Sample Activity – Ratio and Scale Factors via Shrinky Dinks. Shrinky Dinks are large flexible plastic sheets that when heated in an oven, shrink to small hard plates without altering their shape or color. This makes them particularly suitable for exploring ratios, proportions and scaling. Students can create their own designs on the plastic sheets or use pre-prepared designs to color as they choose. Students can explore questions such as, “what size will my shape be after it is heated in the oven?” or the converse question, “if I want my shape to be a certain size after I heat it (say for a necklace), then what must the initial size be?” This project connects well with science, setting up discussions about the impact of heat on the plastic and why certain writing utensils are or are not suitable for use (e.g., oily or waxy items such as crayons melt with the high heat). Ratio, proportions and scaling are challenging concepts for middle school students, yet crucial ones that form the basis for understanding lines, and hence algebra. This activity helps deepen students understanding in a fun, informal setting.
Sample Open-Ended Exploration. Write numbers from 1 to 100 on the board. Select any two of the numbers, erase them, and write on the board the sum plus the product of the two numbers. For example, if you erased 2 and 5, the sum plus the product is 7 plus 10, or 17, and so you write a 17 on the board. Now there are two 17s, but that is okay. Repeat this process of selecting two numbers and replacing them with their sum plus their product. What are the possible outcomes? The mathematical question in this exploration is intentionally open-ended; the point is not to get the “answer,” but rather to question, probe and explore the rich mathematics that arises.