MAT

HEM

AT

ICS

TEACHER’S BOOKLET�

MAT

HEM

AT

ICS

MATHEMATICS SAMPLE ANSWER KEY

33

999-8209-30-7

FCAT Sample Test Materials These sample test materials are designed to help students prepare to answer FCAT questions. These materials introduce them to the kinds of questions they will answer when they take FCAT and include hints for responding to FCAT questions. The FCAT Mathematics sample test materials for Grade 3 are composed of the books described below:

Sample Test Book Includes a mathematics sample test and instructions for completing the sample test. (Copies are available for all students in the tested grade.)

✓ Sample Answer Key Includes answers and explanations for the questions in the sample test. (Copies are available for classroom teachers only.)

✓= This book

Copyright Statement for This Assessment and School Performance Publication

Authorization for reproduction of this document is hereby granted to persons acting in an official capacity within the Uniform System of Public K–12 Schools as defined in Section 1000.01(4), Florida Statutes. The copyright notice at the bottom of this page must be included in all copies.

All trademarks and trade names found in this publication are the property of their respective owners and are not associated with the publishers of this publication.

Permission is NOT granted for distribution or reproduction outside of the Uniform System of Public K–12 Schools or for commercial distribution of the copyrighted materials without written authorization from the Florida Department of Education. Questions regarding use of these copyrighted materials should be sent to the following:

The Administrator Assessment and School Performance

Florida Department of Education Tallahassee, Florida 32399-0400

Copyright © 2004 State of Florida

Department of State

FCAT MathematicsSample

Answer Key

SAMPLE

33This book contains answers to the FCAT Mathematics sample test questions. It also gives the Sunshine State Standards benchmark assessed by each item on the sample test.

In addition, one or more possible approaches to solving the questions are provided. Students may use approaches other than these and still receive credit if they also obtain a correct answer.

Multiple-choice items on FCAT Mathematics tests are scored by awarding one point for each correct answer.

Page 1 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

● 1

SAMPLE 3 FCAT Mathematics Sample Answer Key

The correct answer is C (20 � 4).

Strand: A—Number Sense, Concepts, and Operations

Benchmark: MA.A.3.2.2 The student selects the appropriate operation to solve specific problems involving addition, subtraction, and multiplication of whole numbers, decimals, and fractions, and division of whole numbers.

To solve this problem, first decide whether it is an addition, subtraction, multiplication, or division problem.

The words “all together” indicate that it is either an addition or a multiplication problem. However, since each of the 20 students raised 4 dollars, 20 � 4 (Option A) would not determine the total. Therefore, it is a multiplication problem.

The correct answer is 20 � 4.

Page 2 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

● 2

FCAT Mathematics Sample Answer Key SAMPLE 3

The correct answer is G (5).

Strand: A—Number Sense, Concepts, and Operations

Benchmark: MA.A.4.2.1 The student 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 MA.B.3.2.1 solves real-world problems involving estimates of measurements including length, time, weight, temperature, money, perimeter, area, and volume.)

To solve this problem, ESTIMATE the number of pieces, equal to the size of the piece shown, that could be cut from the remaining pie. The estimate of the total number of pieces into which the pie could be cut should be about 6. Subtract the piece that has already been removed from the pie to find the number of pieces that could be cut from the remaining pie.

6 � 1 � 5.

The number of pieces, each equal to the size of the piece shown, that could be cut from the remaining pie is 5.

Page 3 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

●

● 4

3

SAMPLE 3 FCAT Mathematics Sample Answer Key

The correct answer is D [the grid with the fish located at (1, 2)].

Strand: C—Geometry and Spatial Sense

Benchmark: MA.C.3.2.2 The student identifies and plots positive ordered pairs (whole numbers) in a rectangular coordinate system (graph).

To determine which grid shows the fish located at (1, 2), start at 0 on the grid and countover 1 line to the right.

Then count 2 lines up.

Neither Option A, B, nor C shows the fish located at this point on the grid.

The grid that shows the fish located at (1, 2) is Option D.

The correct answer is F (12 � 4 � �).

Strand: D—Algebraic Thinking

Benchmark: MA.D.2.2.2 The student uses informal methods, such as physical models and graphs, to solve real-world problems involving equations and inequalities. (Also assesses MA.D.2.2.1 represents a given simple problem situation using diagrams, models, and symbolic expressions translated from verbal phrases, or verbal phrases translated from symbolic expressions, etc.)

Jamal spent a total of $12 on 4 tickets that were all of equal price. To find the price of each ticket, divide the total amount spent ($12) by the total number of tickets purchased (4).

