The document discusses different ways of teaching parallel straight lines in geometry. It begins by describing the "old way" of teaching, where the teacher lectures and draws on the blackboard. It then presents the teacher's "new way" of interactive learning using computers. Students work in teams on geometry topics online and with interactive software. They experiment with parallel lines, angles, and properties. Finally, students practice definitions and pair angles on paper through testing.

1. What aboutWhat about
Math…Math…

2. teachingteaching
What aboutWhat about

3. teachteachingI teachI teach math…math…

4. I teachI teach math…math…
…to students who hate Mathematics!

5. I teachI teach math…math…
EuclideanEuclidean
GeometryGeometry

6. Lets talk about ways ofLets talk about ways of
teachingteaching

7. Lets talk about ways ofLets talk about ways of
teaching:teaching:Chapter 4: parallel straight lines

8. ……use the old wayuse the old way
Parallel straight lines through students
school book

9. ……use the old wayuse the old way

10. You could open the book by touching it.
……use the old wayuse the old way

11. What’s the old way?What’s the old way?

12. Me, the teacher
That’s the old way!That’s the old way!

13. Me, the teacher, I talk
That’s the old way!That’s the old way!

14. Me, the teacher, I talk, I talk
That’s the old way!That’s the old way!

15. Me, the teacher, I talk, I talk, I talk
That’s the old way!That’s the old way!

16. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks
That’s the old way!That’s the old way!

17. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions
That’s the old way!That’s the old way!

18. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention
That’s the old way!That’s the old way!

19. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest
That’s the old way!That’s the old way!

20. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once
That’s the old way!That’s the old way!

21. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice
That’s the old way!That’s the old way!

22. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again…
That’s the old way!That’s the old way!

23. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again… again…
That’s the old way!That’s the old way!

24. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again… again…
Some of them are interested
That’s the old way!That’s the old way!

25. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again… again…
Some of them are interested, some of them
answer
That’s the old way.That’s the old way.

26. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again… again…
Some of them are interested, some of them
answer, some of them
That’s the old way!That’s the old way!

27. Me, the teacher, I talk, I talk, I talk, I draw
on the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… once, twice…
again… again…
Some of them are interested, some of them
answer, some of them get bored…
That’s the old way!That’s the old way!

28. Me, the teacher I talk, I talk, I talk, I draw on
the blackboard using chalks, I ask them
simple questions trying to get their
attention and their interest… again and
again…
Some of them are interested, some of them
answer, some of them gt is boring!!!
……using the old wayusing the old way

29. My way now!My way now!

30. My way now!My way now!
1nd
step
Using PC.

31. 1nd
step
I ask students to work in teams of three
using personal computers.
My way now!My way now!
Using PC.

32. 1nd
step
I ask students to work in teams of three
using personal computers.
Then I ask them to take a “walk” on the
Internet geometry books or articles.
My way now!My way now!
Using PC.

33. 1nd
step
I ask students to work in teams of three
using personal computers.
Then I ask them to take a “walk” on the
Internet geometry books or articles.
(I usually give to each team different key
words.)
My way now!My way now!
Using PC.

34. 1nd
step
I ask students to work in teams of three
using personal computers.
Then I ask them to take a “walk” on the
Internet geometry books or articles.
(I usually give to each team different key
words.)
I advise them to use for extra help their
school book.
My way now!My way now!
Using PC.

35. My wayMy way: parallel straight lines
2nd
step
Using PC.

36. My wayMy way: parallel straight lines
2nd
step
Then I give them a GEOGEBRA file I had
prepared to “play” with, to experiment, to
discover, to learn simple facts.
Using PC.

37. My wayMy way: parallel straight lines
2nd
step
Take a
straight
line.
Take a
straight
line.
Using PC.

38. My wayMy way: parallel straight lines
2nd
step
Using PC.

39. My wayMy way: parallel straight lines
2nd
step
You could grab
the line by the
X and move it.
You could grab
the line by the
X and move it.
Using PC.

