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G R A D E3C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsTHE NUMBER SENSE STRANDIn Grade 3, there are two reporting clusters within the Number Sense strand: 1) Place Value, Fractions, andDecimals and 2) Addition, Subtraction, Multiplication, and Division. This booklet contains released testquestions for each of these clusters.The following nine California content standards are included in the Place Value, Fractions, and Decimalsreporting cluster of the Number Sense strand and are represented in this booklet by 16 test questions. Thesequestions represent only some ways in which these standards may be assessed on the Grade 3 CaliforniaMathematics Standards Test.CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTERNumber SenseStandard Set 1.0Students understand the place value of whole numbers:3NS1.1Count, read, and write whole numbers to 10,000.3NS1.2Compare and order whole numbers to 10,000.3NS1.3*Identify the place value for each digit in numbers to 10,000.3NS1.4Round off numbers to 10,000 to the nearest ten, hundred, and thousand.3NS1.5*Use expanded notation to represent numbers (e.g., 3,206 3,000 200 6).Standard Set 3.0Students understand the relationship between whole numbers, simplefractions, and decimals:3NS3.1Compare fractions represented by drawings or concrete materials to showequivalency and to add and subtract simple fractions in context (e.g., 1/2 of apizza is the same amount as 2/4 of another pizza that is the same size; showthat 3/8 is larger than 1/4).3NS3.2*Add and subtract simple fractions (e.g., determine that 1/8 3/8 is the same as1/2).3NS3.3*Solve problems involving addition, subtraction, multiplication, and division ofmoney amounts in decimal notation and multiply and divide money amounts indecimal notation by using whole-number multipliers and divisors.3NS3.4Know and understand that fractions and decimals are two differentrepresentations of the same concept (e.g., 50 cents is 1/2 of a dollar, 75 cents is3/4 of a dollar).* Denotes key standards (Mathematics Framework for California Public Schools)— 2 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions3The following seven California content standards are included in the Addition, Subtraction, Multiplication, andDivision reporting cluster of the Number Sense strand and are represented in this booklet by 15 test questions.These questions represent only some ways in which these standards may be assessed on the Grade 3 CaliforniaMathematics Standards Test.CALIFORNIA CONTENT STANDARDS IN THIS REPORTING CLUSTERNumber SenseStandard Set 2.0Students calculate and solve problems involving addition, subtraction,multiplication, and division:3NS2.1*Find the sum or difference of two whole numbers between 0 and 10,000.3NS2.3*Use the inverse relationship of multiplication and division to compute and checkresults.3NS2.4*Solve simple problems involving multiplication of multi-digit numbers by one-digitnumbers (3,671 3 ).3NS2.5Solve division problems in which a multi-digit number is evenly divided by aone-digit number (135 5 ).3NS2.6Understand the special properties of 0 and 1 in multiplication and division.3NS2.7Determine the unit cost when given the total cost and number of units.3NS2.8Solve problems that require two or more of the skills mentioned above.* Denotes key standards (Mathematics Framework for California Public Schools)— 3 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E3C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsTHE ALGEBRA AND FUNCTIONS STRAND/REPORTING CLUSTERThe following seven California content standards are included in the Algebra and Functions strand/reportingcluster and are represented in this booklet by 12 test questions. These questions represent only some ways inwhich these standards may be assessed on the Grade 3 California Mathematics Standards Test.CALIFORNIA CONTENT STANDARDS IN THIS STRAND/CLUSTERAlgebra and FunctionsStandard Set 1.0Students select appropriate symbols, operations, and