Most children start learning how to multiply in 2nd or 3rd grade. Miquon math has children starting multiplication in 1st grade as an extension of addition. Picture books and stories help make multiplication meaningful and kids can pick up the concept more easily than just with pencil and paper.
Learning to divide is usually learned after multiplication facts are down pat but you can find examples in daily life that can help get the basic concept down painlessly. Some of the books below can help bring this concept to life with pictures and stories. Who says middle elementary math has to be boring and abstract?

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One Grain Of Rice: A Mathematical Folktale
(Multiplication)

Even my older children delighted in this beautifully illustrated traditional tale about a "multiplying" grain of rice.

A Remainder of One by Elinor J Pinczes and Bonnie MacKain (Simple Division)

My son enjoyed this book about some beetles marching along dividing into squadrons. If you like it, you may also want to take a look at the "companion" book: One Hundred Hungry Ants, a book about multiplication.

Amanda Bean's Amazing Dream (Marilyn Burns Brainy Day Books) by Marilyn Burns (Multiplication)

Anno's Mysterious Multiplying Jar by Mitsumasa Anno (Multiplication)

Arctic Fives Arrive by Elinor J. Pinczes (Counting by 5's)

Arithme-Tickle: An Even Number of Odd Riddle-Rhymes
by J. Patrick Lewis and Frank Remkiewicz (Adding, subtracting, multiplying)

Breakfast at Danny's Diner: A Book About Multiplication: A Book About Multiplication (All Aboard Math Reader) by Judith Stamper and Chris L. Demarest (Multiplication)

Can You Count to a Googol? by Robert E. Wells (powers of 10)

Divide and Ride (MathStart 3) by Stuart J. Murphy (Division)

Double the Ducks (MathStart 1) by Stuart J. Murphy and Valeria Petrone (Doubling)

Hershey's Milk Chocolate Multiplication Book by Jerry Pallotta
(Multiplication)

Leaping Lizards (MathStart 1) by Stuart J. Murphy (Multiples of 5)

Math Man by Teri Daniels
(Percentages, fractions, division, multiplication)

Multiplying Menace: The Revenge Of Rumpelstiltskin (A Math Adventure)

(Multiplication of whole numbers and fractions) **Click here for a Multiplying Menace Activity Guide**

One Hundred Hungry Ants Multiplication

This cute little story is the "companion" book to A Remainder of One, a book about division.

Reese's Pieces Count By Fives by Jerry Pallotta (Counting by 5's, a multiplication concept)
My son loves these types of books. Who can resist such a sweet math lesson? ;-)

Spunky Monkeys on Parade (MathStart 2) by Stuart J. Murphy
(Counting by 2's, 3's and 4's - a multiplication concept)

Tally O' Malley by Stuart J. Murphy (tallying)

The Best Of Times by Greg Tang ( Multiplication tricks)

The Great Divide: A Mathematical Marathon by Dayle Ann Dodds (Division)

Too Many Kangaroo Things to Do! (MathStart 3)
by Stuart J. Murphy (Multiplication)

Counting Sheep (Step-Into-Reading, Step 2) Skip counting (multiplication concept)