Clinometer Activity 5p602r

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

Teacher​ ​Candidates​:​ ​Anna​ ​Kusnomo,​ ​Daiva​ ​Ramanauskas,​ ​Paulina​ ​Salata,​ ​Xuewen​ ​Yang Subject:​​ ​ ​Mathematics​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Grade:​​ ​ ​10​ ​Academic Strand:​​ ​Trigonometry​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​ ​Time:​ ​75​ ​min FRAMEWORK Lesson​ ​Specific​ ​Expectation: BIG​ ​IDEA:​ ​Solving​ ​Problems​ ​Involving​ ​the​ ​Trigonometry​ ​of​ ​Right​ ​Triangles Solve​ ​problems​ ​involving​ ​the​ ​measures​ ​of​ ​sides​ ​and​ ​angles​ ​in​ ​right​ ​triangles​ ​in​ ​real​ ​life applications​ ​(i.e.​ ​in​ ​determining​ ​the​ ​height​ ​of​ ​an​ ​inaccessible​ ​object​ ​around​ ​the​ ​school),​ ​using the​ ​primary​ ​trigonometric​ ​ratios​ ​and​ ​the​ ​Pythagorean​ ​theorem. Mathematical​ ​Process​ ​Expectations: In​ ​this​ ​lesson,​ ​students​ ​will​ ​perform​ ​processes​ ​of: ● Problem​ ​solving ● Reasoning ● Selecting​ ​tools​ ​and​ ​computational​ ​strategies ● Representing ● Communicating Learning​ ​Goals: By​ ​the​ ​end​ ​of​ ​this​ ​lesson,​ ​I​ ​will​ ​be​ ​able​ ​to: ● Recall​ ​and​ ​choose​ ​the​ ​appropriate​ ​trigonometric​ ​ratio​ ​to​ ​calculate​ ​the​ ​height​ ​of​ ​an​ ​object (Knowledge​ ​&​ ​Comprehension) ● Relate​ ​basic​ ​trigonometry​ ​ratios​ ​to​ ​a​ ​concrete​ ​real-life​ ​application​ ​(Application) ● Illustrate​ ​observations​ ​using​ ​a​ ​diagram​ ​(Application) ● Devise​ ​a​ ​tool​ ​and​ ​a​ ​strategy​ ​to​ ​measure​ ​the​ ​angle​ ​of​ ​elevation​ ​and​ ​height​ ​of​ ​an​ ​object (Synthesis) ● Compare​ ​answers​ ​and​ ​provide​ ​reasoning​ ​for​ ​discrepancies​ ​(Evaluation) Success​ ​Criteria: To​ ​be​ ​successful​ ​in​ ​this​ ​lesson,​ ​I​ ​will: ● Follow​ ​instructions​ ​to​ ​make​ ​a​ ​clinometer ● Measure​ ​the​ ​angle​ ​of​ ​elevation​ ​of​ ​a​ ​tall​ ​object​ ​using​ ​the​ ​clinometer ● Produce​ ​a​ ​scaled​ ​diagram​ ​of​ ​my​ ​investigation ● Label​ ​my​ ​diagram​ ​accurately ● Calculate​ ​the​ ​height​ ​of​ ​the​ ​classroom​ ​wall​ ​using​ ​the​ ​tools​ ​I​ ​have​ ​and​ ​the​ ​appropriate trigonometric​ ​ratio ● Collaborate​ ​with​ ​my​ ​partner​ ​to​ ​gather​ ​data​ ​and​ ​make​ ​meaningful​ ​conclusions​ ​from​ ​it ● Discuss​ ​my​ ​findings​ ​with​ ​others​ ​using​ ​mathematical​ ​vocabulary​ ​and​ ​conventions 1

