# FCAT Mathematics Sample Items for Grade 5

Document Sample

FCAT Mathematics Sample

All questions are from the FCAT Mathematics Item
Specification for Grades 3 - 5
Table of Content

Strand A        Slides 3 - 16

Strand B        Slides 17 - 22

Strand C        Slides 23 - 31

Strand D        Slides 32 - 39

Strand E        Slides 40 - 53
1) Amy observed some animals and made a chart to
understands the    compare their speeds.
relative size of
whole numbers,
commonly used
fractions,
decimals, and
percents.

According to the chart, which animal was the fastest?
2) Six students ran in the 100-meter race at the City
understands the    Olympics. Their times are shown in the table below. What
relative size of   time listed in the table has the least value?
whole numbers,
commonly used
fractions,
decimals, and
percents.

2 0      67
3) Land covers 1/4 of Earth’s surface. The remaining 3/4 is
understands that         covered by water.
numbers can be
represented in a
variety of equivalent
forms using whole
numbers, decimals,
fractions, and
percents.
Which value below represents the amount of Earth’s
surface covered by water?
(Also assesses A.1.2.1
and A.1.2.3)

4) One bicycle rack at school has enough slots to hold 10
uses place-value        bicycles. Today 7/10 of the bicycle rack is being used. What
concepts of             percent of the bicycle rack is being used today?
grouping based upon
powers of ten
(thousandths,
hundredths, tenths,
ones, tens, hundreds,
thousands) within the
decimal number
system.                           7 0

5) A bolt of lightning can travel at a speed of 334,800,000
understands and           miles per hour. What is the value of the 4 in the number
explains the effects      334,800,000 ?
subtraction, and
multiplication on
whole numbers,
decimals, and
fractions, including
mixed numbers, and
the effects of division
on whole numbers,
including the inverse
relationship of
multiplication and
division.

MC
5) A bolt of lightning can travel at a speed of 334,800,000
understands and           miles per hour. What is the value of the 4 in the number
explains the effects      334,800,000 ?
subtraction, and
multiplication on
whole numbers,
decimals, and
fractions, including
mixed numbers, and
the effects of division
on whole numbers,
including the inverse
relationship of
multiplication and
division.

MC
selects the appropriate   7) The 20 students in Mrs. Meyer’s class collected books
operation to              for a book exchange. Each student collected 3 books, and
solve specific            Mrs. Meyer collected 10 books. Which expression could be
problems involving        used to find the total number of books collected?
and multiplication of
whole numbers,
decimals, and
fractions, and division
of whole numbers.

MC
adds, subtracts, and    8) Dentists tell us we should brush our teeth 2 times a
multiplies whole        day for 3 minutes each time. How many minutes will you
numbers, decimals,      brush your teeth if you do this for 5 days?
and fractions,
including mixed
numbers, and divides
whole numbers to
solve real-world
problems, using
appropriate methods
of computing, such as
mental mathematics,
paper and pencil, and
calculator.

adds, subtracts, and    9) Robert’s father filled the tank of the car with 18 gallons
multiplies whole        of gasoline. The gasoline cost \$1.90 per gallon, including
numbers, decimals,      tax. How much did it cost to fill the tank?
and fractions,
including mixed
numbers, and divides
whole numbers to
solve real-world
problems, using           3 4       20
appropriate methods
of computing, such as
mental mathematics,
paper and pencil, and
calculator.

10) The Martin family moved into a new house and
wanted to plant grass seed in their backyard. They
uses and justifies        measured 2 sides of the backyard and drew the figure
different estimation      below.
strategies in a real-
world problem
situation and
determines the
reasonableness of
results of calculations
in a given problem
situation.

(Also assesses
B.3.2.1)

Estimate the 4 measurements, A, B, C and D that are
missing on the figure and then use those measurements to
uses and justifies        find the total area, in square feet, of the Martins’ backyard.
strategies in a real-
world problem
situation and
determines the
reasonableness of
results of calculations
in a given problem
situation.

(Also assesses
B.3.2.1)

A top-score response would correctly estimate the length of
uses and justifies        the missing sides and the correct area of the Martins’
different estimation      backyard.
strategies in a real-
world problem
situation and
determines the
reasonableness of
results of calculations
in a given problem
situation.

(Also assesses
B.3.2.1)

Continued

uses and justifies
different estimation
strategies in a real-
world problem
situation and
determines the
reasonableness of
results of calculations
in a given problem
situation.

(Also assesses
B.3.2.1)

11) Jack wants to give an equal number of marbles to
each of his 4 friends. At the toy store he sees several
bags of marbles, as shown below. Which bag of marbles
understands and           should Jack buy so that he can give each of his 4 friends
applies basic             an equal number of marbles with none left over?
number theory
concepts, including
primes, composites,
factors, and multiples.

MC
12) Jenna watched someone diving. The diver’s body
made these angles during the different parts of the dive.
solves real-world    Which number labels the picture of the diver’s body
problems             forming an acute angle?
involving length,
weight, perimeter,
area, capacity,
volume, time,
temperature, and
angles.

