When giving talks on Japan in elementary school classrooms in the United States, I chalk the kanji 一, 二, and 三 on the blackboard and ask the children to guess their meanings. "One, two, three!" they shout, easily intuiting three kanji introduced to Japanese schoolchildren in the first grade. Japanese students go on to master more than a dozen other kanji representing numerals — in addition to Arabic numerals — and they also learn to count high numbers in a way alien to their American counterparts.
Numeral kanji, like other Sino-Japanese characters, have undergone major modifications in shape since they were first created in China four millennia ago. Divergent theories on the origins of kanji for numbers often reference hand signals used for counting. 一 (ICHI, one) depicts a single extended forefinger; in 二 (NI, two), a middle finger appears below it. 三 (SAN, three) likely represents a thumb and the first two fingers: Japanese and Chinese have traditionally begun with the thumb when counting from one to five, and they still do so today.
Because 一, 二 and 三 can easily be altered with a stroke or two by unscrupulous people, more graphically complex "formal numbers" (大字, daiji, big/letters) are used on financial and legal documents. Look for 壱 (ICHI, one) on the front of ¥10,000 bills (壱万円, ichimanen, one/10,000/yen) and 弐 (NI, two) on ¥2,000 bills (弐千円, nisenen, two/1,000/yen). 参 (SAN, three), with three hairlike strokes at the bottom, is the formal form of 三.