Module Focus: Geometry – Module 4
Sequence of Sessions
Overarching Objectives of this December 2014 Network Team Institute

Participants will be able to identify, practice, and use best instructional moves and scaffolds for chosen common core standards.
High-Level Purpose of this Session




Participants will be able to identify the major work of each grade using the Curriculum Overview document as a resource in preparation for teaching
these modules.
Participants will draw connections between the progression documents and the careful sequence of mathematical concepts that develop within this
module, thereby enabling participants to enact cross- grade coherence in their classrooms and support their colleagues to do the same.
Standards alignment the major work of the grade in order to fully implement the curriculum.
Participants will be prepared to implement the modules and to make appropriate instructional choices to meet the needs of their students while
maintaining the balance of rigor that is built into the curriculum.
Related Learning Experiences
●
This session is part of a sequence of Module Focus sessions examining the Geometry modules within the curriculum, A Story of Functions.
Key Points
●
●
●
●
●
The work in this module matures students’ understandings of the development of mathematical concepts that connect Algebra and Geometry in terms of
the coordinate plane.
Students will enrich their knowledge and experience in order to implement Module 4 with confidence and success.
Students will use the modeling challenge of “programming” a robot to write and graph inequalities that define a region in the plane.
Students will use the modeling challenge of “programming” a robot to program motion segments parallel and perpendicular to a given segment.
Students will generalize the criterion for perpendicularity of two segments and use slope to recognize pairs of lines as parallel or perpendicular.
Session Outcomes
What do we want participants to be able to do as a result of this
session?

Participants will draw connections between the progression documents
and the careful sequence of mathematical concepts that develop within
this module, thereby enabling participants to enact cross- grade
coherence in their classrooms and support their colleagues to do the
same.
How will we know that they are able to do this?
Participants will be able to articulate the key points listed above.


Participants will be able to articulate how the topics and lessons promote
mastery of the focus standards and how the module addresses the major
work of the grade in order to fully implement the curriculum.
Participants will be prepared to implement the modules and to make
appropriate instructional choices to meet the needs of their students
while maintaining the balance of rigor that is built into the curriculum.
Session Overview
Section
Time
Overview
Prepared Resources
Facilitator Preparation
Introduction
15 min
Introduces Geometry Module 4.


Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review Geometry Module 4
Topic A: Area
91 min
Explores rectangular and
triangular regions defined by
inequalities through a modeling
challenge.


Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review Topic A
Topic B: Volume
90 min
Explores perpendicular and
parallel lines in the Cartesian
Plane by “programming” the
motion of the robot model from
Topic A along segments parallel
and perpendicular to a given
segment and uses slope to
recognize pairs of lines as parallel
or perpendicular.


Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review Topic B
Mid-Module
Assessment
40 min
Allows participants to complete a
Mid-Module Assessment and
engage in a follow-up discussion.


Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review End of Module
Assessment
Topic C: Perimeters
and Areas of
Polygonal Regions in
76 min
Explores using triangle vertices to 
compute the area of a triangular

region, use the distance formula to
Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review Topic C
the Cartesian Plane
calculate perimeter, and the
“shoelace” formula to determine
area.
Topic D: Partitioning
and Extending
Segments and
Parameterization of
Lines
105 min
Explores finding locations on a
directed line segment that
partition the segment into given
ratios, prove classical results in
geometry and use parametric
equations to show coherence
between functions, Algebra, and
coordinate Geometry.


Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review Topic D
End of Module
Assessment and
Conclusion
47 min
Allows participants to complete an 
End of Assessment and engage in a 
follow-up discussion.
Geometry Module 4 PPT
Geometry Module 4
Facilitator Guide
Review End of Module
Assessment
Session Roadmap
Section: Introduction
Time: 15 minutes
In this section, you will be introduced to Geometry Module 4.
Materials used include:
 Geometry Module 4 PPT
 Geometry Module 4 Facilitator’s Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
4 min
Materials Required: Graph paper, patty paper
1.