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

SEQUENCE Assessment​ ​FOR​: This​ ​can​ ​be​ ​done​ ​before​ ​or​ ​after​ ​Minds​ ​On: ● Take​ ​up​ ​homework​ ​from​ ​previous​ ​class ● Review​ ​of​ ​“basic​ ​trigonometric​ ​ratios”​ ​(i.e.​ ​SOH​ ​CAH​ ​TOA)​ ​as​ ​a​ ​class ● Review/introduction​ ​of​ ​the​ ​concept​ ​of​ ​“angle​ ​of​ ​elevation”​ ​and​ ​“angle​ ​of​ ​depression” Minds​ ​On​: Part​ ​1:​ ​FIND​ ​YOUR​ ​PARTNER

This​ ​brief​ ​activity​ ​acts​ ​as​ ​a​ ​way​ ​to​ ​both​ ​review​ ​trigonometric​ ​values​ ​and​ ​partner​ ​students​ ​up ● Each​ ​student​ ​will​ ​randomly​ ​pick​ ​a​ ​small​ ​piece​ ​of​ ​paper​ ​after​ ​entering​ ​the​ ​classroom.​ ​(The following​ ​table​ ​will​ ​be​ ​printed​ ​out​ ​and​ ​cut​ ​into​ ​small​ ​pieces.)​ ​Each​ ​piece​ ​of​ ​paper​ ​either has​ ​a​ ​trig​ ​ratio​ ​or​ ​an​ ​actual​ ​value​ ​written​ ​on​ ​it.​ ​Students​ ​will​ ​look​ ​for​ ​their​ ​partner​ ​by matching​ ​the​ ​trig​ ​ratio​ ​with​ ​the​ ​actual​ ​value.​ ​They​ ​may​ ​use​ ​a​ ​calculator​ ​for​ ​this​ ​activity. sin30​o

0.5

tan15​o

0.2679

sin10​o

0.1736

sin5​o

0.0872

tan21​o

0.3839

sin35​o

0.5736

sin40​o

0.6428

sin45​o

cos45​o

tan12​o

0.2126

cos22​o

0.9272

cos33​o

0.8387

cos55​o

0.5736

cos65​o

0.4226

cos70​o

0.3420

tan80​o

5.6713

Part​ ​2:​ ​ANGLE​ ​OF​ ​ELEVATION​ ​VS.​ ​ANGLE​ ​OF​ ​DEPRESSION ● With​ ​your​ ​partner,​ ​discuss​ ​briefly​ ​the​ ​difference​ ​between​ ​angles​ ​of​ ​elevation​ ​and depression Action: ●

Transition: ○ Have​ ​you​ ​ever​ ​thought​ ​of​ ​how​ ​we​ ​could​ ​measure​ ​the​ ​height​ ​of​ ​a​ ​wall​ ​if​ ​we​ ​did​ ​not have​ ​a​ ​measuring​ ​tape​ ​or​ ​if​ ​it​ ​were​ ​too​ ​high? ○ Would​ ​you​ ​like​ ​to​ ​guess​ ​what​ ​a​ ​Clinometer​ ​is? ○ Today,​ ​we​ ​are​ ​going​ ​to​ ​measure​ ​the​ ​height​ ​of​ ​our​ ​classroom​ ​wall​ ​using​ ​a clinometer.

●

Part​ ​1:​ ​MAKING​ ​A​ ​CLINOMETER​ ​(Pairs) ○ Teacher​ ​hands​ ​out​ ​the​ ​“Making​ ​a​ ​Clinometer”​ ​instruction​ ​sheet​ ​(​Appendix​ ​A​) and​ ​distributes​ ​materials​ ​to​ ​each​ ​pair.​ ​This​ ​activity​ ​should​ ​take​ ​about​ ​15​ ​minutes. ○ Materials​ ​(provided​ ​per​ ​pair): ■ Protractor​ ​template ■ Index​ ​paper ■ Straw 2

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

■ ■ ■ ■ ■ ●

20​ ​cm​ ​string Paperclip​ ​(as​ ​weight​ ​attached​ ​to​ ​the​ ​end​ ​of​ ​the​ ​string) Glue Scissors Cellotape

