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AGENDAS FOR THE WEEK:
September 30 – October 4
MONDAY
Objective(s): SWBAT
*complete an assessment
evaluating their understanding
of the material covered in
Chapter 2
TUESDAY
WEDNESDAY
Objective(s): SWBAT
* identify skew and parallel
lines, planes, and lines cut by a
transversal
*classify types of angles created
by a transversal
*use prior knowledge to prove
theorem 3-1: If two parallel lines
are cut by a third plane, then the
lines of intersection are parallel.
Objective(s): SWBAT
* use technology to identify
the relationship between angles
and parallel lines cut by a
transversal
* solve problems using the
properties parallel lines
Objective(s): SWBAT
* use technology identify the
relationship between angles
and parallel lines cut by a
transversal
* solve problems using the
properties parallel lines
Objective(s): SWBAT
*prove that two lines are
parallel by using theorems
and postulates outlined in Ch.
3-3
CCSS/NGSSS:
CCSS/NGSSS:
MACC.912.G-CO.1.1: Know
precise definitions of angle,
circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions
of point, line, distance along a
line, and distance around a
circular arc.
MACC.912.G-CO.1.1: Know
precise definitions of angle,
circle, perpendicular line,
parallel line, and line segment,
based on the undefined
notions of point, line, distance
along a line, and distance
around a circular arc.
MACC.912.G-CO.3.9: Prove
theorems about lines and
angles.
CCSS/NGSSS:
MACC.912.G-CO.1.1: Know
precise definitions of angle,
circle, perpendicular line,
parallel line, and line segment,
based on the undefined notions
of point, line, distance along a
line, and distance around a
circular arc.
THURSDAY
FRIDAY
CCSS/NGSSS:
MACC.912.G-CO.3.9: Prove
theorems about lines and
angles.
MACC.912.G-CO.3.9: Prove
theorems about lines and angles.
CH. 2
TEST
TODAY
P
Move students’ desks to face
the front of the room, rather
than in their groups. Test
forms A and B can be
distributed amongst the
students in each class to
further deter the temptation to
cheat.
Engage
Engage
Engage
Engage
Bring in a cereal box modeling
parallel planes cut by a third
plane as visuals for the students.
Ask them at the beginning of
class, what does a cereal box
have to do with geometry?
Based on their homework
students should be able to name
the types of lines and planes
contained in the construction of
the box.
Show students the optical
illusion with parallel lines. A
lot can be done with parallel
lines, and with the addition of
surrounding shapes and colors,
one can change the effect that
the image has on the human
eye.
Display the math humor about
parallel lines on the board for
students as they get settled at
the beginning of class.
Have a student volunteer
come to the board and explain
to the class how he/she
completed the proof from last
night on the SmartBoard.
TI-Nspire Warm-up: Have
students answer the questions
outlined in the Warm-up
document on their TI-Nspires.
Discuss the answers together as
a class.
TI-Nspire Warm-up: Have
students answer the questions
outlined in the Warm-up
document on their TI-Nspires.
Discuss the answers together
as a class.
TI-Nspire Warm-up: Have
students answer the questions
outlined in the Warm-up
document on their TI-Nspires.
Discuss the answers together
as a class.
Students will have the whole
class period to complete their
tests.
Elaborate
*Online Homework: students
will watch the following You
Tube video
http://www.youtube.com/watch
?v=Q2ByDKh7Y0g
on the definitions concerning
parallel lines and planes, via
the course website.
L
Explore
Explore
Explore
Explore
Students will be working in
teams to complete the parallel
lines and planes activity
worksheet. Ex. 1 Students must
name the angles created as
alternate interior, same-side
interior, or corresponding
angles. Ex. 2 Students will be
drawing a six sided box and
using it to classify types of lines
in relation to each other. Ex. 3
Students will then use their
knowledge of definitions,
properties and theorems to prove
theorem 3-1 in the textbook: If
two parallel lines are cut by a
third plane, then the lines of
intersection are parallel.
The students will engage in a
TI-Nspires activity in which
they will explore and observe
the properties of angles creates
by parallel lines cut by a
transversal. Students will
follow directions given to them
to complete an activity sheet
that corresponds to the TINspire activity—instructing
them on what to do, and asking
probing questions for them to
consider. Address terms such
as linear angles versus
supplementary angles.
Wrap up the TI-Nspires
activity from yesterday in
which they will explore and
observe the properties of
parallel lines cut by a
transversal.