Copies: ppt slide notes, participant handout, mid and end-of-module
assessments
Welcome to this Grade 10 segment of the NTI. Today we will take a look at
Module 4: Connecting Algebra and Geometry Through Coordinates.
GROUP
Presenter introductions and bios.
You should find a variety of tools and materials where you are seated. First,
you have a copy of the presentation to keep any important notes from the
session. You will also find [in your binder] a Participant Materials packet
that contains all of the problems and diagrams that we will work on
throughout the session. Finally, you will find a copy of the Mid and End-ofModule Assessment and materials.
[Optional] I’ve also provided a parking lot poster for any comments or
questions that you do not want to ask aloud. Please use a post-it note to
leave your comment/question for organizational purposes.
3 min
2.
In order for us to better address your individual needs, it is helpful to know
a little bit about you collectively.
Pick one of these categories that you most identify with. As we go through
these, feel free to look around the room and identify other folks in your
same role that you may want to exchange ideas with over lunch or at breaks.
By a show of hands who in the room is a classroom teacher?
Math trainer?
Principal or school-level leader
District-level leader?
And who among you feel like none of these categories really fit for you.
(Perhaps ask a few of these folks what their role is).
Regardless of your role, what you all have in common is the need to
understand this curriculum well enough to make good decisions about
implementing it. A good part of that will happen through experiencing
pieces of this curriculum and then hearing the commentary that comes from
the classroom teachers and others in the group.
2 min
3.
Our objectives for this session are to:
• Examine the development of mathematical understanding
across the module using a focus on Concept Development.
• Experience the mathematical content that we are going to be
teaching in order to implement that material confidently and
with meaning so that we can genuinely engage our students in
that content in the classroom and beyond.
The goal of this session is to take a look at the content in the lessons of
Module 4 and see how the concepts build upon previous modules and from
lesson to lesson as the module progresses. My hope is that the themes of the
module are clear and that what is changing under the Common Core State
Standards is very apparent.
3 min
4.
Here is our agenda for today and tomorrow. (Review the agenda on the
slide)
If needed, we will start today by orienting ourselves to what the module
materials consist of, however, I’d like to spend the majority of our session
discussing the content and its overarching development throughout Module
4. The idea is for you to leave with an understanding of where the major
shifts in Geometry are, and use examples to make sense of those changes.
[Presenter: Take a fist-to-five poll of the participants as to the level of
knowledge of the module materials. If necessary, take the time to cover the
Module Overview, Topic Openers, Lesson Types, Lesson structures, and
assessment materials.]
Let’s begin with an orientation to the materials for those that are new to the
materials (Skip if participants are already familiar with the materials).
3 min
5.
Here is a quick overview of the Module (read title). Module 4 is a 20 day
module consisting 15 lessons. The module has 4 topics (click through and
read titles).
Section: Topic A: Rectangular and Triangular Regions
Defined by Inequalities
Time: 91 minutes
In this section, you will explore rectangular and triangular regions
defined by inequalities using a modeling challenge.
Materials used include:
 Geometry Module 4 PPT
 Geometry Module 4 Facilitator’s Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
3 min
We begin by looking at Topic A. Topic A can be generalized by the following
points (click through and read points).
6.
GROUP
3 min
7.
Topic A is comprised of four lessons, shown here (click and read one at a
time). You will see the theme of the robot throughout all of the lessons.
6 min
8.
Pose the question to participants and elicit answers. Show the sentence
starters if needed or just tell participants that they are available if needed in
the classroom setting. Show the video.
6 min
9.
Review the exploratory challenge in your handout. You can work
individually, in pairs, or as a table. As you work, think about places that
make cause students to pause and how you can support students’ learning
by asking questions or scaffolding the work.
5 min
10.
As groups finish the work of the exploratory challenge, have them take note
of the questions on the slide. Ask table groups to discuss the answer to each
and consider what background students will need in order to answer the
questions.
