Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency Specification Sheet
2nd Six Weeks: 24 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.
133
6.2C
1
1032 = 320; 2032 = 640; 3032 = 960; 4032 = 1280; 5032 = 1600;
10032 = 3200
2
The use of Landmark numbers will vary depending on how many groups
of 32 are subtracted each time. Here is one possibility. n = 26
1
n
32 832
2-1
136
610
133
2-2
136
610
L
6.12A
6.2C
-320
512
-320
192
-160
32
-32
0
6
=
=
=
10 groups of 32
leftover
10 groups of 32
leftover
5 groups of 32
leftover
1 group of 32
26 groups of 32
1
1027 = 270; 2027 = 540; 3027 = 810; 4027 = 1080; 5032 = 1350;
10027 = 2700
2
The use of Landmark numbers will vary depending on how many groups
of 27 are subtracted each time. Here is one possibility. n = 17
1
n
27 459
L
6.12A
=
-270
189
-189
0
6
=
=
10 groups of 27
leftover
7 groups of 27
17 groups of 27
1
133
6.2C
1
1043 = 430; 2043 = 860; 3043 = 1290; 4043 = 1720; 5043 = 2150;
10043= 4300
2 The use of Landmark numbers will vary depending on how many groups
of 43 are subtracted each time. Here is one possibility. n = 62
n
43 2666
2-3
136
610
L
6.12A
6
Austin ISD Secondary Mathematics Department
-2150
516
-430
86
-86
0
=
=
=
2nd Six Weeks 2009-2010
50 groups of 43
leftover
10 groups of 43
leftover
2 groups of 43
62 groups of 43
Page 1 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
Answer
1
133
6.2C
1
1061 = 610; 2061 = 1220; 3061 = 1830; 4061 = 2440; 5061 = 3050;
10061= 6100
2 The use of Landmark numbers will vary depending on how many groups
of 61 are subtracted each time. Here is one possibility. n = 85
n
61 5185
2-4
2-5
136
L
610
6.12A
6
133
136
605
610
6.2C
L
6.11A
6.12A
1
1
L
133
6.2C
1
605
6.11A
6
610
6.12A
6
2-7
130
133
605
610
L
6.2C
6.11A
6.12A
1
6
6
2-8
130
133
605
610
L
6.2C
6.11A
6.12A
1
6
6
130
L
133
6.2C
2-9
1
2
=
=
=
50 groups of 61
leftover
30 groups of 61
leftover
5 groups of 61
85 groups of 61
$7168
28 haircuts
6
6
130
2-6
-3050
2135
-1830
305
-305
0
7
3
or 1 apples. Both forms of
4
4
the amount are important to discuss. Here is one potential diagram. Each
large square represents one apple. Each small square with horizontal
1
stripes represents one friend’s share from each apple, or of the apple.
4
However, there are 7 small squares with horizontal stripes, so each friend’s
7
3
share is
or 1 apples.
4
4
Diagrams will vary. Each friend will get
2 A
Diagrams will vary.
1
Each friend will get 2
2
brownies.
3
2 C
Diagrams will vary.
1
Each friend will get
2
C
1
of a stick of gum.
3
Diagrams will vary.
1
605
6.11A
6
610
6.12A
6
1
Each friend will get
2
D
Austin ISD Secondary Mathematics Department
3
of a pizza.
8
2nd Six Weeks 2009-2010
Page 2 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
2-10
122
6.2E
1
Answer
1
2
3
2
49
7
1
130
L
133
6.2C
1
605
6.11A
6
610
6.12A
6
130
133
605
610
L
6.2C
6.11A
6.12A
1
6
6
2-11
2-12
2-13
122
6.2E
1
2-14
130
133
605
L
6.2C
6.11A
1
6
610
6.12A
6
130
133
605
610
L
6.2C
6.11A
6.12A
1
6
6
107
L
108
L
2-15
4 cartons
1
2 3 Miles
3
3 3 pieces of ribbon
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 amounts were the 24 team members. The remainder of 8 miles was to
be split evenly among the 24 team members; each of the 24 team members
1
would swim
of a mile of the remaining 8 miles for the mileage to be split
3
evenly.
B
1. A
2. 50
1
1344 miles
1
2 9 Miles
3
Students should be using multiplication and division strategies that make
sense to them, but are also efficient strategies.
1 D
2 C
Students should be using multiplication and division strategies that make
sense to them, but are also efficient strategies.
