Download LAP – Parallel lines and Transversals

Sarah Kanoon
LAP – Parallel Lines and Transversals
I.
Content:
Students will be learning about parallel lines and transversals and the angles that
these lines create. They will investigate the different angle pairs that are created
when parallel lines are cut by a transversal.
II.
Learning Goals:
Students will know and be able to do the following at the end of the lesson:
 Define parallel lines as lines that do not intersect
 Define a transversal as a line that intersects two or more lines that are in the
same plane
 Define corresponding angles(angles on same side of transversal and both
either on the top or bottom of the two lines), alternate interior angles(angles
on opposite sides of transversal and inside the two lines), alternate
exterior(angles on opposite sides of transversal and outside the two lines)
angles, and consecutive interior angles(angles on the same side of transversal
and inside the lines)
 Apply these definitions along with prior knowledge of vertical and
supplementary angles to solve problems
III.
Rationale:
Students will learn about parallel lines and transversals to help them later when they
begin to write proofs that involve these concepts.
IV.
Assessment:
Students will complete class work and homework assignments that will require them
to identify different angle pairs as well find missing angle measures. Once the
students have been introduced to proofs they will also write proofs involving parallel
lines and angles.
V.
Personalization and equity:
I know that many of the students have some trouble using protractors. Instead of
having them measure all eight angles and get frustrated with it, I will have the
students use tracing paper to see that which angles are congruent. Having this visual
in front of them will help all students get a better understanding of the angle pairs.
VI.
Activity description and agenda:
a.
Time
Student Activity
10 min
Enter and begin
working on the
mathercise.
10-15 min Draw two lines on
their paper that are not
perpendicular and a
transversal through
them. Number the
angles 1-8. Using
tracing paper trace
over one of the
intersections, place it
over the other
intersection, compare,
and write what they
notice.
10-15 min Draw two parallel
lines, using their
notebook paper as a
guide, with a
transversal through
them. Number the
angles and repeat the
same process as well
as record which angles
are congruent.
Remaining Discuss as a class
time
what they have found.
Try to make sense of
why this only
happened the second
time.
Day 2
Time
10 min
20 min
Student Activity
Enter and begin
working on the
mathercise.
Actively take notes on
all of the different
Teacher Activity
Greet students and
monitor their progress
on the mathercise.
Give the students step
by step instructions.
Give the students step
by step instructions. I
will also stress to
them to not draw the
transversal
perpendicular to the
parallel lines.
Rationale
Students should be
ready to work as soon
as they get to class.
I first want students to
see what happens
when a transversal
cuts through two lines
that are not parallel to
enforce what they will
discover next. I also
hope giving them the
instructions will help
to keep everyone
together rather than
have some students
wasting all their time.
Seeing what happens
this time will make
more sense after
seeing it first without
parallel lines. I also
do not want them to
get 8 right angles so
they can see the angle
pairs more easily.
Lead the class through
a discussion of what
they have discovered
and begin to introduce
the names for these
pairs of angles.
I want students to
think about why this
happened as well as
try to describe their
locations so that when
the names of these
angles are introduced
they make more
sense.
Teacher Activity
Greet students and
monitor their progress
on the mathercise.
First, I will briefly
review supplementary
Rationale
Students should be
ready to work as soon
as they get to class.
Students will need to
review vertical and
angle pairs.
angles and vertical
angles. I will then
lead the class through
the notes on angle
pairs color coding the
different angle pairs.
Give an example of
how to solve problems
involving these angles.
supplementary angles
since this is from the
beginning of the year
and these ideas will
be useful in solving
problems. They will
also have these notes
and example to use as
a guide when they
begin to practice on
their own.
b. Since some of the students have trouble measuring angles accurately with a
protractor I will not have them get the exact measures. When asking them to record
what they notice this would cause some problems. Using tracing paper to see the
congruent angles will be much simpler and not waste as much time. Also, when
having them draw the parallel lines, I know many of them will just draw a line
straight through, creating right angles. This would not allow them to see what I want
them to, so I will make sure to tell them not to do this.
VII.
Learning standards addressed:
G.CO.9 - Prove theorems about lines and angles. Theorems include: vertical angles
are congruent; when a transversal crosses parallel lines, alternate interior angles are
congruent and corresponding angles are congruent; points on a perpendicular bisector
of a line segment are exactly those equidistant from the segment’s endpoints
VIII.
Reflection:
This lesson went well. There were not too many problems that I noticed during it,
since it was pretty straightforward. I made a last minute decision to have them first
see what would happen if they had parallel lines rather than doing the non-parallel
lines first. Originally I liked having the parallel lines come second because that is the
case we would be focusing on during this unit. However after thinking about it, I
knew that they might not know what to be looking for if I had them write about what
they notice about the non-parallel lines first. Even though I ask this question so that
there is no pressure to have the correct answer, a lot of them still feel like they need to
write the “correct” thing or some of them will get frustrated and not write anything.
By looking at the parallel lines first, they easily see that all of the corresponding
angles are congruent. They then have something to compare the case with nonparallel lines to. This worked out nicely and no one had any trouble writing about
what thy noticed.
While the lesson itself went smoothly, I am not sure how much it helped them
later when we got into all of the angle pairs and their relationships. During the
activity I had them list out all of the angles that they saw were congruent, but not
many of them seemed to think back to this when we were solving problems with
these angles. Another problem I found was that they always wanted to say that all the
angle pairs were equal, forgetting about consecutive interior angles and linear pairs. I
am thinking that I could somehow incorporate a way for them to see that consecutive
interior angles are supplementary into the first activity so that they do not get stuck on
all of the angles being congruent.
After giving them notes with all of the angles color coded, not many of them had
any problems with these angles anymore. While I did give them these notes to have
as a reference, I did want them to eventually be able to think about what the words
meant in the angle pairs and be able to figure out where they were that way. We
talked about what each of the words meant when we wrote our notes, but maybe
having them look them up on their own and try to figure out where they would be on
a diagram that way would help to enforce that the names of the angles actually tell
you exactly where the pairs are.