2 min
11.
In lesson 2, students apply knowledge from grade 9 about inequalities,
systems of inequalities and their graphs. The foundation for this learning
really began in Grade 8 when students first encountered systems of linear
equations and their graphs.
Read the points on the slide.
4 min
12.
The basics are reviewed in the opening exercises. Here you will be able to
tell if students understand how to graph an inequality, whether they
understand that inequalities yield multiple solutions, and if they relate the
solutions to the shading of the appropriate half plane.
5 min
13.
Example 1, shown here, models for students how to describe a rectangular
region in the plane. (Click) We begin by naming three points in the region.
(Ask participants to give three points). (Click) Next they name three points
on the boundary. (Ask participants to give three points). (Click) Now the
interesting questions; how do we describe all the points in the region?
(Click) You can scaffold the work by asking students to first describe all of
the possible values for x, then y. (Ask participants to jot down their
thoughts, bring them back together and record their inequalities on poster
paper). 1</= x </=15 and 2 </= y </=7.
The exercises that follow this example can be used to informally assess
students’ understanding of how to describe a region in the coordinate plane
using a system of inequalities.
6 min
14.
Now in example 2 students are asked to graph three points to form the
triangular region. (click) This sequence of questions begins by asking
students how many half-plane form this region. (Ask participants for
answer). (click) Next students write the slope of the line for one of the
three segments (choose one), what is the slope of the line containing this
segment? (Ask participants for answer). What is the equation that describes
the line? (Ask participants for answer). (click) Jot down the other two
equations. (Ask participants for answers, write the equations on poster
paper as they are given). (click) What do we need to do to our equations to
indicate that shading is needed? (Ask participants for answer and modify
the equations accordingly). Exercise 4 gives students an opportunity to
practice this on their own.
3 min
15.
Now it’s your turn to try a problem.
(Let participants work and share their solutions, if time permits.)
2 min
16.
Now we are ready for lesson 3.
(Read through the points on the slide).
3 min
17.
The opening exercises remind students of how to calculate the distance
between two points on the coordinate plane. This work began in Grade 8,
specifically Grade 8 M2 TD L16 and M7 TC L17. Students complete the
concrete example shown,(click) before generalizing the distance formula
based on the work using the Pythagorean theorem.
6 min
18.
Review example 1 in your handout.
5 min
19.
The work of the example is followed by a discussion with the following
points. (Pause to let participants think about the answer to each as you click
through).
5 min
20.
(Read the problem on the slide, then click to bring in the line). Ask:
How many times does the line y = 2 intersect the boundary of the triangle?
2
Is it easy to find these points from the graph? What can you do to find these
points algebraically?
No, it is not easy because one of the intersection points does not have whole
number coordinates.
We can find the equation of the line that passes through (0, 0) and (2, 6), and
set the equation equal to 2 and solve for x. This gives us the x-coordinate 2/3
of the point (2/3,2).
8 min
21.
(Read part b.) How can we do this?
From graphing the line, we know that the given line intersects AC and BC. We
need to find the equations of AC and BC and put them, as well as the provided
equation of the line 3x –2y=5, into slope intercept form.
AC 
y=12x.
BC 
y=10-2x.
3x-2y=5 
y=1.5x-2.5.
The x-coordinates of the points of intersection can be found by setting each of
AC and BC with the provided equation of the line:
(1) 12x=1.5x-2.5
x=1.25, y=0.625.
(2) 10-2x=1.5x-2.5
x=257, y=207.
(Read part c) How can we determine the length of the segment? approx 3.2
(Read part d) What do we need to do to determine the answer? 12.5
seconds
Consider using poster paper or a document camera to record the answers.
7 min
22.
(Distribute graph paper)
Lesson 4 is all about designing a search robot to find a beacon. Complete the
exploratory challenge in your handout with a partner.
4 min
23.
(Read the sentence). Assuming students believe that the perpendicular is
the shortest distance, what mathematical argument can be used to convince
students it is true? (Ask participants for answers, acknowledge any good
arguments, highlight one that uses the Pythagorean theorem. Once
convinced, click to show the next task).