12 � 4 � 3

Of the equations shown, 12 � 4 � � is the only equation that could be used to determine the price of each ticket.

Page 4 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

FCAT Mathematics Sample Answer Key SAMPLE 3

● The correct answer is D (7 hours).5

Strand: B—Measurement

Benchmark: MA.B.1.2.2 The student solves real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles.

To determine the answer, look at the time shown on each clock.

The first clock shows 6:00 in the morning. The second clock shows 1:00 in the afternoon.

First Strategy:

Look at the face of the first clock. The interval (time) between each number measures one hour. Starting at the 6, move clockwise to the 1. There are 7 one-hour intervals between the 6 and the 1.

OR

Second Strategy:

Subtract 6:00 from 12:00 and get 6 hours. Then count from 12:00 to 1:00 and get 1 hour. Add 6 hours and 1 hour to get an answer of 7 hours.

Melanie and her dad were on their fishing trip for 7 hours.

● The correct answer is F (37).6

Strand: A—Number Sense, Concepts, and Operations

Benchmark: MA.A.3.2.3 The student adds, subtracts, and multiplies whole numbers, decimals, 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.

To solve this problem, subtract the number of white stars on the first United States flag (13) from the number of white stars on today’s United States flag (50).

50 � 13 � 37

There are 37 more white stars on the flag today than there were on the first flag.

Page 5 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

SAMPLE 3 FCAT Mathematics Sample Answer Key

● The correct answer is C (the figure with 4 square tiles lined up in one row).7

Strand: C—Geometry and Spatial Sense

Benchmark: MA.C.3.2.1 The student represents and applies a variety of strategies and geometric properties and formulas for two- and three-dimensional shapes to solve real-world and mathematical problems. (Also assesses MA.C.2.2.1 understands the concepts of spatial relationships, symmetry, reflections, congruency, and similarity.)

To solve this problem, find the perimeter of each of Dante’s figures.

The tiles are square, which means that all of the sides of the tiles are the same length. The picture shows that this length is 1 foot.

Using the formula for perimeter, add the lengths of each outer edge together for each figure.

Figure A is 1 � 3 � 1 � 3 � 8Figure B is 2 � 1 � 2 � 1 � 6Figure C is 1 � 4 � 1 � 4 � 10Figure D is 2 � 2 � 2 � 2 � 8

Since 10 is the largest number, Figure C has the greatest perimeter.

● The correct answer is G (the envelope turned 180°).8

Strand: C—Geometry and Spatial Sense

Benchmark: MA.C.2.2.2 The student predicts, illustrates, and verifies which figures could result from a flip, slide, or turn of a given figure.

To solve this problem, imagine the envelope rotating around a point. As it rotates, the address on the envelope faces different directions.

Turning the envelope 180° moves the envelope halfway around a circle. The address on the envelope is now facing in the opposite direction. It is upside down.

Page 6 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

● 9

FCAT Mathematics Sample Answer Key SAMPLE 3

The correct answer is B (pounds).

Strand: B—Measurement

Benchmark: MA.B.2.2.2 The student selects and uses appropriate standard and nonstandard units of measurement, according to type and size. (Also assesses MA.B.4.2.1 determines which units of measurement, such as seconds, square inches, dollars per tankful, to use with answers to real-world problems.)

To solve this problem, decide which of the units of measurement listed could be used to determine the weight of an elephant.

Inches and yards are used to measure distance or length. Quarts are used to measure liquid capacity.

The only unit of measure listed that could be used to determine the weight of an elephant is pounds.

Page 7 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

● 10

SAMPLE 3 FCAT Mathematics Sample Answer Key

The correct answer is F (the picture of the bear).

Strand: E—Data Analysis and Probability

Benchmark: MA.E.2.2.2 The student predicts the likelihood of simple events occurring.

To solve this problem, look at the sections of the spinner.

The spinner is divided into eight equally-sized sections: 1 bear section, 2 elephant sections, 2 kangaroo sections, and 3 tiger sections. Since the number of bear sections is the least number, it is least likely that the spinner would land on this section.

The spinner is least likely to land on the bear section.

Page 8 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

● 11

FCAT Mathematics Sample Answer Key SAMPLE 3

The correct answer is A (4 years).

Strand: E—Data Analysis and Probability

Benchmark: MA.E.1.2.1 The student solves problems by generating, collecting, organizing, displaying, and analyzing data using histograms, bar graphs, circle graphs, line graphs, pictographs, and charts. (Also assesses MA.E.1.2.3 analyzes

Yea

rs

real-world data to recognize patterns and relationships of the measures of central tendency using tables, charts, histograms, bar graphs, line graphs, pictographs, and circle graphs generated by appropriate technology, including calculators and computers.)

