In Singapore, 16 would be the age for taking "O" levels (British system). If your kid has already passed that equivalent, he/she can move on to the Polytechnic (
http://www.moe.gov.sg/corporate/post_secondary.htm#poly) (couple of them around, Temasek Poly, Singapore Poly, Nanyang Poly, Ngee Ann Poly and Republic Poly). A three year course will lead you to a diploma in (accounting, engineering or business for example, a 3 month attachment (co-orp or apprenticeship if that's how you call it) is compulsory to graduate from this program. The school will arrange the company for the students to be attached to.
Alternatively, if your kid prefers to go the University, he/she can opt to go to the Junior College.
http://www2.moe.edu.sg/schinfo/
http://www.jcguide.org/ (Some of the language is Slingish (singaporean way of speaking, click on the left school logos to learn more)
Two years there will lead you to an "A" level cert and proceed on to the local university, NUS or NTU.
Your younger kid who is 8 years old will fit into the primary school. Primary School Leaving Education (PSLE) is taken at 12 years old before proceeding to a secondary school.