8 min
24.
Shown is the graph of the situation, gray circles represent the beacon, blue
line represents the path of the robot. We can see by the slope triangle that
the path of the robot has a slope of 3, three hundred, to be precise. How can
we use the slope triangle to guide us to find the line perpendicular to the
robot’s path? (Ask participants to respond, once someone says we should
rotate the triangle 90˚ clockwise around point (400, 600), then click to
advance the animation and click again to pose the next question, continue
this process until all questions have been addressed.) The goal of this
lesson is for students to recognize that to find the perpendicular to a
segment by rotating 90˚ around one of the endpoints of the segment.
Secondly, we want students to begin to see the relationship of the slopes of
perpendicular lines. The examples and exercises that follow provide
students opportunities to practice finding the slope of a line perpendicular
to a given segment.
Y-600 = - 1/3 (x-600)
Section: Topic B: Perpendicular and Parallel Lines in the
Cartesian Plane
Time: 90 minutes
In this section, you will explore perpendicular and parallel lines in Materials used include:
the Cartesian Plane by “programming” the motion of the robot
 Geometry Module 4 PPT
model from Topic A along segments parallel and perpendicular to a
 Geometry Module 4 Facilitator’s Guide
given segment and use slope to recognize pairs of lines as parallel or
perpendicular.
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
GROUP
3 min
25.
The remaining topic in this half of the module is topic B. Topic B can be
generalized by the following points (click through and read points).
3 min
26.
Topic B is comprised of four lessons, shown here (click and read one at a
time). Again, you will see the theme of the robot throughout all of these
lessons.
5 min
27.
Allow participants to discuss the question. Elicit responses from the group.
5 min
28.
In Example 1, facts related to the Pythagorean theorem are reviewed. (Read
the first bullet). Share your thoughts with a partner. (Ask participants to
respond, then click to pose the second question). Share your thoughts with a
partner.
4 min
29.
Here is another problem we present to students. Use your graph paper if
necessary. (Ask participants to respond, then click to pose the next question.
Repeat for the last question on the slide). What did all three of these
situations require us to do, mathematically speaking? (Use the converse of
the Pythagorean theorem)
10 min
30.
(Read the theorem). Use the diagram and prompts in your handout to
develop a proof of the theorem.
4 min
31.
(Read through the students outcomes on the slide, then click to pose the
question to the group).
4 min
32.
(Read the prompt and allow participants time to think about the answer.
Elicit responses from the group.)
In the lesson:
We translate the segments so that each has an endpoint at the origin (so we
can use what was learned in the last lesson). We know that segments
translated along a vector have the following properties; the length remains
unchanged, the translated segment will be parallel to the given segment.
That means if we can show that C’D’ is perpendicular to A’B’, then we know
that CD is perpendicular to AB.
Note that AB was translated two units down and two units left so that A was
at the origin. How do the coordinates of B relate to B’?
How was CD translated? How do we determine the coordinates of D’?
4 min
33.
Now that we have segments meeting at the origin, we can use the theorem
from the last lesson to prove that the segments are perpendicular. (Click
and have participants work on the two exercises)
34.
Solution to Exercise 1, if needed.
4 min
35.
In Lesson 7 students work to write equations for normal segments. (Read
bullets on the slide). Read through lesson excerpt in your handout to see
how the work from recent lessons comes together here. Also note any
places that may be points of confusion for students.
5 min
36.
Following the concrete work related to the robot problems, this discussion
generalizes the process. (Read the prompt in black). We want to show that
AB is a normal segment with respect to line l. What was the first thing that
was done in the robot problem? (Elicit answers: translate point A to the
origin, then click to show new graph). Note how the values of the
coordinates have changes due to the translation. Now that we have A’ at the
origin, how do we check for perpendicularity? (Elicit answers: ab+cd=0,
click to next slide).
