How do teachers use math?

It depends on what kind of math teacher you are

Elementary school- arithmetic, fractions, decimals, etc..

Middle school- basic algebra, geometry for some of the more advanced students

High school- pretty much anything, from basic algebra to I've even heard of Calc2 being taught in high school

Surely it depends on the syllabus set by the school's exam board?

The teacher does not set the course content but may have some freedom in planning the order of topics and time devoted to each throughout the School Year.