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Summer holidays are good times to get around to do things that seem to take a back seat during the hectic school year, so we thought that it would be nice to make some suggestions of things to do from the NRICH website. There are ideas for students, parents and teachers.

Each month NRICH creates a new issue on a given mathematical theme. In these issues there are many links between problems. Why not explore an issue that catches your interest and try one problem from each key stage. Depending on your own personal level of mathematical confidence you might be surprised just how accessible part of Stages 4 and 5 are and also how much depth is hidden within Stage
1 and 2 tasks.

September - Great problems for new classes

October - Patterns that lead to algebra and proof

November 2010 - How likely?

January 2011 - Farewell to Jenny Piggott

February 2011 - Thinking about solutions and solution methods

March 2011 - Actions on objects

May 2011 - Mathematics in Science and Technology

June 2011 - Mathematics in Sport

The starter problem selection contains a great list of problems to work through individually. Or, you could take a look at the weekly problems which are taken from UKMT papers. For more advanced students you could try to solve our university
preparation problems or the weekly challenges. Or you could try the 20 fascinating problems selected by members of the Ask NRICH community. We will be making more collections throughout next year. If you are registered then you
will be emailed updates about these.

A large part of mathematics is about working together and discussing ideas. Planning, working, thinking and sharing ideas together is a great thing today. You could form a mini-network amongst friends, other parents or colleagues. Some teachers have taken on the role of 'NRICH ambassadors' in schools to help colleagues find out about NRICH. If you are a teacher then you could try this out; if
you are a student then you could try out some problems for use in maths clubs next year; if you are a parent who wants to help your child with their mathematics then you could try to form a local network with other interested parents.

We think that NRICH problems really help to develop mathematical thinking and a love of mathematics. If you are a teacher then you might want to embed a few problems in your schemes of work. Our curriculum mapping documents have received lots of attention this year across all key stages; the problems on these documents all have 'teachers notes' tabs giving guidance on the use of the tasks in the classroom. If you are a parent then you will be able to use the curriculum mapping documents to help to find problems to enrich your child's mathematical experience; the problems are linked into normal curriculum headings so you should be able to find
relevant material based on their Key Stage. If you need help interpreting the maths jargon, you could ask your child's teacher or you could make a post asking for advice on Ask NRICH, our supportive discussion thread. If you are a student then you could try some problems from the year's work that you have just completed to
consolidate your learning or you could try material from the year ahead, to give yourself a good start to the next year in school.

This one is important! Find yourself a difficult problem and think about it over the course of the holidays. You can use Ask NRICH for hints and help whenever you like.

There are lots and lots of great maths books out there. You can find out about all sorts of wonderful things in mathematics. If something particularly intrigues you then you might well find some related NRICH problems by using the search by topic feature. Or you could just Google NRICH and whatever has caught your attention. If you don't
fancy reading a book you could read one of the many NRICH articles, or some of the articles on the Plus site.

If you haven't registered with us for updates or created a login for Ask NRICH and our blogs, then now is the time to do it! If you are a teacher then you can register to come to work with us on the STEM TI days next year. You can also let us know what you think: feedback is particularly useful to us at the moment as NRICH is developing fast in many exciting ways.

One thing about the rich tasks on offer with NRICH is that they offer great scope for extension with plenty of 'What if ..... ?' and 'Ah, I see....'. Moments. If you are feeling creative then you could try your hand at constructing your own maths tasks. This is a very rewarding activity!

This year we developed the weekly challenges: this are like mini-NRICH problems wrapped up with supporting links. You could try some of the challenges suggested in the celebration article or just go to the weekly challenge list and pick one or two which sound interesting.

Over the past year we have extended stemNRICH down to stages 3 and 4. stemNRICH - Advanced is roughly aimed at post-16; stemNRICH - core is roughly aimed at 11 to 16. If you browse around you will hopefully find many interesting treasures. You could set yourself the challenge of trying to solve a problem from
each of the different sections. Many have full solutions in case you get stuck, and be warned that you might just get hooked on mathematical biology, chemistry or physics!

If you are a student why not take on the role of teacher with a younger child? It is both good fun and also a great way to develop your own mathematics. You could use the curriculum mapping documents for Key Stages 1 to 5 or some of the special new tasks designed for children in early years foundation
stage. The problems on these documents have teachers notes detailing ways in which you might use the tasks.

This year we have started getting ourselves ready for mobile applications. If you know about post-16 maths you can check out our mathmo app. There will be more apps coming over the next year.

The world is full of mathematical structure: mathematics is everywhere. Even the most boring parts of summer holidays can be improved if you keep your eyes open for mathematical structures and symmetry!

We hope that you have a good summer break, and please to get in touch with any comments, queries or suggestions at enquiries.nrich@maths.org.