- Mathematical Investigation inspired by these prehistoric worms -
A worm travels paths of lengths 3, 5, 2 . At the end of each path,
the worm turns right 90 degrees. Practice on grid paper and follow the
picture examples. Remember the starting
direction is up. Good Luck!
STAGE 1:
STAGE 2:
STAGE 3:
STAGE 4:
Results: After four repeats of the pattern, the worm returns to the
starting point.
This spirolateral is closed.
Explain why a pattern works the way it does.
Which patterns are symmetrical?
Which patterns have spirolaterals that do not close?
Try other numbers in the sequence. (1,2,3 or 2,4,6, or 3, 5, 7, you choose!)
Try other sequence lengths (1,2,3,4,5 or 5,4,3,2, you choose !)
Now try some new rules (start down, instead of up!)
Experiment with spirolaterals art pictures. Fill in the grids with different colors and designs.
Remember you can also create a computer program using APPLE LOGO or HYPERSTUDIO HYPERLOGO to show how your spirolaterals work.
Use different types of grids: Square dot paper, Triangular and Isometric dot paper.
You will be turning at an angle of 60 degrees counter clockwise.
If some of your students have trouble understanding "90 degrees right turn" rule,
you can have them set up their grid with the letter "N" for north at the
top of their grid, the letter "E" for East at the right side of their grid,
the letter "S" for South at the bottom of their grid,
and the letter "W" for West at the left side of their grid.
This way the students can remember the path's direction.
First- up North, then East, then South, and then West,
then North, then East, then South, and then West....etc.
(As 5th grade student Fabiola H. explains: it's Never
Eat Shredded Wheat !!)
A special note of credit is extended to the facilators of the Los Angeles Urban Systemic Initative (LA-SI) Phase II Summer Institute '96 for introducing and providing us with inquiry-based activities on "Spirolaterals". The LA-SI is one of 25 Urban Systemic Initiatives funded by the National Science Foundation to improve student outcomes in mathematics and science. Getting kids excited and thinking about Mathematics can only begin when educators/parents/students work together to explore innovative and effective strategies to learning Mathematical concepts. For more information at LA-SI contact LA-SI Facilitor/Resource Teacher, Joe Oliver or LA-SI Project Director, Carol Takemoto.
| September: Math Fun With Spirolaterals |
October: Exploring Number Patterns |
| November: Perimeter, Area, & Volume |
December: Toy Story Math |
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Ave. School