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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Lesson lan: Measuring Angles (This lesson should be adapted, including instructional time, to meet the needs of your students.)
!ac"ground #nformation
Content$Grade Le%el Mathematics Grade 4
&ote: This could easily be a two-day lesson.
Unit$Cluster: 4.M.! Geometric Measurement" #nderstand !oncepts of $ngle and Measure $ngles
'ssential (uestions$'nduringUnderstandings Addressed in t)e
Lesson
%ssential &uestions 'hy do measure angles
'hy do need standardi*ed units of measurement when measuring angles
+ow does what measure influence how measure
'hat types of problems are soled with measurement
'hat are tools used to measure angles and how are they used
'hen is an estimate more appropriate than an actual measurement
'hat strategies help estimate measurements of angles
'hen will use angle measurements in real-life problem soling
%nduring #nderstandings
Measurement describes the attributes of obects and eents.
tandard units of measure enable people to interpret results or data.
$ll measurements hae some degree of uncertainty.
/bects can be described and compared using their geometric attributes. The choice of measurement tools depends on the measurable attribute and the degree of
precision desired.
*tandards Addressed in +)is
Lesson
4.MD.C.5-70ecogni*e angles as geometric shapes that are formed whereer two rays share a
common endpoint, and understand concepts of angle measurement.
4.MD.C.5a$n angle is measured with reference to a circle with its center at the common endpoint
of the rays, by considering the fraction of the circular arc between the points where the two rays
intersect the circle. $n angle that turns through 1235 of a circle is called a 6one-degree angle,7
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
and can be used to measure angles.
4.MD.C.5$n angle that turns through none-degree angles is said to hae an angle measure of n
degrees.
4.MD.C.Measure angles in whole-number degrees using a protractor. 8etch angles of specific
measure.
t is critical that the tandards for Mathematical 9ractice are incorporated in $:: lesson actiities
throughout the unit as appropriate. t is not the e;pectation that all eight Mathematical 9ractices will beeident in eery lesson. The tandards for Mathematical 9ractice ma8e an e;cellent framewor8 on which
to plan your instruction. :oo8 for the infusion of the Mathematical 9ractices throughout this unit.
Lesson +opic Measuring $ngles
ele%ance$Connections !loc8s are circles and the hands form different types of angles as they moe around the cloc8 face
n arious sports, athletes often refer to 6doing a 35, a 1enchmar8 angles of 1
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
*upport +)is Learning Types of angles" acute, obtuse, right, straight angles
#nderstanding that two rays that share an endpoint (erte;) form an angle
orting @uadrilaterals by types of angles
&ote: 9rior to the lesson, consider haing struggling students2%:: students iew one of the ideo clips
listed in the Motiation section to frontload the idea of angle measures in the real world so that they can
contribute to the brainstorming discussion.
Met)od for determining student
readiness for t)e lesson
Materials Aeeded"
0esource heet 1" >ac8ground nformation for the Teacher (0ead prior to lesson.)
0esource heet B" 9retest
0esource heet 3" 9retest $nswer Cey
irections"
istribute 0esource heet B" 9retest to students.
$llow time for them to complete the 9retest.
0eiew their responses based on the notes on 0esource heet 3" $nswer Cey and plan
interentions as needed.
Learning '2perience
Component Details
Which Standards for Mathematical
Practice(s) does this address? How is the
Practice used to help students develop
proficiency?
Warm Up Materials Aeeded"
Dudy cloc8s (one per student and teacher)
M9 ?" #se appropriate tools strategically
tudents will use cloc8 hands to model
and to isuali*e different angles
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
irections
0eiew the types of angles including straight angles
as8ing students to moe the hands of cloc8 to form
different angles.
Motivation Materials Aeeded
/ne of these ideo clips" Cobe >ryant 35 degree dun8
http"22www.youtube.com2watchEf
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
Multiple Means of
0epresentation
Multiple Means for
$ction and
%;pression
Multiple Means for
%ngagementCey &uestions
Jormatie $ssessment
ummary
traws (two or each student)
3-inch pieces of pip cleaner (one for each student)
9art 1
%ach student ma8es an 6angle e;plorer7
Gie each student B straws and a length of pipe cleaner
appro;imately 3 inches long.
tudents bend the pipe cleaner in half and insert each
end into the straws.
9art B
+ae students show different types of angles with their
angle e;plorer (acute, obtuse, right, straight)
iscuss" $ngles are formed by two rays sharing an
endpoint li8e two cloc8 hands. +ae students identify theerte; and the two rays on their angle e;plorer.
+ae students wor8 in pairs.
Gie students different times such as 1"1?, 1B"35, B"3?.
tudents should moe the cloc8 hands to the gien times
and match with angle e;plorer. +ae them identify the
types of angles formed with their partner.
tudents e;plore the relatie si*e of
angles based on the degrees of the
angles.
