Maths National Curriculum
Purpose of study
- 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 for financial literacy and most forms of employment.
- A high-quality mathematics education therefore provides a foundation for understanding the world, the ability to reason mathematically, an appreciation of the beauty and power of mathematics, and a sense of enjoyment and curiosity about the subject.
Aims
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 develop conceptual understanding and the ability to recall and apply knowledge rapidly and accurately
- 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.
(National Curriculum 2014)
Here is the link to download the Maths National Curriculum
National curriculum in England: mathematics programmes of study - GOV.UK (www.gov.uk)
Pupils should be taught to in Y3 and Y4
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 times table and show precision and fluency in their work.
Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.
Pupils should be taught in Y5 and Y6
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.
Maths Curriculum Vision
Long Term Plan (LTP)
The school has formulated alongside the Planpanion Scheme a Long Term Plan for each year group to follow. This is subject to change depending on the needs of the children as some blocks may be longer or shorter depending on the capabilities of the children within the block. Some blocks are also considered 'slider units' so can be slotted at different points within the learning journey.
Calculation Policy
The calculation policy has been produced to ensure that there is progression in the four methods and enable children to be prepared for High School. Children will be taught age appropriate methods, linked to the Calculation Policy below. Although we aim for all children to be at the same stage by the time they leave Anston Park, some children may be working at different stages depending on their mathematical capabilities.
Below is a parent friendly overview of the methods your child will be taught in school. Again, this is a working document and will be refined and reviewed at the end of each academic year.
How do we teach maths?
Arithmetic Sessions
As part of our maths lessons, we recognise the importance of children mastering key mathematical facts and recalling a range of mental strategies. We know that if children are not fluent in recalling specific facts and strategies, they will find it increasingly difficult to reason and problem solve. As a result of this, we spend 15 minutes every day rehearsing key facts and strategies to ensure children are able to apply these effectively when faced with mathematical problems. Children learn strategies and use concrete apparatus and pictorial representations to help them understand why a strategy will work and how to apply this to other calculations. We look at the mathematical structure of problems and don't solely focus on finding an answer. The teacher will model the strategy we expect the children to use, the children will be given a range of questions (where appropriate) for the children to apply the strategy to and finally they will mark the work with the children to ensure the strategy is understood. Sometimes, lessons may be purely practical or teachers may discuss a calculation and find strategies they can use to solve it before deciding on the most efficient. The children understand the value of these sessions and learning is linked back to the Maths lessons so children continually revisit the fundamental strategies and facts.
On the Friday, an arithmetic review is completed by the children to enable them to rehearse skills they have learnt from the week and during the previous weeks to ensure they consolidate strategies and recall facts confidently and fluently (Retrieval Practice). This will allow facts and strategies to be recalled automatically to reduce the cognitive load.
New 2024-2025
Y3- Number Sense (This will form the arithmetic sessions in the Autumn Term)
In Y3, the children will be focusing on the core Addition and Subtraction Fact Grids building on from the programme they studied in the Infant School. These essential facts are the equivalent of times tables for addition and subtraction. Just as all multiplication and division calculations use root times table facts, all future addition and subtraction calculations use these root addition and subtraction facts. The core facts are taught alongside 12 calculation strategies. Learning and applying these strategies gives children a deep understanding of number and number relationships. Using these strategies children can then "use what they know to work out what they don't know". Explicit teaching of derived fact strategies is an effective route to fluency in addition and subtraction facts for all children.
The programme teaches every addition and subtraction fact systematically. Just as schools can tell you where they teach each grapheme-phoneme correspondence in phonics, the Number Sense Maths Fluency Programme systematically teaches the facts and strategies leaving nothing to chance.
The facts and strategies are brought together in a six stage teaching programme. Each stage of the programme is broken down into smaller teaching steps,
1) Visual number formation
2) Make and break numbers to 10
3) Facts and strategies within 10
4) 100 and a bit facts
5) Facts and strategies across 10
6) Extending facts and strategies beyond the grids.