13) For outdoor concerts, Mr. Shannon’s class built a
square stage floor. The top view of the stage floor is shown
solves real-world    below. The area of the stage floor is 400 square feet. What
problems             is the length, in feet, of the stage floor?
involving length,
weight, perimeter,
area, capacity,
volume, time,
temperature, and
angles.
20

14) Deon placed a 4-pound weight on one side of a
balance scale. Then he placed 32 pieces of candy on the
uses direct             other side of the scale to make it balance. Each piece of
(measured) and          candy is the same weight.
indirect
(not measured)
measures to calculate
and compare
measurable
characteristics.

Grades 3–4 MC           How much does one piece of candy weigh?
15) A solar or tropical year is 365 days, 5 hours, 48
minutes and 46 seconds. How many seconds are there in
uses direct             48 minutes?
(measured) and
indirect
(not measured)
measures to calculate
and compare
measurable
characteristics.            28 8 0

16) The height of the Eiffel Tower in Paris, France, is 328
yards. Due to erosion, the Great Pyramid of Giza, Egypt,
uses direct             is now only 450 feet high. How many yards higher is the
(measured) and          Eiffel Tower than the Great Pyramid of Giza?
indirect
(not measured)
measures to calculate
and compare
measurable
characteristics.            17 8

17) Which of these measurements best describes the actual
distance between Orlando, Florida and Miami, Florida?
selects and uses
appropriate standard
and nonstandard units
of measurement,
according to type and
size.

(Also assesses
B.4.2.1)

MC
18) In art class, Sasha drew the rectangular prism
pictured below.
given a verbal
description, draws
and/or models two-
and three-dimensional
shapes and uses
appropriate geometric
vocabulary to write a
description of a figure
or a picture composed
of geometric figures.     Which of the following does line segment EF represent in
the rectangular prism?

MC
19) Which pair of triangles below appears to be a pair
understands the          of similar triangles?
concepts of spatial
relationships,
symmetry, reflections,
congruency, and
similarity.

(Also assesses
B.1.2.1, B.1.2.2,
C.1.2.1, and C.3.2.1)

20) Mr. Gomez is a shopping mall manager. The
shopping mall where he works is divided into sections.
The mall floor plan below shows the location of 2
understands the
stores, the restrooms, and the fountain in the shopping
concepts of spatial
mall.
relationships,
symmetry, reflections,
congruency, and
similarity.

(Also assesses
B.1.2.1, B.1.2.2,
C.1.2.1, and C.3.2.1)

understands the
concepts of spatial
relationships,
symmetry, reflections,
congruency, and
similarity.

(Also assesses
B.1.2.1, B.1.2.2,
C.1.2.1, and C.3.2.1)

understands the
concepts of spatial
relationships,
symmetry, reflections,
congruency, and
similarity.

(Also assesses
B.1.2.1, B.1.2.2,
C.1.2.1, and C.3.2.1)

understands the
concepts of spatial
relationships,
symmetry, reflections,
congruency, and
similarity.

(Also assesses
B.1.2.1, B.1.2.2,
C.1.2.1, and C.3.2.1)

21) Jim reflected the figure below over the dashed line
predicts, illustrates,    and then rotated it 90° clockwise around its center.
and verifies
which figures could
result from a flip
(reflection), slide
(translation), or turn
(rotation) of a given    Which of the following shows the figure after the reflection
figure.                  and 90° clockwise rotation?

MC
22) Raylene plotted points A and B on the coordinate grid
below. If she plots 2 more points, she can connect the points
to create a square. What will be the area of her completed
represents and applies
square?
a variety of strategies
and geometric
properties and
formulas for two- and
three-dimensional
shapes to solve
real-world and
mathematical
problems.

(Also assesses
C.2.2.1 and C.3.2.2)

23) Marcia drew the map below. She included the library,
the park, and her school.
identifies and plots
positive ordered
pairs (whole numbers)
in a rectangular
coordinate system
(graph).

MC

If her house is located halfway between the library and the
park, which ordered pair would best describe the location of
her house?
24) Olga is ordering pencils for her classmates. Each box
of pencils costs 2 dollars. There is an additional shipping
cost of 3 dollars per order.

describes a wide
variety of patterns
and relationships
through models, such
as manipulatives,
tables, graphs, rules
using algebraic
symbols.

What is the total price, in dollars, for an order of 15 boxes of
(Also assesses          pencils?
D.1.2.2)

25) Hallie is making a design with square tiles. The first
design has 6 white tiles in the center and 4 gray legs. As
describes a wide        shown in the pictures below, the legs of each new design
variety of patterns     have more gray tiles than the legs of the design before.
and relationships
through models, such
as manipulatives,
tables, graphs, rules
using algebraic
symbols.

