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2009 TEACHER’S BOOKLET MATHEMATICS MATHEMATICS SAMPLE ANSWER KEY GRADE 999-8729-84-X 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 the FCAT and include hints for responding to FCAT questions The FCAT Mathematics sample test materials for Grade are composed of the books described below: Sample Test Book Includes a mathematics sample test, a sample answer sheet, 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 © 2008 State of Florida Department of State FCAT Mathematics Sample Answer Key SAMPLE This 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 September 2007, the State Board of Education adopted updated benchmarks These new benchmarks are included in this booklet to provide teachers with additional information For more information follow the link to the Florida Standards website at: http://www.floridastandards.org/index.aspx 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 FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAA221ML434 ● The correct answer is B (30) Strand: A—Number Sense, Concepts, and Operations Old 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 New Benchmark: MA.4.A.6.1 Use and represent numbers through millions in various contexts, including estimation of relative sizes of amounts or distances To decide what value the digit has, think about how to read the number and the place each digit holds The number is two thousand, two hundred thirty-five The first is in the thousands place The second is in the hundreds place The is in the tens place, and the is in the ones place The has a value of tens, which is equivalent to 30 04MAA322ML435 ● The correct answer is H (� and �) Strand: A—Number Sense, Concepts, and Operations Old 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 New Benchmark: MA.4.A.4.3 Recognize and write algebraic expressions for functions with two operations To solve this problem, think about the problem If alligators each laid 30 eggs, then � 30 eggs were laid If all but eggs hatched, then those eggs must be removed from the total number of eggs laid, because they did not hatch So � 30 � eggs hatched Therefore, the operation symbols that should be used in the boxes are � and �, respectively Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAE122ML442 ● The correct answer is D (11°F) Strand: E—Data Analysis and Probability Old 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.) New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To find the range of the temperatures shown in the graph, first find the highest and the lowest temperatures The range is the difference between the highest and lowest temperatures The highest temperature shown is for Key West, which is 79°F The lowest is for Jacksonville, which is 68°F The difference can be found by subtracting: 79 � 68 � 11 The range is 11°F Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAD121ML443 ● FCAT Mathematics Sample Answer Key 04MAD121ML443STM.AR1 The correct answer is H (the tile that shows a pair of shoes) Strand: D—Algebraic Thinking Old Benchmark: MA.D.1.2.1 The student describes a wide variety of patterns and relationships through models, such as manipulatives, tables, graphs, rules using algebraic symbols (Also assesses MA.D.1.2.2 generalizes a pattern, relation, or function to explain how a change in one quantity results in a change in another.) New Benchmark: MA.4.A.4.1 Generate algebraic rules and use all four operations to describe patterns, including nonnumeric growing or repeating patterns Note: Although this benchmark will be assessed in Grade 4, the sample provided is not indicative of the way in which the new benchmark will be assessed at Grade in 2011 To find the 11th tile in the pattern, think about how the pattern was made The pattern was made using different tiles, and the pattern repeats after tiles The pattern will be made using tiles in the order: windmill, single daisy, shoes, double tulip The graphics shown below depict the pattern through the 11th tile 10 11 The 11th tile in the pattern will be the tile that shows a pair of shoes Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAB221MI987 ● The correct answer is C (55 inches) Strand: B—Measurement Old Benchmark: MA.B.2.2.1 The student uses direct (measured) and indirect (not measured) measures to calculate and compare measurable characteristics New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To find Jonathan’s height in inches, change the feet into inches and then add the remaining inches Since foot � 12 inches, � 12 inches or 48 inches equals feet Then add inches to get Jonathan’s total height 48 � � 55 Jonathan’s height in inches is 55 inches 04MAB122MI985 ● The correct answer is G (3:40) Strand: B—Measurement Old Benchmark: MA.B.1.2.2 The student solves