GACE Practice Test 2-with correct Answers
1/8 2/5 3/8 4/5 5/8
20% 30% 40% 50% 80%
How many fraction-percent equivalents are listed in the worksheet represented above?
One
Two
Three
Four - Answer-Option (B) is correct. The question requires an understanding of ways to
help students develop a knowledge of fractions as numbers. 1/8 is equivalent to 12.5%;
2/5 is equivalent to 40%; 3/8 is equivalent to 37.5%; 4/5 is equivalent to 80%; and 5/8 is
equivalent to 62.5%.
/.Students in a fourth-grade class are learning how to copy line segments and angles
from their textbook onto a piece of paper. Which of the following tools is appropriate for
the activity?
Select all that apply.
A protractor
A straightedge
A geoboard
A compass - Answer-The correct answers are (A), (B), and (D). The question requires
an understanding of how to draw and identify lines and angles. A geoboard is useful for
illustrating concepts such as area and perimeter but is not useful for measuring angles.
A compass, a protractor, and a straightedge will be useful for the activity.
/.Which of the following activities will best help kindergarten students understand the
concept of negative numbers?
Watching a needle on a dial that shows how fast a wheel is turning
Using a thermometer to illustrate extreme temperatures recorded at the South Pole
Moving the hands of a clock back an hour at the beginning of daylight saving time
Placing money from a change purse into a piggy bank - Answer-Option (B) is correct.
The question requires an understanding of how to help students make sense of
numbers. Kindergarten students need a concrete model when first learning an abstract
concept. From the choices provided, a thermometer showing temperatures above and
below zero will best provide them with an appropriate model to learn about negative
numbers.
/.Green 32%
,Yellow 21%
Blue 20%
Violet 23%
Red ?
The circle graph above shows the distribution, in percents, of various colors of gems in
a collection. What fraction of the collection is red? - Answer-Option (A) is correct. The
question requires an understanding of how to solve problems involving fractions. A
circle graph of percents represents 100% of a group. Based on the information
provided, the total percent of red gems is 4%, which is equivalent to 2/50.
/.The Evergreen Shoe Factory received an order for 100 pairs of shoes. The factory
ships shoes in cartons that each holds up to 12 pairs. How many cartons will the factory
need to ship this order?
Most of the fourth graders who worked on the problem above gave answers such as 8
R4, 8.333, and 8 1/3 . These responses suggest that the students need practice in
rounding down
expressing remainders
applying number sense
using fractions rather than decimals - Answer-Option (C) is correct. The question
requires an understanding of equations and number operations. The responses indicate
that the students do not know how to express a reasonable answer. Since the shoes
are shipped in cartons, the number of cartons should be expressed as a whole number
and not in decimals, fractions, or with a remainder.
/.Second-grade students are using a calculator to total the number of books in their
classroom library. At one point, they mistakenly subtract 12 instead of adding 12. The
calculator display shows a total of 57. What one operation can they do to correct the
mistake?
Add 12
Add 24
Subtract 12
Subtract 24 - Answer-Option (B) is correct. The question requires knowledge of ways to
help students develop an understanding of number operations. The students must add
the 12 books they inadvertently subtracted and then add the 12 they had originally
intended to add. This can be done all at once by adding 24 to the result displayed on
the calculator.
/.A retailer wants to determine the size most often purchased of a certain type of
children's shoe to ensure that enough of that item is available to meet consumer
demand.Sizes sold last month: 2, 2, 2, 3, 5, 5, 7, 8.
, A fifth-grade teacher poses the question above to the class during a lesson. The lesson
most likely addresses which of the following concepts?
Mode
Median
Mean
Range - Answer-Option (A) is correct. The question requires an understanding of how to
represent and interpret data. The mode is the number that occurs most often in a given
set of numbers.
/.Which of the following activities requires a student to perform a mathematical
computation at the most concrete level?
Adding 2+42+4
Joining two blocks and four blocks
Adding two apples and four apples using pictures of the apples
Solving x+4=6 - Answer-Option (B) is correct. The question requires an understanding
of how to help students develop a basic concept of number operations. Teachers must
understand the skills students need to perform specific mathematical tasks, as well as
the proper order for introducing concepts. In this question, the most concrete task is the
one that engages the students in physical manipulation (joining two blocks and four
blocks).
/.19+17+15+13+7+5+3+119+17+15+13+7+5+3+1
A teacher writes an addition problem on the board and asks students to think of other
ways to write the sum, using a different operation. Which of the following represents the
sum of the numbers shown using multiplication?
4×18
4×19
4×20
4×21 - Answer-Option C is correct. The question requires knowledge of ways to help
students develop an understanding of number operations. The numbers can be added
in pairs, with the sum of each pair totaling 20 (19 and 1, 17 and 3, 15 and 5, and 13 and
7). There are four such pairs, so the sum of the eight numbers is 4 x 20.
/.A fourth-grade class is discussing the problem shown.
Sid is traveling by train from Little City to Big City. The train departs Little City at 8:30
A.M. and arrives in Big City at 9:15 P.M. How long does it take the train to travel from
Little City to Big City?
During the discussion, one student says, "All you have to do is subtract 830 from 915,
and you have the answer! It's 85 minutes." For which of the following reasons is the
student incorrect?
