Due to the fact that our cruise line wanted to charge nearly £120 per day for the privilege of unlimited Wi-Fi, I've been without Internet for most of the last week. It's been incredibly relaxing, but I do feel like I've missed a lot on Twitter - I had far too many notifications when I logged in yesterday, and I have a lot of reading to catch up on with all the other#summerblogchallenge posts. I've also gained about thirty new followers this week through tweeting absolutely nothing, which might suggest that I do better when I keep my mouth shut...

I've now managed to post all of the photos from my challenge; here's a quick index:

1. Infinite mirrors
2. Archways
3. Set with playing cards
4. It's all Greek to me...
5. Tiling patterns
6. Triangular bridge
7. More arches in Ancona

There were lots more Roman arches in Ancona, but I also spotted this slightly differently shaped one in a piece of very old wall. A quick Google has told me that this is probably either a lancet arch or an equilateral arch, and I'm going to find out which later by measuring it!

Thursday took us to Dubrovnik, where we played "spot the Game of Thrones filming locations" and tried to avoid melting in the heat. On the way out of the port, I spotted the Franjo Tudman bridge, which is pure geometry in action.

Another day aboard with nowhere to go, hence this slightly tenuous floor tiling pattern - I thought it was quite pretty though!

Today we visited an active volcano near Santorini, which was all very interesting, but had limited opportunities for taking mathematical photos. The best I could find today were some Greek letters on a can of beer and some pretty reflections in the water when we arrived on Mykonos in the evening.

Monday was a day at sea, with not much to do except lounge around in the sun. We retreated to one of the bars in the afternoon when it got too hot, and decided to attempt to play Set with playing cards.

Walking around Split in Croatia gave me lots of opportunities to spot semi-circular or Roman arches - I may turn these into a couple of short problems for starters. There's a good one on NRich already!

As we spent the day driving to Manchester, then flying to Munich and finally on to Venice, then getting a coach to the port, then doing our lifeboat safety drill, I had very little time to spot any maths. However, I decided that the infinite mirrored lifts onboard our boat were definitely mathematical enough to become my first photo in the challenge!

In case you've missed the hashtag #chineseschool on Twitter and the blogs popping up everywhere at the moment, the BBC aired the first programme in a new three-part series on Wednesday night. Titled "Are Our Kids Tough Enough? Chinese School", the programme follows five Chinese teachers as they attempt to teach a group of British pupils using Chinese methodology.

I wrote a post a while back about my philosophy on starters, so thought I'd supplement it with a post about great websites for no-fuss five-minute activities. Most of the starters on these sites require very little or no preparation, so can be used off the cuff. So, in no particular order, here are my top sites for starters:

I wrote a post a couple of weeks ago about the importance of trust, so I thought I'd follow that up today with another tip for NQTs. It's something I need to keep working on myself, although I am getting better - last academic year, I hit the Autumn term exhaustion wall about three weeks before Christmas, as opposed to a week after October half term.

I spent a bit of time playing catch-up with all the #summerblogchallenge posts I'd missed from everyone else today and spotted @DrBennison's Twitter History post. I've seen a couple more Twitter Wordles recently, and quite liked this idea, so thought I'd have a play in today's post.

Here's my Twitter Wordle:

I love how big both #mathschat and #mathsTLP appear; I'm obviously using those a lot, which probably also explains why both @mathsjem and @solvemymaths feature so highly!

I'm also quite enjoying the fact that there are so many positive words on there - I may use this to motivate myself in September when I'm getting the post-holiday blues.

I mentioned a while ago that I was going to do a #summer10 post at some point; despite the fact that I'm two weeks into my holiday, I've pretty much been living and breathing wedding plans and celebrations for most of those, and I realised this morning that I still have nearly five weeks of holiday left, which is incredibly exciting. So here's my #summer10, the ten things I'd like to achieve in the holiday I have left...

Another quick one today to follow on from yesterday's post about the best maths in action I've ever seen, with the promise that more relevant blogging will resume from tomorrow!

Here are a couple of pics of the "scale model" in action...

Another quick post today as I am/will be busy preparing for part two of the wedding celebrations and again am/will be nowhere near a computer (I'm still struggling with tenses - see yesterday's post!).

You know those people that seem to post all the time on Twitter? I've discovered their secret - for me, it was a bit of a necessity if I'm going to manage the #summerblogchallenge, as I got married yesterday and currently have a houseful of people continuing the celebrations until at least Saturday**.

It's a handy little site called Twuffer - you sign up for free with your Twitter account, then simply schedule a Tweet in advance. If you want to schedule a link to a blog post that's not live yet (as I've been doing), you might need a little jiggery-pokery with the url of your post, but it's fairly simple to work out.

I'll admit to having to cheat a little bit on this challenge; this post is one of the few I had to write ahead of time and schedule to post later. I have a good excuse - I'm getting married today, and I imagine that, even though my fiance is very understanding about the amount of time and energy I put into teaching, even he would object if I blogged during our wedding day.

​While I've been organising over the summer, I realised that my resource collection has grown exponentially again this year. I made the move to storing resources electronically this year, which has meant I'm drowning in far fewer bits of paper and it's much easier to find the worksheet I want than rifling through folders. Despite this, I still have my entire cupboard under the stairs full of bits and pieces that need transferring or updating - I think it's going to be an endless task.

Finding, developing and trying new resources is one of my favourite parts of teaching, which is one of the reasons I started the resources pages on my site - it's far easier to link to a page at home, then find that again at school, rather than email things to myself, which I then forget about the following year. As above, this project is still unfinished, but I hope to put a big dent in it over the next few weeks. But what makes a good resource?

Starters can be a contentious issue; the term "starter" is a hangover from the days of three-part lessons in bite-size chunks, which seem to have fallen from vogue now. However, they are still a key part of my teaching, and today's SBPC looks at why.

In my mind, my lesson "starters" fall into three categories, and they're not mutually exclusive. Sometimes it's appropriate to have a couple of "starter" activities (I'm dropping the quote marks now because I'm irritating myself). I once had a lesson starter that went on for the entire lesson, as it became painfully apparent that the class had completely forgotten to solve simultaneous equations, so my quick prior knowledge check turned into an off-the-cuff revision session.

At the most recent Maths Conference in London, I spent one session sitting at a table with three NQTs, and was asked by one of them what my "top tips" were for surviving their NQT year. For a bit of context, I've now been teaching for six years if you include my GTP year, which I do, as I was thrown in the deep end with my own classes and found that year very challenging. As a result, I found my NQT year relatively straightforward, as I wasn't in the position that many new teachers are: suddenly having to take on sole responsibility for the classes in front of me.

It still baffles me a little bit that people would ask me for advice, as I still consider myself a fairly "new" teacher, but I did my best with a few bits of advice. There are far more comprehensive guides on the Internet - I'd recommend checking out TM4T's NQT guide, which has some fantastic tips for time management. Furthermore, I found it much more useful talking to colleagues working in my school for advice on how they manage day-to-day teaching, as every setting is different, and every school will have different policies and procedures that need to be followed.

Regardless, I thought a small series of "Tips for NQTs" might be a good use of some of my SBPC posts, if only to remind myself of the fundamentals of my teaching practice before September. Today's is probably my most important tip: