Lesson Plan
Course Title: Engineering Design and Presentation
Session Title: How to Draw and Plot Polar Coordinates
Performance Objective:
Upon completion of this lesson/assignment the student will be able to plot or draw coordinates
given, and then draw their own problem and correctly plot the coordinates for his/her drawing.
Specific Objectives:
 Identify what direction they need to draw based upon the angle given
 Be able to find specific coordinates given
 Be able to plot their own coordinates
Preparation
TEKS Correlations:
This lesson, as published, correlates to the following TEKS. Any changes/alterations to the
activities may result in the elimination of any or all of the TEKS listed.
Engineering Design and Presentation:

130.365 (c)(1)(E)
...identify and use appropriate work habits;

130.365 (c)(3)(A)(B)
...use time-management techniques to develop and maintain work schedules and meet
deadlines;
...complete work according to established criteria;

130.365 (c)(5)(G)(H)(J)
...draw developments using radial line, parallel line, and triangulation methods;
...construct piercing points and intersection of planes using edge-view and cutting plane
methods;
...demonstrate knowledge of effective file structure and management.

130.365 (c)(6)(B)(C)(D)
...think critically, identify the system constraints, and make fact-based decisions;
...use rational thinking to develop or improve a product;
...apply decision-making strategies when developing solutions;

130.365 (c)(8)(D)
...produce engineering drawings to industry standards;
Interdisciplinary Correlations:
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Geometry:

111.34 (b)(4)
...select an appropriate representation (concrete, pictorial, graphical, verbal, or symbolic)
in order to solve problems;

111.34 (b)(5)(A)(B)(C)(D)
...use numeric and geometric patterns to develop algebraic expressions representing
geometric properties;
...use numeric and geometric patterns to make generalizations about geometric
properties, including properties of polygons, ratios in similar figures and solids, and
angle relationships in polygons and circles;
...use properties of transformations and their compositions to make connections between
mathematics and the real world, such as tessellations;
...identify and apply patterns from right triangles to solve meaningful problems, including
special right triangles (45-45-90 and 30-60-90) and triangles whose sides are
Pythagorean triples;

111.34 (b)(10)(A)
...use congruence transformations to make conjectures and justify properties of
geometric figures including figures represented on a coordinate plane;