Part​ ​2:​ ​USING​ ​THE​ ​CLINOMETER​ ​(Pairs) ○ Once​ ​the​ ​clinometers​ ​are​ ​ready​ ​to​ ​use,​ ​send​ ​the​ ​pairs​ ​to​ ​different​ ​parts​ ​of​ ​the classroom​ ​(or​ ​any​ ​other​ ​room​ ​in​ ​the​ ​school)​ ​to​ ​measure​ ​the​ ​height​ ​of​ ​the​ ​room’s wall.​ ​Preferably,​ ​students​ ​measure​ ​the​ ​height​ ​of​ ​walls​ ​in​ ​the​ ​same​ ​room,​ ​so​ ​that at​ ​the​ ​end​ ​of​ ​the​ ​class,​ ​pairs​ ​can​ ​compare​ ​results. ○ Teacher​ ​will​ ​distribute​ ​the​ ​handout​ ​“Using​ ​the​ ​Clinometer”​ ​(A ​ ppendix​ ​B​)​ ​and optionally​ ​the​ ​pre-designed​ ​organizer​ ​“Using​ ​Trigonometry​ ​to​ ​Calculate​ ​the Height​ ​of​ ​the​ ​Classroom​ ​Wall”​ ​(​Appendix​ ​C​)​ ​prior​ ​to​ ​the​ ​start​ ​of​ ​the​ ​activity. ○ Materials​ ​(per​ ​pair): ■ Scientific​ ​calculator​ ​(own) ■ Ruler​ ​&​ ​stationery​ ​(own) ■ Blank​ ​paper​ ​or​ ​pre-designed​ ​organizer​ ​(provided) ■ Measuring​ ​tape​ ​(provided​ ​-​ ​to​ ​share​ ​with​ ​the​ ​whole​ ​class) ○ Assessment​ ​AS​:​ ​Checklist​ ​for​ ​Clinometer​ ​(Appendix​ ​D) This​ ​is​ ​done​ ​by​ ​the​ ​teacher​ ​as​ ​students​ ​are​ ​working​ ​on​ ​the​ ​above​ ​activities​ ​to check​ ​for: ● Student​ ​readiness ● Understanding​ ​of​ ​instructions ● Correct​ ​execution​ ​of​ ​activity ● Collaboration

Consolidation​​ ​(Assessment​ ​AS)​: Teacher​ ​provides​ ​opportunity​ ​for​ ​pairs​ ​to​ ​share​​ ​their​ ​investigation​ ​findings​ ​through​ ​one​ ​of these​ ​ways: ○ Volunteers​ ​(​3-4,​ ​preferably​ ​those​ ​who​ ​have​ ​approached​ ​the​ ​problem​ ​differently)​ could​ ​be​ ​asked​ ​to​ ​go​ ​up​ ​to​ ​the​ ​board​ ​and​ ​explain​ ​their​ ​process​ ​and​ ​solution ○ Pairs​ ​pair​ ​up​ ​with​ ​other​ ​pairs​ ​to​ ​compare​ ​their​ ​results ○ Gallery​ ​walk​ ​around​ ​the​ ​classroom ● Teacher​ ​will​ ​hold​ ​a​ ​class​ ​discussion​​ ​on​ ​the​ ​following: ○ Why​ ​were​ ​some​ ​of​ ​the​ ​results​ ​different?​ ​(Possible​ ​points:​ ​taking​ ​the​ ​wrong reading​ ​for​ ​angle​ ​of​ ​elevation,​ ​excluding​ ​height​ ​of​ ​the​ ​person​ ​measuring​ ​(at​ ​eye level)​ ​in​ ​calculating​ ​the​ ​total​ ​height,​ ​rounding​ ​angles​ ​or​ ​mid-calculations​ ​too​ ​early in​ ​the​ ​process,​ ​etc.) ○ What​ ​would​ ​happen​ ​to​ ​the​ ​angle​ ​of​ ​elevation​ ​if​ ​you​ ​were​ ​standing​ ​closer​ ​or farther​ ​away​ ​from​ ​the​ ​wall? Possible​ ​Next​ ​Step: ●

