OPErations Workshop

Why teach number operations? Growing in fluency with the four operations allows children to think about the underlying maths, as opposed to the procedure of adding or subtracting. Being able to use number operations appropriately is a life skill. Becoming competent with these will prepare children for secondary school and beyond. The aim is that children use mental methods where appropriate, but for calculations they cannot do in their heads, to use efficient written methods confidently. By the end of Y6 students should be able to use all 4 operations effectively and use methods for calculating with fractions decimals and percentages.

What is more important? Written methods? Mental calculation?

Different methods are appropriate for different circumstances. In order to become competent at maths, it is important to be able to choose the best method. We need to encourage children to look first at the problem, and then decide which method: pictures, jottings, mental calculations, or structured recording. This method might not necessarily be a formal written method, however mental strategies play an important role, whichever is chosen. The methods that might be appropriate develop and change through primary:

If we push children to use written methods too early, it can result in a lack of mathematical understanding. So, it is important to help children develop their mathematical thinking and understanding, at the same time as giving them a range of strategies to solve problems. What is the misunderstanding here? 2 4 3 9 5 1 3 +

Before attempting any problem, children should be encouraged to ask themselves the following questions:

What are the four operations? With your child, can you name the Four Operations? Can you give examples of what each one is?

Addition – Subtraction – Multiplication - Division Children learn these operations by first using real objects to help structure their thinking. Once they have a good understanding of how to apply these in real life situations, they begin to represent the concrete objects using pictures or other representations. Then children can begin to transition to using numbers to solve these problems. What does this look like?

You try: Can 11 be shared equally between 3? Ask your child if there are any physical objects that might help them solve this problem. Ask your child if there are any drawings/representations that they could make to help solve this problem. Solving problems in this way helps to expose the deeper thinking that children have around mathematical concepts. It is a small step to replace representations with numbers and symbols, but a bigger step to go back and build understanding for a child who is not confident using numerical methods.

You Try Discuss with your child the methods they know for approaching these problems: 4232 x 2 234 x 21 222 ÷ 2 234 ÷ 2

How can I help? If you are stuck, ask your child to explain the method they used at school. Use the resource uploaded on the blog to help support you with this. If children are stuck, encourage them to go back to more concrete representations or objects. Ask questions like can you draw it? What is the question asking you to do? For children to become truly fluent, they must be secure in their number facts and times tables. Take every opportunity to practice! Even 10 minutes a day helps! Take an interest! Talk to your children about the maths they have learned in school, and see if they can teach you the methods they have learned. Research shows that children who feel that their parents are interested in their school work achieve better.

What is ‘Maths Mastery?’ Put simply: Encouraging a deeper understanding of maths. Involves a set of key principles: Success for all - Every child can enjoy and succeed in mathematics as long as they are given the appropriate learning opportunities. A growth mindset enables pupils to develop resilience and confidence. Problem-solving - Enabling learners to solve new problems in unfamiliar contexts is the ultimate aim of mathematics education. Identifying, applying and connecting ideas enables pupils to tackle new and more complex problems. Mathematical language - Mathematical language strengthens conceptual understanding by enabling pupils to explain and reason. This must be carefully introduced and reinforced through frequent discussion to ensure it is meaningfully understood. Deeper understanding - Pupils must be given time and opportunities to fully explore mathematical concepts. The challenge comes from investigating ideas in new and complex ways – rather than accelerating through new topics. Mathematical thinking - Successful mathematicians are known to develop mathematical ‘habits of mind’. To encourage this, we must support pupils to be systematic, generalise and seek out patterns. Questioning is a key element of this. Multiple representations - Objects, pictures, numbers and symbols enable pupils to represent ideas and make connections in different ways. This develops understanding and problem solving skills – while making lessons engaging and fun.

“I’m really clever. Maths is easy.” Do either of the following statements sound familiar? Do you think these are good ways to think about your learning?  Talk to your children. “I’m no good at maths.” “I’m really clever. Maths is easy.”

Success for All Both statements on the prior slide are examples of “fixed mindsets”. They both encourage the idea that you are always ’good’ or ‘bad’ at something, and that this can never change. Studies have shown that praising children for ‘being clever’ encourages the idea that a child has been born with a gift or special brain – this can make it devastating when that child comes across challenges, later on and can encourage children to slack off. Instead, we should praise children for working hard. This nudges children towards valuing hard work, as opposed to innate talent. As teachers and parents we need reinforce an expectation that all pupils are capable of achieving high standards in mathematics. Developing a growth mindset is useful when encountering problems in any aspect of life!

Problem Solving One of the core reasons to learn maths is to be able to solve problems that apply in the real world…. Being able to subtract accurately is useless if you don’t know that you have to subtract to work out how much change you get at the shop, or how much time you have left to get to work! Learning number facts, times tables and maths operations is really important, as it creates fluency, which makes maths so much easier. However, children need the opportunity to apply these skills in a variety of contexts…. Can you think of any ways that you could give children experience in problem solving and in real life maths at home?

Deeper Understanding When developing mathematicians it is important to enable them to make connections rather than skipping forward topics. Rich tasks, not rushing! Simple concepts should be presented in challenging ways, to extend thinking. Have a go at these problems: Is the result the same for any odd numbers? Is there a pattern? Can you prove it?

Mathematical Thinking The thinking behind maths is as important as the procedures of calculation. To develop into more competent mathematical thinkers, children need to be presented with high level questions. The sorts of questions that children can be asked every day to develop their ability to reason include: What do you notice? True or false? Can you give another example of…? Can you explain how you….? Can you spot the error here? What is the pattern here? Can you convince me/prove that this is true? Why?

HOW TO HELP! Be a maths enthusiast! Get them to talk about the maths they have done each day, and explain it! Support them through practice with memory aspects of maths Vocabulary Facts Procedures Encourage them to make connections between different areas of maths and real life. Wherever you are, you can be practicing maths! Keep it simple! Maths isn’t always about ‘big’ numbers and times tables – it is about being able to apply concepts to different situations, problem solve, and find different strategies to check. Days, calculating, positional language, shape, problem solving, counting, time, money, measure (weight, length and capacity)

Useful websites www.nrich.maths.org  Excellent maths investigations www.mathsisfun.com  Lots of definitions and exercises to help with tricky concepts, AND a great maths puzzles section https://www.ncetm.org.uk/resources/46689  Some activities to help to teach to a mastery level http://www.mathsphere.co.uk/fun/#mathspuzzles  Good range of puzzles www.kahoot.it  Set up maths quizzes to challenge your child, and track their score