To answer the question, look at the bar graph. The animals are named across the bottom (x-axis) of the graph. The numbers along the left side (y-axis) of the graph show the number of years in the animals’ life spans.

ANIMALS' LIFE SPANS 20

18

16

14

12

10

876

432

0 Mouse Hamster Starfish Queen Ant Octopus

Animal

The starfish is the third bar from the left. To read the number of years in its life span, look to see to what number the top of the bar corresponds. The bar seems to be about halfway between the 6 and the 8, which would be 7.

The octopus is the fifth bar from the left. To read the number of years in its life span, look to see to what number the top of the bar corresponds. The bar seems to be about halfway between the 2 and the 4, which would be 3.

To determine how much longer a starfish lives than an octopus, subtract the life span of the octopus (3) from the life span of the starfish (7).

7 � 3 � 4

A starfish lives 4 years longer than an octopus.

Page 9 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

SAMPLE 3 FCAT Mathematics Sample Answer Key

● The correct answer is H (2 � t).12

Strand: D—Algebraic Thinking

Benchmark: MA.D.2.2.1 The student represents a given simple problem situation using diagrams, models, and symbolic expressions translated from verbal phrases, or verbal phrases translated from symbolic expressions, etc. (Also assesses MA.D.2.2.2 uses informal methods, such as physical models and graphs, to solve real-world problems involving equations and inequalities.)

To solve the problem, determine whether it is best to use addition, subtraction, multiplication, or division.

The phrase “2 times the weight” indicates that this is a multiplication problem. The weight of an adult Diplodocus was 2 times the weight of an adult Tyrannosaurus Rex, which is represented by t.

The correct answer is 2 � t.

● The correct answer is C (6 inches).13

Strand: E—Data Analysis and Probability

Benchmark: MA.E.1.2.2 The student determines range, mean, median, and mode from sets of data. (Also assesses MA.E.1.2.3 analyzes real-world data to recognize patterns and relationships of the measures of central tendency using tables, charts, histograms, bar graphs, line graphs, pictographs, and circle graphs generated by appropriate technology, including calculators and computers.)

To solve this problem, begin by ordering each of the given heights from shortest to tallest:

4, 5, 6, 7, 7

The median is the middle number, or 6.

The median height of Phoebe’s plants is 6 inches.

Page 10 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

FCAT Mathematics Sample Answer Key SAMPLE 3

● The correct answer is H Q5R.14 2

Strand: A—Number Sense, Concepts, and Operations

Benchmark: MA.A.1.2.4 The student understands that numbers can be represented in a variety of equivalent forms using whole numbers, decimals, fractions, and percents. (Also assesses MA.A.1.2.1 names whole numbers, combining 3-digit numeration (hundred, tens, ones) and the use of number periods, such as ones, thousands, and millions and associates verbal names, written word names, and standard numerals with whole numbers, commonly used fractions, decimals, and percents; and MA.A.1.2.3 understands concrete and symbolic representations of whole numbers, fractions, decimals, and percents in real-world situations.)

To solve this problem, look at the pictures. There are 2 types of shovels, a spade shovel and a garden shovel. Maria has a total of 5 garden tools in the whole set.

The fraction that shows the number of shovels (2) compared to the whole set (5) is 2 5.

● The correct answer is D (Neptune).15

Strand: A—Number Sense, Concepts, and Operations

Benchmark: MA.A.2.2.1 The student uses place-value concepts of grouping based upon powers of ten (thousandths, hundredths, tenths, ones, tens, hundreds, thousands) within the decimal number system.

To solve this problem, look at the table. The table shows the planet names in the left column and the distances around the planets in the right column.

Since each of the planets in the table contains the numeral 3 in its distance, look at the place value at which the 3s are located:

Jupiter’s distance has a 3 in the tens place.Mars’s distance has a 3 in the ones place.Mercury’s distance has one 3 in the thousands place and another 3 in the tens place.Neptune’s distance has one 3 in the ten-thousands place and another 3 in the onesplace.

Neptune is the only planet in the table with a “distance around (in miles)” that includes the numeral 3 in the ten-thousands place.

Page 11 FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

Notes

Page 12FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

Notes

Page 13FCAT 2005 Sample Test Materials © 2004 Florida Department of Education

MAT

HEM

AT

ICS

Assessment and School PerformanceFlorida Department of Education

Tallahassee, Florida

Copyright © 2004 State of Florida Department of State