SUBJECT: Geometry
GRADE: High School
TECHNOLOGY: Geo-Logo Turtle Paths
BY: Megan Stewart
Interior Angles of Polygons
Target Grade/Subject:
High School Geometry class. The target grades for this lesson are 8-12. After learning about the interior angles of polygons, students will go to the computer lab and will free explore using Geo-Logo Turtle Paths. This lesson is targeted for a block class or any other class with an extended length of time.
Objectives:
1) Students will gain practice in angle measurements and lengths of segments in a proportion.
2) Students will discover the relationship between the in-class lesson on interior angles of polygons and free explore on Geo-Logo.
3) Students will use this relationship to fill out a worksheet that asks them to draw and record the commands necessary to produce various regular polygons.
4) Students will have the opportunity to explore the other activities on Geo-Logo if time permits.
The criteria for assessing mastery will be a small grade on the worksheet and the teacher’s observation of the students using this program.
Materials:
Either a computer lab or enough computers in the classroom for students to work alone or in pairs. Use a computer program called Geo-Logo Turtle Paths. This program has a variety of activities students can use such as, Get the Toys, Feed the Turtle, Triangles, Missing Measures, 200 Steps, Geo-Face, and Free Explore.
Students will be given a worksheet that gives them the basic commands to use in Logo and activities to complete. These activities will emphasize the previous in-class lesson on interior angles of a polygon.
Lesson Description:
1) Pass out a worksheet and go over it with the students. Explain the commands needed to move the turtle around. Some of the basic commands to go over are:
Shorthand - Means - Meaning
pd - Pendown - The turtle will now leave a track
fd x - Forward x - Turtle moves forward x steps
bk x - Back x - Turtle moves backward x steps
rt x - Right x - Turtle turns right x degrees
lt x - Left x - Turtle turns left x degrees
pu - Penup - Turtle no longer leaves a track
If time permits, students will be able to explore the other activities in Logo. Inform students that in Feed the Turtle, the steps are in multiples of 10 and the degrees are in multiples of 30.
2) Get all students to do basic commands so they can see how the turtle moves. Get the students to type in: fd 10 (return) fd 40 (return) rt 60 (return) lt 180 (return) fd 20 (return) and bk 30 (return).
Show students that they can go up to the Command Center (where the commands they typed in are displayed) and edit their previous commands.
Answer any questions they may have. One question that may arise - What does it mean to get an error message? Students may have an extra return in their command. Delete the command and retype it. This should resolve the problem.
3) Allow students to work on worksheet alone or in pairs. Walk around the room and assess their progress. (Worksheet included at the bottom of this document.)
The primary focus of this lesson is for students to decide what angle measurements to use to form various interior angles of polygons. Students should use their knowledge from the previous lesson to determine what the interior angle will be. I hope students will use the knowledge that n-2 triangles (n being the number of sides of the polygon) can be formed within each polygon. Each triangle is made up of 180 degrees. Multiply and find out the total angle measurement of the regular polygon. Then dividing that number by n they will arrive at the angle measurement for each angle. Using this knowledge the students should be able to arrive at their commands more quickly rather than using trial and error method to come up with the correct measurements. Students must discover this relationship on their own, hence the purpose of this lesson.
Evaluation Procedure:
Assess student feedback by walking around the room answering questions and checking on their progress. Also, collect the worksheets, pass them back, and go over them in a class discussion.
Worksheet
Record your procedures and answers to the following questions to use in class discussions.
Part I
1) Have the turtle draw your first initial. Record the commands you used.
2) Draw a square that is 60 turtle steps on a side. Record the commands you used.
3) Draw a rectangle that is 50 turtle steps by 70 turtle steps. Record your commands.
4) You can use a short cut to writing all the commands out. For example, if I wanted to make a rectangle 70 turtle steps by 20 turtle steps, I could type in the commands fd 70 rt 90 fd 20 rt 90 fd 70 rt 90 fd 20 or I could use a repeat command to repeat the parts that are done over.
It would look like this: repeat 2[fd 70 rt 90 fd 20 rt 90]
Draw a square that is 90 turtle steps on a side using the repeat command.
Part II
1) You can teach the turtle vocabulary so you don’t have to type in the set of commands every time. Press the “Turtle Teach” button in the upper left part of the screen and name the procedure when asked. The computer will add the word “end” to the procedure and move it to the teach screen.
Let’s define a procedure for making a square 70 steps on a side.
Type repeat 4[fd 70 rt 90] and press return.
Now press the Teach-Turtle button. Type the word square and press return. What happened? Now type Square in the command center and press return. Did the turtle follow your directions?
2) Make a square that is 40 steps on a side. Go to the Teach section. What do you have to change in your procedure to make the new square? Go ahead and change it using the arrow key and the delete key to move around the screen. Try out your new procedure.
Part III
1) It can be an awful nuisance to keep editing to get different squares. Wouldn’t it be nice if we could tell the turtle how long we wanted a side of the square to be when we ran the procedure? We can do that using variables for the things we want to change. For example, go to the Teach Section
and let’s edit the procedure you have for a square.
to square
repeat 4[fd 40 rt 90]
end
to look like this:
to square :side
repeat 4[fd :side rt 90]
end
The way Logo designates a variable is to put a colon in front of the variable name, which can be a single letter or a series of letters. When you run the procedure, you type in the name of the procedure (square in this case) and what number you want used for the variable. The computer will take that value and plug it in wherever it finds the variable.
Part IV
1) Make a procedure for a square using one variable for the length of a side.
2) Make a procedure for an equilateral triangle using one variable for the length of the side.
3) Make a procedure for a regular pentagon using one variable for the length for the side.
4) Make a procedure for a regular hexagon.
5) Make a procedure for a regular decagon.
6) Make a procedure for a regular n-gon using one variable for the length of a side.
7) What connection do you see between our lesson on interior angles of a polygon and the way you came up with the procedure for a polygon, hexagon, decagon, and n-gon?
8) Did you discover any other interesting procedures?