properties torepresent, describe, simplify, and solve simple number relationships:3AF1.1*Represent relationships of quantities in the form of mathematical expressions,equations, or inequalities.3AF1.2Solve problems involving numeric equations or inequalities.3AF1.3Select appropriate operational and relational symbols to make an expressiontrue (e.g., if 4 3 12, what operational symbol goes in the blank?).3AF1.4Express simple unit conversions in symbolic form (e.g., inches feet 12).3AF1.5Recognize and use the commutative and associative properties of multiplication(e.g., if 5 7 35, then what is 7 5? and if 5 7 3 105, then what is7 3 5?).Standard Set 2.0Students represent simple functional relationships:3AF2.1*Solve simple problems involving a functional relationship between two quantities(e.g., find the total cost of multiple items given the cost per unit).3AF2.2Extend and recognize a linear pattern by its rules (e.g., the number of legs on agiven number of horses may be calculated by counting by 4s or by multiplyingthe number of horses by 4).* Denotes key standards (Mathematics Framework for California Public Schools)— 4 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions3THE MEASUREMENT AND GEOMETRY STRAND/REPORTING CLUSTERThe following ten California content standards are included in the Measurement and Geometry strand/reporting cluster and are represented in this booklet by 16 test questions. These questions represent only someways in which these standards may be assessed on the Grade 3 California Mathematics Standards Test.CALIFORNIA CONTENT STANDARDS IN THIS STRAND/CLUSTERMeasurement and GeometryStandard Set 1.0Students choose and use appropriate units and measurement tools toquantify the properties of objects:3MG1.1Choose the appropriate tools and units (metric and U.S.) and estimate andmeasure the length, liquid volume, and weight/mass of given objects.3MG1.2*Estimate or determine the area and volume of solid figures by covering themwith squares or by counting the number of cubes that would fill them.3MG1.3*Find the perimeter of a polygon with integer sides.3MG1.4Carry out simple unit conversions within a system of measurement (e.g.,centimeters and meters, hours and minutes).Standard Set 2.0Students describe and compare the attributes of plane and solid geometricfigures and use their understanding to show relationships and solveproblems:3MG2.1*Identify, describe, and classify polygons (including pentagons, hexagons, andoctagons).3MG2.2*Identify attributes of triangles (e.g., two equal sides for the isosceles triangle,three equal sides for the equilateral triangle, right angle for the right triangle).3MG2.3*Identify attributes of quadrilaterals (e.g., parallel sides for the parallelogram, rightangles for the rectangle, equal sides and right angles for the square).3MG2.4Identify right angles in geometric figures or in appropriate objects and determinewhether other angles are greater or less than a right angle.3MG2.5Identify, describe, and classify common three-dimensional geometric objects(e.g., cube, rectangular solid, sphere, prism, pyramid, cone, cylinder).3MG2.6Identify common solid objects that are the components needed to make a morecomplex solid object.* Denotes key standards (Mathematics Framework for California Public Schools)— 5 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E3C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsTHE STATISTICS, DATA ANALYSIS, AND PROBABILITY STRAND/REPORTINGCLUSTERThe following three California content standards are included in the Statistics, Data Analysis, and Probabilitystrand/reporting cluster and are represented in this booklet by five test questions. These questions represent onlysome ways in which these standards may be assessed on the Grade 3 California Mathematics Standards Test.CALIFORNIA CONTENT STANDARDS IN THIS STRAND/CLUSTERStatistics, Data Analysis, and ProbabilityStandard Set 1.0Students conduct simple probability experiments by determining thenumber of possible outcomes and make simple predictions:3PS1.1Identify whether common events are certain, likely, unlikely, or improbable.3PS1.2*Record the possible outcomes for a simple event (e.g., tossing a coin) andsystematically keep track of the outcomes when the event is repeated manytimes.3PS1.3*Summarize and display the results of probability experiments in a clear andorganized way (e.g., use a bar graph or a line plot).