1 2.7 or 2.70
2
3
2
2-16
2-17
110
6.1A
1
217
6.3B
2
107
108
110
L
L
6.1A
3
Two and seven tenths or two and seventy hundredths
1
2
3.1 or 3.10
1
Austin ISD Secondary Mathematics Department
3
4
2nd Six Weeks 2009-2010
Page 3 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
NF
Problem
2-18
2-19
Matrix
#
TEKS
#
TAKS
Obj #
217
6.3B
2
107
L
108
L
110
6.1A
1
217
6.3B
2
107
L
108
L
110
6.1A
1
217
6.3B
2
107
L
108
L
110
6.1A
1
217
6.3B
2
108
L
127
6.2B
1
217
6.3B
2
108
L
127
6.2B
Answer
3
Three and one tenth or Three and ten hundredths
1
2
1.25
3
1
2
3
1
2
3
0.1
zero and nine hundredths or nine hundredths
See additional answers.
2.3
2.2
2.2
Two and twenty-seven hundredths
1-3
See additional answers below.
4
1.72 + 0.20 = 1.92
1-2
1
One and twenty-five hundredths
0.09
0
2-20
2-21
2
1
3
4
See additional answers below.
3.40 – 1.86 = 1.54
2 13 10
2-22
217
6.3B
108
L
3.40
- 1.86
1.54
2
1-2
3
4
See additional answers below.
1.75 – 0.89 = 0.86
0 16 15
2-23
127
6.2B
1.75
- 0.89
0.86
1
kkk
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 4 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
NF
Problem
Matrix
#
TEKS
#
TAKS
Obj #
217
6.3B
2
Answer
1 a = 579
5 e = 333
2-24
108
L
127
6.2B
610
6.12A
1
6
2 b = 57.9
6 f = 33.3
3 c = 5.79
7 g = 3.33
4 d = 0.579
8 h = 0.333
9 When adding decimals, only the common place values can be operated on
together (i.e. tenths can be added only to other tenths, hundredths can only
be combined with other hundredths, etc). The same rule applies for
subtraction. It is far more important for students to understand this idea
rather then simply saying “line up the decimals” for the reason given in the
“Did You Know?” note below.
Did You Know? Note how this is actually the same rule for adding and
subtracting fractions – only fractions with common denominators can be
operated on together. Later in the year students will connect their
understanding of fractions to their understanding of decimals. Students come
to see that decimals are special fractions with denominators limited to only
1
1
1
powers of 10 (i.e. tenths , hundredths , thousandths , etc.)
100
10
1000
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 5 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-1
1
Compute the following factor pairs to get some Landmark
Numbers for 32.
Landmark Numbers
10  32 = _____
20  32 = _____
30  32 = _____
40  32 = _____
50  32 = _____
100  32 = _____
2
Use Landmark Numbers for 32 to find the value of n that
makes the following division problem true.
n
32 832
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 6 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-2
1
Compute the following factor pairs to get some Landmark
Numbers for 27.
Landmark Numbers
10  27 = _____
20  27 = _____
30  27 = _____
40  27 = _____
50  27 = _____
100  27 = _____
2
Use Landmark Numbers for 27 to find the value of n that
makes the following division problem true.
n
27 459
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 7 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-3
1
Compute the following factor pairs to get some Landmark
Numbers for 43.
Landmark Numbers
10  43 = _____
20  43 = _____
30  43 = _____
40  43 = _____
50  43 = _____
100  43 = _____
2
Use Landmark Numbers for 43 to find the value of n that
makes the following division problem true.
n
43 2666
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 8 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-4
1
Compute the following factor pairs to get some Landmark
Numbers for 61.
Landmark Numbers
10  61 = _____
20  61 = _____
30  61 = _____
40  61 = _____
50  61 = _____
100  61 = _____
2
Use Landmark Numbers for 61 to find the value of n that
makes the following division problem true.
n
61 5185
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 9 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-5
1
Stylists at a hair salon charge $16 for each
haircut. If the stylists gave 448 haircuts during
the last month, how much money did they
collect, not including tips?
2
Rebecca is a stylist at a hair salon. Last week
she made $448 giving haircuts. If each haircut
costs $16, how many haircuts did Rebecca give?
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 10 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-6
1
Draw a diagram to answer the following
question. Write the answer in a sentence.
There are 7 apples. Four friends will share the
apples equally. How many apples will each
friend get?
2
There are 7 apples. Four friends will share the
apples equally. Which of the following
expressions does NOT represent this situation?
Be prepared to justify your answer.
A
47
B
47
C
74
D
7
4
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 11 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-7
1
Draw a diagram to answer the following
question. Write the answer in a sentence.
There are 8 brownies. Three friends will share
the brownies equally. How many brownies will
each friend get?
2
There are 8 brownies. Three friends will share
the brownies equally. Which of the following
expressions does NOT represent this situation?
Be prepared to justify your answer.
A
83
B
8
3
C
38
D
38
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 12 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-8
1
Draw a diagram to answer the following
question. Write the answer in a sentence.
There is one stick of gum. Three friends will
share the gum equally. How much gum will each
friend get?
2
There is one stick of gum. Three friends will
share the gum equally. Which of the following
expressions does NOT represent this situation?
Be prepared to justify your answer.