111.34 (b)(7)(A)
...use one- and two-dimensional coordinate systems to represent points, lines, rays, line
segments, and figures;
Teacher Preparation:
Coordinate System lessons should be taught in this order: Absolute, Relative, and Polar.
Read through the PowerPoint provided. Watch the video(s) as needed. Practice drawing it
yourself before the students draw.
References:
Texas approved publishers are:
Goodheart-Willcox
Delmar Learning
Prentice Hall
All have companion workbooks with more problems. Recommend using one of these or any
other approved textbook, (i.e., if you teach ATC or TechPrep and must teach using local college
textbook).
Also “Google” and you can find tons of information on these subjects!
Instructional Aids:
1. PowerPoint
2. How to video
3. Coordinates graph paper
4. Coordinates problem
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Materials Needed:
1. 2 copies of the coordinate systems graph paper for each student
2. 1 copy of the coordinate problem for each student
Equipment Needed:
1. Each student needs a pencil to draw with
2. Data projector for Power Point file or put on PC’s
3. Optional access to the demo video for student or class use
4. Overhead projector or document camera
Learner Preparation:
Students must be able to know angle/directions.
Students must understand Pythagorean Theory or a2 + b2 = c2
3 = 4.24
4 = 5.66
etc….
So 1 = 1.41
2 = 2.82
Introduction
Introduction (LSI Quadrant I):
SAY: Today we are going to learn about Polar coordinates.
ASK: Why do we need to know these coordinate systems?
SAY: Because this is how any CAD system understands how to draw. You tell it what to do, like
draw a line, and then this tells it where to start and go.
SAY: Think of it as a foreign language for the computer, but it’s based on mathematical
concepts.
SHOW: Show the PowerPoint presentation.
ASK: Does anyone know what direction 0 is? = Right
ASK: Does anyone know what direction 90 is? = Up
ASK: Does anyone know what direction 180 is? = Left
ASK: Does anyone know what direction 270 is? = Down
ASK: Does anyone know what direction 45 is? = Right and Up
ASK: Can you tell me what the difference is between Absolute and Relative and now Polar
coordinates?
SAY: Absolute and Relative are based on the X and Y axis or plane. Polar is all distance and
direction.
ASK and SHOW: Does anyone want to volunteer to draw the first set of points given? (Try to
get a student to do it first. If not, then you show them how to draw the whole 1st set or letter
given.)
SAY: Okay now you all draw the others on your own. (Teacher walks around and monitors for
about 15 minutes.)
ASK and SHOW: Does anyone want to volunteer to draw their Birth month or Year and plot the
coordinates? (Try to get a student to do it first. If not, then you show them how to draw and plot
yours.)
SAY: Okay now you draw and plot your own coordinates on your own. Write these coordinates
in the space provided in the worksheet. (Teacher walks around and monitors for about 15
minutes.)
Optional Say: Tomorrow we will draw YOURS in Auto CAD or ACAD
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Outline
Outline (LSI Quadrant II):
Instructors can use the PowerPoint presentation, slides, handouts, and note pages in
conjunction with the following outline.
MI
Outline
Notes to Instructor
Teacher shows the
I. Discuss terms
A. What are Coordinate Systems and why do PowerPoint
presentation.
we need to know them?
B. What are Polar coordinates?
SAY: Today we are going to learn about Polar
coordinates.
ASK: Why do we need to know these coordinate
systems?
SAY: Because this is how any CAD system
understands how to draw. You tell it what to do, like
draw a line, and then this tells it where to start and go.
SAY: Think of it as a foreign language for the
computer, but it’s based on mathematical concepts.
II. Explain the difference between the various
directions
A. Right
B. Up
C. Left
D. Down
E. Right and Up
.
Teacher shows these
on the board or in
PowerPoint
presentation, or draws
on the board.
ASK: Does anyone know what direction 0 is? =
Right
ASK: Does anyone know what direction 90 is? =
Up
ASK: Does anyone know what direction 180 is? =
Left
ASK: Does anyone know what direction 270 is? =
Down
ASK: Does anyone know what direction 45 is? =
Right and Up
III. Explain why the Pythagorean Theory or
a2 + b 2 = c 2
So 1 = 1.41
2 = 2.82
3 = 4.24
etc….
Explain even though
VISUALLY it looks like
one square,
mathematically it is
more and this is why
we have to follow this
theory when drawing.
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IV. Explain the differences between Absolute,
Relative, and Polar coordinates
A. Absolute and Relative are based on the X
and Y axis or plane.
B. Polar is all distance and direction.
Teacher discusses the
differences.
ASK: Can you tell me what the difference is between