real-world problems involving length, weight, perimeter, area, capacity, volume, time, temperature, and angles New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To solve the problem, read the clock that shows the time Kenny finished practicing The clock shows the time as 4:10 Kenny practiced for 30 minutes, so he must have started practicing 30 minutes before the time shown on the clock To find the time he started practicing, count 30 minutes by 5s counterclockwise, which is 3:40 Kenny started practicing at 3:40 Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAA421M4422 ● FCAT Mathematics Sample Answer Key 04MAA421M4422STM.AR1 The correct answer is C (210) Strand: A—Number Sense, Concepts, and Operations Old 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.) New Benchmark: MA.4.A.6.6 Estimate and describe reasonableness of estimates; determine the appropriateness of an estimate versus an exact answer First Strategy: 15 15 15 15 Oranges 20 20 20 20 20 20 20 20 About 18 oranges It appears that each bag can be divided into sections Since 18 is an estimate (about 18 oranges) and the bag isn’t a perfect rectangle, 15 can be used as an estimate of the top narrower section of the bags and 20 in the middle and bottom sections There are top sections of 15 oranges each, or 15 � � 60 There are remaining sections of 20 oranges each, or 20 � � 160 60 � 160 � 220 Second Strategy: To find the number of oranges that are needed to fill all bags to the top, first look at the number of oranges in the first bag There are about 18 oranges in the bag, and the bag is about one-third full So the first bag holds about 18 � oranges, or 54 oranges Each bag holds the same amount, so bags each hold about 54 oranges, and 54 � � 216 The answer choice closest to 216 is 210 The other answer choices are not as close to 216 as 210 The best answer choice is 210 Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 05MAE121M0066 ● The correct answer is I (1) Strand: E—Data Analysis and Probability Old 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 New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To solve this problem, decide how to find the combined number of fruit and vegetable servings You must add the number of servings of fruits and vegetables, and then subtract that sum from the number of servings of bread According to the graph there are servings of fruits and servings of vegetables, � � According to the graph there are servings of bread, � � There is more serving of bread than servings of fruits and vegetables combined 04MAA323ML444 ● The correct answer is A ($6.38) Strand: A—Number Sense, Concepts, and Operations Old 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 New Benchmark: MA.4.A.6.1 Use and represent numbers through millions in various contexts, including estimation of relative sizes of amounts or distances To solve the problem, decide which operation is needed to find the change Donna should receive from the $20.00 she used to pay the dinner bill To find change, Donna should begin with $20.00 and subtract the amount she owes, 20.00 � 13.62 � 6.38 Donna should receive $6.38 in change from the $20.00 Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAA124ML445 10 ● FCAT Mathematics Sample Answer Key 04MAA124ML445STM.AR1 The correct answer is H Q14R Strand: A—Number Sense, Concepts, and Operations Old 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 three-digit numeration [hundreds, 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.) New Benchmark: MA.4.A.2.3 Relate equivalent fractions and decimals with and without models, including locations on a number line First Strategy: To solve the problem, note that the garden is divided into 20 equal sections Of those 20 sections, are planted with beans Therefore 20 of the garden is planted with beans Since the fraction 20 is not one of the answer choices an equivalent fraction must be found The number is a common factor of and 20 5�5 � 20 � Therefore, 14 of the garden is planted with beans Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key OR Second Strategy: To solve the problem, look at how the garden is divided The garden is divided into equal rows that have five sections each Of those rows, row is planted with beans That means that 14 of the rows in the garden is planted with beans VEGETABLE GARDEN Corn Corn Corn Corn Corn Corn Corn Corn Corn Corn Beans Beans Beans Beans Beans Tomatoes Tomatoes Squash Squash Lettuce The fraction 14 represents the part of the garden that is planted with beans 03MAB222MI991 11 ● The correct answer is B (gram) Strand: B—Measurement Old 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.) New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To answer the question, think about what the word “mass” means The mass is the amount