The above skills are fundamental skills that the children need to have mastered for learning in the rest of the key stage.
Y4 and Y5 KS2 Mastering Number Programme
Y4 and Y5 will be taking part in a pilot KS2 Mastering Number programme focussing on learning their times tables facts and division facts. This is in conjunction with the South Yorkshire Maths Hub.
Y4 Overview of the programme (Y5 will be published once the programme has started in September)
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Autumn Term |
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· Represent ‘many as 1’ using a unitised counter and stamping gesture, · Use the ‘five and a bit’ structure to double, connect this to recalling products when one of the factors is 2 or 4, · Practise recalling products when one of the factors is 5 or 10, · Explore ‘square’ numbers, · Use the distributive property to explore the x9, x11 and x12 facts, · Become familiar with the core multiplication facts (CMF) table and practise saying the smaller factor first regardless of the position of the factors, |
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Spring Term |
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Going for Gold · The intention is that, over the course of this term, will develop automaticity in all the multiplication facts, both those in the Core Multiplication Fact Table (CMF) and others with the set of 144 facts, · Recap- Quick review of previously- learnt facts using the oral pattern as the initial prompt, · Understand- this provides an opportunity for pupils to explore, in more depth, the structure of the 2 focus tables, · Explain- Continue to develop and use good number sense to check answers eg explaining why 7x9 gives a product that is less than 70 and must be an odd number because at least one of the factors is odd, · Say- this provides an opportunity for pupils to practise saying the fact using the oral pattern of factor, factor, product, alongside the representation used. |
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Summer Term |
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· Connect contexts to writing and interpreting equations and connect multiplication equations and multiplication equations with a missing factor to division, · Know that the product in a multiplication equation is equivalent to the dividend in the corresponding division equation.
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Times Tables
As a school, we value the importance of children learning their times tables and related division facts. These facts help the children to unlock many other areas of maths learning for example ratio and area. Also when fluent, it allows children to focus on the strategy needed for problem solving or reasoning instead of having to count on to find the relevant times tables.
In school, we focus on teaching the conceptual understanding of times tables and what they mean in Y3 so children are really secure about how to represent a times tables in an array, that it is an equal group of and the difference between grouping and sharing. This forms the basis of our times tables and children apply this learning for the rest of their time in school. Y3 do not focus on times table teaching until the Spring Term to ensure they fully understand what multiplication and division is before they start their times table journey and are solid with their addition and subtraction facts.
In Y4 and Y5, the children will be participating in the KS2 Mastering Number Times Table pilot with the Maths Hub. The approach focuses on making connections between tables and related division facts and look at using what they know to help them derive other facts eg if you know 5x6 = 30 you also know 6x6 (5x6+6)
In Y6, each class, linked to the fluency document or gaps their class have, practise a table across one, two or three weeks. Children are given fact cards and they group them into facts they know and facts they don't. The teacher assesses what the majority of the class knows and compiles a list of facts that the children will start their journey with. The children choral chant the tables, starting with the ones they know, each day and the end of a session, the children will complete a speed sheet with the table facts they know. This allows children to consolidate the facts they know and recall them at speed. Over the subsequent sessions, when the children are ready, a new fact is introduced. The children have rapid fire questions regarding the new fact and then choral chant the facts they know. They then complete the speed sheet at the end of the session. This continues until all facts have been learnt. Division facts are introduced when the Class Teacher thinks they are ready and these are then incorporated into the speed sheets. Once the children are fluent in this times tables, the class teacher will select a new times table and repeat the above steps. Every week children will look back at their fact cards to ensure that they revisit the times tables to ensure they move into their long term memory.
Here is an example of the choral counting your child will do in school.
