Austin Independent School District
Department of Curriculum and Instruction
Mathematics
Numerical Fluency
Grade 6
Mathematics
1st Six-Weeks
2009-2010
Numerical Fluency Problems #1-1 through 1-25
(1-26 through 1-28 OPTIONAL)
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 1 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency Specification Sheet
1st Six Weeks: 29 Days
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
Discuss Numerical Fluency Problems by having students share their multiple strategies.
This sharing will help students become flexible, efficient, and accurate with numerical
reasoning while learning the TEKS deeply.


1-1
128
L

1-2
112
6.1E
128
L
133
6.2C
1
112
6.1E
1
133
6.2C
225
L
1
There are many possible rectangular arrays for 36 students.
1 row with 36 students, 2 rows with 18 students each, 3 rows with 12 students
each, 4 rows with 9 students each, 6 rows with 6 students each, 9 rows with 4
students each, 12 rows with 3 students each, 18 rows with 2 students each,
and 36 rows with 1 student each
Number of
Rows, r
1
2
4
5
10
20
25
50
100
1
1-3
128
L
205
L
128
L
205
L
1-4
1-5
Strategy #1: Changing the order of the factors does not change the
product such as 4  5  20 and 5  4  20 .
Strategy #2: Double a column to obtain twice as much such as doubling
the products of the 3’s column gives the products to the 6’s column. For
example, 3  4  12 so 6  4  2  12  24 .
Strategy #3: Use the 5’s as a benchmark and add groups of a number to
the product of the 5’s. For example, to recall 8  8 , do
5 × 8 + 3 × 8 = 40 + 24 = 64 .
Number of
Students in Each
Row, s
100
50
25
20
10
5
4
2
1
1
2
3
4
5
1
2
3
Since 5 groups of 8 are 40, one more group of 8 added to 40 makes 48.
6  8 = (5  8) + (1  8)
Since 3 groups of 8 are 24, 6 groups of 8 would be twice as much or 48.
6  8 = (3  8)  2
6  8 = 48, 8  6 = 48, 48  8 = 6, 48  6 = 8
Since 5 groups of 8 are 40, two more groups of 8 added to 40 makes 56.
7  8 = (5  8) + (2  8)
Since 10 groups of 8 are 80, three groups of 8 or 24 less than 80 makes
56.
4 7  8 = (10  8) - (3  8)
5 7  8 = 56, 8  7 = 56, 56  8 = 7, 56  7 = 8
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 2 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
121
TAKS
Obj #
L
1-6
610
6.12A
121
6
L
1-7
610
6.12A
6
112
6.1E
1
610
6.12A
6
135
6.2D
1
1-8
1-9
136
L
130
L
133
6.2C
1
605
6.11A
6
610
6.12A
6
6.2C
1 Answers will vary. Here are some possible number sentences.
4  15 = (4  5) + (4  5) + (4  5)
4  15 = (2  15) + (2  15)
4  15 = (4  10) + (4  5)
2
4  15 = 60, 15  4 = 60, 60  4 = 15, 60  15 = 4
1 Answers will vary. Here are some possible number sentences.
29  15 = (20  15) + (9  15)
29  15 = (10  15) + (10  15) + (9  15)
29  15 = (30  15) – 15
2 29  15 = 435, 15  29 = 435, 435  15 = 29, 435  29 = 15
1 Answers will vary. Here are some possible factor pairs.
10  25, 3  25, 20  13, 5  13, 30  25, 7  25
2 Answers will vary. Here are some possible number sentences.
13  25 = (10  25) + (3  25)
13  25 = (20  13) + (5  13)
13  25 = (30  25) - (7  25)
3 13  25 = 325, 25  13 = 325, 325  13 = 25, 325  25 = 13
50 groups of 18 is closer to the product of 47  18 because it is 3 groups
of 18 more than the product, whereas, 40 groups of 18 is 7 groups of 18
less than the product.
2 20(17) is closer to 22  17 because it is 34 less 22  17, whereas, 25  17
is 51 more than 22  17.
1
1
2
1-10
133
Answer
1
2 pieces of rope
3 buses
1
3 2 dollars or $2.50
2
Help students think about remainders. Depending on the context of the
situation, remainders are dropped sometimes, sometimes they are rounded
up, and sometimes a fractional remainder makes sense. Do NOT teach
division with fractions or decimals at this time. Help students make sense of
the remainder by thinking about what the whole amount. In this case the
whole amount were the 40 band students. The remainder of $20 was to be
split evenly among the 40 band students; each of the 40 band students gets
$0.50 of that remainder of $20.
