This is a brief summary of some of the most important maths concepts to be taught in Year 3 by way of challenges and investigations. 1. Choosing appropriate number operations An important aspect of Using and Applying Maths is concerned with children choosing and using the most appropriate number operations to answer questions and solve problems. A good way to introduce this is to ask children to make up number stories from given maths statements, using all four rules. In this way children can show that they understand the meaning of the number sentences and can put them into a real context. When asking which number operation is best, activities can arise easily from practical work and everyday situations and can be answered orally. Children should be starting to make more complex, and more interesting, number stories corresponding to the sums. Another activity, following on from year 2, is a where a sign has been omitted or replaced by a  star or shape .  This again makes children think what is happening in the sum and is a good introduction into algebra. 2. Open and closed questions Solving problems and investigating continue in three year. Some of these problems are ‘closed’, in other words they only have one, or a few possible answers. Others are ‘open’ and can have many possible answers. The open questions are ideal for assessing how well children use their knowledge and how imaginative they can be. Exercises such as the magic triangle look closed to begin with but there is plenty of potential to change totals or even change the numbers that are put in. Because of the open nature of most of these problems we have not included answers for the majority – it is an excellent idea for children to check both their own and other children’s solutions to see if they fit the criteria. 3. Working in a systematic way A key feature of this work is that children should become more systematic in their approach, checking as they go and looking for answers which are the same. They should be able to talk about their work, especially about how they are tackling the investigation, what the rules are and any findings they have. Children should be given the opportunity to give examples to match statements. It should help them clarify some of the basic concepts, such as an even number and an odd number will always add up to an odd number etc. It also re-inforces much of the mathematical language used so far, such as multiple, odd, even, right angle etc. 4.  Solving problems In year 3 children are expected to use any of the four operations to solve ‘story’ problems. Once again, these problems can be divided into one step and two step problems – the latter meaning that two calculations have to be done in order to get the answer. Children should explain orally how they set about answering the questions and then move on to written methods using simple number sentences. There are also similar modules on money, time and measurement. Money continues to be an important area of work in year 3, especially as a means of re-enforcing place value. Working with coins should remain a priority, and children will begin to give change for amounts up to £1. An emphasis is made on converting pounds to pence and vice versa. Especially important is to recognise the need to place a nought in the ten pence column when converting amounts such as 203p into pounds. When working out change, 'counting on' from the units should be encouraged, eg:    Change from £1 when spending 67p 3p makes 70p,     add another 30p to the 70p to make 100p:   answer 33p Note: Working in this way should avoid the all too common erroneous answer of 43p, which is reached by adding 40 to 60 and then a further 3 to the 7 to make 10 (in reality this comes to 110p) Go to Year 3 Challenges: Using and Applying Maths