1/8 2/5 3/8 4/5 5/8
20% 30% 40% 50% 80%
How many fraction-percent equivalents are listed in the worksheet represented above?
One
Two
Three
Four - Answer-Option (B) is correct. The question requires an understanding of ways to
help students develop a knowledge of fractions as numbers. 1/8 is equivalent to 12.5%;
2/5 is equivalent to 40%; 3/8 is equivalent to 37.5%; 4/5 is equivalent to 80%; and 5/8 is
equivalent to 62.5%.
/.Students in a fourth-grade class are learning how to copy line segments and angles
from their textbook onto a piece of paper. Which of the following tools is appropriate for
the activity?
Select all that apply.
A protractor
A straightedge
A geoboard
A compass - Answer-The correct answers are (A), (B), and (D). The question requires
an understanding of how to draw and identify lines and angles. A geoboard is useful for
illustrating concepts such as area and perimeter but is not useful for measuring angles.
A compass, a protractor, and a straightedge will be useful for the activity.
/.Which of the following activities will best help kindergarten students understand the
concept of negative numbers?
Watching a needle on a dial that shows how fast a wheel is turning
Using a thermometer to illustrate extreme temperatures recorded at the South Pole
Moving the hands of a clock back an hour at the beginning of daylight saving time
Placing money from a change purse into a piggy bank - Answer-Option (B) is correct.
The question requires an understanding of how to help students make sense of
numbers. Kindergarten students need a concrete model when first learning an abstract
concept. From the choices provided, a thermometer showing temperatures above and
below zero will best provide them with an appropriate model to learn about negative
numbers.
/.Green 32%
,Yellow 21%
Blue 20%
Violet 23%
Red ?
The circle graph above shows the distribution, in percents, of various colors of gems in
a collection. What fraction of the collection is red? - Answer-Option (A) is correct. The
question requires an understanding of how to solve problems involving fractions. A
circle graph of percents represents 100% of a group. Based on the information
provided, the total percent of red gems is 4%, which is equivalent to 2/50.
/.The Evergreen Shoe Factory received an order for 100 pairs of shoes. The factory
ships shoes in cartons that each holds up to 12 pairs. How many cartons will the factory
need to ship this order?
Most of the fourth graders who worked on the problem above gave answers such as 8
R4, 8.333, and 8 1/3 . These responses suggest that the students need practice in
rounding down
expressing remainders
applying number sense
using fractions rather than decimals - Answer-Option (C) is correct. The question
requires an understanding of equations and number operations. The responses indicate
that the students do not know how to express a reasonable answer. Since the shoes
are shipped in cartons, the number of cartons should be expressed as a whole number
and not in decimals, fractions, or with a remainder.
/.Second-grade students are using a calculator to total the number of books in their
classroom library. At one point, they mistakenly subtract 12 instead of adding 12. The
calculator display shows a total of 57. What one operation can they do to correct the
mistake?
Add 12
Add 24
Subtract 12
Subtract 24 - Answer-Option (B) is correct. The question requires knowledge of ways to
help students develop an understanding of number operations. The students must add
the 12 books they inadvertently subtracted and then add the 12 they had originally
intended to add. This can be done all at once by adding 24 to the result displayed on
the calculator.
/.A retailer wants to determine the size most often purchased of a certain type of
children's shoe to ensure that enough of that item is available to meet consumer
demand.Sizes sold last month: 2, 2, 2, 3, 5, 5, 7, 8.
, A fifth-grade teacher poses the question above to the class during a lesson. The lesson
most likely addresses which of the following concepts?
Mode
Median
Mean
Range - Answer-Option (A) is correct. The question requires an understanding of how to
represent and interpret data. The mode is the number that occurs most often in a given
set of numbers.
/.Which of the following activities requires a student to perform a mathematical
computation at the most concrete level?
Adding 2+42+4
Joining two blocks and four blocks
Adding two apples and four apples using pictures of the apples
Solving x+4=6 - Answer-Option (B) is correct. The question requires an understanding
of how to help students develop a basic concept of number operations. Teachers must
understand the skills students need to perform specific mathematical tasks, as well as
the proper order for introducing concepts. In this question, the most concrete task is the
one that engages the students in physical manipulation (joining two blocks and four
blocks).
/.19+17+15+13+7+5+3+119+17+15+13+7+5+3+1
A teacher writes an addition problem on the board and asks students to think of other
ways to write the sum, using a different operation. Which of the following represents the
sum of the numbers shown using multiplication?
4×18
4×19
4×20
4×21 - Answer-Option C is correct. The question requires knowledge of ways to help
students develop an understanding of number operations. The numbers can be added
in pairs, with the sum of each pair totaling 20 (19 and 1, 17 and 3, 15 and 5, and 13 and
7). There are four such pairs, so the sum of the eight numbers is 4 x 20.
/.A fourth-grade class is discussing the problem shown.
Sid is traveling by train from Little City to Big City. The train departs Little City at 8:30
A.M. and arrives in Big City at 9:15 P.M. How long does it take the train to travel from
Little City to Big City?
During the discussion, one student says, "All you have to do is subtract 830 from 915,
and you have the answer! It's 85 minutes." For which of the following reasons is the
student incorrect?