1
2
3
4  26 = (2  26) + (2  26)
4  26 = (4  20) + (4  6)
26
1-11
135
136
6.2D
1
L
Austin ISD Secondary Mathematics Department
X
4
24
=
(4 x 6) =
4 rows of 6
80
=
(4 x 20) =
4 rows of 20
104
1st Six Weeks 2009-2010
Page 3 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
1
133
6.2C
1
2
3
The missing dimension on the left is 9. The missing dimension on the top
is 20.
9  28 = (9  20) + (9  8)
28
X
1-12
135
6.2D
9
72
=
(9 x 8)
180
=
(9 x 20) =
1
=
9 rows of 8
9 rows of 20
252
136
L
4
1
2
112
6.1E
1
9  28 = 252; 28  9 = 252; 252  28 = 9; 252  9 = 28
432 pencils
The table below shows all the possible arrangements of cement squares
for the patio.
Number of Rows, r
1-13
128
L
133
6.2C
1
2
3
4
6
8
12
16
24
48
1
1
133
6.2C
2
10 x 20 = 200
10 x 20 = 200
10 x 20 = 200
4 x 20 = 80
10 x 6 = 60
10 x 6 = 60
10 x 6 = 60
6 x 4 = 24
1
1-14
136
Number of Cement
Squares in Each Row,
s
48
24
16
12
8
6
4
3
2
1
26
x 34
24
80
180
600
884
=
=
=
=
4x6
4 x 20
30 x 6
30 x 20
34 x 26
34 x 26 = 884
L
3 34  26 = 884; 26  34 = 884; 884  26 = 34; 884 34 = 26
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 4 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
1
133
6.2C
10 x 10
10 x 10
10 x 10
10 x 10
2 x 10
7 x 10
7 x 10
7 x 10
7 x 10
7x2
42 x 17
1
1-15
136
= 100
= 100
= 100
= 100
= 20
= 70
= 70
= 70
= 70
= 14
= 714
2
42
X
17
14
280
20
400
714
=7x2
= 7 x 40
= 10 x 2
= 10 x 40
= 42 x 17
L
3 42  17 = 714; 42  17 = 714; 714  42 = 17; 714  17 = 42
1 Answers will vary. Here is one possibility.
45  39 = 40  39 + 5  39 = 1560 + 195 = 1755
133
6.2C
1
2
45
X 39
45
360
150
1200
1755
1-16
136
Answers will vary Here is one possibility.
L
=9x5
= 9 x 40
= 30 x 5
= 30x 40
= 45 x 39
Strategies will vary. Efficient methods should be both accurate and quick.
1 72  14 = 10  72 + 4  72 = 720 + 288 = 1008
133
6.2C
1
2
1-17
136
L
3
Austin ISD Secondary Mathematics Department
27
X 56
42
120
350
1000
1512
=6x7
= 6 x 20
= 50 x 7
= 50x 20
= 56 x 27
32(95) = 100  32 – 5  32 = 3200 – 160 = 3040
1st Six Weeks 2009-2010
Page 5 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
1
112
6.1E
441
420
399
378
357
336
315
294
273
252
231
210
189
168
147
126
105
84
64
42
21
1
1-18
1-19
133
6.2C
1
112
6.1E
1
133
6.2C
1
136
1-20
L
133
6.2C
1
133
6.2C
1
1-21
136
L
2
3
4
5
10
10
10
Answers will vary. Here are a
few possibilities.
a
3
5
10
13
15
b
63
105
210
273
315
1
2
3
4
5
6
7
8
9
10
420
20
20
210
420
630
840
1050
1680
2100
1
21 crayons
2
Students should be using division strategies that make sense to them, but are
also efficient strategies.
1 Both Marta and James arrange their division problems vertically and write
their groups of 21 to the right side of the problem. Both Marta and James
subtract groups of 21 until no groups of 21 remain of the original 504.
James method is different than Marta’s method because he subtracts 20
groups of 21 as a first step, whereas Marta only subtracts 10 groups of 21
as the first step.
2 n = 24
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 6 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
1
135
6.2D
378
360
342
324
306
288
270
252
234
216
198
180
162
144
126
108
90
72
54
36
18
1
1-22
136
L
38  18 = 20  18 + 10  18 + 8  18 = 360 + 180 + 144 = 684
2
Miguel’s method
3
n
18 576
- 180
10 groups of 18
396 left over
- 360
20 groups of 18
36 left over
- 36
2 groups of 18
0
32 groups of 18
4
Gloria’s method
n
18 576
-540
36
- 36
0
1
133
6.2C
groups of 18
groups of 18
groups of 18
10 x 18 = 180; 20 X 18 = 360; 30 x 18 = 540; 40 x 18 = 720; 50 x 18 =
900; 100 x 18 = 1800
1
2
1-23
136
30
left over
2
32
900 = 50 group of 18
54
54 = 3 groups of 18
0
L
1-24
133
136
6.2C
1
L
1-25
128
L
1
1-26
optional
108
127
L
6.2B
1
n
18 954
1
2

54
86
Strategy #1: Changing the order of the factors does not change the
product such as 4  5  20 and 5  4  20 .
