What mathematics do students need before high school?

I was at my master's summer school unit and caught up with my high school mathematics teacher. We started talking about what was needed before starting high school in mathematics.

I knew the year 7 teachers from her feeder schools (albeit a few years ago I had done my practicums at both schools). The year 7 teachers were proactive teachers, and had started topics like volume and Pythagoras' theorem. In my naievity, I had thought this a good thing.

She quickly set me straight and said that these were easy things to teach if the basics were in place. Without the basics they were quickly forgotten.

So I started thinking to myself, what were the basics?

1. Did they have one-to-one number correspondence (could the children identify 1 with one of something, 2 as two of something so on and so forth)?
2. Could the children read the time?
3. Did children understand their four operations?
4. Did they know their tables?
5. Could they add and subtract one and two digits without a calculator?
6. Could they recognise basic units of measure?
7. Could they manage small amounts of money?
8. Did they understand place value?
9. Were students aware of order of operations?
10. Can they recognise basic shapes?
11. Can they identify uses of maths in their environment?

By the time I arrived at 8, I quickly understood her meaning. If students were able to do pythagoras, but were unable to recognise 4 lots of something was a multiplication sum then time was probably better spent sorting out operations.

These topics are easily tested by parents and school instruction can be complemented by a number of readily available books and websites.