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Fourth GradeCore IdeaNumber OperationsMars 2006Overview of ExamTask DescriptionsTaskWhat’s My Number?The task asks students to use and to write clues involving multiplies to find a givennumber. Successful students can work with multiples of 2, 3,5,6,7, and 9. Theyunderstand order of numbers, such as larger and smaller. They can write explanationsto show the logic of how a number fits a set of clues.Number OperationsCookies, Muffins & BrowniesThe task asks students to use multiplication and division to reason about packagingfood for a school fair. Successful students can recognize multiplication situations anduse multiplication to reason about students, each making groups of cookies, browniesor muffins, to find the total number of baked goods. Students could then use divisionto package the food into equal-size containers.Data AnalysisDinosaur DataThe task asks students to relate a table of data to a bar graph and make comparisonstatements about data on the graph. Successful students could work with scales of 5’sand reason about bars falling between the lines. Students could make conclusionsabout data and write comparison statements using multiplication or subtraction.Geometry andMeasurementStarsThe task asks students to work with symmetry and area of shapes in a tessellation.Successful students could reason about area and how half squares fit together to makea whole. Students could use spatial visualization to identify and shade hexagons in alarger design, identify attributes of shapes, and recognize shapes that have beenrotated.Patterns, Functions,and AlgebraBikes and TrikesThe task asks students to use solve number problems using multiplication and divisionin the context of wheels in a bicycle shop. Successful students could identifymultiplication situations in context and multiply one-digit numbers with accuracy.They could reason about combining two groups of items and solve a multi-stepproblem involving multiplication and addition.Fourth Grade – 2006pg.1(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 20

What’s My Number?This problem gives you the chance to: solve “what’s my number?” problemsMandy and David play a number game.My number is: smaller than 20a multiple of 3a multiple of 51. What is Mandy’s number?Show how you figured it out.My number is: larger than 20smaller than 30a multiple of 7a multiple of 22. What is David’s number?Show how you figured it out.3. Mandy thinks of the number 18.Write three clues that will help David to guess her number correctly.9Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Page 1Fourth Grade – 2006What’s My Number?Test 4pg.4(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 21

What’s My NumberRubricThe core elements of performance required by this task are: .solve “what’s my number?” problemsBased on these, credit for specific aspects of performance should be assigned as follows1.2.Gives correct answer: 151Shows work such as:The multiples of 3 that are less than 20 are: 3, 6, 9, 12, 15, 18The multiples of 5 that are less than 20 are: 5, 10, 15orShows that 3 and 5 are factors of 15 e.g. 3 x 5 1511or2Gives correct answer: 281Shows work such as:The multiples of 7 that are between 20 and 30 are: 21, 28The multiples of 2 that are between 20 and 30 are:22, 24, 26, 28orShows that 7 and 2 are factors of 28or2Makes two true statements.Makes a statement that makes the number 18 unique(1)32 x 1.139Total PointsFourth Grade – 2006311Partial creditGives a number larger than 20 and smaller than 30 that is a multiple ofeither 7 or 23.sectionpoints pointspg.5(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 22

Cookies, Muffins and BrowniesThis problem gives you the chance to: solve number problems with multiplication and division in a real context1. Four students bake cookies for the school fair.Each student bakes twelve cookies.They are going to sell the cookies in bags of three.How many bags do they need?bagsShow how you figured it out.2. Five students bake muffins for the school fair.Each student bakes twenty muffins.They are going to sell the muffins in boxes of four.How many boxes do they need?boxesExplain how you figured it out.Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Page 2Fourth Grade – 2006Cookies, Muffins and BrowniesTest 4pg.21(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 23

3. Ten students make brownies for the school fair.Each student makes six brownies.They put the same number of brownies in each of twelve boxes.How many brownies do they put in each box?Explain how you figured it out.Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Page 3Fourth Grade – 2006Cookies, Muffins and BrowniesTest 4pg.922(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 24