Students will be working in
groups to complete the 3-3
Proofs worksheets. Circulate
throughout the room
answering any questions
students may have, and
posing probing questions to
them.
(Students will be saving their
document in the folder that
corresponds to their period, so
that they will be able to pick
up where they left off
tomorrow, if necessary)
Elaborate
Explain
Call student’s attention to the
front of the room. Display each
problem/diagram on the
SmartBoard for students to see.
Call on volunteers to come to the
board to explain their reasoning
for classifying the lines and
angles in the diagram.
For the last exercise, pass around
a 3-D model of the figure
described by the theorem, for
students to physically see.
Explain
After the activity/during the
activity call students’ attention
to the board to discuss their
results and observations after
certain important concepts
arise. (i.e. When two parallel
lines are cut by a transversal,
corresponding angles have the
same angle measure.)
Elaborate
If time remains, have students
use classroom protractors to
measure the angles formed by
the transversal and the parallel
lines in the first exercise.
Students will begin to see a trend
occurring as they record the
angle measurements. This
activity serves as a great Segway
Address the theorems from last
night (3-2) that pertain to the
activity on parallel lines.
Prompt students to take notes
and/or refer to their notes from
last night. (*Note: Students
will probably not finish the
activity. Provide them with a
brief overview of the new
concepts that they have
Explain
Call students’ attention to the
front of the room to review
their results, and discuss their
findings. Elaborate on the
theorems and postulates that
pertain to their results.
Continue to discuss the
theorems and postulates in
Ch. 3.2 and 3.3 as a class by
having students work a couple
proofs at their desks presented
to them on the SmartBoard
(these proofs are listed in the
in-class proofs document).
Then take a volunteer to come
to the SmartBoard to
explain/teach the class their
reasoning.
Pass out the 3-3 Worksheet,
and have the students work in
their groups to complete.
Circulate throughout the room
answering questions and
asking probing questions.
Most likely students will not
be able to get through the
entire worksheet. Pick a few
harder questions that multiple
groups had questions about to
work together as a class on the
board. Students should
complete the worksheet, if
Explain
Students will volunteer to
come to the SmartBoard to
explain each proof.
(Advanced Prep: The teacher
should copy and paste the
proofs into a SmartBoard
document so that students
will be able to fill in the
blanks with the pen tool,
while “teaching” the class.
The teacher should clarify
student reasoning for further
understanding.
Elaborate
*Online HW: Students will be
taking notes on the following
proof of the theorem: the sum
of the measures of the angles
in a triangle is 180 degrees.
You Tube video:
https://www.khanacademy.or
g/math/geometry/paralleland-perpendicularlines/triang_prop_tut/v/proof--sum-of-measures-of-anglesin-a-triangle-are-180
into tomorrow’s exploration on
properties of parallel lines!
discovered, and continue
where they left off tomorrow)
they hadn’t already done so,
as homework in addition to
the proof discussed below.
*Online HW: Students will be
taking notes on the 3.2 You
Tube video:
http://www.youtube.com/watch?
v=AztmdWk_BF4 given to them
via the course website, as well as
the 3-2 PowerPoint
Elaborate
Evaluate and Summary
Evaluate and Summary
Evaluate and Summary
Evaluate and Summary
The evaluation of tonight’s
homework will be assessed in
tomorrow’s warm-up.
The evaluation of tonight’s
homework will be assessed in
tomorrow’s warm-up
The evaluation of tonight’s
homework will be assessed in
tomorrow’s warm-up
Students will be completing a
proof given to them via the
online website, and bringing it
to class tomorrow.
Chapter 2 Tests
(form A and B)
Warm-up Questions
Parallel Lines & Planes
Worksheet
3-2 PPT
TI-Nspires
Protractors
Cereal Box
Intersecting planes model
Warm-up Questions
TI-Nspires Activity Sheet
TI-Nspires directions
3-3 PPT
TI-Nspires
Math Humor
Warm-up Questions
TI-Nspires Activity Sheet
TI-Nspires directions
In-class proofs
3-3 Worksheet
Online HW: Proof
TI-Nspires
Students will be taking notes
on the 3.3 video given to them
via the course website. You
Tube video:
http://www.youtube.com/watc
h?v=ubDalX0vokQ as well as
on the 3-3 PowerPoint slides.
A
N
Resources:
Evaluate and Summary
3-3 Proofs Worksheet
SmartBoard