It is an 11-fold increase with four attacks in 2014 compared to 44 the next year, including January 2016.
The change in tactics reflects the loss of territory in Nigeria by the group.
The seven-year insurgency, which has mainly affected north-eastern Nigeria as well as its neighbours around Lake Chad, has left some 17,000 people dead.
Unicef says up to 1.3 million children have been forced from their homes across four countries: Cameroon, Chad, Nigeria and Niger.
More on Boko Haram`s teenage bombers:
The UN report has been released as Nigeria approaches the second anniversary of the kidnapping by Boko Haram of more than 200 girls from their boarding school in the Nigerian town of Chibok.
Their abduction sparked the global campaign Bring Back Our Girls, but none of the girls have yet been found.
The report, Beyond Chibok, says that boys abducted and recruited into Boko Haram`s ranks are forced to attack their own families to demonstrate their loyalty.
Girls are exposed to severe abuse including sexual violence and forced marriage to fighters.
The girls who are used for bombings are often drugged and then explosives are strapped to their bodies.
According to the report, Cameroon has the highest number of child suicide attacks, involving children who are as young as eight.
Boko Haram, which means "Western education is forbidden", has often targeted schools during its insurgency.
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