Geometry Activity - TEACHER'S GUIDE
Assumed Prior Knowledge
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Definition of a regular polygon
Definition of exterior and interior angles
Sum of interior angles in a triangle and square
How to label angles on a shape
Objectives – Students will be able to
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Label the exterior and interior angles on a polygon
Look at data, observe a pattern, and apply the pattern to making inferences
Calculate the sum of the exterior angles of any n-sided polygon
Calculate the sum of the interior angles of any n-sided polygon
Draw any n-sided regular polygon in StarLogo Nova
Part 1: Introduction to the Activity - Looking at the Code
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Go to http://tinyurl.com/geo-activity
Remix the Project and rename it: Geometry Activity (Your Name)
Click the "Run Code" button
Scroll down to the WorkSpace and you should see the following code in "The World" page
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When the user presses “setup”, Spaceland will be cleared, and one turtle will be created
This turtle will stamp the terrain white and then delete itself
At the same time, another turtle will be created. This turtle will be purple.
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The Turtle will put its “pen” down onto the ground so that a trail is left behind him
whenever he moves (think Hansel and Gretel!)
You may change the Turtle color from purple to another color. In order to change the pen
color, you must change the turtle's color.
Switch to the Turtle page by clicking on the Turtle tab in Workspace
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Look over the code and then go back to the SpaceLand screen and click the “Draw
My Shape” button. Observe what happens.
What shape is drawn? Square
Look back at the code and make predictions about how the blocks specify
instructions for the turtle to follow
Draw the shape below in the box:
What do you think the number in the "repeat___ times" block represents (see
screenshot above)? Your answer should relate to both the shape that was drawn, as
well as the movement of the turtle. This number represents the number of sides on
the shape, and the number of times that the turtle repeats the command.
What do you think the number in the "forward___" block represents? Again, answer
both in terms of the shape that was drawn, as well as the movement of the turtle.
This number represents the side length of the shape, and the number of steps that
the turtle takes.
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What do you think the number in the "left by ___ degs" represents? Again, answer
both in terms of the shape that was drawn, as well as the movement of the turtle.
You should use the term “exterior angle” and/or “interior angle” in your answer.
This number represents measure of the exterior angle (students may think it is the
interior angle at this point still) of the square. The turtle turns this many degrees
after each line segment that it draws.
On your drawing above, mark the location of the angle you described in #4 on your
shape.
Note: The yield blocks in between simply slow down the turtle’s movement so that we can see him
move step by step.
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Part II. Test Your Prediction (based on what you wrote down for the pink number blocks above)
a. Adjust the numbers in the blocks to values that you believe would instruct the turtle to
draw a regular triangle with the same side length as the original shape that was drawn in
Part I.
b. Fill in your adjusted code below:
Students will likely fill in numbers from one of two options shown below:
 Option 1: 3, 15, 60
 Option 2: 3, 15, 120
c. Return to Spaceland, click “Setup” to reset Spaceland and then “Draw My Shape” and
observe what happens. Draw the shape produced in the box below.
Based on the two options indicated above:
Option A
Option B
d. On your drawing above, label/mark:
i. Your turtle’s start point with a circle
ii. The path that the turtle would take if it ignored its coded instructions and did not
turn after starting to move forward and instead kept walking straight forward
iii. The angle between the turtle’s extended path (from ii) and the side of the drawn
shape.
 What kind of angle is this? Exterior
e. Try drawing a regular hexagon and repeat steps (a through d from above)
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f.
If you did not produce a triangle earlier, try again below:
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Part III. Check Understanding
a. Definition of Interior vs. Exterior Angles
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For each question, circle one of the italicized terms
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Angle 1 is the interior/exterior angle of the triangle.
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Angle 2 is the interior/exterior angle of the triangle.
b. Measures of Interior and Exterior Angles for Various Regular Polygons
 Assuming the triangle above is a regular triangle, what is the measure of
A. Angle 1? 120°
B. Angle 2? 60°
C. The total interior degrees? 180°
D. The Total exterior degrees? 360°
Hint for Students:
Total interior degrees = # of corners * measure of one interior angle
Angle 2 = total exterior degrees = number of corners * measure of one exterior angle
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Repeat the above steps for a square:
A. Angle 1: 90°
B. Angle 2: 90°
C. Total interior degrees: 360°
D. Total exterior degrees: 360°
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Repeat the above steps for a hexagon:
A. Angle 1: 60°
B. Angle 2: 120°
C. Total interior degrees: 720°
D. Total exterior degrees: 360°
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Repeat the above steps for a pentagon:
A. Angle 1: 72°
B. Angle 2: 108°
C. Total interior degrees: 540°
D. Total exterior degrees: 360°
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c. How do Angle 1 and Angle 2 relate to one another?
 Angle 1 + Angle 2 = 180°
d. What name is given to angles which exhibit such a relationship?
 Supplementary Angles
e. Based on your answers above, fill out the table below and answer the questions that follow:
Shape Name
Number of Sides (n)
Triangle
Square
Pentagon
Hexagon
3
4
5
6
i.
Total Interior Degrees
(TID)
180
360
540
720
Total Exterior Degrees
(TED)
360
360
360
360
How does the total interior degrees of a triangle relate to the total interior degrees
of a square? How does the total interior degrees of a square relate to the total
interior degrees of a pentagon? How does the total interior degrees of a pentagon
relate to the total interior degrees of a hexagon? In general, how does adding one
side change the total interior degrees?
 Each time we add a side, the total interior degrees increases by 180°
ii. How does the total interior degrees relate to the number of sides? Write a formula
for TID (the total interior degrees) that includes “n” – the number of sides. Hint:
think about your answer to part i)!
 TID = (n – 2) * 180°
iii. What is the pattern you observe among the total exterior degrees?
 Total exterior degrees always equals 360°
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Based on your observations and inferences, fill out the following information for a decagon
(has 10 sides)
 Measure of a single exterior angle: 144°
 Measure of a single interior angle: 36°
 Total interior degrees: 1440°
 Total exterior degrees: 360°
g. And for a regular polygon with 100 sides:
 Measure of a single exterior angle: 3.6°
 Measure of a single interior angle: 176.4°
 Total interior degrees: 17640°
 Total exterior degrees: 360°
f.
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Part IV. Extensions
a. Create more different shapes by adjusting the code in StarLogo.
b. Create multiple turtles during setup so that more than one shape is drawn at one time.
c. Replace the Draw My Shape button and blocks with a toggle button widget and
“while___toggled” block, to draw the shape over and over but with slightly different colors or
starting headings each time.
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