3

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

Plotting​ ​or​ ​organizing​ ​the​ ​class’​ ​data​ ​from​ ​Activity​ ​-​ ​Part​ ​2​ ​to​ ​identify​ ​the​ ​range​ ​of​ ​data​ ​values and​ ​possible​ ​outliers​ ​-​ ​for​ ​further​ ​discussion​ ​that​ ​leads​ ​into​ ​Data​ ​Management. Mid-​ ​Unit​ ​Assignment​ ​(Assessment​ ​OF)​: Now​ ​it​ ​is​ ​your​ ​job​ ​is​ ​to​ ​create​ ​a​ ​scenario​ ​where​ ​you​ ​need​ ​to​ ​use​ ​trigonometry​ ​to​ ​calculate​ ​an object​ ​that​ ​is​ ​either​ ​taller​ ​than​ ​you​ ​or​ ​higher​ ​than​ ​you.​ ​It​ ​is​ ​up​ ​to​ ​you​ ​where​ ​it​ ​takes​ ​place.​ ​It​ ​can take​ ​place​ ​in​ ​your​ ​home,​ ​your​ ​neighbourhood​ ​or​ ​on​ ​Pluto.​ ​This​ ​is​ ​your​ ​opportunity​ ​to​ b ​ e creative​! What​ ​needs​ ​to​ ​be​ ​included: ❏ A​ ​description​​ ​of​ ​the​ ​scenario. ❏ The​ ​question​.​ ​(ie.​ ​Find​ ​the​ ​height​ ​of​ ​the​ ​tower.) ❏ A​ ​diagram​​ ​of​ ​the​ ​scenario​ ​you​ ​are​ ​describing.​ ​It​ ​must​ ​be​ ​LABELED! ❏ A​ ​detailed​ ​solution​.​ ​Show​ ​ALL​​ ​your​ ​work​ ​and​ ​thinking. ❏ A​ ​concluding​ ​statement​​ ​that​ ​answers​ ​the​ ​question​ ​you​ ​posed. ❏ Work​ ​must​ ​be​ ​organized​. Accommodations: ● For​ ​English​ ​Language​ ​Learners​: ○ Provide​ ​an​ ​oral​ ​component​ ​of​ ​the​ ​instructions​ ​(i.e.​ ​reading​ ​aloud​ ​by​ ​the​ ​teacher) ○ Provide​ ​a​ ​visual​ ​component​ ​of​ ​the​ ​instructions​ ​(i.e.​ ​visualization​ ​on​ ​PPT) ● For​ ​students​ ​struggling​ ​in​ ​math​: ○ Provide​ ​pre-designed​ ​organizers​ ​to​ ​document​ ​observations,​ ​calculations,​ ​and results ○ Provide​ ​extra​ ​time ○ Divide​ ​and​ ​deliver​ ​the​ ​task​ ​in​ ​smaller​ ​components ○ Have​ ​an​ ​Educational​ ​Assistant​ ​in​ ​larger​ ​classrooms ● For​ ​students​ ​in​ ​need​ ​of​ ​breaks​​ ​(to​ ​get​ ​up​ ​and​ ​move​ ​around) ○ Minds​ ​on​ ​activity​ ​and​ ​the​ ​clinometer​ ​measuring​ ​activity gets​ ​the​ ​students​ ​up​ ​and​ ​moving​ ​while​ ​they​ ​are​ ​learning ● For​ ​more​ ​advanced​ ​students​: ○ Introduce​ ​a​ ​Clinometer​ ​app​ ​in​ ​addition​ ​to​ ​the​ ​Clinometer device​ ​students​ ​made ○ Provide​ ​blank​ ​instead​ ​of​ ​pre-designed​ ​organizers​ ​to diagram​ ​observations

