Explain the differences among rote counting, counting on, counting back, and skip counting.

Rote counting is counting by making a one-to-one correspondence. When counting on, we begin at a certain plane in the number word sequence and rote-count from that number. When counting back, we begin at one place in the number word sequence and count backward. When skip-counting, we begin at one place in the number word sequence and count one by 2s, 5s, 10s, or other values.