Canister Conundrum

Home , Conundrum (Dallas)

unknown filmcanister TEACHER 5 knownfilmcanisters balance GROUP EACH MATERIALS RESOURCES AND Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. at online us Visit reserved. rights Texas. All Dallas, Initiative, +Science Math National ©2013 Copyright 1 boxpaperclips,jumbo I should beperformedinconjunctionwith“Barbie graphing, slope,andlinearregression. This activity This activityreliesonstudents’ priorknowledgeof canister usinganindirectmethodofmeasurement. presented here. protocol thatwillallowthemtosolvethepuzzle Doll BungeeJumping,”wherestudentslearna ABOUT THIS LESSON THIS ABOUT IndirectlyDetermining Mass Canister Conundrum Middle Grades:General LEVEL Students will: OBJECTIVES Generateagraphofthatdataanddecidewhat the • Constructadatatableanddeterminewhat to • Createaproceduretodeterminethemassofan • of onepaperclipandthemassanemptyfilm world scenarioandthetaskoffindingmass n thisinquirylesson,studentsaregivenareal- resulting linearregressionrepresents collect object object withoutdirectlymeasuringthemassof Middle Grades Science ®

i TEACHER PAGES NEXT GENERATION SCIENCE STANDARDS PLANNING/CARRYING OUT ETS1: ENGINEERING INVESTIGATIONS PATTERNS DESIGN Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. at online us Visit reserved. rights Texas. All Dallas, Initiative, +Science Math National ©2013 Copyright SCALE, PROPORTION, INTERPRETING DATA ANALYZING AND AND QUANTITY embedded inthislesson: The followingtypesofformativeassessmentsare ASSESSMENTS Visual assessmentofstudent-generateddata • Middle Grades Science –Canister Conundrum tables andgraphs ii TEACHER PAGES between dependentandindependentvariables. Represent andanalyzequantitativerelationships (MATH) 6.EE.C experiments, ortechnicalprocesses. narration ofhistoricalevents,scientificprocedures/ Write informative/explanatorytexts,includingthe WHST.6-8.2 (LITERACY) content. Write arguments focusedondiscipline-specific WHST.6-8.1 (LITERACY) diagram, model,graph,ortable). information expressedvisually(e.g.,inaflowchart, expressed inwordsatextwithversionofthat Integrate quantitativeortechnicalinformation RST.6-8.7 (LITERACY) technical tasks. out experiments,takingmeasurements,orperforming Follow preciselyamultistepprocedurewhencarrying RST.6-8.3 (LITERACY) science andtechnicaltexts. Cite specifictextualevidencetosupportanalysisof RST.6-8.1 (LITERACY) STATE STANDARDS CORE COMMON Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. at online us Visit reserved. rights Texas. All Dallas, Initiative, +Science Math National ©2013 Copyright (MATH) 8.F.A simultaneous linearequations. Analyze andsolvelinearequationspairsof (MATH) 8.EE.C relationships, lines,andlinearequations. Understand theconnectionsbetweenproportional (MATH) 8.EE.B solve real-worldandmathematicalproblems. Analyze proportionalrelationshipsandusethemto (MATH) 7.RP.A numerical andalgebraicexpressionsequations. Solve real-lifeandmathematicalproblemsusing (MATH) 7.EE.B Investigate patternsofassociationinbivariatedata. (MATH) 8.SP.A quantities. Use functionstomodelrelationshipsbetween (MATH) 8.F.B Define, evaluate,andcomparefunctions. Middle Grades Science –Canister Conundrum iii TEACHER PAGES T activity iftheyhavecompletedthelesson,“Barbie y formula foraline( SUGGESTIONS TEACHING is consistent. dated post-1982),nickels,oranythingwithamass that The paperclipscouldbereplacedwithpennies(all approximate mass. or papersolongasallcontainersmaintainthesame opaque, youcouldcovertheoutsidewithpaint,tape, mass inallcases.Ifthecontainerisnotnaturally are thatthecontainerremainssealedandhasasimilar other packagingcontainerscouldbeused. The criteria with lids,babyfoodcontainers,paddedenvelopes,and If filmcanistersarenotavailable,condimentcups (interpolation). the numberofpaperclipsinan“unknown”canister the massofemptycontainer( determine themassofasinglepaperclip(slope), the knownpaperclipcontainersanduseagraphto canister. They willmeasurethemasses ofeach the numberofpaperclipsinunknownopaque to determineboththemassofasinglepaperclipand containing aknownnumberofpaperclipsandasked Students areprovidedwithfivesealedfilmcanisters graphing skillstoindirectlyfindatomicmass. various scientificendeavors,forexample,utilizing relationships. This activityhasmanyimplicationsfor insight intotheirtrueunderstandingofthese concepts tosolveaproblemandgivetheteacher This activitywillallowstudentstoapplythese Doll BungeeJumping.” -intercept ofalinerepresentpriortocompletingthis and linearregression.Studentswillknowthe students’ priorknowledgeofgraphing,slope, his activityisaninquirylabthatdrawson Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. at online us Visit reserved. rights Texas. All Dallas, Initiative, +Science Math National ©2013 Copyright y = mx + b ) andwhattheslope y -intercept), and ®

SAMPLE PROCEDURE, DATA, ANALYSIS AND PROCEDURE, SAMPLE . Thesloperepresentsthemassofonepaperclip, 4. . Determinetheslope 3. Graphmassvs.numberofpaperclips,including 2. Determinethemassofcanisterswith 1. Middle Grades Science –Canister Conundrum canister. and the line ofmanualfit. the lineofmanualfit. known numberofpaperclips. Paper Clips Figure A. Massvs.numberofpaperclips Number of nnw Varies Unknown 318.88 13 117.38 11 15.04 12.76 10.73 9 7 5 y -intercept representsthemassoffilm Table A.SampleData èø ç ç ç æö D D y x ÷ ÷ ÷ and with Paper Clips(g) Mass ofContainer y -intercept ofthe iv TEACHER PAGES Middle Grades Science – Canister Conundrum