40. My wayMy way: parallel straight lines
2nd
step
Take one more
straight line,
parallel to the
first one.
Take one more
straight line,
parallel to the
first one.
Using PC.

41. My wayMy way: parallel straight lines
2nd
step
Using PC.

42. My wayMy way: parallel straight lines
2nd
step
Remember you
could play moving
the lines using X as
a handle.
Remember you
could play moving
the lines using X as
a handle.
Using PC.

43. My wayMy way: parallel straight lines
2nd
step
Take a
transversal line.
Take a
transversal line.
Using PC.

44. My wayMy way: parallel straight lines
2nd
step
Using PC.

45. My wayMy way: parallel straight lines
2nd
step
“Show” me
all the
angles!
“Show” me
all the
angles!
Using PC.

46. My wayMy way: parallel straight lines
2nd
step
“Show” me
all the angles
around A!
“Show” me
all the angles
around A!
Using PC.

47. My wayMy way: parallel straight lines
2nd
step
Using PC.

48. My wayMy way: parallel straight lines
2nd
step
Using PC.

49. My wayMy way: parallel straight lines
2nd
step
Using PC.

50. My wayMy way: parallel straight lines
2nd
step
Using PC.

51. My wayMy way: parallel straight lines
2nd
step
Do the same
for B!
Do the same
for B!
Using PC.

52. My wayMy way: parallel straight lines
2nd
step
Using PC.

53. My wayMy way: parallel straight lines
2nd
step
Using PC.

54. My wayMy way: parallel straight lines
2nd
step
Using PC.

55. My wayMy way: parallel straight lines
2nd
step
Using PC.

56. My wayMy way: parallel straight lines
2nd
step
Move the lines
if you like.
Move the lines
if you like.
Using PC.

57. My wayMy way: parallel straight lines
2nd
step
Using PC.

58. My wayMy way: parallel straight lines
2nd
step
Now keep all the
interior angles!
Now keep all the
interior angles!
Using PC.

59. My wayMy way: parallel straight lines
2nd
step
Now keep all the
interior angles!
Now keep all the
interior angles!
Using PC.

60. My wayMy way: parallel straight lines
2nd
step
Now keep all the
interior angles!
Now keep all the
interior angles!
Using PC.

61. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep all the
exterior angles!
Now keep all the
exterior angles!

62. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep all the
exterior angles!
Now keep all the
exterior angles!

63. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep all the
exterior angles!
Now keep all the
exterior angles!

64. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep 2 alternate
angles!
Now keep 2 alternate
angles!

65. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep 2 alternate
angles!
Now keep 2 alternate
angles!

66. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now keep 2 alternate
angles!
Now keep 2 alternate
angles!
ΕΝΑΛΛΑΞ!

67. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now find another pair
of alternate angles!
Now find another pair
of alternate angles!

68. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now find another pair
of alternate angles!
Now find another pair
of alternate angles!

69. My wayMy way: parallel straight lines
2nd
step
Using PC.
Now find another pair
of alternate angles!
Now find another pair
of alternate angles!
ΕΝΑΛΛΑΞ!

70. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of angles at
the same side!
Find a pair of angles at
the same side!

71. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of angles at
the same side!
Find a pair of angles at
the same side!

72. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of angles at
the same side!
Find a pair of angles at
the same side!
ΕΠΙ ΤΑ ΑΥΤΑ!

73. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of alternate
interior angles!
Find a pair of alternate
interior angles!

74. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of alternate
interior angles!
Find a pair of alternate
interior angles!

75. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of alternate
interior angles!
Find a pair of alternate
interior angles!
Yeah!

76. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of alternate
interior angles!
Find a pair of alternate
interior angles!
Move the ε line!
Did you notice
anything?
Move the ε line!
Did you notice
anything?

77. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find another pair of
alternate interior
angles!
Find another pair of
alternate interior
angles!

78. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of same side
angles, one interior and the
other exterior!
Find a pair of same side
angles, one interior and the
other exterior!

79. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of same side
angles, one interior and the
other exterior!
Find a pair of same side
angles, one interior and the
other exterior!

80. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of same side
angles, one interior and the
other exterior!
Find a pair of same side
angles, one interior and the
other exterior!
Choose another pair like this one!

81. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of same side
angles, one interior and the
other exterior!
Find a pair of same side
angles, one interior and the
other exterior!

82. My wayMy way: parallel straight lines
2nd
step
Using PC.
Find a pair of same side
angles, one interior and the
other exterior!
Find a pair of same side
angles, one interior and the
other exterior!
Choose another pair like this one!

83. My wayMy way: parallel straight lines
2nd
step
Using PC.

84. My wayMy way: parallel straight lines
2nd
step
Using PC.

85. My wayMy way: parallel straight lines
2nd
step
Using PC.
and so on…

86. My wayMy way: parallel straight lines
3nd
step
Using paper
At this stage students have to use their
pencils and work on papers in pairs.

87. My wayMy way: parallel straight lines
3rd
step
Using paper

88. My wayMy way: parallel straight lines
3rd
step
Using paper

89. My wayMy way: parallel straight lines
3rd
step
the definition
Using paper

90. My wayMy way: parallel straight lines
3rd
step
Using paper

91. My wayMy way: parallel straight lines
3rd
step talking about anglesUsing paper

92. My wayMy way: parallel straight lines
3rd
step
•pairing angles
•giving angles 2 names
Using paper

93. My wayMy way: parallel straight lines
3rd
step
•pairing angles
•giving angles 2 names
«εντός» “interior”
Using paper

94. My wayMy way: parallel straight lines
3rd
step
•pairing angles
•giving angles 2 names
«εκτός» “exterior”
«εντός» “interior”
Using paper

95. My wayMy way: parallel straight lines
3rd
step
•pairing angles
•giving angles 2 names
«εκτός» “exterior”
«εντός» “interior” «εναλλάξ» “alternate”
Using paper

96. My wayMy way: parallel straight lines
3rd
step
•pairing angles
•giving angles 2 names
«εκτός» “exterior”
«εντός» “interior” «εναλλάξ» “alternate”
«επί τα αυτά» “same side”
Using paper

97. My wayMy way: parallel straight lines
3rd
step
test 1:
Using paper

98. My wayMy way: parallel straight lines
3rd
step
I give you a pair of angles.
Name them please!
test 1:
Using paper

99. My wayMy way: parallel straight lines
3rd
step
Using paper

100. My wayMy way: parallel straight lines
3rd
step 1st
question:Using paper

101. My wayMy way: parallel straight lines
3rd
step
do you remember
anything
about angles 1 and 3
Using paper 1st
question:

102. My wayMy way: parallel straight lines
3rd
step
do you remember
anything
about angles 1 and3
vertical
angles
1st
question:Using paper

103. My wayMy way: parallel straight lines
3rd
step
do you remember
anything
about angles 1 and3
vertical
angles
equal
1st
question:Using paper

104. My wayMy way: parallel straight lines
3rd
step
Using paper

105. My wayMy way: parallel straight lines
3rd
step 2nd
question:Using paper

106. My wayMy way: parallel straight lines
3rd
step
could u find more pairs
of vertical angles?
(like 1 and 3)
Using paper 2nd
question:

107. My wayMy way: parallel straight lines
3rd
step
Using paper

108. My wayMy way: parallel straight lines
3rd
step test 2:Using paper

109. My wayMy way: parallel straight lines
3rd
step
I give you e1//e2 and e.
You have 8 angles.
(φ (φ phi)phi) is an interior angle
Find the one which is
interior and alternate to φφ..
Think and name the angle!
Using paper test 2:

110. My wayMy way: parallel straight lines
5th
step
Using tablets (or mobiles)
At this stage students have to work as a
unit and they try to win the “game”.

