There are five major offerings described in the Old Testament (Leviticus 1-5): burnt, meat, peace, sin, and trespass. One them, the meat offering, does not use an animal sacrifice. The other four do. However, the offerings differ in whether the animals are to be male or female. Here is how they are specified. The burnt offering is to be a male (Leviticus 1:3, 10). The peace offering can be either male or female (Leviticus 3:1, 6). The sin offering is to be male when offered for "a ruler" of the people (Leviticus 4:22-23) but a female when offered for "one of the common people" (Leviticus 4:27-28). Finally, the trespass offering is to be a female (Leviticus 5:6). The question is why.
Much of God's creation is marked by the number three. This makes sense since God Himself is a trinity. There are three kinds of vegetation: grass, herbs and trees (Genesis 1:11). There are three kinds of lights in the sky: the sun, the moon and the stars (Genesis 1:16). There are three kinds of animals: fish, fowl and land animals. There are three kinds of land animals: cattle, creeping things and beasts (Genesis 1:24). Man has three parts: spirit, soul, and body (1Thessalonians 5:23). There are three basic colors and three states of matter (solid, liquid and gas). If you think about it, you can find other examples.
Of the 17 times the word firmament is used in the Bible, over half (or 9) of the times are found in Genesis One. Firmament means an expanse or expansion of space and it refers to the expansion of space between the earth and God's heavenly abode. It is bound by the waters above and the waters below (Genesis 1:6-8). This explains why there are "waters that be above the heavens" (Psalm 148:4). Of the three heavens indicated in 2Corinthians 12:2, the firmament includes the first two heavens while the third heaven refers to God's dwelling place. The first heaven is the "open firmament of heaven" where the birds fly (Genesis 1:20). The second heaven is "firmament of the heaven" where the planets and stars reside (Genesis 1:14-15). As known to anyone who has considered the heavens as the work of God's finger (Psalm 8:3), the firmament exalts God. As the psalmist proclaims in Psalm 19:1, "The heavens declare the glory of God; and the firmament sheweth his handywork."
Here is a site that has pictures of the Jewish practice of Kapparot. "Kapparot, which is from the same Hebrew root as Yom Kippur and literally means "atonements", is a custom which aims to awaken the drive toward repentance while engaging in charity on the eve of Judaism's central day of prayer. The practice of kapparot using live fowl entails the following: A male or female chicken is taken in hand, corresponding to the gender of the taker or family members on whose behalf they are performing the ritual. Psalm 107:17-20 and Job 33:23-24 are recited and the live bird is swung around the person's head three times. While swinging, the person recites the following three times: 'This be my substitute, my vicarious offering, my atonement. This cock (or hen) shall meet death, but I shall find a long and pleasant life of peace.'"