 Strategy #2: Double a column to obtain twice as much such as doubling
the products of the 3’s column gives the products to the 6’s column. For
example, 3  4  12 so 6  4  2  12  24 .
 Strategy #3: Use the 5’s as a benchmark and add groups of a number to
the product of the 5’s. For example, to recall 8  8 , do
5 × 8 + 3 × 8 = 40 + 24 = 64 .
1 $47.16
Austin ISD Secondary Mathematics Department
2 $12.89
3 0.124
1st Six Weeks 2009-2010
4 $70.01
Page 7 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
NF
Problem
1-27
optional
1-28
optional
Matrix
#
108
127
108
227
223
TEKS
#
L
6.2B
L
6.2B
6.5A
TAKS
Obj #
1
1
2
Answer
9.5 – 2.75 = 6.75 inches
1
2
Austin ISD Secondary Mathematics Department
C
$50.05
1st Six Weeks 2009-2010
Page 8 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-1
Complete the following multiplication table.
X 1 2
1
2
2 2
3 3 6
4 4 8
5 5 10
6 6 12
7
8 8 16
9 9 18
10 10 20
11 11 22
12
3
3
6
4 5 6 7 8 9
4 5 6
8 9
8 10 12
16 18
12
18
24
12
20 24
15 20
30 35
45
18 24 30
54
35
24
45 54 63
30 40
60 70
90
10
10
20
30
40
50
60
11
11
22
12
60
90
60
List 3 strategies you used to recall facts you did not
know.
1.
2.
3.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 9 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-2
The Super Bowl is going to be held in Austin this year.
The Super Bowl Committee has decided that the 36
students in Ms. Grant’s class at Fulmore Middle School
will march in the pre-game parade. They will march in a
variety of rectangular arrays such as the one shown
below.
Write down as many of the possible marching
arrangements for the 36 students that you can.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 10 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-3
The Super Bowl Committee changed their minds. They decided
all 100 sixth graders at Fulmore Middle School may march in the
pre-game parade. The 100 students will march in a variety of
rectangular arrays.
One of the Fulmore sixth graders wrote the following equation to
help find all the possible arrangements.
r  s  100
A variable, often a letter of the alphabet, represents a quantity
that changes. In the equation above, the variable r represents the
number of rows. The variable s represents the number of
students in each row.
Create a table of data for the two variables. In the table write as
many possible marching arrangements for the 100 students that
you can.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 11 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-4
1
Describe in words how to use 5  8 to find the
product of 6 8 .
2
Write a horizontal number sentence using 5  8
that shows how to find the product of 6 8 .
6 8 = _______________________
3
Describe in words how to use 3 8 to find the
product of 6 8 .
4
Write a horizontal number sentence using 3 8
that shows how to find the product of 6 8 .
6 8 = _______________________
5
What is the multiplication and division fact
family for 6 8 ?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 12 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-5
1
Describe in words how to use 5  8 to find the
product of 7 8 .
2
Write a horizontal number sentence using 5  8
that shows how to find the product of 7 8 .
7 8 = _______________________
3
Describe in words how to use 10 8 to find the
product of 7 8 .
4
Write a horizontal number sentence using 10 8
that shows how to find the product of 7 8 .
7 8 = _______________________
5
What is the multiplication and division fact
family for 7 8 ?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 13 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-6
Multiplication Cluster
45
2  15
4  10
4  15
1
Using one or more factor pairs from the Multiplication
Cluster, write a horizontal number sentence that
shows how to find the product of 4  15.
4  15 = ________________________________
2
What is the multiplication and division family for
4  15?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 14 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-7
Multiplication Cluster
10  15
20  15
30  15
9  15
29  15
1
Using one or more factor pairs from the Multiplication
Cluster, write a horizontal number sentence that
shows how to find the product of 29  15.
29  15 = ________________________________
2
What is the multiplication and division family for
29  15?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 15 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-8
There are 13 classes of 6th grade mathematics at Porter
Middle School. Each class has 25 students.
1
Create a cluster of factors pairs that could be used to
find the total number of students in the 13 classes.
