Latin verb parts

[Sophia]

My 9 y.o. uses a different latin curriculum than my older two.

She was taught the four verb parts are:
amo, amare, amavi, amatum.

My older dc's book says:
amo, amare, amavi, amatus.

What am I missing here?
Why the different endings on the fourth part?

tia..

[LisaNY]

Using "amatum" instead of "amatus" avoids limiting the participle to either masculine or feminine. "-um" is also the ending identical to the supine.

Both listings are okay - it's just a difference of opinion as to what is the best/optimal way to list the verb form.