The basic purpose of flowers is sex.

Sex, as in the exchange of genetic material between two parents and the production of off-spring. Here we will look at the basic structure of a grass flower, the floret. Grass flowers that have both male and female flower parts are called perfect, but I prefer the term bisexual. Florets may be sterile (lacking both male and female flowers), male (stamens), female (pistil), or bisexual.

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this lovely drawing is by Agnes Chase, from her First Book of Grasses.

The female grass flower is a pistil, which is made up of the stigma, style, and ovary. The stigma is a feathery plume used to catch air-borne pollen, the style holds the stigmas up in the air and transports pollen to the ovary where it fertilizes the ovule.

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stigma

ovary

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The ovary matures into a seed, sometimes called a grain, caryopsis, or urticle. Technically, these are different, but to reduce the number of terms for you to deal with, I'll use the word seed for everything. The seed is made up of an embryo at the base and a starchy endosperm which is the food the developing plantlet will use to grow. The seed detaches from the plant, it leaves a scar called the hilum at the base of the seed.  

Now for the male flowers:

These are the stamens, which have two parts, the anther (which contains the pollen) and the filament, which is the thin stalk that bears the anther. Anthers release the pollen by splitting lengthwise or by little slits at the tips. The pollen becomes airborne, causing various kinds of excitement, including allergies in humans and fertilization of gametes in grasses.

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a word of warning about anthers. Some anthers fail to develop to maturity. These are sometimes called vestigial anthers, in which case the flower is effectively female. Bluegrasses (Poa species) are prone to playing around with male and female flowers on separate plants and sometimes you will find vestigial anthers in the female florets. 

Mature anthers are plump and often split open. Never use a slender, shriveled anther for a measurement in a key. It will lead you astray.

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The two structures that protect the flower parts and complete the floret are called the lemma and the palea. The lemma is the outer part and has an odd number of veins with one vein running down the center of the back. The base of the palea is inside the lemma. The palea always has two veins.