* Denotes key standards (Mathematics Framework for California Public Schools)— 6 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions1 4 How is eight thousand, seventy-sixwritten in standard form?Which digit is in the hundreds place inthe number 3174?A 8067A 1B 8076B 3C 8706C 4D 8760D 7CSM204622 Which set of numbers is in order fromgreatest to least?CSM204645 What does the 3 represent in the numberbelow?3051A 147, 163, 234, 275B 275, 234, 163, 147A 3C 275, 163, 234, 147B 30D 163, 275, 234, 147C 300D 3000CSM015933 3CSM02188Which number has a 4 in the tens placeand a 4 in the hundreds place?A 64246 Sophie has 527 seashells in her collection.Which of these equals 527?B 6244A 5 2 7C 4462B 5 20 700D 6442C 500 20 7D 500 200 70CSM01057CSM00051— 7 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E3 7C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions Which number is 4000 80 5?9A 458The circle shows1shaded.4B 485C 4085 1–4D 4805CSM105768 Which number means 1000 600 8?Which fractional part of a circle below1is equal to ?4A 168B 1068C 1608 3–8D 1680 2–6CSM00094AC2 –8B 1–6DCSM02123— 8 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions 12 1 2 4 410AB6626BrandCostA 31.47B 34.71How much more does Brand B cost thanBrand A?34A 3.24CSM0220311 Reggie compared the prices of tworadios. The table below shows theprices.Cost of Radios2C3D3B 3.26A pie was divided into fifths. Emily ate12of the pie. Tony ateof the pie. Jenny551ateof the pie. How much of the pie5was left?A45C 3.34D 3.36CSM0217413 Adam has 5.00 to buy an airplane thatcosts 4.28. How much change should heget back?3B5A 70 25C 75 CB 72 D 82 1D5CSM01079CSM02175— 9 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E3 14C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions 16Carmen bought these three things.Donna shaded1of the figure.10 3.45 4.10 1.75Which decimal equalsWhat was the total cost of these threeitems?A 0.01A 9.30B 0.1B 9.20C 0.110C 8.30D 1.01?10D 8.20CSM01089CSM0218215 Lisa rented 4 videotapes for 4.80. Howmuch did each tape cost to rent?17 9000 3782 A 5218B 5328A 1.20C 6782B 8.80D 12,782C 12.00CSM02197D 19.20CSM20665— 10 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions18 21 Look at the number sentence below.67 1213The figure below is a model for themultiplication sentence.8 4 32Which number will make the numbersentence true?A 54B 56C 64D 68CSM1043119 Which number is 6 more than 1026?Which division sentence is modeled bythe same figure?A 1022A 8 4 2B 1032B 12 4 3C 1122C 24 8 3D 1132D 32 8 4CSM01096CSM10424 20The town of Milburg has 5256 grown-upsand 2987 children. How many people livein Milburg?22 Lily did this division problem.375 25 15A 7133Which problem could she do to checkher answer?B 8133A 25 15 C 8243B 25 15 D 8343C 25 15 D 25 15 CSM10580CSM01040— 11 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E323 C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsA company has 6 big trucks. Each truckhas 18 wheels. How many wheels is thisin all?26 There are 124 students making 3 starseach for the school wall. How many starswill they make all together?A 24A 127B 96B 357C 108C 362D 116D 372CSM0104524 CSM1068727 On Friday, 1250 people visited the zoo.Three times as many people visited onSaturday than on Friday. How manypeople visited the zoo on Saturday?How much is nine times four hundredfifty-eight?A 4042A 3615B 4122B 3650C 4311C 3750D 4589CSM10589D 375328 CSM1010625 Third-grade students went to a concertin 8 buses. Each bus took 45 students.How many students went to the concert?During Field Day, 1624 students fromGlen Hill School were equally dividedinto 8 different events. How