A
13
B
1
3
C
13
D
31
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 13 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-9
1
Draw a diagram to answer the following
question. Write the answer in a sentence.
There are 3 pizzas. Eight friends will share the
pizzas equally. How much pizza will each friend
get?
2
There are 3 pizzas. Eight friends will share the
pizzas equally. Which of the following
expressions does NOT represent this situation?
Be prepared to justify your answer.
A
38
B
3
8
C
83
D
8
3
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 14 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-10
Simplify the following expressions using the correct
order of operations.
1
24  3  3 2
2
(45  20)  3  8
3
8  (16  4)  3
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 15 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-11
1
One day at the Barrera family farm, the chickens
laid 80 eggs. The eggs were placed in cartons
that hold 24 eggs each. How many cartons were
needed for the 80 eggs?
2
To raise money, the 24 members of the swim
team got pledges for a swim marathon. The
team goal is to swim 80 miles while sharing the
swimming equally. How many miles will each
team member swim?
3
There are 80 yards of ribbon on a roll. How
many pieces of ribbon each 24 yards long can be
cut from the roll?
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 16 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-12
The Robinson family bought a phone card
containing 10 hours of phone time. There are 6
people in the Robinson family. They will share the
phone time equally. Which of the following does
NOT show how much time each Robinson family
member will get to talk.
A
100 minutes
B
0.6 hour
C
1
D
1 hour 40 minutes
2
hours
3
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 17 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-13
1
Choose the letter of the correct answer. What is
the value of the following expression?
8(15  3  2)
2
A 56
B 42
C 24
D 20
Record your answer and fill in the bubbles below
your answer. Use the correct place value.
Find the value of the following expression:
150  (50  2)  4
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 18 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-14
1
During summer, Melinda drove 112 miles each
day for 12 days. How many miles did she travel
altogether?
2
Lance rode his bicycle 112 miles in 12 hours.
How many miles did he ride per hour?
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 19 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-15
1
2
At the Graham Packaging Company, 744 ounces of fruit juice
will be placed in bottles. Each bottle will hold 32 ounces of
fruit juice. How many bottles of juice can the company fill?
A
23
3
bottles
4
B
13
1
bottles
4
C
24 bottles
D
23
1
bottles
4
The Florida Juice Company has an agreement with a grocery
store. During the next year, they will make 32 deliveries to
the grocery store. Each time they will deliver 744 bottles of
fruit juice. How many bottles of fruit juice will Florida Juice
Company deliver to the grocery store in that year?
A
776 bottles
B
26808 bottles
C
23808 bottles
D
2368 bottles
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 20 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-16
1
If the complete shaded area below represents 1
whole,
what value does the total shaded area below
represent?
2
Find and label this value on the number line below.
0
3
1
2
3
4
5
Write this value using words.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 21 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-17
1
If the complete shaded area below represents 1
whole,
what value does the total shaded area below
represent?
2
Find and label this value on the number line below.
0
3
1
2
3
4
5
Write this value using words.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 22 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-18
1
If the complete shaded area below represents 1
whole,
what value does the total shaded area below
represent?
2
Find and label this value on the number line below.
0
3
1
2
3
4
5
Write this value using words.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 23 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-19
1
If the complete shaded area below represents 1
whole,
what value does the total shaded area below
represent?
2
Find and label this value on the number line below.
0
3
0.1
0.2
0.3
0.4
0.5
Write this value using words.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 24 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-20
1
If the complete shaded area below represents 1
whole,
shade in the area that represents the value 2.27.
2
Find and label this value on the number line below.
2.2
3
2.3
2.4
2.5
2.6
2.7
Write this value using words.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 25 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-21
=1
1
Shade in the value that represents 1.72.
2
Shade in the value that represents 0.2.
3
Shade in the value that represents the sum of
1.72 + 0.2.
4
Show how to compute the sum of 1.72 + 0.2.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 26 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-22
=1
1
Shade in the value that represents 3.4.
2
From that value, remove 1.86. Shade in the
remaining value below.
3
Write a number sentence that represents this action.
4
Show how to record these actions symbolically.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 27 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-23
=1
1
Shade in the value that represents 1.75.
2
From that value, remove 0.89. Shade in the
remaining value below.
3
Write a number sentence that represents this action.
4
Show how to record these actions symbolically.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 28 of 29
Grade 6 Mathematics---------------------------------------------------------Numerical Fluency Problems
Numerical Fluency #2-24
Find the value of the variable that makes each
equation below true.
1
123 + 456 = a
5
456 – 123 = e
2
12.3 + 45.6 = b
6
45.6 – 12.3 = f
3
1.23 + 4.56 = c
7
4.56 – 1.23 = g
4
0.123 + 0.456 = d
8
0.456 – 0.123 = h
9
Write an algorithm that can be used to add and
subtract decimals.
Austin ISD Secondary Mathematics Department
2nd Six Weeks 2009-2010
Page 29 of 29