# Maths

Mathematics is a creative and highly inter-connected discipline that has been developed over centuries, providing the solution to some of History’s most intriguing problems. It is essential to everyday life, critical to science, technology and engineering, and necessary in most forms of employment.

At Sandown Primary School we believe a high-quality mathematics education provides a foundation for understanding the world, the ability to reason mathematically, and a sense of enjoyment and curiosity about the subject.

**The National Curriculum** 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.

Mathematics is an interconnected subject in which pupils need to be able to move fluently between representations of mathematical ideas. The programmes of study are, by necessity, organised into apparently distinct domains, but 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.

The expectation is that the majority of pupils will move through the programmes of study at broadly the same pace. However, decisions about when to progress should always be based on the security of pupils’ understanding and their readiness to progress to the next stage. Pupils who grasp concepts rapidly should be challenged through being offered rich and sophisticated problems before any acceleration through new content. Those who are not sufficiently fluent with earlier material should consolidate their understanding, including through additional practice, before moving on.

By the end of each key stage, pupils are expected to know, apply and understand the matters, skills and processes specified in the relevant programme of study.

**Early Years- Reception** In Reception, Maths involves providing children with opportunities to develop and improve their skills in counting, understanding and using numbers, calculating simple addition and subtraction problems; and to describe shapes, spaces, and measures.

**Key Stage One- Years 1 and 2** The principal aim is to ensure that pupils develop confidence and mental fluency with whole numbers, counting and place value. This should involve working with numerals, words and the four operations, including with practical resources. Pupils should begin to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. They should know a range of measures to describe and compare different quantities such as length, mass, capacity/volume, time and money. By the end of Year 2, pupils should know number bonds to 20 and be precise in using and understanding place value. Children should be able to fluently recall their 2x, 3x, 5x and 10x table by the end of Year 2 and be able to recall the related division facts. Pupils should read and spell mathematical vocabulary, appropriate to their level.

**Lower Key Stage Two – Years 3 and 4** The principal focus of mathematics teaching in lower Key Stage 2 is to ensure that pupils become increasingly fluent with whole numbers and the four operations, including number facts and the concept of place value. This should ensure that pupils develop efficient written and mental methods and perform calculations accurately with increasingly large whole numbers. At this stage, pupils should develop their ability to solve a range of problems, including with simple fractions and decimal place value. Teaching should also ensure that pupils draw with increasing accuracy and develop mathematical reasoning so they can analyse shapes and their properties, and confidently describe the relationships between them. It should ensure that they can use measuring instruments with accuracy and make connections between measure and number. By the end of Year 4, pupils should have memorised their multiplication tables up to and including the 12 multiplication table and show precision and fluency in their work. Children should also be able to recall the division facts for their multiplication tables. Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.

**Upper Key Stage Two – Years 5 and 6** The principal focus of mathematics teaching in upper Key Stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio. At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation. With this foundation in arithmetic, pupils are introduced to the language of algebra as a means for solving a variety of problems. Teaching in geometry and measures should consolidate and extend knowledge developed in number. Teaching should also ensure that pupils classify shapes with increasingly complex geometric properties and that they learn the vocabulary they need to describe them. By the end of Year 6, pupils should be fluent in written methods for all four operations, including long multiplication and division, and in working with fractions, decimals and percentages. Pupils should read, spell and pronounce mathematical vocabulary correctly.

The aim of our Calculation Policy is to ensure all children leave Sandown Primary School with a secure understanding of the four operations and can confidently use both written and mental calculation strategies in a range of contexts. This policy states the required mental strategies and sets out the progression of written procedures that the children will use as they progress in their understanding of the four operations. In order for children to develop a full understanding of the written procedures, they must first have a firm understanding of place value. It is expected that the majority of pupils will progress through the calculation stages as stated in this policy. However, children should not be made to go onto the next stage if: - They are not ready. - They are not confident. Children who do grasp concepts rapidly should be challenged through sophisticated and diverse problems, before being accelerated through new content. Furthermore, it is essential that at each stage, children are making choices about whether to use a mental or written method. Finally, it is essential that the strategies in this policy are being taught through mathematical problems and activities that are contextualised, relevant and rich in key mathematical vocabulary.

