Eighth Grade · Math · week 35

Design project with transformations

Design a simple pattern using a sequence of transformations on a starting figure, describing each step precisely with coordinates.

Real design -- logos, tile patterns, snowflakes -- often repeats one shape transformed several times. This project applies the whole transformation toolkit (translations, reflections, rotations, and dilations) to build something out of one starting figure.

Keep straight which figure each new transformation starts from: transforming the ORIGINAL every time gives a "starburst" of copies around one shape, while transforming your PREVIOUS result each time gives a "chain" of copies.

📋 For the teacher
Teach it (10–15 min):
  • This project is open-ended in spirit (design your own pattern) but precise in execution -- every move must be describable with exact coordinates.
  • Keep straight which figure each transformation starts from -- transforming the original each time gives a "starburst," transforming the previous result each time gives a "chain."
  • Encourage a rough sketch (even just described in words) of what the finished arrangement looks like -- a pinwheel, a row, a snowflake-like burst?
  • Every property from the last two weeks still applies: translated, reflected, or rotated copies are CONGRUENT to the original; dilated copies are SIMILAR (unless the scale factor is exactly 1).
Talk about it:
  • What is the difference between transforming the original shape each time versus transforming your last result each time?
  • Of the copies in your design, which are congruent to the original, and which are only similar?
  • If you wanted a snowflake-like repeating design, which transformation would you lean on most, and why?

Mastery looks like: Given a starting figure, they apply a sequence of at least three different transformations, correctly computing coordinates at each step and identifying which copies are congruent versus similar.

Common stumbles: Losing track of which figure (original vs. previous result) a new transformation should start from; applying a transformation rule meant for one axis to the other axis.

See it visually

Interactive, spoken-aloud tools that show this idea in motion.

Coordinate PlanePlot points and explore the four quadrants.try →
Homework for this lessonType it, write it with a stylus, or print it for pencil & paper.open →
Records attendance + 15 min of Math for this learner.
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