PROCEDURE DATA AND OBSERVATIONS

SAMPLE PROCEDURE SAMPLE DATA 1. Mass the canisters with the known number of paper clips. Table B. Sample Data Number of Mass of Container 2. Graph mass vs. number of paper clips, including Paper Clips with Paper Clips (g) the line of manual fit. 5 10.73 æö çDy÷ ç ÷ 3. Determine the slope èøçDx and y-intercept of the 7 12.76 line of manual fit. 9 15.04 4. The slope equals the mass of one paper clip and 11 17.38 the y-intercept equals the mass of the canister. 13 18.88 Unknown Varies ANSWER KEY

Figure B. Mass vs. number of paper clips

ANALYSIS CONCLUSION QUESTIONS

1. Determine the number of paper clips in your 1. Did the two methods for determining the number unknown canister using two methods: of paper clips in your unknown canister yield a. Place an “X” on your graph at the point that the same result? Justify your answer by citing represents the mass and number of paper clips evidence from your data. in your unknown sample. Record the number Student answers will vary, but the two methods of paper clips in the space provided. should yield similar results. The number varies depending on the number 2. Would your graph allow you to determine the of paper clips. However, students should use mass of 10 nickels? Why or why not? interpolation to determine the even number of No, this graph only applies to the size of paper paper clips in their canister clips used. No other objects could be determined b. Using the formula for the line of best fit from using this graph. your graph, determine the number of paper 3. Would this type of graph allow you to determine clips in your unknown sample. Show your the mass of 10 seashells? Why or why not? work and record your answer in the space No, seashells vary in mass and thus this method provided. would not work. Final answers will vary based on the unknown 4. Chemists use a similar concept to count atoms. canister. Explain how the mass of a sample of atoms can y = 1.046x + 5.544 provide an accurate count of the number of atoms based on what you have experienced in this massunknown = 1.046(numberpaper clips) + 5.544 activity. mass- 5.544 Once the mass of an individual atom is known number = unknown paper clips 1.046 (from the periodic table) the number of grams ANSWER KEY 2. Use your graph to determine the mass of your of sample can be divided by the mass of the canister containing 15 paper clips. Place a small individual atom to yield the number of atoms circle on your graph at the point that represents present. the mass, and record this value in the space In chemistry, because atoms are so small we provided. use a unit called the mole to represent a group 23 Students should inspect the graph for the of 6.02 × 10 atoms. The atomic mass on the intersection of the plotted line and x = 15 (paper table represents the mass in grams that has to be 23 clips). The y-value of the intersection of these measured to contain exactly 6.02 ×10 atoms of two lines will represent the mass of 15 paper that element. clips. For the sample data, the mass of 15 paper For example, if you have a sample of gold that clips is most nearly 21 g. weighs 196.97 g, there will be almost exactly 23 3. What would be the mass of a canister with 100 6.02 × 10 atoms of gold in that sample. paper clips? Show your work and record your answer in the space provided.

masscanister = 1.046(numberpaper clips) + 5.544

masscanister = 1.046(100) + 5.544 = 110.1 g

Copyright © 2013 National Math + Science Initiative, Dallas, Texas. All rights reserved. Visit us online at www.nms.org. vi Middle Grades Science Middle– Canister Grades Conundrum Science Canister Conundrum Determining Mass Indirectly

paper clip packaging company has had a major malfunction with its counting machine. The company cannot get the machine fixed or A replaced for five days. Not wanting to shut down the company for this time period, they are looking into alternative ways of counting paper clips. MATERIALS Counting 100 paper clips is a tedious task when done by hand. Instead of counting balance the paper clips individually, the company would like to package the paper clips by 5 known film canisters mass. If they do not get the correct mass, the number of paper clips in the package unknown film canister will not be correct and this could affect profits. They have asked you to determine the mass of one paper clip using indirect methods of measurement. The task given to you is to find the mass of one paper clip and the mass of the empty packaging canister.

PURPOSE

In this activity, you will determine the mass of a single object without directly measuring the mass of that object.

PROCEDURE

Record the procedures you developed to determine the mass of one paper clip and the mass of the empty canister.

DATA AND OBSERVATIONS

Create your data table here.

Mass of one paper clip = ______

Mass of the empty canister = ______

ANALYSIS

1. Determine the number of paper clips in your unknown canister using two methods: a. Place an “X” on your graph at the point that represents the mass and number of paper clips in your unknown sample. Record the number of paper clips in the space provided.

b. Using the formula for the line of best fit from your graph, determine the number of paper clips in your unknown sample. Show your work and record your answer in the space provided.

2. Use your graph to determine the mass of your canister containing 15 paper clips. Place a small circle on your graph at the point that represents the mass, and record this value in the space provided.

3. What would be the mass of a canister with 100 paper clips? Show your work and record your answer in the space provided.

CONCLUSION QUESTIONS

1. Did the two methods for determining the number of paper clips in your unknown canister yield the same result? Justify your answer by citing evidence from your data.

2. Would your graph allow you to determine the mass of 10 nickels? Why or why not?

3. Would this type of graph allow you to determine the mass of 10 seashells? Why or why not?

4. Chemists use a similar concept to count atoms. Explain how the mass of a sample of atoms can provide an accurate count of the number of atoms based on what you have experienced in this activity.