4

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

APPENDIX​ ​A Making​ ​a​ ​Clinometer Did​ ​you​ ​know? Captain​ ​Jack​ ​Sparrow​ ​used​ ​a​ ​clinometer​ ​in​ ​the movie​ ​Pirates​ ​of​ ​the​ ​Caribbean​.​ ​A​ ​clinometer​ ​is​ ​a useful​ ​piece​ ​of​ ​equipment​ ​for​ ​measuring​ ​angles and​ ​calculating​ ​approximate​ ​heights.​ ​It​ ​is​ ​used frequently​ ​in​ ​forestry,​ ​engineering​ ​and astronomy.​ ​It​ ​was​ ​invented​ ​over​ ​1,000​ ​years​ ​ago and​ ​was​ ​an​ ​important​ ​piece​ ​of​ ​equipment​ ​for early​ ​navigators.​ ​You​ ​can​ ​use​ ​it​ ​here​ ​today​ ​to estimate​ ​the​ ​height​ ​of​ ​our​ ​classroom​ ​wall! Let’s​ ​make​ ​a​ ​Clinometer! 1. Cut​ ​out​ ​the​ ​protractor template​ ​below​ ​and​ ​glue​ ​it​ ​on INDEX​ ​paper. 2. Tape​ ​the​ ​20​ ​cm​ ​string​ ​to​ ​the flat​ ​edge​ ​of​ ​the​ ​protractor,​ ​so that​ ​the​ ​end​ ​of​ ​the​ ​string touches​ ​the​ ​vertical​ ​line​ ​in the​ ​centre.​ ​To​ ​make​ ​sure​ ​it​ ​is secure,​ ​tape​ ​the​ ​string​ ​to​ ​the back​ ​of​ ​the​ ​protractor​ ​and wrap​ ​it​ ​around​ ​the​ ​bottom. 3. Tie​ ​a​ ​paperclip​ ​to​ ​the​ ​other end​ ​of​ ​the​ ​string.​ ​Let​ ​it​ ​swing freely. 4. Now,​ ​glue​ ​a​ ​straw​ ​to​ ​the​ ​flat edge​ ​of​ ​the​ ​clinometer.​ ​The​ ​finished​ ​product​ ​should​ ​look​ ​like​ ​the​ ​figure​ ​on​ ​the​ ​right.

5

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

Protractor​ ​Template:

6

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

APPENDIX​ ​B Using​ ​the​ ​Clinometer​ ​to​ ​Find​ ​The​ ​Height​ ​of​ ​our​ ​Classroom​ ​Wall You​ ​can​ ​now​ ​put​ ​your​ ​clinometer​ ​to​ ​use.

Find​ ​the​ ​angle​ ​of​ ​elevation​ ​by​ ​looking through​ ​the​ ​straw​ ​to​ ​line​ ​up​ ​the​ ​top​ ​of​ ​the wall.​ ​The​ ​string​ ​hanging​ ​down​ ​will​ ​show you​ ​an​ ​angle​ ​reading,​ ​which​ ​you​ ​must subtract​ ​from​ ​90​ ​degrees​ ​to​ ​get​ ​the angle​ ​of​ ​elevation​. Let’s​ ​measure​ ​the​ ​height​ ​of​ ​our​ ​classroom​ ​wall: 1. Work​ ​in​ ​pairs​ ​-​ ​one​ ​holding​ ​the​ ​clinometer​ ​and​ ​the​ ​other​ ​measuring​ ​and​ ​recording information. 2. Stand​ ​a​ ​distance​ ​away​ ​from​ ​the​ ​wall​ ​and​ ​measure​ ​the distance​ ​between​ ​the​ ​wall​ ​and​ ​observer. 3. View​ ​the​ ​top​ ​of​ ​the​ ​wall​ ​using​ ​the​ ​clinometer​ ​through​ ​the straw​ ​so​ ​that​ ​the​ ​string​ ​is​ ​vertical. 4. Record​ ​the​ ​angle​ ​reading​ ​where​ ​the​ ​string​ ​falls​ ​and calculate​ ​the​ ​angle​ ​of​ ​elevation. 5. Draw​ ​a​ ​diagram​ ​in​ ​the​ ​paper/grid​ ​provided​ ​(​Appendix​ ​C​) and​ ​label​ ​all​ ​your​ ​measurements​ ​correctly. 6. Now,​ ​use​ ​the​ ​correct​ ​trigonometric​ ​ratio​ ​to​ ​measure​ ​the approximate​ ​height​ ​of​ ​the​ ​wall. (If​ ​you​ ​were​ ​measuring​ ​the height​ ​of​ ​a​ ​tree)

