Matt:

A way to decide the most important task would be to determine most essential concept(s) of a unit to be studied. Identifying the essential concepts brings focus to the abstract which your learners must master.

I have observed many math teachers and found that the most important teaching point is an introduction that will surprise students by its connection to mathematics. Finding even a remote but visual link to the topic can both generate student interest and facilitate teaching of even the most challenging topics. 

Students like to be able to take something concrete away from their lessons let the connection between the task and your students be relevant to them to achieve successful learning. Whilst there are many excellent resources available they still need to be tailored to meet the needs of the specific audience.

I agree with Maryam. The key point is often relevance particularly in lower secondary schol pupils who are beginning to question the relevance of Mathematics to their future and the often repeated mantra - everything is Maths based - doesn´t always convince them. Real world problems, not just those in textbooks, particularly when explained in Maths terms can sometimes help this choice of teaching tasks and the aspects whihc take the fore.

Many thanks for these replies.  I can see how an early element of surprise can act as a 'hook', and successful in terms of motivating students.  This might be designed to exploit cognitive conflict between the structure of a particular mathematical situation and what we know / anticipate students might initially think, what Bruner describes as a 'disturbance', which needs resolution.  

This situates the key teaching point well; given two, three different hooks which a teacher might use, how do we discriminate between them?  How do we perceive the mathematical value in a given activity, approach?  

The first thing is the teacher must have a conceptual understanding of the task. Next, is to identify the key concepts in the task and explain them at the level of the students' understanding. A number of strategies or approaches may be employed in the explanation as appropriate. It should be stressed that the teacher's knowledge of the subject-matter plays an important role in this activity.

Your title mentions secondary teachers but this might provide some interesting information:

Son, J. W., & Kim, O. K. (2015). Teachers’ selection and enactment of mathematical problems from textbooks. Mathematics Education Research Journal, 1-28.

Have you already heard about Variationt Theory and Learning Studies, which are done in Sweden and Hong Kong? They can help to identify these important teaching points.

 Thanks again to colleagues for your answers.  Michele - that paper is very relevant to my interest, thank you so much for signposting it, it will make a real difference. 

Susanne, thank you also.  Yes I have read some Marton, and also Runesson on Variation Theory and Learning Study, but should read more.  I have found articles in this field which identify a 'critical aspect', and then detail building a learning study to that end, but less on how we might identify the implied critical aspects within an existing activity.  My interest is in teachers' perception and appreciation of key mathematical concepts in activities, and whether it is possible to develop this.  

Previous student performance on related mathematics tasks often times drives the decision-making.

Just to add to the mix. We are often obsessed with the start of the learning story. What will we get out of this, what is the hook that will get them in? These are great and not to be belittled. However, how often do people look at an activity at the END and ask what was the important bit of that? What was the learning intention? I always say there are 3 things we tried to do today and then stand back and be amazed at what the students think was important. Sometimes they are looking at an angle that I totally am not and many times they are focussed on something and want an "A HA" or lightbulb moment. It is actually fun, occasionally silly but always enlightening.