6 min
37.
(Click, then read the information regarding the substitution). What does the
equation A(x-a)+b(y-b)= 0 represent? (Elicit answers: It is the equation of
the line that passes through A and is perpendicular to AB, click to reveal
conclusion).
10 min
38.
(Give time for participants to work and share their solution with the whole
group. Solution is provided, if needed).
5 min
39.
The opening challenges students to examine what happens when the
endpoints of a segment, perpendicular to another segment, are manipulated,
i.e., moved along the segment. They should note that the sum does not
change, it always remains zero. (If possible, show this using geometry
software). Why do you think this is so?
2 min
40.
Continue with property 6 as with the previous slides.
Say: This last volume property is very important for establishing the
volume formula for a general cylinder and therefore warrants a closer look.
6 min
41.
10 min
42.
We want to develop the relationship between two coplanar lines that are
perpendicular to the same line. You can use construction tools for this
activity or a sketch. (Click to advance through each step). (Beginning on
line 4: the relationship is that the lines are parallel because when
corresponding angles of a pair of lines are equal, the lines must be parallel,
the slopes of l_1 and l_2 must be –(1/m), which are obviously equal. Since
the lines have the same slopes we know they are parallel.)
Section: Mid-Module Assessment
Time: 40 minutes
In this section, you will complete a Mid-Module Assessment and
follow up discussion.
Materials used include:
 Geometry Module 4 PPT
 Geometry Module 4 Facilitator’s Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
40 min
Provide 25-30 minutes for participants to complete the Mid-Module
Assessment. Then conduct a 5-10 minute discussion about the lessons from
which the assessment items stem from, the provided sample work,
scaffolding issues, use of items as Topic A,B quiz questions, etc.
43.
Section: Topic C: Perimeters and Areas of Polygonal
Regions in the Cartesian Plane
GROUP
Time: 76 minutes
In this section, you will explore using triangle vertices to compute Materials used include:
the area of a triangular region, use the distance formula to calculate
 Geometry Module 4 PPT
perimeter, and the “shoelace” formula to determine area.
 Geometry Module 4 Facilitator’s Guide
Time Slide Slide #/ Pic of Slide
#
Script/ Activity directions
3 min
The second half of the module begins with Topic C. Topic C can be
generalized by the following points (click through and read points).
44.
GROUP
3 min
45.
Topic C is comprised of three lessons, shown here (click and read one
at a time). Again, you will see the theme of the robot throughout all of
these lessons.
10
min
46.
(Distribute graph paper. Lead participants through the steps in
Example 1. Have participants share their solutions. The decomposition
method is on the next slide, if needed.)
47.
10
min
48.
(Give participants time to work. Find a volunteer to share their
solution or use the one on the slide, if needed). If we labeled our points
differently we may have derived the equivalent formula: ½ (x_2 y_1 –
x_1 y_2).
8 min
49.
Part of the discussion in the example challenges students to think about
whether the formula derived from the decomposition method would
work for triangles beyond those in quadrant one. What do you think?
(Elicit answers, click through the next two points, again asking
participants for their input).
8 min
50.
The last question posed in example 1 motivates the work in example 2.
If there is no vertex at the origin, we can use what we know about
translation and its effect on coordinates, so that we can use the formula.
(Read the information on the slide and click to show the development
of the simplified formula).
51.
(This slide can be used to describe the shoelace area formula, or you
can show how the shoelaces are developed using the document
camera). To ensure students always end up with a positive area we
have them (1) pick a starting point, (2) walk around the figure in a
counterclockwise direction, then (3) once they return to the starting
point, reverse the direction.
4 min
52.
(Provide participants time to discuss the question on the slide. Have
participants share their thoughts. Acknowledge all comments but
highlight the comment that mentions decomposing the quadrilateral
into two triangles. Click to show the decomposed quadrilateral).
10
min
53.