Multiplication Cluster
______________
______________
______________
______________
13  25
2
Using one or more factor pairs from the Multiplication
Cluster, write a horizontal number sentence that
shows how to find the product of 13  25.
13  25 = ____________________________
3
What is the multiplication and division family for
13  25?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 16 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-9
Without doing any calculations, decide which expression
is a closer estimate to the multiplication problem in each
rectangle. Explain your reasoning.
40 groups of 18
1
47  18
50 groups of 18
2
20(17)
22  17
Austin ISD Secondary Mathematics Department
25  17
1st Six Weeks 2009-2010
Page 17 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-10
1
A rope is 100 feet long. How many pieces of
rope, each 40 feet long, can be cut from the
rope?
2
100 people from Lamar Middle School are going
on a field trip. Each bus holds 40 people. How
many buses are needed for the field trip?
3
A $100 prize was given to 40 band students who
entering a marching contest. If the money is
shared equally, how much will each student
receive?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 18 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-11
The array below models the multiplication problem 4  26.
1
The following array shows a way to divide the array above
into groups.
26
2
2
Using the dimensions from the array above, write a horizontal
number sentence that shows how to find the product of 4  26.
4  26 = ____________________________________
2
The following array shows another way to divide the array
into groups.
6
20
4
Using the dimensions from the array above, write a horizontal
number sentence that shows how to find the product of 4  26.
4  26 = ____________________________________
3
Complete the following vertical number sentence for 4  26.
26
X 4

Austin ISD Secondary Mathematics Department
(4 x 6)
(4 x 20)
1st Six Weeks 2009-2010
4 rows of 6
4 rows of 20
Page 19 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-12
The array below models the multiplication problem 9  28.
1
The following array shows a how to divide the array above
into groups to find the product of 9  28. Find each missing
dimension.
8
2
Using the dimensions from the array above, write a
horizontal number sentence that shows how to find the
product of 9  28.
9  28 = ____________________________________
3
Complete the following vertical number sentence for 9  28.
28
X 9

4
(9 x 8)
(9 x 20)
9 rows of 8
9 rows of 20
What is the multiplication and division family for 9  28?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 20 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-13
1
At the Austin ISD Warehouse, there are 72 pencils in
each box. The Mathematics Department at Murchison
Middle School ordered 6 boxes of pencils. How many
pencils were ordered?
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
2
Eric bought 48 cement squares to make a rectangular
patio. He created an equation, r  s = 48, to find the
different rectangular arrangements for the patio. If r
represents the number of rows and s represents the
number of squares in each row, what are all the
possible arrangements for the rectangular patio?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 21 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-14
1
To multiply 34  26, Janie used the following array model.
Complete the multiplication equations and find the total
product.
20
6
10
10 x 20 = ______
10 x 20 = ______
10 x 20 = ______
4 x 20 = ______
10 x 6 = ______
10 x 6 = ______
10 x 6 = ______
6 x 4 = ______
4
34 x 26 = ______
10
10
2
To multiply 34  26, Greg used the following array model.
Complete the vertical multiplication strategy to find the total
product.
20
6
26
x 34
4x 6
4 x 20
30 x 6
30 x 20
30
34 x 26
4
Austin ISD Secondary Mathematics Department
3
What is the multiplication and division
family for 26 x 34?
1st Six Weeks 2009-2010
Page 22 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-15
To multiply 17  42, Roy used the following array model. Complete
the multiplication equations and find the total product.
1
10
7
10 x 10 = ______
10 x 10 = ______
10 x 10 = ______
10 x 10 = ______
2 x 10 = ______
7 x 10 = ______
7 x 10 = ______
7 x 10 = ______
7 x 10 = ______
7 x 2 = ______
10
10
10
10
2
42 x 17 = ______
To multiply 17  42, Sandra used the following array model. Complete
the vertical multiplication strategy to find the total product.
7
10
2
42
x 17
7x 2
7 x 40
10 x 2
10 x 40
40
42 x 17
2
Austin ISD Secondary Mathematics Department
3
What is the multiplication and division
family for 42 x 17?
1st Six Weeks 2009-2010
Page 23 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-16
In recent Numerical Fluency problems you have used the
following multiplication strategies.




Clusters
Horizontal number sentences
Arrays
Vertical number sentences
1
Compute 45  39 using one of the above strategies.
2
Compute 45  39 using another one of the above
strategies.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 24 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-17
Use an efficient method to compute each of the following
problems. Be prepared to explain why your method
makes sense and why it is efficient.
1
72  14
2
27  56
3
32(95)
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 25 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-18
1
Complete the Multiple Tower below for 21.