7

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

APPENDIX​ ​C​ ​http://www.projectmaths.ie/documents/T&L/IntroductionToTrigonometry.pdf

Using​ ​Trigonometry​ ​to​ ​Calculate​ ​the​ ​Height​ ​of​ ​the​ ​Classroom​ ​Wall With​ ​your​ ​partner,​ ​record​​ ​your​ ​observations​ ​in​ ​the​ ​chart​ ​provided. Height​ ​from​ ​ground​ ​to observer’s​ ​eye

Distance​ ​between​ ​observer and​ ​wall

Angle​ ​of​ ​elevation​ ​to​ ​the​ ​top of​ ​the​ ​wall

Draw​ ​a​ ​diagram​​ ​of​ ​the​ ​scenario​ ​in​ ​the​ ​space​ ​below.​ ​In​ ​your​ ​diagram​ ​mark​ ​the​ ​right​ ​angle,​ ​the angle​ ​of​ ​elevation,​ ​the​ ​hypotenuse,​ ​and​ ​the​ ​adjacent​ ​and​ ​opposite​ ​side​ ​with​ ​respect​ ​to​ ​the​ ​angle of​ ​elevation.​ ​Make​ ​sure​ ​all​ ​sides​ ​are​ ​labelled​ ​and​ ​measurements​ ​are​ ​included​.

Now​ ​it​ ​is​ ​time​ ​to​ ​calculate​ ​the​ ​height​ ​of​ ​the​ ​wall​.​ ​Look​ ​back​ ​to​ ​your​ ​diagram.​ ​What​ ​are​ ​your givens?​ ​What​ ​side​ ​length​ ​are​ ​you​ ​trying​ ​to​ ​find?​ ​What​ ​trigonometric​ ​ratio​ ​uses​ ​these​ ​two​ ​sides?

8

Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D November​ ​2,​ ​2017

APPENDIX​ ​D Assessment​ ​AS​ ​Checklist​​ ​(used​ ​during​ ​group​ ​activities) Learning​ ​Goal: We​ ​are​ ​learning​ ​to measure​ ​the​ ​height​ ​of an​ ​object​ ​using​ ​tangent ratio.

Success​ ​Criteria: 1.​​ ​ ​ ​ ​I​ ​made​ ​the​ ​clinometer​ ​following​ ​instructions. 2.​​ ​ ​ ​ ​I​ ​measured​ ​the​ ​angle​ ​of​ ​elevation​ ​using​ ​the​ ​appropriate technique. 3.​​ ​ ​ ​ ​I​ ​measured​ ​all​ ​distances​ ​needed​ ​for​ ​solving​ ​the​ ​problem correctly.

Student Name

Discussed Angles

Discussed Data Collection

Discussed Trig​ ​Ratios

Drew​ ​a diagram​ ​to represent​ ​the scenario

Other​ ​Notes

I​ ​–​ ​student​ ​initiated​ ​the​ ​discussion E​ ​–​ ​student​ ​expanded​ ​on​ ​the​ ​topic​ ​discussed O​ ​–​ ​student​ ​observed​ ​the​ ​discussion​ ​and​ ​seemed​ ​engaged,​ ​without​ ​necessarily​ ​adding​ ​to​ ​it 9