Grade 8
Mathematics
Unit: 01 Lesson: 01
Rational Number Application KEY
Select the most appropriate answer choice for each question. Indicate why each answer
choice is or is not the appropriate choice.
1. Gaona Construction is currently building four houses. There is a work crew at each of the
1
1
3
2
3
8
four job sites. The construction company has completed
of one job,
of another job,
3
4
of a third job, and
of the last job. Select the list that shows the fraction of work
completed at the job sites in ascending order.
Justify Reasoning
Compare the fractions after writing the fractions with the
3 1 1 3
9
8 12 18
A.
8 3 2 4
, , ,
24 24 24 24
same
denominator.
,
, different denominators:
Fractions with the same, numerator,
1 1 3 3
1
1
B.
2 3 4 8
2
3
, , ,
the fraction with the smaller denominator is greater.
>
Fractions with the same numerator, different denominators:
3 1 3 1
3
3
C.
4 2 8 3
4
8
, , ,
the fraction with the smaller denominator is greater.
>
Compare the fractions after writing the fractions with the
1 3 1 3
8
9 12 18
D.
3 8 2 4
24 24 24 24
, , ,
same denominator.
,
,
,
2. The competition in the 2004 Summer Olympics Men’s Team Final Gymnastics was fierce.
For example, in the horizontal bar event, the U.S.A. scored 28.636, Germany scored 28.7,
Romania scored 27.962, and China scored 28.537 points. Which list shows these scores in
descending order?
Justify Reasoning
A.
28.636, 28.537, 28.7, 27.962
B.
28.7, 28.636, 28.537, 27.962
C.
27.962, 28.7, 28.636, 28.537
©2012, TESCCC
Line up the decimals based on corresponding place
value positions. Compare the whole number portion
first, then the decimal portion. Not descending order
because 28.636 < 28.7.
Line up the decimals based on corresponding place
value positions. Compare the whole number portion
first, then the decimal portion. Decimals in
descending order.
Line up the decimals based on corresponding place
value positions. Compare the whole number portion
first, then the decimal portion. Not descending order
because 27.962 < 28.7.
05/15/12
page 1 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
D.
©2012, TESCCC
27.962, 28.537, 28.636, 28.7
Line up the decimals based on corresponding place
value positions. Compare the whole number portion
first, then the decimal portion. Decimals in ascending
order, not descending order.
05/15/12
page 2 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
Rational Number Application KEY
Select the most appropriate answer choice for each question. Indicate why each answer
choice is or is not the appropriate choice.
3. Jill is ranking the different tasks at her job based upon amount of time spent on each task.
Select the list that shows the tasks ranked in ascending order. Reading and responding to
7
16
emails: 18.75% of the work day, sales calls:
of the workday, designing ads for clients:
1
2
0.25 of the day, and business meetings: 12 % of the day.
Justify Reasoning
7
1
Write in decimal form and compare the corresponding place value
positions. 0.4375, 0.25, 0.1875, 0.125  descending order, not
A.
16
2
, 0.25, 18.75%, 12 % ascending order.
7
1
Did not look at place value positions as significant. Looked at
B.
16
2
digits  7, 12, 18, 25.
, 12 %, 18.75%, 0.25
C.
0.25, 18.75%, 12
D.
12
1
2
1
2
%,
%, 18.75%, 0.25,
7
16
Did not look at place value positions as significant. Looked at
digits and wrote in descending order  25, 18, 12, 7.
7
16
Write in decimal form and compare the corresponding place value
positions. 0.125, 0.1875, 0.25, 0.4375
4. Ms. Jones had her class keep track of the losses and gains of a particular stock in the stock
market during the first few days of the month. Which list shows the losses and gains ranked
in ascending order?
Justify Reasoning
Write in decimal form, rank according to left or right of 0
3
7
7
3 3
3
A.
16
8
12 16 8
and distance from 0  −1.2, −1.1875, −0.875,
− 0.58 ,
−1.2, −1
,− ,−
,
,
B.
−1
C.
©2012, TESCCC
3
16
,−
7
8
7
3 3
12 16 8
, −1.2, −
,
,
3 3
7
7
3
8 16
12
8
16
,
,−
, − , −1
, −1.2
0.1875, 0.375
3
−1
16
and -1.2 are found between consecutive integers -2
7
−
8
and -1.
is found between consecutive integers -1 and 0
3
−1
When placing positive and negative
16rational numbers in
ascending
order,
negative
rational
numbers
are located to
and cannot be placed between
and -1.2
the left of the positive rational numbers: here positives are
placed to the left of negatives
05/15/12
page 3 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
D.