Sandown Primary School aims to promote pupils’ spiritual, moral, social and cultural development and prepares all pupils for the opportunities, responsibilities and experiences of life. Mathematics contributes to our SMSC development through:

Social development: through helping children work together productively on complex mathematical tasks and helping they see that the result is often better than any of them could achieve separately.

Moral development: helping children recognise how logical reasoning can be used to consider the consequences of particular decisions and choices and helping them learn the value of mathematical truth.

Spiritual development: through helping children obtain an insight into the infinite, and through explaining the underlying mathematical principles behind natural forms and patterns.

Cultural development: through helping children appreciate that mathematical thought contributes to the development of our culture and is becoming increasingly central to our highly technological future, and through recognising that mathematicians from many cultures have contributed to the development of modern day mathematics.

Every class has the opportunity to access Mathletics once a week during Maths. Children have their own log in and have learning tasks assigned to them which are personalised to their ability. Teachers closely match the assigned tasks to complement what children are learning in class or to revise a specific curriculum area that has been previously taught.

Mathletics club is held at lunchtimes: - Tuesday- Year 1 and 2 - Wednesday- Year 3 and 4 - Friday- Year 5 and 6.

Click on the image to go to Mathletics.

In order to become a competent mathematician, children need to develop a secure understanding of number facts in all four operations: addition, subtraction, multiplication and division. Through their practise and application of these number facts, they will enhance their development in all areas of mathematics, especially problem solving. We have now introduced Maths Passports to support your child in learning and recalling their number facts. Maths Passports begin in the Early Years and progress through too Year 6. Your child’s Passport journey begins in the British Isles and then progresses around the world. Your child’s teacher has assessed their mental maths strengths and next steps, allowing them to be given a passport, which is appropriate for them. Your child will be able to choose a target from their passport and practice this at home to support them with their learning at school; this helps achieve our vision statement ‘Bringing home and school together’. Once your child successfully completes a target they get it ticked off. Each target has to be achieved 3 times in order for us to be sure that the facts are embedded. Once all targets have been completed, your child will receive a certificate and then will then progress onto a new passport. Please click on the areas below to access the targets your child is working on. England Scotland Northern Ireland Wales Ireland Jersey Guernsey Alderney Sark Europe Asia Africa Antarctica Australasia North America South America Globetrotter Pangea Atlantis

Take a look at this exciting new Maths programme that will teach your child about the representation of numbers. Be warned, the tunes are catchy and your child may be singing them to you!

Day Three- Today's activity involved us engaging with visual and creative mathematical thinking. Children took on the role of the sceptic and the convincer for this activity which encouraged reasoning using the correct mathematical language. The video we watched explained to children that sometimes speed in Maths is not always a good thing; when we want to learn something deeply, you need to go slowly and look for patterns and relationships. Follow these instructions to have a go at this activity:

1) You will need 3 squares of paper each.

2) Using your first square of paper can you, construct a square that is exactly 1/4 the area of the original square. Convince your partner that it is a square with 1/4 of the area.

3) Using your third square of paper can you, construct a triangle that is exactly 1/4 of the area of the original square. Convince your partner that it is a triangle with 1/4 of the area.

4) Using your fourth square of paper can you, construct a triangle that is exactly 1/8 of the area of the original square. Convince your partner that it is a triangle with 1/8 of the area.

Have a look at some of our photographs to see how we completed the activity.

Day Five: What a fantastic end to the week! The children have surpassed their own imagination of what they could achieve mathematically this week.

In our video from today's session the children learnt that it is ok to make mistakes as long as they work hard to uncover why they made the mistake and retry the problem; we understand that this is perseverance. In fact we learn more when we make mistakes and unpick them.

