Host, breaking over the chalice

In three places in the Roman Missal and the GIRM (all quotes are from the 2011 USCCB official English translation), it mentions breaking the host over the paten. The reason for this is most likely to prevent particles of the Body of Christ from scattering and being lost. It is an act of respect for the Eucharist. 

 

Order of Mass (pg. 667 or pg. 665 in the pdf) #129: 

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"then he [the priest] takes the host, breaks it over the paten, and places a small piece in the chalice [...]"

 

GIRM, Chapter IV, #155:

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"After this, the Priest takes the host, breaks it over the paten [....]."

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GIRM, Chapter IV, #267:

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"Then, while he says the Agnus Dei (Lamb of God) with the minister, the Priest breaks the host over the paten."