of matter in an object, often measured in milligrams, grams, or kilograms Look at the answer choices The first choice, centimeter, is used for measuring the length of something, not the mass of it The third choice, kilometer, is used for measuring the length of something, not the mass of it The fourth choice, liter, is used to measure amounts of liquid in containers, not the mass of objects The only answer choice that is used for measuring mass is the unit gram Page FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAD221ML446 12 ● The correct answer is F (45 � � w) Strand: D—Algebraic Thinking Old 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.) New Benchmark: MA.4.A.4.2 Describe mathematics relationships using expressions, equations, and visual representations To solve this problem, decide which operation is used to find the total number of milliliters of water Gerald poured into the sugar solution over the 5-day experiment He poured 45 milliliters each day for days, so he poured 45 � 45 � 45 � 45 � 45 milliliters or 45 � milliliters into the solution Since w represents the total number of milliliters, 45 � � w, or � 45 � w The equation that best shows this is 45 � � w Page 10 FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAE221ML447 13 ● The correct answer is B (6) Strand: E—Data Analysis and Probability Old Benchmark: MA.E.2.2.1 The student uses models, such as tree diagrams, to display possible outcomes and to predict events New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To solve the problem, think about the possible combinations of two colors that Sierra could use on her poster List the combinations and check your list to be sure no combinations are repeated.* The possible combinations are: Red and Yellow (RY)* Red and Black (RB) Red and Green (RG) Yellow and Black (YB) Yellow and Green (YG) Black and Green (BG) A total of combinations using colors can be made * Please note that order of appearance does not affect combinations For example, Red and Yellow (RY) and Yellow and Red (YR) are different representations of the same combination and would be counted as combination Page 11 FCAT 2009 Sample Test Materials © 2008 Florida Department of Education SAMPLE FCAT Mathematics Sample Answer Key 04MAC322ML448 14 ● The correct answer is H (5, 2) Strand: C—Geometry and Spatial Sense Old Benchmark: MA.C.3.2.2 The student identifies and plots positive ordered pairs (whole numbers) in a rectangular coordinate system (graph) New Benchmark: after 2010 Note: This benchmark will not be assessed in Grade To solve the problem, think about the properties of a rectangle A rectangle is a four-sided figure with two sets of parallel sides and four right angles, and its opposite sides are equal Picture a rectangle with three vertices shown Decide where the fourth vertex should be located to complete the rectangle: To satisfy the properties of a rectangle, the fourth vertex should be located three units down from the point drawn at (5, 5) This would be represented by the ordered pair (5, 2) The fourth vertex should be the ordered pair (5, 2) 04MAC222M7263 ● 15 04MAC222M7263STM.AR1 The correct answer is A Strand: C—Geometry and Spatial Sense Old Benchmark: MA.C.2.2.2 The student predicts, illustrates, and verifies which figures could result from a flip (reflection), slide (translation), or turn (rotation) of a given figure New Benchmark: MA.4.G.5.2 Identify and describe the results of translations, reflections, and rotations of 45, 90, 180, 270, and 360 degrees, including figures with line and rotational symmetry To solve this problem, find the symbol in the chart that represents “Sad.” It looks like this To turn this symbol clockwise 90 degrees, you must turn it to the right until the eyes are at the top and the frown is at the bottom The sad symbol turned clockwise 90 degrees is Page 12 FCAT 2009 Sample Test Materials © 2008 Florida Department of Education Notes Page 13 FCAT 2009 Sample Test Materials © 2008 Florida Department of Education Copyright © 2008 State of Florida Department of State 10 11 12 A B C D E MATHEMATICS Assessment and School Performance Florida Department of Education Tallahassee, Florida ... is 3 :40 Kenny started practicing at 3 :40 Page FCAT 2 009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAA421M 442 2 ● FCAT Mathematics Sample Answer Key 04MAA421M 442 2STM.AR1... Page FCAT 2 009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAA124ML 445 10 ● FCAT Mathematics Sample Answer Key 04MAA124ML 445 STM.AR1 The correct answer is H Q14R Strand:... The range is 11°F Page FCAT 2 009 Sample Test Materials © 2008 Florida Department of Education SAMPLE 04MAD121ML 443 ● FCAT Mathematics Sample Answer Key 04MAD121ML 443 STM.AR1 The correct answer
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