M9 " $ttend to precision
tudents use appropriate symbols ()
and unit of measurement (degrees).
M9 I" :oo8 for and ma8e use of structure
tudents recogni*e that a 4?is half of
=5angle and so on.
tudents recogni*e that a =5angle is
still a =5angle regardless of its
orientation.
M9
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
#: !omponents
Multiple Means of
0epresentation
Multiple Means for
$ction and
%;pression Multiple Means for
%ngagement
Cey &uestions
Jormatie $ssessment
ummary
student)
irections"
$s8 students if they 8now how a circle is measured.
0efer bac8 to the Motiation $ctiity.
iscuss that a full circle is 35and that circles and
angles are measured in degrees. The anglemeasurement is measuring the spread of the rays in a
circle. ntroduce the degree symbol. 0elate to cloc8s
and the moement of the cloc8 hands.
Gie each student a paper circle with the center point
mar8ed from 0esource heet 4" 9aper !ircle.
+ae students fold the circle in half and then trace oer
the line. %ncourage them to be as e;act as possible.
$s8" f a circle e@ual 35, what would K circle e@ual
:abel half circle 1
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
Aote" tudents who hae difficulty isuali*ing the parts of a
circle could color the angles as shown aboe.
+ae students use their angle e;plorer from $ctiity 1 toform =5angle and a 1
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
$ction and
%;pression
Multiple Means for
%ngagement
Cey &uestions
Jormatie $ssessment
ummary
Ma8ing and #sing a 'a; 9aper 9rotractor
1. 9ass out s@uare of wa; paper and 0esource heet ?"
$ngle 'or8sheet (which displays 3 circles L, 12
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
Learning '2perience
0esource heet I" %;it Tic8et
'rap #p"
1) istribute 0esource heet I" %;it Tic8et and allow time
for students to complete it.B) !ollect the %;it Tic8et from each student and as8 them to
oin you up front for a class discussion.3) iscussion" 0efer bac8 to the motiation.
Tal8 about why something is called a 1&
$s8 student how many turns is a 1B5 9roe your
answer.
the reasoning of others
tudents ustify their reasoning when
discussing types of angles in the realworld.
M9 4" Model with mathematics
tudents apply the math they 8now to
sole problems arising in eeryday life
*upporting #nformation#nter%entions$'nric)ments
pecial %ducation2truggling
:earners
%::
Gifted and Talented
pecial %ducation2truggling :earners and %:: students"
9rior to the lesson, consider haing struggling students2%:: students iew one of the ideo clips listed
the Motiation section to frontload the idea of angle measures in the real world so that they can
contribute to the brainstorming discussion.
tudents who hae difficulty isuali*ing the parts of a circle could color the angles as shown in $ctiity
%:: students
9roide a ocabulary sheet identifying and illustrating the different types of angles (acute, obtuse, righ
straight)
Gifted and Talented
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http://www.youtube.com/watch?v=qIr2ki4nWkUhttp://www.youtube.com/watch?v=oF-jmHTYLBQhttp://www.youtube.com/watch?v=oF-jmHTYLBQhttp://www.youtube.com/watch?v=qIr2ki4nWkUhttp://www.youtube.com/watch?v=oF-jmHTYLBQ7/23/2019 Lesson Plan (Geometry).docx
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
>abylonians share what they learn
!hallenge problems are included on the e;it slip for enrichment purposes
Materials 0esource heet 1" >ac8ground nformation for the Teacher (0ead prior to lesson.)
0esource heet B" 9retest
0esource heet 3" 9retest $nswer Cey
Dudy cloc8s (one per student and teacher)
/ne of these ideo clips"
Cobe >ryant 35 degree dun8
o http"22www.youtube.com2watchEf
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: Understand Concepts of Angle andMeasure Angles
and the margin of error is only 1.
$lien$ngles game"
www.mathplayground.com/alien angles .html
$lien $ngles game" 9ractice estimating angles with this game. t is challenging and some students might
find it frustrating.
!reating 9ractice 'or8sheets"
www.worksheetworks.com/math/geometry/ measuring -angles .html
This site allows the teacher to create a practice wor8sheet that proides students with a set of angles that
they measure with a protractor. Teachers are able to specify the range of angles used on the wor8sheet
and are able to ma8e the measuring easier by not rotating the angle, which will 8eep the base of the angle
always hori*ontal on the wor8sheet.