Work with a partner to develop the general shoelace formula for the
quadrilateral in your handout. (Give participants time to work, then
ask for someone to share their solution). (The two slides that follow
show the development of the general formula, use if needed, but make
sure to mention that this formula is known as “Green’s theorem”.)
2 min
54.
Green’s theorem is a high school Geometry version of the exact same
theorem that students learn in Calculus III (along with Stokes’ theorem
and the divergence theorem). Students only need to know that the
shoelace formula can also be referred to as Green’s theorem.
55.
Green’s theorem is a high school Geometry version of the exact same
theorem that students learn in Calculus III (along with Stokes’ theorem
and the divergence theorem). Students only need to know that the
shoelace formula can also be referred to as Green’s theorem.
56.
(Read the title and student outcomes on the slide).
6 min
57.
Now we show how that the shoelace method produces the normal area
formula for a parallelogram. (Click) Beginning with the upper left
vertex of the parallelogram, let’s identify the coordinates of each vertex.
(Elicit answers from participants, click until all four vertices are named,
then click to show the use of the formula). If we begin at the origin and
move counterclockwise we are guaranteed to get a positive area.
5 min
58.
In example 2, we show that the shoelace method gives the normal area
formula for triangles. Again we begin by naming the coordinates (click
to show coordinates), then apply the formula (click), thus proving the
shoelace methods validity.
7min
59.
(Provide participants time to work. Circulate to find a participant to
volunteer their solution, given below).
Perimeter is approx. 20.26 units
Area is 24 sq un
Section: Topic D: Partitioning and Extending Segments
and Parameterization of Lines
Time: 105 minutes
In this section, you will explore finding locations on a directed line Materials used include:
segment that partition the segment into given ratios, prove classical
 Geometry Module 4 PPT
results in geometry and use parametric equations to show
coherence between functions, Algebra, and coordinate Geometry.

Geometry Module 4 Facilitator’s Guide
Time Slide Slide #/ Pic of Slide
#
Script/ Activity directions
3 min
60.
Now we are at the last topic of the module. Topic D can be generalized
by the following points (click through and read points).
3 min
61.
Topic D is comprised of four lessons, shown here (click and read one at
a time). Again, you will see the theme of the robot throughout all of
these lessons.
6 min
62.
We begin by drawing the slope triangle between the two points. (Click
to advance). Our goal is to determine the coordinates of the shown
point M and write a formula to find it (Click). The midpoint “formula”
shown actually describes the process used to find the midpoint. That is,
take half of the horizontal distance between the two points (half of
16=8), to determine the x-coordinate of the midpoint, start from the left
point (-4) and go 8 units to the right (half the horizontal distance
between the two points). Repeat the process for the vertical distance.
GROUP
6 min
63.
(Present the general midpoint formula. Click to advance. Instruct
participants to discuss the two questions. They should recognize that
both questions are asking the same thing. To find one-fourth, the ½ is
replaced with ¼ in the formula.)
10
min
64.
(Instruct participants to complete the work for example 1. Ask
participants the first question on the slide. Elicit responses: We can
write the equation of the line and then determine if the point C is a
solution to the equation. Ask the second question. Elicit response: No,
the points would not coincide.)
7 min
65.
Let’s take a look at exercise 4. (Read the prompt and part a). Since we
are looking for where the robot is at the end of the third hour and the
robot reaches point be in 10 hours, we need to locate the point that is
3/10 along the segment starting at point A. (Click to show the solution,
then read part b). How will we determine the location this time? (Elicit
responses, then click to show solution. Read part c). What are the
implications of this part? (Elicit responses, show solution).
5 min
66.
(Read information on the slide, click to reveal the question. Elicit
responses, then show answer). Note that in Module 1 when students
found the point of concurrency by construction we said that the point
of concurrency would be found two-thirds of the way along the median
from the vertex of the triangle. Do these statements contradict one
another? (Elicit responses: No, they say the same thing. The only
difference is the starting point).
10
min
67.
