What is the phrase used to convey the meaning of "to clock in and to clock out"?

Solution 1:

Consider, punch the clock

1. to record on a special clock when you arrive and leave work e.g. "In our factory, if you don't punch a clock, you don't get paid"

2. to go to work every day e.g. "One I retire I won't have to punch the clock every day"

Idiomhq

1. To register one's arrive or departure at a job.

2. To be employed at a job with regular hours.

FOD

Ngram

Solution 2:

Note that you should say either "In order to track employee attendance..." or "In order to keep track of employee attendance...".

I would simply say:

In order to track employee attendance, the company prompts employees to clock in and out on weekdays.

or perhaps "sign" instead:

In order to track employee attendance, the company prompts employees to sign in and out on weekdays.

In both cases the language is a little outdated: they are not putting cards in a clock which stamps them (like people used to) and they're not actually signing anything either. But the language persists because they are effectively performing the same function.

For a more up-to-date version, you could say "swipe" instead of "sign" or "clock", reflecting the fact that it is usually done by swiping a card across or near a card reader, and the verb "swipe" has become synonymous with the process of presenting a card to a card-reading device.