Cookies, Muffins and BrowniesRubricThe core elements of performance required by this task are: solve number problems with multiplication and division in a real contextpointssectionpointsBased on these, credit for specific aspects of performance should be assigned as follows1.Gives correct answer: 161Shows correct work such as:12 x 4 48or12 3 448 3 4x4 11Accept repeated addition/subtraction or diagrams2.3Gives correct answer: 251Gives correct explanations or shows that:5 students bake 20 x 5 100 muffins,They need 100 4 25 boxes.orEach student needs 20 4 5 boxes,Five students need 5 x 5 25 boxes.11or11Accept repeated addition/subtraction or diagrams3.3Gives correct answer: 51Gives correct explanations or shows that:10 students bake 10 x 6 60 brownies,In each box they put 60 12 5 brownies.orEach student puts one brownie in 6 (half) of the boxes,Ten students put 5 brownies in twelve boxes.11or11Accept repeated addition/subtraction or diagrams39Total PointsFourth Grade – 2006pg.23(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 25

Dinosaur DataThis problem gives you the chance to: relate a table of data and a bar graph derive informationSangita and Zach are doing a project about dinosaurs.They have discovered the facts shown in the table below.Name of dinosaurFood dinosaurs eatEstimated length in They use the numbers in the table to draw this bar nosaurus seismosaurusCopyright 2006 by Mathematics AssessmentResource Service. All rights reserved.diplodocusPage 4Fourth Grade – 2006allosaurusbrachiosaurusDinosaur DataTest 4pg.49(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 26

1. The students have made a mistake.One of the bars on the graph is wrong.Which one is it?Explain your answer.2. Using the table on the opposite page, the students have written someinformation about these dinosaurs.One of the sentences is not correct. Underline the incorrect sentence. A brachiosaurus can be about twice as long as a tyrannosaurus. Meat eating dinosaurs are longer than plant eaters. An allosaurus is shorter in length than a seismosaurus.Explain what is wrong with the information in the sentence you have underlined.3. Using the facts on the opposite page, write two sentences of your owncomparing the length of these dinosaurs.Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Page 5Dinosaur DataTest 47Fourth Grade – 2006pg.50(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 27

Dinosaur DataRubricThe core elements of performance required by this task are: relate a table of data and a bar graph derive informationBased on these, credit for specific aspects of performance should be assigned as follows1.2.3.pointsGives correct answer: diplodocus1Gives correct explanation such as:On the bar chart this is recorded at about 37 (accept 36 to 38 inclusive)rather than 27 meters.2Partial creditFor a partially correct/inaccurate answer.(1)Underlines “Meat eating dinosaurs are longer than plant eaters”.1Gives correct explanation such as:From the table it would appear that the plant eating dinosaurs are longerthan the meat eaters.1Writes correct statements such as:The seismosaurus is (about 15 meters) longer than the brachiosaurus.The shortest of these dinosaurs is the allosaurus.sectionpoints211Total PointsFourth Grade – 20063pg.2751(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 28

StarsThis problem gives you the chance to: work with symmetry and area of shapes in a tessellation1. How many sides does this shaded starshape have?2. Explain why the area of the star is 3 squares.This pattern is made from lots of stars. Some of them are flipped.Hexagons are made between the stars.Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Page 6Fourth Grade – 2006StarsTest 4pg.62(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 29

3. Shade three of the hexagons in the diagram.4. How many stars are there in the diagram?5. Is the area of the hexagon bigger or smaller than the area of the star?Explain how you figured it out.Fourth Grade – 2006pg.63(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 30

StarsRubricThe core elements of performance required by this task are: work with symmetry and area of shapes in a tessellationBased on these, credit for specific aspects of performance should be assigned as followspointssectionpoints1.Gives correct answer: 8112.Gives a correct explanation such as:There is one whole square and four half squares.223.Shades three hexagons.114.Gives correct answer: 16115.Gives correct answer: biggerandExplains that there are 4 whole squares and 4 half squares, or 6 wholesquares227Total PointsFourth Grade – 2006pg.64(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsPage 31