Absolute and Relative and now Polar coordinates?
V. Demonstrate how to draw using the coordinates
given
ASK and SHOW: Does anyone want to volunteer to
draw the first set of points given?
SAY: Okay now you all draw the others on your own.
VI. Demonstrate how to draw their Birth Month or
Year and how to plot its coordinates
ASK and SHOW: Does anyone want to volunteer to
draw their Birth Month or Year and plot the
coordinates?
SAY: Okay now you draw and plot your own
coordinates on your own.
Teacher tries to get a
student to draw first. If
not, the teacher will
show them how to
draw the whole 1st set
of coordinates or letter
given.
Teacher walks around
the room for about 15
minutes and
checks/monitors for
understanding as
students work
independently.
Teacher tries to get a
student to draw theirs
first. If not then the
teacher shows them
how to draw and plot
hers.
Students write these
coordinates in the
space provided in the
worksheet “Polar
Coordinate Drawing.”
Teacher walks around
the room for about 15
minutes and
checks/monitors for
understanding as
students work
independently.
How to video:
http://www.vimeo.com/user1000605/videos
Use the “How to” video
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VII. Assessment
A. Teacher will ask review questions
B. Monitor students as they work
C. Each student’s drawing should match the one
demonstrated in class.
as supplemental for
those students who
need even more help.
Teacher will monitor
students as they work
and ask review
questions.
Teacher checks to see
if each student did
their own drawing and
coordinates. They
receive 50 points for
each.
Verbal
Linguistic
Logical
Mathematical
Visual
Spatial
Musical
Rhythmic
Bodily
Kinesthetic
Intrapersonal
Interpersonal
Naturalist
Existentialist
Application
Guided Practice (LSI Quadrant III):
The teacher must explain the PowerPoint during the lesson. Do NOT just read it or let students
read it. Explain and give personal examples as you go. Demonstrate how to do the assignment,
part of it, but not the whole thing. Use the video as supplemental for those students who need
even more help.
Independent Practice (LSI Quadrant III):
Draw the coordinates given. Then draw own birth month or year and plot the coordinates.
Summary
Review (LSI Quadrants I and IV):
Q: Randomly ask what directions
A: Varies based upon what you ask
Q: What is the difference between Absolute and Relative and now Polar coordinates?
A: Absolute and Relative are based on the X and Y axis or plane. Polar is all distance and
direction
Evaluation
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Informal Assessment (LSI Quadrant III):
Walk around the room and monitor the students as they work.
Formal Assessment (LSI Quadrant III, IV):
Their drawing should match the practice one you did. Check to see if they did their own drawing
and coordinates. 50 pts for each.
Extension
Extension/Enrichment (LSI Quadrant IV:
Tomorrow draw their coordinates in ACAD. Do the hand drawing and computer drawing match?
They should if done correctly.
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POLAR COORDINATE DRAWING”
DIRECTIONS: Draw on the graph paper given to you the problem by following the
directions. For example @2<90 means you draw a line that is 2 squares long and up.
You must start where indicated. Shading when done drawing will help you to see the
picture better. What does your picture look like? Is it correct when you show it to your
teacher or compare to your neighbors? If yes, now on the other side of this graph
paper draw YOUR Birth month or Year. Plot out the coordinates, using Absolute X, Y
for the starting points. Good luck and have FUN!
POLAR = @ Distance < Angle
Ex: 4 squares to the right would be @4<0
NOTE: When dealing with angled measurements like @1<45; we must use the
Pythagorean Theory or a2 + b2 = c2 So 1 = 1.41 2 = 2.82
3 = 4.24
4=
5.66 etc….
1st Letter SP= 25,13
1
@2.82<135
2
@2.82<225
3
@1<180
4
@1<90
5
@1<0
6
@1.41<45
7
@2<90
8
@1.41<135
9
@1<180
10 @1<90
11 @1<0
12 @2.82<315
13 @2.82<45
14 @1<0
15 @1<270
16 @1<180
17 @1.41<225
18 @2<270
19 @1.41<315
20 @1<0
21 @1<270
22 @1<180
2nd Letter SP= 11,13
1
@6<90
2
@3<0
3
@1.41<315
4
@1<270
5
@1.41<225
6
@1.41<315
7
@2<270
8
@1<180
9
@1<90
10 @2.82<135
11 @3<270
12 @1<180
3rd Letter SP= 18,13
1 @1<180
2 @1.41<135
3 @4<90
4 @1.41<45
5 @1<0
6 @1.41<315
7 @4<270
8 @1.41<225
4th Letter SP= 17,14
1 @4<90
2 @1<0
3 @4<270
4 @1<180
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Draw your Birth Month or Year on the graph paper provided. Write down your
coordinates on the space below. You will be typing in these into ACAD tomorrow. Your
grade will be based upon your accuracy NOT looks.
Objective is for what you draw on the paper to match what you draw on the computer!
You will staple all together and turn in as one assignment.
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