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U n t er r i ch t spl a n
Ang l e M e as ure s
Altersgruppe: 4 t h Gr ade , 5 t h Gr ade
Texas - TEKS: G4 .1.M P S .C , G4 .6.GM .A , G4 .6.GM .B ,
G4 .6.GM .C
Riverside USD Scope and Sequence: 4 .M D.5 [4 .7 ]
Oklahoma Academic Standards Mathematics: 4 .GM .1.1, 4 .GM .2.1,
4 .GM .2.2
Virginia - Mathematics Standards of Learning (2009): 4 .10a, 5 .11,
5 .9
Common Core: 4 .M D.C .5
Mathematics Florida Standards (MAFS): 4 .M D.3 .5
Alaska: 4 .M D.7 a, 4 .M D.7 b, 4 .M P .6e , 4 .M P .6f
Minnesota: 4 .3 .2.1, 4 .3 .2.2
Fairfax County Public Schools Program of Studies: 4 .10.a.1,
4 .10.a.3 , 5 .11.a.1, 5 .11.a.3 , 5 .9.a.1, 5 .9.a.2
Nebraska Mathematics Standards: M A .4 .3 .1.e
South Carolina: 4 .M DA .5 , 4 .M DA .6, 4 .M DA .7
Indiana: 4 .M .5 , 4 .M .6, 4 .P S .7
Georgia Standards of Excellence: M GS E 4 .M D.5
Online-Ressourcen: W hat ' s Y o ur A ngl e ?
Opening
T eacher
present s
St udent s
play
Class
discussion
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15
10
3
min
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ZIE L E :
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Closing
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E x pe r i e nc e manipulating sectors within a circle
P r ac t i c e finding the measure of an angle
L e ar n to identify acute, right, obtuse, and straight angles
De v e l o p geometry skills
Ope ni ng | 7 min
Display the following sentence:
“The principal said she would never agree to an ice cream social, but then she
did a 180.”
A sk the students to talk in pairs. Ask: In this sentence, what does
“did a 180” mean?
When the students have talked in their pairs for a minute, share.
A sk: In this sentence, what does “did a 180” mean?
It means to change her mind entirely or to do the opposite. It
means the principal agreed to the ice cream social.
S ay: The expression comes from the fact that a circle contains
360 degrees. So if you make a 360 degree turn, you have “come
full circle”, turned around one full revolution, and arrived back at
your original ideas. But to “do a 180” is to turn 180 degrees, which
means that your ideas are the opposite of what they once were.
So what does a 180 degree turn look like?
A 180 degree turn is to turn halfway around so that you are
facing the opposite direction.
Display the following:
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S ay: We can cut the circle up further into smaller wedges. Rather
than making a 180 degree turn, we could make a quarter turn, or 90
degree turn. This is called a r i ght angl e .
Write on the board:
R ig h t a n g le – a 90 degree angle (a quarter turn)
A c u t e a n g le – an angle between 0 and 90 degrees
Ob t u s e a n g le – an angle between 90 and 180 degrees
S t r a ig h t a n g le – a 180 degree angle
T e ac he r pr e se nt s W hat ’ s Y o ur A ngl e ? | 12 min
Present Matific ’s episode W hat ’ s Y o ur A ngl e ? - Quant i f yi ng
P ar t s o f a C i r c l e to the class, using the projector.
The goal of the episode is to determine the measure of an angle by
determining how many sectors fit in a circle.
E x a m p le :
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S ay: The episode wants us to determine the measure of the given
angle. Let’s see how many wedges fit inside the circle.
Move the sector onto the circle. Continue placing sectors onto the
circle until the circle is completely covered.
A sk: How many wedges does it take to cover the circle?
Students can answer based on the episode.
A sk: How do we determine the measure of angle A? How do you
know?
We divide 360 by the number of times that the wedge fits inside
the circle. The measure of the whole circle is 360 degrees, so we
divide to find the angle of each piece.
A sk: So what is the measure of angle A?
Students can do the division to calculate the answer.
Click on the
to enter the value that the students offer.
If the answer is correct, the episode will demonstrate the division involved in
the problem.
If the answer is incorrect, the question will wiggle.
A sk: Is angle A acute, right, or obtuse?
Students can answer based on the episode.
Click on the
to proceed to the next question.
The episode will present a total of six questions.
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S t ude nt s pl ay W hat ’ s Y o ur A ngl e ? | 15 min
Have the students play W hat ’ s Y o ur A ngl e ? - Quant i f yi ng
P ar t s o f a C i r c l e on their personal devices. Students should also
have time to play W hat ’ s Y o ur A ngl e ? - N ami ng A ngl e s .
Circulate, answering questions as necessary.
C l ass di sc ussi o n | 10 min
Display the following:
A sk: What kind of angle is made by the hands of the clock?
The hands of the clock form a right angle.
A sk: Is three o’clock the only right angle that can be made with the
hands of the clock?
No. A right angle occurs at nine o’clock also. We can make other
right angles, too, such as 4:05. (Of course, to be precise, the hour
hand may have moved slightly away from the 4 at 4:05.)
A sk: If we place the hour hand on one number of the clock and the
minute hand on the next number (see diagram below), what is the
measure of the angle formed? How do you know?
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The angle measures 30 degrees. Since there are 360 degrees in a
circle and the clock is divided into 12 sections, we divide 360 by 12
to get 30.
Ask: How could we make a 120 degree angle? How do you know?
Responses may vary. A possible response: At 4:00, a 120 degree
angle occurs. The minute hand is on the 12 and the hour hand is on
the 4. The measure between consecutive numbers is 30 degrees.
So we have 4 sets of 30 degrees from 12 to 4. Four sets of 30 is
120 degrees.
Ask: Is this the only way to make a 120 degree angle?
No. Any time the two hands are four numbers apart on the clock, a
120 degree angle is formed.
Ask: What kind of angle is a 120 degree angle?
It is an obtuse angle.
Display the following:
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A sk the students to copy and complete the table. They should
complete the table by writing the times from the box in the correct
column. They should consider the angle formed between the hands
of the clock. (No reflex angles should be considered.)
Review answers.
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C l o si ng | 3 min
A sk: True or False? A 360 degree turn is a half revolution.
False. A 360 degree turn is a full revolution.
A sk: True or False? An acute angle is smaller than a right angle.
True. An acute angle is smaller than a right angle.
A sk: True or False? Two identical acute angles next to each other
could form a right angle.
True. Two 45 degree angles together form a right angle.
A sk: True or False? Two obtuse angles next to each other form a
straight angle.
False. Two right angles together form a straight angle.
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