. 2 #3 adj.
2
Problem #1–10
A.1B
1
Problem #1-11
A.6A
3
TAKS Grade 8 2003 #29
TAKS Study Guide Grade 9 #17
modified
Discovering Algebra page 208 i, iii, v
(Algebra TEXTEAMS)
Problem #1–12
A.6D
3
Discovering Algebra page 211 #3a
Problem #1–13
A.2C
2
Rev. TAKS SG Gr. 10 Obj. 2 p. 41
Problem #1–14
A.2C
2
TAKS Grade 9 2006 #51
C
Problem #1–15
A.1B
1
TAKS Study Guide Grade 10 #3
C
Problem #1–16
A.1B
1
Problem #1–17
Problem #1–18
A.1A
A.1A
1
1
TAKS Grade 10 2006 #14 mod.
TAKS Study Guide Grade 10 #1
Problem #1–19
A.1A
1
TAKS Test 2003 Grade 9 #42
B
C
B
Problem #1–20
A.1C
1
TAKS Study Guide Grade 9 #16
modified
A
Problem #1–21
A.1D
1
B
Problem #1–22
A.2D
2
Algebra 1 EOC 2002 #3 mod.
Algebra two year workbook page
37 #37
Problem #1–23
A.2D
2
TAKS Grade 9 2006 #33 mod.
A
Problem #1–24
Problem #1–25
A.3B
A.5C
2
3
TAKS Grade 8 SG #19 mod.
TAKS Exit Feb 2006 #3
B
C
Austin ISD Secondary
Mathematics Department
Discovering Algebra page 185 #6
Discovering Algebra page 171 #1
1+2+3+4+5+6+7+8·9 = 100
1.
2.
(3 + 2) (5) – 7 = 18
(8 – 5) – 6 – 7 = -10
C
B
A
F
C
D
D
A
Accept reasonable student
responses.
Accept reasonable student
responses; d = 6 -.2t
Accept reasonable student
responses.
D
See below for answers.
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Answer Key
Problem #1–21
1)
2)
3)
4)
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–1
Show all your work for the following problems.
This problem, sometimes referred to
as Einstein’s problem, is quite
challenging. “Use the digits 1, 2, 3, 4,
5, 6, 7, 8, 9, and any combination of
the operations (+, -, ×, ÷) to write an
expression that equals 100. Keep the
numbers in consecutive order and do
not use parentheses.”
Here is one solution:
123 – 4 – 5 – 6 – 7 + 8 – 9 = 100
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–2
Show all your work for the following problems.
Insert operation signs, parentheses, or both
into each string of numbers to create an
expression equal to the given answer.
1. 3
2 5 7 = 18
2. 8
5 6 7 = -10
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–3
For each answer choice you do not choose, provide
the coordinates of that point.
Which point on the grid below best
represents the coordinates
4 4
 , 
3 3
?
A Point K
B Point M
C Point R
D Point U
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–4
Be prepared to justify your answer.
Which graph below best represents the linear
parent function?
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–5
Answer the question below and then choose one
other graph that does not represent the relationship
stated below and write your own story about the
graph.
Which graph best represents the relationship
between the height of a burning candle and
the amount of time that passes as the candle
burns?
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–6
Identify the graph that best represents the
relationship between the number of gallons of
gasoline Mr. Saenz purchased at $3.79 a
gallon and the total cost of his gasoline.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–7
Below are congruent isosceles triangles
arranged in a sequence to obtain a
geometric pattern.
Which expression can be used to find the
perimeter of a composite figure made up of
t triangles arranged in this pattern?
A 12t − 5
B 5t + 2
C 2t + 10
D 12t
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–8
Choose the correct algebraic expression modeled by
the pattern, and then create a pattern that models
one of the other algebraic expressions.
The pattern of dots shown below continues
infinitely, with more dots being added at each
step.
Which expression can be used to determine
the number of dots in the nth step?
A 2n
B 6n
C 4n + (n + 1)
D 4n + 2
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–9
Be prepared to justify your answer.
Which expression can be used to find the nth
term in the following arithmetic sequence,
where n represents a number’s position in
the sequence?
A
n+4
B
3n +4
C
5n
D
4n + 1
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–10
Be prepared to justify your answer.
