Telling time to the half-hour involves reading a clock when the minute hand points to 6 and the hour hand is halfway between two numbers. Times are expressed as '_____ thirty' or 'half past _____'.
Think of the clock face as a circular track that the minute hand runs around once every hour. When you first learned to tell time, the minute hand was at the "start" — pointing straight up at the 12, meaning zero minutes had passed since the hour. Now the minute hand has traveled halfway around that track and stopped at the 6. That half-lap takes exactly 30 minutes.
The hour hand tells an interesting story at this moment. Because 30 minutes is exactly half of one full hour, the hour hand has moved exactly halfway between two numbers. If the time is "3 thirty," the hour hand sits exactly between the 3 and the 4 — it has started its slow journey toward 4 o'clock but hasn't arrived yet. This is why we call half-hour times "half past" the hour: the time is halfway past the previous o'clock mark.
When reading a half-hour time, always check the minute hand first. If it points to the 6, you know it's "thirty." Then look at the hour hand. Since it's between two numbers, name the number it most recently passed — the one behind it in the direction the hand travels. If the hour hand is between 7 and 8 with the minute hand on 6, the time is 7:30, or "half past seven."
A common mistake is naming the number the hour hand is pointing toward rather than the one it just left. Remember: the hour hand shows which hour is currently happening, not which hour is coming next. At 7:30, the clock is still in the 7 o'clock hour — it won't be 8 o'clock until the minute hand completes its full loop back to the 12.