manystudents were in each event?A 203A 320B 206B 360C 221C 380D 224D 3240CSM10107CSM00052— 12 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions29 What number can be multiplied by 5768to give the answer 5768?5768 32 5768Mr. Guzman bought 48 doughnuts packedequally into 4 boxes. Which numbersentence shows how to find the number ofdoughnuts in each box?A 0A 48 4 B 1B 48 4 C 2C 48 4 D 10D 48 4 CSM1059230 CSM02176Mr. Brown bought 6 towels. All thetowels were the same price. The totalcost was 84. How much money did eachtowel cost?33 The Sumata family took a five-day vacationby car. Each day they drove 250 miles.Which number sentence could be used tofind out how many total miles they drove?A 11A 250 5 B 14B 250 5 C 78C 250 5 D 504D 250 5 CSM0213431 3CSM10599Tony had 20. He paid 8 for a ticket toa baseball game. At the game, he boughta hot dog for 3. What amount of moneydid Tony have then?34 A 5If Mai bought apples for 2.50 and she paidwith a 10 bill, which expression shows thecorrect amount of change?A 10 2.50B 10 2.50B 9C 10 2.50C 11D 10 2.50D 15CSM10097CSM02117— 13 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D EC A L I F O R N I A S TA N DA R D S T E S T335 MathReleased Test Questions38 What number makes this numbersentence true?3 5 2Which of the following is used to find outhow many inches are in 5 feet?A 5 12A 3B 12 5B 4C 5 12C 5D 12 5D 6CSM20848CSM0212136 What number makes this numbersentence true?39 If 7 11 13 1001, then whatis 11 7 13 ?A 776 9 3 B 91A 18C 143B 19D 1001CSM10058C 16D 17CSM0042537 40 Which sign goes in the box to make thenumber sentence true?One stamp costs 34 . Two stamps cost68 . Three stamps cost 1.02. If the costof each stamp remains the same, howmuch would 4 stamps cost?A 1.2648 6 8B 1.34A C 1.36B D 12.16C CSM02192D CSM01071— 14 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions41 The table shows the number of coloredpencils needed for different numbers ofstudents.43 3Look at the linear pattern below.3, 6, 9, 12, 15, 18,What number comes next in this pattern?Colored PencilsA 19Numberof StudentsNumberof Pencils14C 2128D 22312B 20CSM10046If each student gets the same number ofpencils, how many are needed for6 students?A 22B 24C 26D 27CSM0219442 If bananas cost 35 per pound, howmuch will 4 pounds cost?A 0.39B 1.20C 1.29D 1.40CSM10690— 15 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E344 C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsWhich of the following objects is heavierthan 1 pound?45 What is the area of this figure? 1 square unitA 2 square unitsPencilAB 3 square unitsC 4 square unitsD 6 square unitsCSM0107846 What is the volume of this solid figuremade with cubes?BackpackBA 10 cubic unitsB 17 cubic unitsPaperC 20 cubic unitsCD 22 cubic unitsCSM01099EraserDCSM10440— 16 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S T47 3MathReleased Test Questions48 A basketball court is shaped like arectangle 20 meters long and 10 meterswide.What is the perimeter of the figure?4 inches5 inches7 inches10 meters7 inches20 meters5 inches4 inchesWhat is the perimeter in meters of thecourt?A 18 inchesA 30 metersB 22 inchesB 50 metersC 24 inchesC 60 metersD 32 inchesD 200 metersCSM21415CSM0010449 Look at the polygon below.10 cm1 cm4 cm2 cm1 cm6 cm1 centimeter 1 cmWhat is the perimeter of the polygon?A 16 cmB 20 cmC 24 cmD 28 cmCSM10447— 17 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E350 C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsThere are 1,000 meters in 1 kilometer.How many meters are in 5 kilometers?52 Which sign is shaped like a pentagon?A 1,000 metersB 50 metersC 200 metersD 5,000 metersACBDCSM0039951 Which of these is a hexagon?CSM00088A53 CAn isosceles triangle MUST haveA 4 sides that are the samelength.B 3 sides that are the samelength.C 2 sides that are the samelength.BD no sides that are the samelength.DCSM01070CSM00620— 18 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions54 What measurement is missing on theequilateral triangle below?56 3How many right angles are in