Class Teachers teach the tables for four days and on Thursday and Friday the children are given 3 minutes to complete 60 questions on the Time Table Rockstar sheet. The challenge is to complete the sheet as quickly as they can to gain the coveted Rock Hero status. You can help your child by encouraging them to play at home on the website on the Garage section as they can practise the times table they are working on in school. School competitions take place termly, where classes take on other classes in school to become the Times Table Champions.
Below is an example of the way the TTRockstars are presented. The children need to try and beat their time each week. The ultimate aim is to answer all of the questions in less than 1 minute.
Click on the image below to go to the TTRockstars website. Children will have their usernames and passwords within the first week of school.
Maths Lessons
The school are continuing to develop the mastery approach to the teaching of maths. This involves the children being exposed to teaching that develops a deep understanding of mathematical concepts through the use of practical apparatus and uses visual representations to support them (CPA model of teaching). The children are encouraged to think deeply about concepts and make connections which are guided by the teachers. The learning is interlinked across the learning journey and they see the concepts in a variety of contexts (variation) which enable children to 'master' their mathematical thinking. Where differentiation is needed, the children are given learning that will meet their needs or enabling prompts (scaffolds) will be given to support them when accessing the task. Children will constantly deepen their learning both within a lesson and as part of the learning journey.
We have been working on providing children with more problem solving/reasoning activities in their learning as this encourages them to apply their learning across a range of contexts. It also encourages the children to reason with number which is a key driver in the maths curriculum. The children are also encouraged to explain how they have calculated the answers to some questions as this also encourages the children to further deepen their understanding.
Children are encouraged to correct their mathematical errors using a green pen. The green pen shows the teacher that the children have responded to their marking and corrected the errors they have made. Sometimes prompts will be given to aid the corrections, they may be pulled together into a group if children have similar misconceptions or the children may simply have made errors in their calculations so they can put it right independently. The children complete their green pen edits before the next maths lesson eg at the start of the day or at the start of the maths lesson.
Scheme of Learning
The school follows the Planpanion (formerly Deepening Understanding) Scheme of learning. This resource :
- Enables children to build their confidence, consolidate their learning and ultimately challenge their thinking to equip every child with the skills and knowledge needed to become fluent and confident mathematicians.
- Enables children to build their number sense, develop their fluency, make connections, develop their mathematical vocabulary, reason mathematically, revisit prior learning and create capable problem solvers.
- Is matched to the NC and any DfE guidance. It links in prior learning and these should be investigated before teaching age related expectations eg through a quick recap or whiteboard work. These are not designed to be complete lessons unless the children need it.
- Applies consistent and relevant teaching pedagogies acting upon recent educational research and work with focus groups of teachers/advisors to shape the materials.
- Is planned in small steps and resources are not differentiated but staff will scaffold learning where appropriate.
- Gives pupils the opportunities to build fluency, reason and problem solve within their year group expectations.
How will we fit in our lessons?
Learning will be streamlined to allow for completion of all steps. Learning is broken down into 5 key areas:
Recall,
Mental Maths,
Skills,
Practical
Theory.
The children are taught the following blocks of learning:
Place Value,
Addition and Subtraction skills,
Multiplication and Division skills,
Application blocks for the 4 operations
Fractions
Geometry,
Measurement,
Algebra/Ratio and Proportion (Y6 only)
These are not all taught as discrete blocks of learning but instead a skill is taught and then it is applied in a range of different contexts eg addition skills are taught and it is applied through a perimeter/angle context.
Throughout their time in school, the skills that they are taught progress and they continually revisit and consolidate to ensure the concepts stay in their Long Term Memory.
Parent Support
Although the school does not use the White Rose Scheme of Learning, they have produced a series of home videos to support your child in each aspect of the maths curriculum which are still applicable when supporting parents in the new methods we use. They are very visual and use the CPA model of teaching. They will talk through strategies and model the way problems can be approached. Simply click on the link below and then click on the year group of your child. Look for area of Maths you are looking for support with and click on the link.
