Math from the heart, not the textbook
Find what you love. Do more of that. What do you love? How can you incorporate more of that in what you do? Not the first thing that comes to mind. What is the underlying principle that speaks to your mathematical soul, to your teacher's heart?
For Christopher, it's ambiguity.
Which One Doesn't Belong?
Kids notice corners and points before sides. They notice how shapes are built. The top right picture is the only one that can't be built from the top left triangle. Doing these activities brings out vocabulary, composing and decomposing shapes, and orientation.
Using spirals as shapes, we don't have vocabulary for the properties. We decide on what's important and then name it.
Kids notice things we don't and name it with the vocabulary they have. Zero belong because they can't be colored in (not closed polygons).
Top left doesn't belong because if it rained, it's the only the shape that would hold water.
Top right doesn't belong because both ends are not facing the same direction.
The bottom two look roughly the same length. Kids debate that the bottom right has further space from the end to the inner so it should be longer.
On this picture, there is debate about number of corners or vertices. Does the top left have one or two? Does the top right have two or three? Does the bottom right have zero or eight?
How far can the parabola tilt and still be a function?
Decide what you love and then explore it!
What's your niche?