Talking Math with Adults - Complementary Fractions

During a New Years party I was making a few new cards for the fraction wars deck, when an adult acquaintance asked what I was doing (rightly so — I probably should have been doing something more celebratory to ring in the new year). I explained that the goal is to figure out what fraction of each card is shaded and showed them the following example.

Their response was “I have no idea how I would figure that out!” with a chuckle. At this point I shared the inverse image of the one above,

When I asked them how much of this image was shaded, they said “Well, the bigger piece is half, and the smaller piece….is a quarter.” “So how much of the first card is shaded?” I asked. “One quarter” they replied.

While I doubt that this discovery was the best part of their New Years Eve 2018-2019 experience, I like to think that this positive experience inspired some confidence and curiosity. What this experience illustrated to me was that inversely shaded images can be extremely helpful in helping us make sense of things.

Here are a few of my favourite complementary fractions thus far, I hope you enjoy them.