arectangle?A 1B 27 inches?C 3D 47 inchesCSM20168A 1 inch57 B 7 inchesLook at the four angles marked on thepicture of a house.C 14 inchesD 49 inches2CSM21491355 4One side of a rectangle is 8 feet long.Another side of the rectangle is 10 feetlong. What are the lengths of the other2 sides of the rectangle?A They could be any length.1B 10 feet and 8 feetC 10 feet and 10 feetWhich angle is a right angle?D 8 feet and 8 feetA angle 1B angle 2CSM02180C angle 3D angle 4CSM00108— 19 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D E358 C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test Questions59 Which object is a cylinder?Which shapes make up this solidobject?ABACCCerealA cone and cylinderB circle and triangleC triangle and cylinderD rectangle, triangle, and circleBDCSM10134CSM10521— 20 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S T60 3MathReleased Test QuestionsMiriam put 10 marbles in a paper sack.Six of the marbles were black, three weregray, and one was white.61 Miriam closed her eyes and took onemarble out of the sack. Is it certain,likely, unlikely, or impossible that themarble she picked was white?A certainA spinner landed on “Red” 6 times,“Blue” 4 times, and “Green” 5 times.Which tally chart shows these results?Spin ResultsSpin ResultsRedRedBlueBlueGreenGreenACSpin ResultsSpin ResultsRedRedBlueBlueGreenGreenBB likelyDC unlikelyCSN00095D impossibleCSM10615— 21 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D EReleased Test QuestionsA group of children tossed a coin 10 times. The coin landed on heads 4 times and tails 6 times.Which tally chart shows these tosses?e rti blyIN GOD WETRUST1 9 8 9e rtibe rtiblyylIN GOD WETRUSTIN GOD WETRUST1 9 8 91 9 8 9ACe rtibyye rtibl62 Mathl3CA L I F O R N I A S TA N DA R D S T E S TIN GOD WETRUSTIN GOD WETRUST1 9 8 91 9 8 9BDCSM10068— 22 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsDanny tossed 2 nickels 10 times. The results are shown in the tally chart below.Lusd we trnngoTY 1973ERgoIBTY 1973ERd we trLtIBustiiLEPLURIBUS UNUMMECARIESPLURIBUS UNUCAEMM O N T I C E L L ODEESITITNTUNUNFIVS T E CE A MATE S O FNTS T E CE A MATE S O FFIVNTSCAURIBUS UNUFIVRIEPLM O N T I C E L L ODDRIgonITEM O N T I C E L L OUNTY 1973ERd we trIBusti63 3S T E CE A MATE S O FEWhich graph shows these results?Coin Toss ResultsCoin Toss Results2 headsResult2 heads1 head,1 tailResult2 tails1 head,1 tail2 tails0 1 2 3 4 5 6Number of Times0 1 2 3 4 5 6Number of TimesACCoin Toss ResultsCoin Toss Results2 headsResult2 heads1 head,1 tailResult2 tails1 head,1 tail2 tails0 1 2 3 4 5 6Number of Times0 1 2 3 4 5 6Number of TimesBDCSN00330— 23 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D EReleased Test QuestionsJosie, Mary, and Susana were tossing a coin to see how many times it would land on tails. Theyeach tossed the coin 10 times and recorded their results with tally marks.Coin TossNameTailsJosieMarySusanaWhich graph shows their results?654321Coin TossTails654321JMSCoin TossJMSNameACCoin TossJ654321NameTailsTails64 MathTails3C A L I F O R N I A S TA N DA R D S T E S TMS654321Coin TossJMSNameNameBDCSM20866— 24 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

G R A D ECA L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsQuestion NumberCorrect AnswerStandardYear of — 25 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.3

G R A D E3C A L I F O R N I A S TA N DA R D S T E S TMathReleased Test QuestionsQuestion NumberCorrect AnswerStandardYear of 2200663D3PS1.3200464A3PS1.32006— 26 —This is a sample of California Standards Test questions. This is NOT an operational test form. Test scores cannot be projectedbased on performance on released test questions. Copyright 2007 California Department of Education.

Introduction - Grade 3 Mathematics The following released test questions are taken from the Grade 3 Mathematics Standards Test. This test is one of the California Standards Tests administered as part of the Standardized Testing and Reporting (STAR) Program under policies set by the State Board of Education.