The dosage is based on weight, not age. For fever and pain relief, the dosage is 25 - 50 mg/kg/day, given in four divided doses. For inflammation, the dose is 50 - 100 mg/kg/day in four divided doses. Doses in that higher range should be monitored by periodic salicylate levels.

The acute toxic dose for a toddler would be around 200 mg/kg. 

Because of the risk of Reye Syndrome, medications such as acetaminophen (Tylenol and others) have overtaken aspirin in popularity and safety.

If you gave the average 10 year old weighing 35 kg, one and a quarter adult aspirin or five baby aspirins, you would approach a relatively safe level of under 50 mg/kg. As stated earlier, there are better options using other drugs.