Download Bits and Pieces Ace 3

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Comparing Bits and Pieces
(INVESTIGATION 3)
Background Information and ACE Practice Problems
A C E
Applications | Connections |
Extensions
(INVESTIGATION 3)
Bits and Pieces
Applications
1. Describe, in writing or with pictures, how 73 compares to 2 13 .
2. Multiple Choice On a number line from 0 to –10, where is
 13
3
located?
A. between 0 and −1
B. between −4 and −5
C. between −5 and −6
D. between −6 and −7
3. Copy the number line below. Locate and label marks
representing
9
2 1 , 1 , and 15 .
4 10
4
For Exercises 5–8, write each mixed number as an
improper fraction.
5. 1 32
7. 9 7
6. 6 3
8. 4 2
9
4
7
For Exercises 9–12, write each improper fraction as a
mixed number.
9. 22
4
10. 10
6
11.  17
12.  36
5
8
1
13.What numbers have an absolute value of 2 1 ?
2
In many cold places, weather reports often include wind chills, the
temperature of how cold it feels outside when you include the wind
making it feel colder. For Exercises 16–19, write an inequality
statement for the wind chills of the two locations.
16.Lincoln, NE compared to New Albin, IA 15°F
example answer: 15° F >
17. Viroqua, WI compared to Toledo, OH −8°F
5° F
6°F
18. Minneapolis, MN compared to Duluth, MN −10°F
19. Bozeman, MT compared to Rapid City, SD −5°F
–25°F
−3°F
5 °F
20. Mr. Bergman is having an end-of-the-year trivia contest. Each
correct answer is worth 100 points, and each incorrect answer is worth
–50 points. At the end of the contest Mr. Bergman is surprised by the
final scores.
Blue Team
Orange Team
Purple Team
–50 points
–250 points
–200 points
The Blue team says they win because they have the
highest score. The White team says that 250 is greater
than 50, so they win. Which team should be called the
winner? Explain.
3
23. Franklin Middle School is having an end-of-the-year carnival with
different games. One of the games is a bean-bag toss. The object is to
get zero, or as close to zero as possible on the toss. Joseph’s bag lands
on an area labeled –3. Jeremiah’s bag lands on an area labeled 2.
Joseph says, “I win because –3 < 2.”
Jeremiah says, “No, we have to decide whose score is
closer to zero.
Since  3  3 and 2  2 , my score is closer to zero. I
win.”
Who is correct? Explain.
As Rosemary works through some homework problems, she
notices that negative numbers can often be rewritten using
positive numbers if you change what you are talking about. For
example, a golf score was given as –4 but Rosemary rewrote this as
“4 shots under par.” For Exercises 25–28, rewrite each negative
situation using a positive value.
25.A savings account balance is − $15.00.
26.The elevation of a city is −20 feet.
27.A quarterback ran for −8 yards.
28.The amount of money a lemonade stand made on a
rainy day was
− $10.00.
For Exercises 29–40, compare each pair of fractions using
benchmarks, number lines, and other strategies. Then use a less
than (<), greater than (>), or equal to (=) symbol to complete each
number sentence.
8
29. 10
3
8
30. 32
4
9
31. 53
5
12
32. 13
2
3
35.  8
6
9
9
36. 10
10
11
40.  54
7
8
example answer: >
33.
3
4
37.  3
12
3
5
7
12
34. 3
2
38.  56
7
6
12
5
8
39.  73
6
14
For Exercises 45–50, between which two benchmarks
(of 0, 1 , 1, 1 1 , and 2) does each fraction fall? Tell which
2
2
is the nearer benchmark.
46. 1 62
45. 53
47. 12
10
answer:
between ½ and 1
nearer to ½
2
48. 18
8
49. 110
50. 112
15
5.
51. Multiple Choice Which fraction is greatest?
F. 76
G. 89
13
H. 12
J.
14
15
52. Multiple Choice Find the opposite of each number below. Which
one is greatest?
A. 7
6
B. 89
C. 13
12
D. 14
15
For Exercises 60–63, write a decimal equivalent to the
fraction.
60. 3
4
61.
7
50
62.  13
25
7
63.  10
answer: 0.75
For Exercises 66–68, a full one-hundredths grid
represents the number 1. What fraction and decimal is
represented by each of the shaded parts?
66.
Answer: 40/100 or 4/10 or 0.4
68.
67.
For Exercises 70–72, copy the part of the number line
given. Then find the “step” by determining the
difference from one mark to another. Label the
unlabeled marks with decimal numbers.
Sample:
The step is 0.1.
70.
71.
72.
7
For Exercises 77–82, insert < , >, or = to make a true statement.
77.
0.205
0.21
78. 0.1
79.
−0.04
−0.050
80. −1.03
81.
5
10
0.6
82.  53
0.1000
−0.03
−0.3
For Exercises 83 and 84, rewrite the numbers in order
from least to greatest.
83.
45
0.33, −0.12, −0.127, 0.2, 10
3 , –0.005, 0.34
84.  45 , 1000
10
85. Multiple Choice The orchestra at Johnson School is
responsible for cleaning up a 15-mile section of
highway. There are 45 students in the orchestra. If each
orchestra member cleans the same-size section, which
of the decimals indicates the part of a mile cleaned by
each student?
F. 0.25
Connections
G. 0.33
H.0.333… J.
0.5
(Investigation 3)
Bits and Pieces
For Exercise 89, use the following information. Each student
activity group at Johnson School agreed to pick up litter along a
ten-mile stretch of highway
89. Kelly and Sean work together to clean a section of
highway that is 10
miles long. Write this distance as a
3
mixed number.
9
Extensions
(INVESTIGATION 3)
Bits and Pieces
8 and  4 .
97. Find five fractions between  10
5
11