111. My wayMy way: parallel straight lines
5th
step
NowNow
test 2
in a different way
Using tablets (or mobiles)

112. My wayMy way: parallel straight lines
5th
step
Using tablets (or mobiles)

113. My wayMy way: parallel straight lines
5th
step
Using tablets (or mobiles)
NowNow
We play kahoot!

114. …and playing this
“game”, my way of
teaching comes to
an end.

115. Let’s talk about both
ways…

116. Which way is the best?Which way is the best?
Let’s talk about both
ways…

117. Which way is the best?Which way is the best?
Old way?Old way?

118. Which way is the best?Which way is the best?
Old way?Old way? ““My” way?My” way?

119. Which way is the best?Which way is the best?
Old way?Old way? ““My” way?My” way?
Easy or difficult?

120. Which way is the best?Which way is the best?
Old wayOld way ““My” wayMy” way
Easy or difficult?
Teacher’s opinion:

121. Which way is the best?Which way is the best?
Old wayOld way ““My” wayMy” way
Easy or difficult?
Teacher’s opinion:
Less work preparing how to teach the old way.

122. Which way is the best?Which way is the best?
Old wayOld way ““My” wayMy” way
Easy or difficult?
Teacher’s opinion:
Less work preparing how to teach the old way.
On contrary, there is immense work using “my”
way.

123. Which way is the best?Which way is the best?
Old way?Old way? ““My” way?My” way?
Easy or difficult?

124. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?

125. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:

126. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…

127. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..

128. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..
In Geometry you have
to use your
imagination… shapes
on the blackboard are
very flat.

129. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..
In Geometry you have
to use your
imagination… shapes
on the blackboard are
very flat.
Difficult to realize
what the teacher
asks…

130. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..
In Geometry you have
to use your
imagination… shapes
on the blackboard are
very flat.
Difficult to realize
what the teacher
asks…
I don’t pay attention…
I am no good at this.

131. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..
In Geometry you have
to use your
imagination… shapes
on the blackboard are
very flat.
Difficult to realize
what the teacher
asks…
I don’t pay attention…
I am no good at this.
I prefer Algebra

132. Which way is the best?Which way is the best?
Old wayOld way
Easy or difficult?
Students opinion:
Easy?
Easy to understand?
Sometimes…
Old way?
You mean the usual way?
Well… I don’t like
geometry..
In Geometry you have
to use your
imagination… shapes
on the blackboard are
very flat.
Difficult to realize
what the teacher
asks…
I don’t pay attention…
I am no good at this.
I prefer Algebra
It is ok, but the
other way is
more fun.

133. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:

134. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer

135. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.

136. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used this
way… but I learn
things withoutstudying

137. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used this
way… but I learn
things withoutstudying
I like that we work
in teams.

138. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun

139. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.

140. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.

141. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way

142. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way
I think I am
good at this!

143. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way
I think I am
good at this!
I like that time
passes quickly

144. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way
I think I am
good at this!
I like that time
passes quickly
We do a variety
of things…
I like that.

145. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way
I think I am
good at this!
I like that time
passes quickly
We do a variety
of things…
I like that.
I like that I help
the others.

146. Which way is the best?Which way is the best?
““My” wayMy” way
Easy or difficult?
Students opinion:
I like that we use
computer
I use to work
alone, now Ishouldcooperate.
I am not used in this
way… but I learn
things withoutstudying
I like that we work
in teams.
It’s fun
I discover things by
myself! It’s good.
I don’t have to
work at home. I
remember
almost
everything.
We use papers too,
but in a different way
I think I am
good at this!
I like that time
passes quickly
We do a variety
of things…
I like that.
I like that I help
the others.
Can we do it
always this way?
Pleaseeee…

147. Can we do it
always this way?
Pleaseeee…

148. No, we could not.
Can we do it
always this way?
Pleaseeee…

149. For many reasons
we could not do it
every time.

150. Even it’s more
successful than the
old way.

151. Lack of equipment,

152. not always available
computer room

153. too many to be
taught in one hour
pro week…

154. Even though the
students gain
confidence and
knowledge, it is not
possible to teach this
colorful way every
time.

155. 