©2012, TESCCC
3 3
7
7
3
8 16
12
8
16
,
,−
, −1.2, − , −1
When placing positive and negative rational numbers in
ascending order, negative rational numbers are located to
the left of the positive rational numbers: here positives are
placed to the left of negatives
05/15/12
page 4 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
Rational Number Application KEY
Select the most appropriate answer choice for each question. Indicate why each answer
choice is or is not the appropriate choice.
5. Joe is trying to graph the fraction
5
12
on the class number line by placing a green dot on
5
12
the correct location. Mrs. Garcia told Joe that
is between one pair of fractions already
5
12
graphed on the number line. The fraction
is found between which pair of fractions on
the number line?
Justify Reasoning
A.
1
4
B.
8
16
C.
1
4
D.
6
16
and
5
16
and
and
1
2
1
2
and
9
24
6
Convert to decimal form: 0.25 and 0.3125  0.41 is
not between.
8
1
16
2
Simplify
 equivalent to
6
Convert to decimal form: 0.25 and 0.5  0.41 is
between.
6
9
3
16
24
8
Simplify
and
 both equivalent to
6. Identify the group that does NOT contain equivalent fractions, decimals, and percents.
Justify Reasoning
A.
B.
C.
©2012, TESCCC
3
16
11
12
, 0.1875, 18
3
4
Convert to decimal form: all = 0.1875
%
6
, 0.91 , 91.6%
5
2
6
12
3
, 0.41 , 41 %
Convert to decimal form: first two = 0.91
last one = 0.916
Convert to decimal form: all = 0.41
05/15/12
6
6
page 5 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
D.
©2012, TESCCC
2
3
6
, 0.6 , 66
2
3
%
Convert to decimal form: all = 0.6
05/15/12
6
page 6 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
Rational Number Application KEY
Select the most appropriate answer choice for each question. Indicate why each answer
choice is or is not the appropriate choice.
7. It is estimated that only 7.5% of today’s junior high students will be employed as adults in a
job requiring little computer skills. Which number is NOT equivalent to 7.5%?
Justify Reasoning
A.
3
40
B.
7.5
100
C.
0.075
D.
7.5
10
Convert to decimal form: 0.075
Divide by 100: 0.075
Compare to other answers
Divide by 10: 0.75
8. Which pair of rational numbers is −
7
8
NOT between?
Justify Reasoning
A.
− 100% and − 50%
B.
− 1 and −
C.
−
D.
−
©2012, TESCCC
7
12
15
16
7
12
and −
and −
3
4
13
16
Common denominators and compare: −
Common denominators and compare:
24
21
14
24
24
24
−
<−
<−
Common denominators and compare:
21
18
14
7
24
24
24
8
−
<−
<−
 − is not between.
Common denominators and compare:
15
14
13
16
16
16
−
<−
<−
05/15/12
8
8
<−
7
8
<−
4
8
page 7 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
©2012, TESCCC
05/15/12
page 8 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
Rational Number Application KEY
Select the most appropriate answer choice for each question. Indicate why each answer
choice is or is not the appropriate choice.
9. Create an example for ordering rational numbers including integers, percents, positive and
negative decimals and fractions. Explain the strategy you would use to arrange the
numbers from your example in ascending order.
Sample Answer:
3
3
16
5
Arrange the following numbers in ascending order: 1
, − 0.3, − , − 0.375, 1, and 115%.
Write the numbers in decimal form, compare place value positions, and put in order.
1.1875, − 0.3, − 0.6, − 0.375, 1.0, and 1.15  − 0.6, − 0.375, − 0.3, 1.0, 1.15, 1.1875
10. Which number is NOT between −
A.
− 75%
B.
2
3
−
C.
−
D.
3
7
− 0.7
3
5
and − 80%? −
The numerator in −
3
7
> − 50%.
3
5
3
7
and − 80% < − 50%
is less than half the denominator, so −
11. Four cities in North Texas recorded temperatures below zero during a very strong cold
front. Amarillo recorded a temperature of −14.2 oF. Canyon recorded a temperature of
1
2
−14 oF. Hereford recorded a temperature of −14.09 oF. Canadian recorded a temperature
of −15 oF. Which list shows the cities in order of temperatures from least to greatest?
A.
Hereford, Amarillo, Canyon, Canadian
B.
Canadian, Hereford, Amarillo, Canyon
C.
Canadian, Canyon, Amarillo, Hereford
©2012, TESCCC
05/15/12
page 9 of 10
Grade 8
Mathematics
Unit: 01 Lesson: 01
D.
©2012, TESCCC
10
Canadian, Amarillo, Hereford, Canyon
05/15/12
page 10 of