Each is a 5-10 minute starter.
Watch as you and your class discover and explore the fundamental structures of mathematical calculation.
One of the most surprising things which reliably emerged with my classes was their insight into reciprocals.
They're always looking for short cuts so they rapidly spot the links in the results for division:
4 and 1/4
3 and 1/3
2/5 and 5/2
7 and 1/7
They're reciprocal pairs. Even though they only get half a mark for a second quotient calculated in this way, they still spot the pattern. So my students have a strong familiarity with reciprocal pairs and an insight into their relevance for multiplication and division from early in year 7 (age 11) when I first teach them. I'm sure that younger students could cope with this too.
It's so easy and natural but I've never seen this understanding in other classrooms. Usually in the UK reciprocals are taught as a disconnected entity at GCSE level or are found in algorithms, again without their connected context. Yet a structural understanding of them is clearly there in the Chinese classrooms described by Liping Ma. Chinese teachers use them fluently and flexibly for calculation.
Of course I'm not saying that the Chinese teachers taught this in the way I did. I'm just trying to convince teachers that it is possible to replicate significant aspects of the Chinese teaching strategies with classes of students and teachers who have never thought structurally about calculations before. Oh and I always taught in tough schools. No docile classes for me. And I found that students were more settled if I taught them in this way. It suited them to focus on structures rather than to learn recipes. They felt more in control of what they were doing and their education became more relevant to them. They weren't good at 'learning recipes'.
There's more to come....