Published September 2010,September 2012,February 2011.

What does your first lesson with a new class look like? Mine always features a paired games activity. You can tell so much from observing the children playing a simple game. When the whole class is playing the same (or very similar) game, you and any support staff are able to focus on observing the children and getting a feel for their understanding of, and attitude to, mathematics.

Having made myself a class observation list, I set up the headings so that I only need to add a quick tick or cross, though I do leave room for a comment too. The choice of game depends on the year group, but needs to be a fairly straightforward one, leaving you free to circulate and listen in.

After a quick warm up, explain the game and allow the children to pair up with whoever they wish. Put copies of the game with sufficient dice and counters in the middle of the tables so that the children have to organise themselves.

Use any simple track game, for example Incey Wincey Spider or Tug of War. If the track is numbered and has optional routes so that children have to make decisions, so much the better. Look out for children who:

- Organise themselves
- Take turns
- Move the correct number of spaces
- Include the space the player is on as the beginning of the count
- Follow the numbers
- Can play with a variety of children
- Could be potential talk partners

Ask questions about what number the player will land on if they throw a 2, or 5 etc. Listen out for allegations of cheating. What has the accused done? What is the accuser saying has happened? Allegations and responses sometimes reveal misunderstandings about how to play the game.

It just has to be snakes and ladders. Make sure the children know how to play - more and more children do not. Play in pairs. Look out for the same skills as above, but focus on whether or not the children follow the numbers correctly, particularly at the end of each row. You can bring in higher-order thinking skills by throwing two dice: children can choose which dice they use, or
they could add/subtract the numbers on the dice so that decision-making is also involved. This is great played as a knockout contest to find the class Snakes and Ladders Champion. As players are knocked out and watch new games, listen to their comments. Are they supportive of each other? Do they encourage, remind and advise? Listen out for allegations of cheating as above.

There are plenty of games on NRICH to give you ideas, for example: Strike It Out, First Connect Three, Got It! ... . Alternatively, you could download or access a version of 'Who wants to be a millionaire?' from the internet. Board
games such as 'Trilemma', 'What's the Point?', 'Nubble!' or 'Triolet', my favourite, are useful. Most are four-player games so you do not need many copies for a class set. Alternatively, some have computer versions. Pool resources from other classes and check out which games are on your school system. Look out for all the characteristics mentioned above, as well as any knowledge needed to play
the game. 'What's the point?' uses decimals, fractions and percentages, whilst 'Trilemma' includes questions about prime numbers, factors, square numbers and square roots and more. Watch out for those who need support. Do they receive help from the other players?

My second session usually involves a digit game. Can the children play with numbers? Use their first solution to find others? Explore and test their ideas? I usually specify that they must work with someone they did not work with yesterday so that I can see how other pairings and groupings work.

After you have explored the children's understanding of digits, give a set of digit cards per pair and ask them to make 10. Demonstrate first. They must use the one and the zero to make ten, a good test in itself, then explore ways of solving the calculation. Provide sticks of 10 interlocking cubes for support. Challenge the more able by including a third number to add to make 10 or by
moving the calculation around to make 10 - ? = ? or by removing the stipulation that the total must be 10.

Look out for children who can:

- Organise themselves
- Take turns
- Discuss solutions
- Record their solutions clearly
- Use the previous solution to make a new one

Children who worked well together on both days could be potential talk partners.

Play 'The Digit Game' as a starter. With one set of digit cards, challenge the class to beat you. You will need to decide whether you are playing to make the highest or lowest numbers. Pick a digit out of a bag without looking and decide where to place it. Verbalise your thinking to model the process for the children. Once placed, digits cannot be moved! It might be better to make
three-digit numbers in Year 2, challenging those who are working well to move on to four digits. Who won? How much did they win by? What is the difference between the winning number and the highest number possible? Did the placed digits make the highest/lowest number possible with those digits? Could they be rearranged to make a higher/lower number? There are many questions you can ask and the
answers tell you a great deal about the children's understanding of and facility with numbers.

The children can then play in pairs, making the highest number, lowest number, nearest to 5000 etc. Ask them to come up with their own versions for others to try. At the end of the session, discuss who liked which particular version and why. Have a look at NRICH's version of this game, Nice and Nasty, which takes the ideas a bit
further.

Alternatively, challenge them to find two two-digit numbers to add together to make 100 or even two three-digit numbers to make 1000. You have to allow the 100 or 1000 to be written without using any of the digits provided since they would not have enough zeros to make it!

After a quick warm-up and demonstration, give each pair a set of digit cards and ask them to solve one or all of the following digit problems. Allow them to choose which one to start work on, but allow them to change if they feel they have found all possible solutions or are getting frustrated.

What if the total was a four digit number?

Change any of the operation signs and explore further. Alternatively, ask the children to write a set of five questions which use up all the digits. Can the rest of the class solve these puzzles? You may also like to look at Dicey Operations.

All of these activities will tell you so much about the children's understanding of number and their attitude to mathematics. You will be able to see how flexible they are, whether or not they can explore and persevere and you will get a good idea of who works well with whom. Then you have the whole year ahead to investigate and discover mathematics together!

References and resources:

Orchard Toys Incey Winsey Spider http://www.orchardtoys.com/products/insey-winsey-spider/

'Who wants to be a millionaire?' http://www.woodlands-junior.kent.sch.uk/maths/mathionaire

Who want's to be a Mathionaire? http://www.superteachertools.com/millionaire/

'Trilemma' http://www.greenboardgames.com/store/index.php?route=product/product&filter_name=Trilemma&product_id=279

Electronic version http://www.keen2learn.co.uk/product/Trilemma.php

'What's the Point?' http://www.keen2learn.co.uk/product/What-s-The-Point.php

Electronic version http://www.virtualimage.co.uk/html/nubble__deluxe.html

'Who wants to be a millionaire?' http://www.woodlands-junior.kent.sch.uk/maths/mathionaire

Who want's to be a Mathionaire? http://www.superteachertools.com/millionaire/

'Trilemma' http://www.greenboardgames.com/store/index.php?route=product/product&filter_name=Trilemma&product_id=279

Electronic version http://www.keen2learn.co.uk/product/Trilemma.php

'What's the Point?' http://www.keen2learn.co.uk/product/What-s-The-Point.php

Electronic version http://www.virtualimage.co.uk/html/nubble__deluxe.html