There are 13 types of frogs that live in Michigan:

most lay eggs in the spring, from which we first get tadpoles, which move on to become frogs (usually later in the summer). I pulled the following information off of Michigan's website:

The frog you might be talking about is the Northern Spring Peeper, whose eggs hatch very quickly, but the tadpoles still need to go through weeks of metamorphosis before becoming frogs.

Blanchard's Cricket Frog (Acris crepitans blanchardi)
-Breed from mid-May to mid-July. Transform into tadpoles in late summer.
Bull Frog (Rana catesbeiana)
-Breed from June-July. Tadpoles need 2 to 3 summers before becoming frogs.
Eastern American Toad (Bufo americanus americanus)
-Breed from April-May. Blackish tadpoles transform into toadlets in June or July.
Fowler's Toad (Bufo woodhousei fowleri)
-Breed from May-June. Tadpoles transform in mid to late summer.
Gray Tree Frog (Hyla versicolor and Hyla chrysoscelis)
-Breed in May. Transformation of tadpoles by mid to late summer.
Green Frog (Rana clamitans melanota)
-Breed from May-July, in permanent waters. Tadpoles often take two seasons to transform into frogs.
Mink Frog (Rana septentrionalis)
-Breed from June-July. Tadpoles may require more than one summer to become frogs.
Northern Leopard Frog (Rana pipiens)
-Breed from April-early May. Tadpoles transform into frogs by mid summer.
Northern Spring Peeper (Pseudacris crucifer crucifer)
-Eggs may hatch within four days or may take up to two weeks during cooler periods. After another two to three months, tadpoles are fully transformed.
Pickerel Frog (Rana palustris)
-Breed from April-May. Tadpoles transform into frogs in late summer.
Western Chorus Frog (Pseudacris triseriata triseriata)
-Breed from March-May. Tadpoles transform into frogs in 2 to 3 months.
Wood Frog (Rana sylvatica)
-Breed from March-April. Tadpoles will transform about 2 months later