(Also assesses
D.1.2.2)

According to the pattern, how many tiles will Hallie use all
together to make a design that has 5 tiles in each leg?

describes a wide
variety of patterns
and relationships
through models, such
as manipulatives,
tables, graphs, rules
using algebraic
symbols.                    26

(Also assesses
D.1.2.2)

26)

generalizes a pattern,
relation, or function to
explain how a change
in one quantity results
in a change in another.

(Also assesses
D.1.2.1)

assessed)
generalizes a pattern,
relation, or function to
explain how a change
in one quantity results
in a change in another.

(Also assesses
D.1.2.1)

assessed)
27) Let n represent the number of papers Mrs. Zapata graded
represents a given       Mr. Goldberg graded 2 times the number of papers Mrs.
simple problem           Zapata graded, plus 15 papers from his after-school program.
situation using          Which expression could be used to find the number of papers
diagrams, models, and    Mr. Goldberg graded?
symbolic expressions
translated from verbal
phrases, or verbal
phrases translated
from symbolic
expressions, etc.

(Also assesses
D.2.2.2)

MC
28) Look at the two inequalities below.

uses informal
methods, such as         Which of the number lines below shows a graph of all the
physical models and      whole numbers that h could represent to make both
graphs, to solve real-   inequalities true statements?
world problems
involving equations
and inequalities.

(Also assesses
D.2.2.1)

29) Dwayne’s fifth grade class bought 35 key lime pies to
sell at the school’s fair this year. If Dwayne’s class had
bought 1 more pie, the number of pies this year would have
been twice the number of pies sold last year. Let p represent
uses informal            the number of pies sold last year. What is the value of p in
methods, such as         the equation below?
physical models and
graphs, to solve real-
world problems
involving equations
and inequalities.
18
(Also assesses
D.2.2.1)

30) The chart below shows 3 types of drinks and the
number of gallons of each type of drink purchased in a
school cafeteria last week.
solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

Grades 3–4 MC             Which graph displays this information correctly?
Which graph displays this information correctly?

solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

choose their favorite cafeteria lunches. The results are
shown below.
solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

Count the number of students who prefer each type of
lunch and write the numbers in the chart below.
solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)
On the grid, make a bar graph showing the number of
students who prefer each type of lunch.
Grade 5 MC, GR, ER        Be sure to include:

a title                             labels for the axes;
appropriate and consistent scales   all the data
solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

A top-score response includes a correctly constructed bar
solves problems by        graph and two statements of comparison, including
generating, collecting,
organizing, displaying,   A valid bar graph similar to one of the two examples shown
and analyzing data        below;
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

solves problems by
generating, collecting,
organizing, displaying,
and analyzing data
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.

(Also assesses
E.1.2.3)

32) At a school dance, the disc jockey asked 40 students to
choose the type of music they wanted to hear. The circle
graph below shows the percent of students who chose each
solves problems by        type of music.
generating, collecting,
organizing, displaying,   According to the graph, how many of the 40 students
and analyzing data        chose jazz?
using histograms, bar
graphs, circle graphs,
line graphs,
pictographs, and
charts.                    12
(Also assesses
E.1.2.3)

33) Mrs. Terry posted the scores from this week’s science
quiz on the board as shown below.

determines range,
mean, median, and
mode from sets of
data.

(Also assesses
E.1.2.3)

Grades 3–4 MC       What is the range of the scores shown in the stem-and-leaf plot?
34) The chart below shows the names of seven kinds of
cloud formations. It also shows some of their recorded
distances above Earth. What is the median distance above
determines range,   Earth, in miles, of the cloud formations listed in the chart
mean, median, and   above?
mode from sets of
data.

(Also assesses
E.1.2.3)
4
35) Krista (K), Juan (J), and Rosie (R) will compete against
each other in the 50-yard dash. After the race, they will each
uses models, such as   be awarded one of the ribbons shown below.
tree diagrams, to
display possible
outcomes and to
predict events.

In the space below, list all the different ways these 3
Grades 3–4 MC          students could place first, second, or third in the race. You
Grade 5 SR             may use the first letter of each student’s name in your list
(for example, K, J, R).

What is the total number of ways these 3 students could
place in the race? ___________
uses models, such as
tree diagrams, to
display possible
outcomes and to
predict events.

36) At the cookie sale, Marc bought 3 sugar, 8 oatmeal, 5
predicts the likelihood
peanut butter, and 4 chocolate chip cookies that were all the
of simple events
same size and shape. All the cookies were placed in one bag.
occurring.
Since Marc’s friend likes all of the cookies, he will choose 1
cookie from the bag without looking. What is the probability
that Marc’s friend will choose a chocolate chip cookie?
MC
37) Dean is collecting data on his classmates’ favorite and
least favorite cafeteria foods. He plans to present his results
designs experiments to     to the cafeteria manager. Which of the following is the best
answer class or            survey for Dean to use to collect his data?
personal questions,
collects information,
and interprets the
results using statistics
(range, mean, median,
and mode) and
pictographs, charts, bar
graphs, circle graphs,
and line graphs.

(Also assesses E.3.2.2)