Suppose you are racing around a track and they want you to keep track of the number of laps. Every time someone runs a lap you need to write it down.

If you write down the numbers with a pencil you can keep erasing them but will be messy. You could keep crossing out the score, so by the time they have run \(5\) laps it looks like this. \[\not 1\not 2\not 3\not 4 5\]

An easier way is to use tallies. Suppose every time someone ran a lap you drew a line, and every \(5\) laps you drew a diaganol line.

Here is what the tallies \(1\) through \(5\) look like.

\(1 \rightarrow\)

\(2 \rightarrow\)

\(3 \rightarrow\)

\(4 \rightarrow\)

\(5 \rightarrow\)

\(6 \rightarrow\)

By making a diagonal line every \(5\) strokes, you can count the tallies using counting by \(5\)'s. Here is the number \(17\) shown in tallies. It is three \(5\)'s and two \(1\)'s.