Bikes and TrikesThis problem gives you the chance to: solve number problems in a real contextThe cycle shop on Main Street sells bikes (two wheels) and trikes (three wheels).1.Yesterday, Sarah counted all of the cycles in the shop.There were seven bikes and four trikes in the shop.How many wheels were there on these eleven cycles?Show your calculation.2.Today, Sarah counted all of the wheels of all of the cycles in the shop.She found that there were 30 wheels in all.There were the same number of bikes as there were trikes.How many bikes were there?How many trikes were there?Show how you figured it out.8Copyright 2006 by Mathematics AssessmentResource Service. All rights reserved.Grade Four – 2006Page 8Bikes and Trikespg.(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/marsTest 481Page 32

Bikes and TrikesRubricThe core elements of performance required by this task are: solve number problems in a real contextBased on these, credit for specific aspects of performance should be assigned as follows1.pointsGives correct answer: 26 wheels1Shows work such as:7 x 2 and 4 x 314 12 2sectionpointsAccept repeated addition or diagrams2.3Gives correct answers: 6 bikes and 6 trikes2Gives correct explanation such as:6 bikes 12 wheels6 trikes 18 wheelsin all 30 wheels3May list or draw diagrams1 bike and 1 trike 2 3 5 wheels2 bikes and 2 trikes 4 6 or 2 x 5 10 wheels3 bikes and 3 trikes 6 9 or 3 x 5 15 wheels4 bikes and 4 trikes 8 12 or 4 x 5 20 wheels5 bikes and 5 trikes 10 15 or 5 x 5 25 wheels6 bikes and 6 trikes 12 18 or 6 x 5 30 wheelsTotal PointsGrade Four – 2006pg.(c) Noyce Foundation 2006. To reproduce this document, permission must be granted by the Noyce Foundation:info@noycefdn.org.MARS Tasks – Grade 4www.scoe.org/mars5882Page 33

Fourth GradeMars 2007Overview of ExamCore IdeaTaskTask DescriptionsScoreLooking at PatternsAlgebraThe task asks students to follow a pattern for doubling and subtracting and find theresulting patterns. Students needed to show an understanding of odd and even.Successful students could describe repeating patterns and explain why the rules of thepattern produced odd numbers.Number OperationsThe BakerThe task asks students to use multiplication and division to reason about packagingbaked goods into bakery boxes. Successful students could use division and reasonabout the remainder in a context. Successful students could justify which type ofbaked goods would exactly fill 8 boxes.GeometryStained GlassThe task asks students to work with line symmetry. Students needed to draw in linesof symmetry in geometrical designs and find the number of lines of symmetry for acomplex design. Successful students could also fill in missing parts of a design usinglines of symmetry as clues.Dinosaurs and DragonsData AnalysisThe task asks students to identify an error made when transposing information from aline plot to a bar graph and to make their own bar graph from a frequency table .Successful students could also compare and contrast the data shown in the two bargraphs.Picking FractionsNumber PropertiesThe task asks students to pick equivalent fractions from a given list and make theirown equivalent fractions. To meet standards, students should be able to work withunit fractions like 1/2, 1/4, and 1/3. Successful students could also reason aboutfractions like 2/3 and 3/4.th4 grade - 20071Copyright 2007 by Noyce FoundationResource Service. All rights reserved.MARS Tasks – Grade 4www.scoe.org/marsPage 34

Looking At PatternsThis problem gives you the chance to: recognize and use patterns1. Here is part of a repeating pattern.Draw the next 4 shapes in this pattern.2. Here is a number pattern game. Write a number between 1 and 5 in the first circle.Double the number and write it in the next circle.Keep doing this, but if the number is more than 10 subtract 10 before you write thenumber in the next circle. Carry on until all the circles are full.Describe what happens to the numbers in your pattern.3. Here is another number pattern game.Write a small odd number greater than 1 in the first circle.Now follow this rule: Double the number, then subtract one.Write this number in the second circle. Keep doing this until all the circles are full.What pattern do you see in these numbers?Explain why this happens.8Copyright 2007 by Mathematics AssessmentResource Service. All rights reserved.MARS Tasks – Grade 44www.scoe.org/marsLooking at Patterns Test 4Page 35

