My first example of inspiration is "Math Photo Challenge," a summer photo taking challenge for math-minded Twitter peeps (not on Twitter? check out the website). Each week there is a different theme/challenge. It's a great way to see the math in your everyday life.
The collection of pictures from everyone is also great images to use in your classroom in the fall. You can show pictures and ask your students what they notice/wonder. Or you can use pictures for specific standards and ask students what problems they can come up with that match the image. I'm even thinking about how I can have my students use their iPads to take pictures with a different theme each week so they are inspired to see math everywhere just like I have been!
Here are a few examples of my pictures. Check out @mathphoto16 and #mathphoto16 on Twitter to see what others have shared as well!
Here is #lines:
Another source of inspiration for seeing math everywhere is "Talking Math with Your Kids" by a passionate educator, Christopher Danielson (@Trianglemancsd). Check out the blog as well as #tmwyk on Twitter. By reading how other parents talk about math with their kids (no matter how young or old), it has me inspired to see the math in conversations I have with my 2-year old.
Being a middle school math teacher, I might not have seen the sometimes simple conversations I have with Natalie to be that "mathy," when in fact they are really laying the foundation for her understanding of shapes, numbers, and how math works!
Also, I see mathematical ideas in some of her toys. This creation I made and tweeted was liked and retweeted many times letting me know that others love seeing math in the world as well! :)