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

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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

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■ 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:
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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

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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.

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 Mathematics​ ​Lesson​ ​Plan​ ​-​ ​EDFE​ ​3200​ ​D
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Protractor​ ​Template:

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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)

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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 Distance​ ​between​ ​observer Angle​ ​of​ ​elevation​ ​to​ ​the​ ​top
observer’s​ ​eye and​ ​wall 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?

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APPENDIX​ ​D

Assessment​ ​AS​ ​Checklist​​ ​(used​ ​during​ ​group​ ​activities)

Learning​ ​Goal: Success​ ​Criteria:

We​ ​are​ ​learning​ ​to
measure​ ​the​ ​height​ ​of 1.​​ ​ ​ ​ ​I​ ​made​ ​the​ ​clinometer​ ​following​ ​instructions.
an​ ​object​ ​using​ ​tangent
ratio. 2.​​ ​ ​ ​ ​I​ ​measured​ ​the​ ​angle​ ​of​ ​elevation​ ​using​ ​the​ ​appropriate
technique.

3.​​ ​ ​ ​ ​I​ ​measured​ ​all​ ​distances​ ​needed​ ​for​ ​solving​ ​the​ ​problem
correctly.

Drew​ ​a
Discussed
Student Discussed Discussed diagram​ ​to
Data Other​ ​Notes
Name Angles Trig​ ​Ratios represent​ ​the
Collection
scenario

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