Making line designs is an excellent extended project for a 4th or 5th grade class. It integrates many skills and concepts, and students get to take something home they can display. A class can complete a line design, starting with an 11” square with only a large circle with the center marked on it, in 3 class periods.
Prerequisites for this include the ability to measure and draw angles and lines accurately. Some familiarity with the relationship between circles and angles is very helpful.
Included here is the slideshow that I used in a December, 2015 presentation at the annual conference of Associated Teachers of Mathematics in Connecticut (ATOMIC). This focuses on the steps of creating line designs.
Perhaps the best extended project I’ve ever done is to make string designs. As a math coach, I conduct after-school Math groups, which is the only time I can do them nowadays. With testing such a focus, it’s hard to find the time to work on threading needles, stringing yarn, and so on in classes. But if you can swing it this is one of those projects your students will remember for a long time.
I’m including my notes on making string designs from that ATOMIC conference. It’s a little light on pictures illustrating the process. I tend not to think about taking pictures in class, but I do take pictures of each student after they complete their design. Some of the pictures from my last group to do string designs, in May of 2015, are here. All of these were done by 3rd, 4th, and 5th graders.
And if you’re seriously thinking about string designs, get your hands on Victoria Pohl’s 1986 book, How to Enrich Geometry Using String Designs, published by the NCTM. This is a wonderful book, well-
sequenced and illustrated in great detail. It’s out of print now, but still available from used booksellers.