I love the The Mathematics Calendar 2018.
It has an equation or other statement about math for every day, often linked to that day (like, the January 13th entry is "the sixth prime number"). Some entries are little mat quizzes for you to fugue out. Some are funny jokes, like the entry for Thanksgiving (any guesses as to what that might be? Hint: It is a formula.) The level of difficulty of understanding the reference or solving the problem ranges from suitable for a smart 7 year old (Huxley has figured some out) up through college level. Also, the picture that go with each moth are totally cool and, of course, mathy.
The calendar is complied by Rebecca Rapoport, of Harvard. She is also the author of Math Lab for Kids, which is not a dog, but a book, that looks good but that I've not seen.
I'm tagging this post with the keyterm "holiday shopping" to hopefully remind me to remind you that this is a great holiday gift for that special math nerd or math teacher in your life.
Other publications that make good browsing material are:
The Penguin Dictionary of Curious and Interesting Numbers one of a number (sorry) of books in an intriguing series by David Wells,
also this tome Mathematics: From the Birth of Numbers.
One that involves much deeper thought is, and I am out of allowable links this post, 'Gödel, Escher, Bach: An Eternal Golden Braid' by Douglas Hofstadter. Being a fan of both Escher and Bach JS and having done coding including messing about with fractals and appreciating Lewis Carroll (there are a number of books published exploring that vein) I was naturally drawn to this book.
There is also a series of math-related videos on youtube, called Numberphile.
Usually good, sometime great, discussions of items related to different areas of mathematics.
And remember, if you know someone who is troubled by improper fractions, there is a help line available 24/7.
Also, check out the calendar of the same name by Theoni Pappas. I've been getting that every year that it is available for the last 10 years or so. On that calendar, the answer to the problem is always the day of the month, so you always know the answer, the fun is in trying to figure out how to get there. There are also interesting mathematics related articles each month on the calendar.
Pappas' calender is also at the link you provided above.
I'm glad to know that there is an alternative since the Pappas calendar has missed a couple of years lately. I may get both this year.
Lionel A recommended "also this tome Mathematics: From the Birth of Numbers."
This is a very nice book. I purchased it in 1998 and have used it to refresh myself when helping my children through High School math classes (especially pre-calc and calc subjects).