The statement shown here is how students know it from Module 1
(Click), for this exercise, prove the location of the point of concurrency
by doing the following (read the “do so” statement). (Instruct
participants to complete exercise 1, have someone share their
solution).
5 min
68.
In Exercise 2 students prove that the diagonals bisect one another, i.e.,
they are concurrent at their midpoints.
4 min
69.
(Read the student outcome, then click to show the description of
parametric equations). Note that this is an optional lesson so if time is
an issue, the teacher may skip this lesson without worry about missing
a standard.
8 min
70.
(Give participants time to work on Example 1, then click to reveal one
question at a time. Elicit responses from the group for each. Answers
are given below).
-The triangles formed are similar triangles by the AA criterion.
-The robots have been moving for a longer period of time.
-If the robot continues to move along the same path the robot will pass
point b.
-The location of the robot will be at (1/2, 0).
Ask, what did you need to know to determine the location of the robot
in the last question? (You need to know how to find the midpoint of a
segment).
8 min
71.
Give participants time to review example 2. Allow time for table
discussions about student struggle, then ask for tables to share
concerns and possible scaffolding strategies. (Click to show the next
question, it may be necessary to allow tables to discuss again, click to
reveal answer if needed.)
5 min
72.
(Read through the information on the slide. Ask participants to explain
how to find the solution for part a, click to reveal answer, then ask
about part b, click to reveal answer). What skills are being reinforced
in this lesson? (Elicit responses from group. Acknowledge all
appropriate responses and make clear that skills related to work in
Lesson 12: Dividing Segments Proportionately are being reinforced.
Therefore, a teacher who feels students need extra practice with this
may choose to use this lesson since it is “optional”.
10
min
73.
(Read the lesson title. Click to reveal the steps for the basic
construction, then the task. Provide participants time to develop an
argument and ask participants to share their arguments).
15
min
74.
In Module 1 students learned how to construct the perpendicular to a
line (or segment) through a point on or off the line. (Click) The goal
now is figure out how to determine the location of the point of
intersection algebraically. (Click) Take a look at the proof given in your
handout. As you review, think about how you will explain it to students
(or any audience).
(Do “Practice Perfect” with the participants.)
-Select one part of the proof, something that can be explained in about a
minute. “Practice” explaining to a partner. If you are listening to an
explanation, you are responsible for giving feedback. If you are
explaining, be prepared to use the feedback you have been provided.
Repeat this process twice so that the person who is practicing the
explaining part gets to practice three times. Then switch roles. The
new explainer should select a new part of the proof to present.
75.
Consider having participants who practiced this part of the proof
explain it to the whole group.
76.
Consider having participants who practiced this part of the proof
explain it to the whole group.
77.
Consider having participants who practiced this part of the proof
explain it to the whole group.
Section: End of Module Assessment
Time: 47 minutes
In this section, you will complete an End of Module Assessment and Materials used include:
participate in a follow-up discussion.
 Geometry Module 4 PPT
 Geometry Module 4 Facilitator’s Guide
Time Slide # Slide #/ Pic of Slide
Script/ Activity directions
40 min
78.
Provide 25-30 minutes for participants to complete the End-of-Module
Assessment. Then conduct a 5-10 minute discussion about the lessons from
which the assessment items stem from, the provided sample work,
scaffolding issues, use of items as Topic C,D quiz questions, etc.
2 min
79.
5 min
80.
Take a few minutes to reflect on this session. You can jot your thoughts on
your copy of the PowerPoint. What are your biggest takeaways?
(click)
Now, consider specifically how you can support successful implementation
of these materials at your schools given your role as a teacher, school leader,
administrator or other representative.
GROUP
Use the following icons in the script to indicate different learning modes.
Video
Reflect on a prompt
Turnkey Materials Provided
●
●
Geometry Module 4 PPT
Geometry Module 4 Facilitator’s Guide
Additional Suggested Resources
●
●
●
How to Implement A Story of Functions
A Story of Functions Year Long Curriculum Overview
A Story of Functions CCLS Checklist
Active learning
Turn and talk