Shapes
A square was sitting quietly
Outside his rectangular shack
When a triangle came down--kerplunk!--
"I must go to the hospital,"
Cried the wounded square.
So a passing rolling circle
Picked him up and took him there.
Shel Silverstein in A Light in the Attic
There are many ways to teach math concepts, and math lessons don't necessarily have to be boring. Think about this poem by Shel Silverstein and what it teaches. What would this poem look like in pictures? Tell the story in a comic strip. Draw a square. Draw a rectangle. Can you find some triangles in this room? Some circles?
The National Research Council recently released a report suggesting that a child should begin learning about numbers, spatial thinking, and measurement at a very early age. I would suggest that intuitive math learning can begin and go on at any age. One of the reasons that I liked geometry in high school was that I was better at spatial thinking than I was at abstract algebraic equations. I think that if I had been taught to think mathematically, algebra would have been easier for me.
I happened upon a list of some favorite picture books that encourage mathematical thinking at many ages, but particularly for preschool and elementary school children. A book such as Each Orange Had Eight Slices by Paul Giganti Jr. can be used with a preschooler as a counting book and a third grader for a unit on fractions. Young children love How Much is a Million? by David Schwartz to teach really big thinking as much as a first or second grader will love it because they love really big numbers. And everybody loves Math Curse by Jon Sciezka, Thunder Cake by Patricia Polacco, and The Doorbell Rang by Pat Hutchins.
A few of the following books are available online, some are available in video on YouTube, but all will be available at your local library. They are arranged by mathematical concept. Many thanks to a middle school librarian on a wiki website from Blytheville, Arkansas for this list.
This blog posting will consider the basic math concepts of counting, addition and subtraction. The next posting will include books that are about higher level math concepts. 
Counting
100 Monsters from My School by Bonnie Bader
Animal 1 2 3! by J. Douglas Lee
Bears on Wheels by Stan & Jan Berenstain
Chicken Little Count to Ten by Margaret Friskey
Click, Clack, Splish, Splash: a Counting Adventure by Doreen Cronin
Count and See by Tana Hoban
Counting on Frank by Rod Clement
A Dozen Dogs by Harriet Ziefert
Each Orange had 8 Slices by Paul Giganti, Jr.
The Handmade Counting Book by Laura Rankin
Mouse Count! by Felicia Law
Too Many Balloons by Catherine Matthias
Addition
365 Penguins by Jean-Luc Fromental
The 500 Hats of Bartholomew Cubbins by Dr. Seuss
Addition Annie by David Gisler
Blueberries for Sal by Robert McCloskey
Imogene's Antlers by David Small
Math Potatoes by Greg Tang
The Mission of Addition by Brian Cleary
The Rainbow Fish by Marcus Pfister
The Very Hungry Caterpillar by Eric Carle
Subtraction
The Action of Subtraction by Brian Cleary
Blueberries for Sal by Robert McCloskey
Hershey Kisses Subtraction Book by Jerry Pallotta
The Rainbow Fish by Marcus Pfister
Happy Reading! Happy counting, and adding, and subtracting!