Therefore today's challenge was a head scratcher. The children were given the first three cases of a growing pattern and they had to work out how it was growing. The children came up with loads of different ideas which we named 'the raindrop effect', 'the rainbow', 'the rocket' and 'the bridge' (have a look at e pictures to see if you can work out which name belongs to which pattern!). These names helped to explain the different patterns and where the growth was. Children were given the opportunity to build the first three cases with cubes or Cuisennaire rods and then build the next two cases. Once we put the data that we had found out into a table, the children began to spot patterns with the numbers. The children made conjectures e.g. "I think you double and add 1", "I think that the pattern is going up by 2 each time" and "I think that the pattern is growing in odd numbers". We proved and disproved our conjectures and went on to spot further patterns. With a little support we were able to see that each number was a square number. This helped us to be able to say how many cubes we would need for the 6th and 7th cases as well as make a generalisation. We spotted that if we added 1 to each case name e.g. case 1 would we 1+1=2, we would have to square that number to work out the total number of cubes e.g. 2 squared =4. We then wrote this as 'total number of cubes=(c+1) squared'. We worked out that to make case 99 we would need 10,000 cubes. Have a look at our jottings to find out what else we discovered!

We hope that you are as inspired as we are to continue with some of our learning.

**Peer tutoring**is an structured learning experience in which a Year 5 child acts as a teacher and the Year 3 child is the learner. It gives both students an opportunity to use their mathematical knowledge in a meaningful, social experience whilst developing their understanding of Maths.

In lesson 2 the children recapped their counting in tens before moving onto new learning. The Year 5 teachers were impressed at how well the Year 3 children had retained their learning. After this the Year 5s taught the Year 3s how to count in 3s using multiple representations. The children used counters, bead string, subsets and number lines. The children then drew arrays to show the 3x table. Have a look at some of the pictures to see their super teaching and learning.

Mrs Tugwell and a Mrs Harley were lucky enough to run Double Trouble this week and see the fantastic learning that the Year 3s are being taught by the Year 5s. The Year 5s were rather nervous about being 'observed' but coped well and showed off their super teaching skills! The Year 5s focused on doubling this week as well as recapping the children's knowledge of their 10 times table. The children had the chance to draw aliens with lots of arms, legs, eyes and noses so that they could then draw the aliens twin. Once completing their pictures they had to work out how many arms, legs, eyes and noses there were altogether by doubling numbers.

In this session we looked at counting on in tens from any number. The Year 5 children taught this using a range of resources e.g. Place value counters and dienes. Once the Year 3s had a secure understanding of adding ten to any number and could spot the pattern, the Year 5s taught them a game to play on a blank one hundred square. Take a look at some of the pictures to see the children enjoying their Maths learning.

**Lesson 5**

In lesson 5 the the Year 3 children enjoyed playing games which helped them to become mor fluent with their addition and subtraction knowledge. The Year 5 children taught them the rules of the game and then played alongside them encouraging them to use mental strategies rather than counting on in ones or using their fingers. The children also continued to practise their understanding of doubling by using resources to show that it is the same as multiplying by two or adding the same number together.

__Lesson 6__At Sandown Primary school we are continually striving to 'Bring Home and School Together'. Every year group holds a 'Teach My Family' Maths Party during the year where children share their maths learning with their families. Children create a personal invitation that they send home to their parents and create a maths party bag full of mathematical resources and games. During the event the parents watch part of a maths lesson and then the children share their mathematical learning with their families. Take a look at some of the pictures from previous 'Teach My Family' Maths parties to see the children enjoying their maths learning.

As you will be aware, the Year 3-6 children are now being rewarded with times table wristbands for learning their times table and division facts. Children will earn them in numerical order (1-12) and will be tested on times table and division facts for each times table. For every band they earn, they need to be able to recall facts from the previous times tables e.g. if they are wearing the 5x table band, they will be tested on their 1x, 2x, 3x and 4x tables with the corresponding division facts. To challenge our more able children, they will be being asked 'challenge questions'. These may include:

Super-size times tables: multiplying multiples of 10, 100 and 1,000 e.g. 700x4=

Super-skinny times table facts: multiplying decimals and fractions e.g. 0.6x9=

Please remember that learning all times table and division facts up to 12x12 is a Year 4 objective. Conquering these facts early will allow children to move onto more complex maths.

Once the children have mastered all times table and division facts up to 12x12, children will be rewarded with a Times Table Champion pin badge to wear with pride.