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Activity Networks and Critical Paths

When I first came to teach Activity Networks and Critical Paths I couldn’t really remember being taught them. I knew I had studied critical path analysis, but my memories of them were no less vague than that. In order to teach them I refreshed my memory using an edexcel textbook, as it was the board we used, and I got to grips with the “on arc” method.


This year I’ve been teaching a class as part of the core maths early adopters programme and we have selected the AQA qualification. For our optional content we chose the critical path option (option 2b). When browsing the mark scheme for the specimen paper I saw this:


Apparently the “on node” method. When I first looked at it it seemed strange. I had a good think about it and once I’d got my head past the fact that the “late time” was the latest an activity could finish, rather than the latest an activity could start – as in the “on arc” method, I think I actually prefer it.

The thing my students find hardest every year is drawing an activity network, especially where dummies are involved, and it seemed to me that this “on node” method would be much easier in this respect, and that dummies wouldn’t need to be considered. I did worry that actually identifying critical activities, and hence the critical path, might be a little more difficult, but I still didn’t think it would be too taxing.

So when I came to teach my year 12 core maths class activity Networks I went with this “on node” method. I’ve never known a class get the hang of drawing activity networks so quickly, and as this was a core maths class, rather than an a level class, their GCSE grades are much lower – mainly Cs compared to mainly As.

They also didn’t have a problem with the early and late times or identifying critical activities. I much prefer this method.

It got me thinking about the validity of each method and whether either would be allowable in an exam. I feel that both methods are valid and that we should be teaching how to solve these problems using maths, so each method should be allowable, but I’m not sure whether the exam boards agree.

Close inspection of the specimen mark scheme for AQA core maths paper 2b certainly implies that either method is allowable:


However a look at the Edexcel markscheme doesn’t:


If you look at the question paper and answer book there is in fact the heavy implication that only one method will suffice, as there is an explicit mention of dummies and the network is already set up for this method to be filled in:



Do you have a strong preference to either method? Do you think exam boards should be prescribing which method to use? Do you have any further insights into which method the other exam boards favour or prescribe? If so, I’d love to hear about it.

  1. Mark Wilson
    March 12, 2016 at 3:50 pm

    Hi, I don’t/have never taught this but I will be next year. When I learnt this I learnt both methods and I think that the “on node” method makes perfect sense. I don’t think boards should prescribe methods at all in any situation, problem solving is just that. I will be investigating this further, we do MEI by the way

    • March 12, 2016 at 4:36 pm

      I’m in agreement there. I had a discussion on twitter earlier with someone who does MEI and he said they prescribed the on arc method.

  1. March 26, 2016 at 9:26 am

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