Helping your child make good progress in mathematics Brightwalton Parents Meeting January 2015

What do we want for our children? they enjoy mathematics they find mathematics interesting and challenging they want to continue to study mathematics they see mathematics as relevant to their lives – a life skill they are competent and confident mathematicians NB Appear on click. 1.Want them to enjoy learning in maths, learning should be enjoyable, should build self-esteem and motivation to learn more. A maths lesson every day – need to enjoy it 2 maths is a vast subject – there should be something to interest everyone in interviews many children tell us that they like maths because it is challenging 3 children will be studying mats for a long time – need to want to do this 4 a purpose for learning is very powerful 5 confidence key Would anyone like to add anything?

What does the new mathematics curriculum want for our children? The national curriculum for mathematics aims to ensure that all pupils: become fluent in the fundamentals of mathematics, including through varied and frequent practice with increasingly complex problems over time, so that pupils have conceptual understanding and are able to recall and apply their knowledge rapidly and accurately to problems reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language can solve problems by applying their mathematics to a variety of routine and non-routine problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions.

NC key messages - making connections ‘ ……….pupils should make rich connections across mathematical ideas to develop fluency, mathematical reasoning and competence in solving increasingly sophisticated problems. They should also apply their mathematical knowledge to science and other subjects.’ Within maths lessons and across the curriculum

NC key messages - mathematical language The quality and variety of language that pupils hear and speak are key factors in developing their mathematical vocabulary and presenting a mathematical justification, argument or proof. They must be assisted in making their thinking clear to themselves as well as others and teachers should ensure that pupils build secure foundations by using discussion to probe and remedy their misconceptions.

Ofsted: In the best schools.... ...problem solving and investigative skills... were at the heart of learning mathematics.

If you would like to have a go at this , you have about 5 minutes – if you don’t, don’t worry. Don’t do it on your own –have ago as a group. It’s not about getting the right answers – it’s about having a go, enjoying the challenge – all the things on slide 1. Which year group might tackle this problem – actually matches well with NC expectations for Y4. Recall multiplication and division facts to 12 x 12 Mulitply by 0 and 1 Solve problems involving multiplying

What problem solving skills did you use? apply the mathematics you know in a new context? identify relevant information in the problem? find a starting point? decide what mathematics and resources to use? overcome difficulties/ try different approaches? work in a methodical or systematic way? check your solution? There’s a lot of choice and decision making and therefore a lot of independence in problem solving – this is where the best assessment information can be gathered. Not handed to pupils on a plate – they need to think and work hard.

Did you use the language of reasoning? It could be ... because ... It cannot be ... because ... It will not work because ... It will work when ... It will only work if ... If ... then ... Since ... is true, ... must also be true Since ... is true, it follows that ... In that case ... Therefore ...

Ofsted: In the best schools……. Pupils of all ages and abilities tackled varied questions and problems, showing a preparedness to grapple with challenges, and explaining their reasoning with confidence.

Developing conceptual understanding – a multi-sensory approach doing maths concrete resources language symbols images seeing visualising understanding the abstract knowing the conventions This is what teachers consider when planning work in maths – a rich experience in which pupils see visual images to support internal visualisation, do – handle practical objects, have hands-on experiences and talk – mathematical dialogue. listening understanding and use of mathematical language speaking - articulating thinking

10 + = 2 5 8 addition concrete resources language symbols images sum plus equals This is what it might look like – Y1/Y2 Symbols – abstract – need to be underpinned by a mental image. If you can visualise – internalise the models and images you have seen and handled – you can understand. Hopefully this slide suggests rich learning experiences for children in maths active learning independence choices/decisions communicating reasoning questioning thinking ‘hands-on’ add add together more total

The importance of visualisation If you can visualise something, it is a good indication that you understand it. Children who struggle with mathematics often have little or no mental imagery to draw on. Mental imagery is built up by regularly seeing and discussing visual images.

Number line The empty number line is a powerful model for developing children’s calculation strategies and developing their understanding. Draw yourself a number line like this one and mark 60 on it – think about the number knowledge you drew on to make your decision, tell the person next to you how you worked out where it was. Where would you place 5. 97 etc. 100

Looking at the calculation and making a choice 103 – 98 3004 – 2996 84 - 7 We want children to be able to visualise the numberline stretching on for ever. Then they are in a position to make good calculation choices.

Building mental fluency – making good calculation choices 61 – 4 61 – 41 61 – 32 61 – 58 61 – 43 Calculations presented horizontally – have a go. Children will look at each calculation and decide on the most efficient method to use - all accessible mentally. With standard method works for all numbers – no need to look at the numbers anymore.

Jottings illustrating mental fluency a personal record of intermediate steps in a calculation that the person calculating feels the need to record as support Good example of a child working mentally at what we might traditionally have considered to be a pencil and paper method – but it shows the child is looking at the numbers involved and making connections noting the relationship between 17 and 34 and therefore between 17 and 340, adjusting the calculation to make it more accessible. Working it mentally with a few jottings along the way to keep track of thinking.

When do we need a written calculation? When numbers are too big or complex to hold in our heads. Then we choose a written method Explain decomposition is required emphasising the language of place value. Children are now expected to be able to do this by the end of Y3 – but remember it is not enough to be able to follow the process – they also need the conceptual understanding.

Combining images Model difference ITP and multiplication facts ITP.

Partitioning This child is beginning the move to formal written addition. She is using Dienes apparatus to support her with this – she can see clearly what each part of the number she is dealing with re

Activity What would happen if the number was 347 not 346 – child would have 10 units and would exchange these for another 10 leaving no units to be recorded in the units column. Have a go! Try adding 2 3-digit numbers of your choice.

Partitioning for multiplication

Partitioning for division – an informal method 84 ÷ 7 54 ÷ 4

The process of moving towards the standard written method - addition A number line is a method of informal calculation that works for any size of number. 8+7, 48+36

Partitioning Record steps in addition using partitioning: 47 + 76 = 40 + 70 + 7 + 6 = 110 + 13 = 123 Partitioned numbers are then written under one another; the expanded method

Expanded method in columns Adding the tens first: Adding the ones first: 4 7 + 7 6 1 3 1 1 0 1 2 3

Column method

As well as number there is Measurement Geometry – properties of shapes Geometry – position and direction Statistics

Which year group? (Y1-Y6) recognise and know the value of different dominations of coins and notes tell and write the time from an analogue clock, including using Roman numerals from I to XII, and 12-hour and 24-hour clocks compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and shapes interpret and construct simple pictograms, tally charts, block diagrams and simple tables interpret and construct pie charts and line graphs and use these to solve problems draw given angles and measure them in degrees Y1 Y3 Y4 Y2 Y6 Y5

How can parents support their children with mathematics? exhibit a positive attitude towards mathematics be overt about your own use of mathematics ask children what they have learnt in maths rather than what they have done value children’s mathematical thinking – don’t focus solely on correct answers and speed of response find ways to engage children with maths in everyday life e.g. finding the heaviest and lightest tin in the food cupboard

Any questions?