Which sequence uses the algebraic expression
3n + 5 to describe the relationship between a
term in the sequence and its position, n, in
the sequence?
A 8, 11, 14, 17, 20, …
B 8, 11, 15, 18, 21, …
C 8, 13, 18, 23, 28, …
D 5, 6, 7, 8, 9, …
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–11
Write a set of walking instructions, if
possible, for each graph. Your instructions
should include information about where the
walk begins, how fast the walker is walking,
and whether the walker is walking toward or
away from the zero mark.
1.
meters
seconds
Two graphs are on the next sheet.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
2.
Numerical Fluency Problems
meters
seconds
3.
meters
seconds
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–12
Show all your work for the following problem.
Write one or two sentences that describe the
walk represented by the data in the table.
What is the function rule for this data?
Austin ISD Secondary
Mathematics Department
Time in
seconds
0
Distance
in meters
6
1
5.8
2
5.6
3
5.4
4
5.2
5
5
6
4.8
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–13
Terri placed a pot of water on the stove to
boil. The temperature of the water in terms
of the time it was on the stove is represented
by the graph.
Write a reasonable interpretation of the graph.
Be sure to include as many details as possible
about what happened at the beginning, in the
middle and at the end.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–14
Be prepared to justify your answer.
Look at the graph below.
Which is the best interpretation of this graph?
A A runner runs at a constant rate of 2 miles
every 30 minutes.
B Jorge earns $20 for each hour worked.
C For every 10 pieces of candy Stacey buys,
she pays $1.
D For every 10 students at a dance, 2
teachers are needed as chaperones.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–15
Be prepared to justify your answer.
Which of the following tables does not
represent a function?
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–16
Be prepared to justify your answer.
Which relationship does not represent a
function?
A
D
x
y
0
4
–5
0
13
6
7 –11
B
C
-2
-1
0
1
4
2
f(x) = 3x + 7
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–17
Be prepared to justify your answer.
The table below shows the relationship
between p, the number of cell phones a
company produces, and d, the number of cell
phones that are defective.
Which equation can be used to describe this
relationship?
A d = 20p
B d = p/20
p  90
d
C
2
D d = p – 95
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–18
Be prepared to justify your answer.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–19
Be prepared to justify your answer.
For a car traveling at a speed of 50 miles per
hour, the relationship between the distance
traveled, d, and the time traveled, t, is
described by the function d= 50t. Which
statement is true?
A The time traveled depends on the distance
traveled.
B The distance traveled depends on the time
traveled.
C The speed of the car depends on the
distance traveled.
D The speed of the car depends on the time
traveled.
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–20
Be prepared to justify your answer.
Jaime is six feet tall. He climbs a ladder to
paint some trim on his house. For each rung
that he climbs, Jaime is 1.6 feet higher above
the ground. Which expression could you use
to calculate the distance from the top of
Jaime’s head to the ground if r represents the
number of ladder rungs he has climbed?
A 1.6r + 6
B 1.6r
C r+6
D 6r + 1.6
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–21
Be prepared to justify your answer.
Which function includes all of the ordered
pairs in the table?
A
B
C
D
x
–5
–3
0
1
4
f(x)
13
9
3
1
–5
3x + 2
–2x + 3
–3x – 2
2x – 3
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–22
Sketch a trend line through each scatter plot.
1)
2)
3)
4)
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–23
Be prepared to justify your answer.
The graph below shows the relationship between the
distance in miles a delivery truck traveled and the
number of hours each delivery took.
Which best describes the relationship shown on the
graph?
A Positive Correlation
B Negative Correlation
C No Correlation
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–24
Be prepared to justify your answer.
Let n represent a term’s position in a sequence.
Which algebraic expression can be used to find
the nth term of the sequence below?
4, 8, 12, 16, 24, 28, …
A
B
C
D
2n(n + 1)
4n
4n2
3n + 1
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009
Algebra 1
Numerical Fluency Problems
Numerical Fluency Problem #1–25
Be prepared to justify your answer.
Which table identifies points on the line defined
by the equation y − 5x = −9?
Austin ISD Secondary
Mathematics Department
1st 6 Weeks Fall 2009