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https://exchange.ccboe.com/owa/redir.aspx?C=060da758a346408aa6f13698b1a378c8&URL=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dmeasuring%2520angles%2520practice%26source%3Dweb%26cd%3D2%26ved%3D0CCQQFjAB%26url%3Dhttp%253A%252F%252Fwww.mathplayground.com%252Falienangles.html%26ei%3DFECIUNWSGIyq0AGijYGwAw%26usg%3DAFQjCNGcPog8W2j-Tp2Z_WKq-ZaWE5MK9Ahttp://www.mathplayground.com/alienangles.htmlhttps://exchange.ccboe.com/owa/redir.aspx?C=060da758a346408aa6f13698b1a378c8&URL=http%3A%2F%2Fwww.worksheetworks.com%2Fmath%2Fgeometry%2Fmeasuring-angles.htmlhttp://www.worksheetworks.com/math/geometry/measuring-angles.htmlhttp://www.worksheetworks.com/math/geometry/measuring-angles.htmlhttps://exchange.ccboe.com/owa/redir.aspx?C=060da758a346408aa6f13698b1a378c8&URL=http%3A%2F%2Fwww.google.com%2Furl%3Fsa%3Dt%26rct%3Dj%26q%3Dmeasuring%2520angles%2520practice%26source%3Dweb%26cd%3D2%26ved%3D0CCQQFjAB%26url%3Dhttp%253A%252F%252Fwww.mathplayground.com%252Falienangles.html%26ei%3DFECIUNWSGIyq0AGijYGwAw%26usg%3DAFQjCNGcPog8W2j-Tp2Z_WKq-ZaWE5MK9Ahttp://www.mathplayground.com/alienangles.htmlhttps://exchange.ccboe.com/owa/redir.aspx?C=060da758a346408aa6f13698b1a378c8&URL=http%3A%2F%2Fwww.worksheetworks.com%2Fmath%2Fgeometry%2Fmeasuring-angles.htmlhttp://www.worksheetworks.com/math/geometry/measuring-angles.html7/23/2019 Lesson Plan (Geometry).docx
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet 1 !ac"ground information for t)e teac)er
Mesopotamia Mat)ematics and t)e -Degree Circle
The Mesopotamians are credited with inenting
mathematics. The Mesopotamians numerical
system was based on multiples of and 15. The
first round of numbers were based on ten li8e
ours, but the ne;t round was based on multiples
of si; to get 5 and 55. 'hy it was based on
multiples of si;, no one 8nows. 9erhaps it is
because the number 5 can be diided by many
numbers" B, 3, 4, ?, , 1B, 1?, B5 and 35.
The umerians deeloped a numerical system
based on 5. The base numerical system is the
reason why >abylonians chose 1B months instead
of 15 for their calendar and why hours and
minutes are diided into 5 units and why we
hae do*ens and a circle has 35 degrees. >abylonian astronomers 8new the true number of
days in a year, but 8ept it at 35 because that number was belieed to be possessed with
magical properties.
>abylonians deised the system of diiding a circle into 35 degrees (some say it was the
$ssyrians who first diided the circle). The tiny circle as a sign for a degree was probably
originally a hieroglyph for the sun from ancient %gypt. $ circle was used by the ancient
>abylonian and %gyptian astronomers to the circle the *odiac. The degree was a way of
diiding a circle and designating the distance traeled by the sun each day. t is no
coincidence then that the number of degrees in a circle (35) corresponds with the days of
the year on the >abylonian calendar.
*ource: http"22factsanddetails.com2world.phpitemidE1?11QcatidE?QsubcatidE33
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet B" retest
Aame ate
Directions: &ame t)e t3pes of angles s)o1n elo1.
1. B. 3.
4. ?. .
Directions: Ans1er 6uestions 7-8 3 listing t)e letters of t)e appropriate 6uadrilaterals.
I. 'hich @uadrilaterals hae only right angles
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet 3" retest - A&*9' 0'
+eac)er &ote$Loo" fors:
Did students generall3 "no1 t)e different t3pes of angles;
#f students t)oug)t
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
Did students see t)e connection et1een t)eir ans1ers in 7-8; @or e2ample, an3
6uadrilateral 1it) an acute angle must also )a%e an otuse angle. +)e onl36uadrilaterals 1it)out acute and otuse angles are t)ose 1it) all rig)t angles.
0esource heet 4" aper Circle
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet ? A&GL' 9/0*''+
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet MA0#&G A 9AB A' /+AC+/
1. tart with a s@uare sheet of paper, appro;imately 4 inches ; 4 inches.
B. Jold the s@uare in half, creating a rectangle. !rease the fold.
3. Jold the rectangle in half, creating a new s@uare. !rease the fold.
4. Jold the new s@uare in half li8e a triangle.
?. Jold the triangle in half, ma8ing a narrower triangle.
. !ut off the top edge, ma8ing all the edges een.
I. #nfold
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Grade 4: Unit 4.MD.C.5-7, Geometric Measurement: UnderstandConcepts of Angle and Measure Angles
0esource heet I '2it *lip
Aame ate
1. +ow many one-degree angles are in a full circle
B. $n angle that ma8es a full turn through a circle measures degrees.
3. 'hat fraction of a circle is a 1