Task 1: Looking at PatternsRubricThe core elements of performance required by this task are: recognize and use patternspointssectionpoints11Based on these, credit for specific aspects of performance should be assigned as follows1.Draws the next four shapes correctly2.Dependent on the starting number, produces pattern such as:3Partial creditOne error with correct follow through.Two errors.3(2)(1)Gives correct explanations such as:The numbers repeat (dependent on a correct pattern).Dependent on the starting number, produces pattern such as the top line inthe table.33569517103311orGives second row of table and states: They are alternate odd and even.Gives explanation such as: Double an odd number gives an even number.Subtract one gives an odd numberTotal PointsMARS Tasks – Grade 45www.scoe.org/mars41Gives correct answer such as: They are all odd numbers.Gives correct explanations such as:The starting number was odd. By doubling an odd number get an evennumber, but you had to take one away. This means you have an odd number.So all the numbers are odd.Copyright 2007 by Mathematics AssessmentResource Service. All rights reserved.1113or118Looking at Patterns Test 4Page 36

The BakerThis problem gives you the chance to: choose and perform number operations in a practical contextThe baker uses boxes of different sizes to carry her goods.Cookie boxes hold 12 cookies.Donut boxes hold 4 donuts.Muffin boxes hold 2 muffins.Bagel boxes hold 6 bagels.Bagel boxes hold 41. On Monday she baked 24 of everything.bagels.How many boxes did she need? Fill in the empty spaces.cookie boxesdonut boxesmuffin boxesbagel boxes2. On Tuesday she baked just bagels. She filled 7 boxes.How many bagels did she make?Show your calculations.3. On Wednesday she baked 42 cookies.How many boxes did she fill?How many cookies were left over?Explain how you figured this out.4. On Thursday she baked 32 of just one item and she filled 8 boxes.What did she bake on Thursday?Show how you figured this out.Copyright 2007 by Mathematics AssessmentResource Service. All rights reserved.MARS Tasks – Grade 41024www.scoe.org/marsThe Baker Test 4Page 37

Task 2: The BakerRubricThe core elements of performance required by this task are: choose and perform number operations in a practical contextpointssectionpointsBased on these, credit for specific aspects of performance should be assigned as follows1.2.3.Gives correct answers:1x42 cookie boxes6 donut boxes12 muffin boxes4 bagel boxes4Gives correct answer: 421Shows 6 x 7 42. Accept repeated addition.1Gives correct answers: 3126Gives a correct explanation such as:She filled 3 complete boxes: 3 x 12 36 and 42 – 36 6.This means that 6 were left overorShows 42 12 3, remainder 6.4.12Gives correct answer: donuts1Shows work such as:4 x 8 32Accept diagrams.1Total PointsCopyright 2007 by Mathematics AssessmentResource Service. All rights reserved.MARS Tasks – Grade 425www.scoe.org/mars210The Baker Test 4Page 38

Stained GlassThis problem gives you the chance to: work with line symmetryMaddie loves the symmetrical designs in stained glass windows.1. Here is one design that she likes.Draw in the line of symmetry for Maddie.2. Maddie has begun to draw a window with two linesof symmetry.The dot lines () show the two lines of symmetry.Complete the drawing so that it is symmetrical.3. This window is Maddie’s favorite.How many l

MARS MARS Tasks Grade 4 Page Name of MARS Task Year Math Strand Notes * Shapes with Straws 2003 NO, GM Prob. @ divisors, multiples in geo. figures * Number Trains 2003 PFA, NO Prob. @ factors, multiples in toy trains * Hexagon Desks 2003 PFA Find, analyze # of chairs needed, graph * Flow