Year 5/6 Mathematics.

I was looking for something different for the students to use with regards to perimeter and area. Looking at the Maths 300 website I found the Sphinx. The shape of it was great in view of the fact that I had just been looking at the area of a parallelogram (being that of the rectangle made when translating the right-angled triangle).

We had also looked at the area of a triangle being half of the area of a rectangle it formed from the base.

The Sphinx, because of its unique shape, could be dissected into an equilateral triangle and a parallelogram. It was easy then to use the formula already discovered for the parallelogram and the triangle to work out the area. The perimeter was also interesting because of the shape and ratio of the length of the sides.

The class created a size 64 Sphinx using four size 16 Sphinx of different colours.

AppleMark

Using logo programming:

Having worked with the shape most students had little trouble in creating a Sphinx in MicroWorlds using logo programming. Initially I suggested they work with 100:200:300 for ease. The angles the turtle needed to turn because of the shapes were 60 or 120 degrees. That was the easy part. Now I wanted them to create a size 2 Sphinx using four smaller ones and some were up to the challenge.

Three Sphinx are the same orientation, i.e. 3 is a translation of 1, 2 is a rotation of 1, but 4 is reflected and rotated.

Student 1                               Student 2

to Sphinx
pd rt 90
fd 100
rt 60
fd 100
rt 120
fd 300
rt 120
fd 200
rt 120
fd 100
end
to Sphinx2
Sphinx lt 60
fd 100 rt 90
Sphinx
end
to Sphinx3
bk 100
rt 60
fd 200 seth 0
pd lt 210
fd 100
lt 60

fd 100
lt 120
fd 300
lt 120
fd 200
lt 120
fd 100
rt 60
fd 100
lt 60
end
to Sphinx4
fd 100
rt 60
fd 100
rt 90
rt 30
fd 300
end
to Sphinx5
Sphinx2
Sphinx3
Sphinx4
end

to Sphinx
pu
lt 120
fd 400
rt 120
pd
rt 90
fd 300
lt 120
fd 100
lt 60
fd 100
rt 60
fd 100
lt 120
fd 200
lt 120
fd 300
lt 60
fd 200
rt 180
lt 30
rt 90
fd 300

lt 120
fd 100
lt 60
fd 100
rt 60
fd 100
lt 120
fd 200
lt 120
fd 300
lt 60
fd 200
rt 180
rt 60
fd 300
lt 90
rt 90
fd 300
lt 120
fd 100
lt 60
fd 100
rt 60
fd 100

t 120
fd 200
lt 120
fd 300
lt 120
fd 100
fd 300
lt 120
fd 200
end

 

Student A programmed each individual size 1 Sphinx and then put them together to create a size 2 Sphinx.

 

Student B just followed his nose and had the size 2 Sphinx created in no time.

 

Student 1                                                       Student 2      

                                                                                                

I was happy to see the students working towards the goal. Personally I would have created one Sphinx of each orientation (steeple left and steeple right), and put them together to form the four, but with further exposure to programming and a little prompting, this may become an option (as repeat does in creating regular polygons). It is always interesting to me to see how different minds work.

The next challenge:

Student 2 went on with ease to create three size 3 Sphinx which I had copied from the web page: http://www.blackdouglas.com.au/project/Sphinx/sfnx3sol.htm

We simply imported the pictures onto the MicroWorld’s screen page by page and he programmed as before following the shape of the picture. He seemed to do this in record time so obviously has a good visual perception.