2
How many multiples of 21
does it take to get to 210?
3
What value of x makes the
following equation true?
x  21 210
4
What value of y makes the
following equation true?
210  21  y
5
_____
63
42
21
Use the Multiple Tower for 21
to find at least 3 pairs of
numbers that make the
following equation true.
a 21  b
Save your Multiple Tower for use
during the next few days.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 26 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-19
Use the Multiple Tower you built for 21 to answer
the following problems.
1
After 210, what is the next multiple of 21 that
has a 0 in the ones place value?
2
What value of a makes this equation true.
a  21 = 420
3
What value of r makes this equation true?
420  21 = r
Compute the following factor pairs to get some
Landmark Numbers for 21.
_____
63
42
21
3
10  21 = ______
4
20  21 = ______
5
30  21 = ______
6
40  21 = ______
7
50  21 = ______
8
80  21 = ______
9
100  21 = ______
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 27 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-20
There are 129 crayons. Six children will share the
crayons equally. How many crayons will each child
receive?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 28 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-21
Marta and James looked at the Multiple Tower for 21 and then
used different methods for the same division problem.
1
2
Be prepared to explain the similarities and differences of
their methods.
Find the value for n that makes the division problem true.
441
420
399
378
357
336
315
294
273
252
231
210
189
168
147
126
105
84
63
42
21
Austin ISD Secondary Mathematics Department
Marta’s method
n
21 504
- 210
10 groups of 21
294 left over
- 210
10 groups of 21
84 left over
- 84
4 groups of 21
0
n groups of 21
James’ method
n
21 504
- 420
20 groups of 21
84 left over
- 84
4 groups of 21
0
n groups of 21
1st Six Weeks 2009-2010
Page 29 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-22
1
Complete the Multiple Tower for 18. (Keep it
for tomorrow’s Numerical Fluency.)
2
Solve 38  18 by using a horizontal number
sentence.
3
Complete Miguel’s division problem below and
find the value of n that makes the problem
true.
Miguel’s method
n
18 576
- 180
10 groups of 18
396 left over
20 groups of 18
left over
-
? groups of 18
n groups of 18
1
4
Complete Gloria’s division problem below and
find the value of n that makes the problem
true.
Gloria’s method
n
18 576
30 groups of 18
18
left over
0
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
? groups of 18
n groups of 18
Page 30 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-23
1
Compute the following factor pairs to get some Landmark
Numbers for 18.
Landmark Numbers
10  18 = _____
20  18 = _____
30  18 = _____
40  18 = _____
50  18 = _____
100  18 = _____
2
Use your Multiple Tower for 18 and the Landmark Numbers
for 18 to find the value of n that makes the following division
problem true.
n
18 954
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 31 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-24
Record your answer and fill in the bubbles below your
answer. Be sure to use the correct place value.
1
There are 972 seats in the Austin High School Theater.
There are 18 seats in each row. How many rows of
seats are in this theater?
2
There are 1806 peach trees in the orchard. There are
21 rows of peach trees. How many trees are in each
row of the peach orchard?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 32 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-25
Complete the following multiplication table.
X
1
2
3
4
5
6
7
8
9
10
11
12
1
2
3
4
5
6
2
2
3
3
6
4 5 6 7 8
4 5 6
8 10 12
6
12
18
2
8 12
20 24
10 15 20
30 35
12 18 24 30
35
24
9
10 11 12
List 3 strategies you used to recall facts you did not know.
1.
2.
3.
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 33 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-26
Use an algorithm to find the value of the variable that
makes each equation true.
1
$ 35.17 + $ 11.99 = w
2
15.7 – 2.81 = n
3
z + 37.6 = 37.724
4
$100 - x = $ 29.99
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 34 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-27
Harold made a drawing of his rectangular kitchen.
The length of the drawing was 9.5 inches, and the
width of the drawing was 2.75 inches less than the
length. Find the width of the drawing.
Kitchen
9.5 inches
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 35 of 36
Grade 6 Mathematics------------------------------------------------------Numerical Fluency Problems
Numerical Fluency 1-28
David bought 2 shirts at Foleys. One shirt cost $23.50.
The other shirt was on sale for $5.95 off of the original
price of $32.50.
1
2
Which equation can be used to find n, the total
amount David paid for the 2 shirts?
A
n = 23.50 + (5.95 + 32.50)
B
n = (32.50 – 5.95) – 23.50
C
n = (32.50 – 5.95) + 23.50
D
n = (32.50 – 23.50) – 5.95
How much did David pay for the two shirts?
Austin ISD Secondary Mathematics Department
1st Six Weeks 2009-2010
Page 36 of 36