Educational Activities The Winnipeg School Division No. 1
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Mathematics Geometry Programming
(MSWLogo - Geometry Programming - SS-II.3.5)

(Originally from the Inner City Technology Goals Document – June 1997)

Description:
Students design geometric shapes in LOGO, then compute the perimeter and/or area of the shape.

Math: Yes

TypeLessonPlan: Unit Plan - complete unit

TechnologySkills: Programming

SoftwareUsed: MSW Logo

EarlyYears:

MiddleYears: Yes

S1-S4:

SpecificGrade:

Submittedby: Brian Proctor

E-mail: proctor@minet.gov.mb.ca

Details:
The first step is to design and execute a shape. The shape can be any geometric figure, however rectangles and squares are easiest to start with. Logo commands are displayed in bold text. e.g. fd 100 rt 90 fd 50 rt 90 . Repeat 2 [fd 100 rt 90 fd 50 rt 90] will execute a rectangle of length 100 pixels, width 50 pixels. (about 1 mm. per pixel ). The perimeter of this figure can be calculated by simply adding the lengths of the sides of the rectangle. P =100 + 50 + 100 + 50 = 200. Similarly, the perimeter of a 20 x 40 rectangle would be 40 + 20 + 40 + 20 = 120 etc. It should become apparent that the perimeter of a rectangle can be calculated by adding the length to the width and multplying by 2 e.g. P = (L+W)2. Actually creating the rectangles in LOGO should enable the students to more clearly understand what the formula actually means.

Similarly LOGO will execute any rectangle in the same way. The use of the repeat command in LOGO uses the same basic mathematical structure as the formula for perimeter, with only the addition of the degree inputs. e.g. repeat 2 [ fd 100 rt 90 fd 50 rt 90 ] will execute the first rectangle, repeat 2 [ fd 40 rt 90 fd 20 rt 90] will execute the second. LOGO will also output perimeter by executing show ( 100+50)*2 for the first rectangle or show (40+20)*2 for the second rectangle. Again note the mathematical nature of the programming language. The only difference is the use of the * symbol for multiplication.

To have LOGO calculate the perimeter of any rectangle create the following procedure:
to perimeter :length :width
show (:length + :width)*2
end

Students need only execute the following command, e.g. perimeter 100 50 for the first rectangle or perimeter 40 20 for the second rectangle. This is a fine, simple way of demonstrating to children both the meaning of perimeter and the mathematical nature of computer programming.

Extensions:
MSWLOGO can be programmed to output any mathematical formula.
e.g. volume of a cube
to volume :length :width :depth
show (:length * :width *:depth)
end

or, area of a rectangle
to area :length :width
show (:length*:width)
end

The key here is to use LOGO to demonstrate what the mathematical symbols really mean. At the same time, the students have an opportunity to realize the mathematical nature of computer programming.






Filename:  Mathematics Geometry Programming.htm