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.
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 nonroutine 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.
The national curriculum for mathematics reflects the importance of spoken language in pupils’ development across the whole curriculum – cognitively, socially and linguistically. 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.
Mathematics in the Early Years
This involves providing children with opportunities to:
- practise and improve their skills in counting numbers, calculating simple addition and subtraction problems
- describe shapes, spaces, and measures
- Children count reliably with numbers from 1 to 20, place them in order and say which number is one more or one less than a given number
- Using quantities and objects, they add and subtract 2 single-digit numbers and count on or back to find the answer
- They solve problems, including doubling, halving and sharing
Shape, space and measures:
- Children use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems
- They recognise, create and describe patterns
- They explore characteristics of everyday objects and shapes and use mathematical language to describe them
Key Stage 1- year 1 and 2
The principal focus of mathematics teaching in key stage 1 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 [for example, concrete objects and measuring tools].
At this stage, pupils should develop their ability to recognise, describe, draw, compare and sort different shapes and use the related vocabulary. Teaching should also involve using 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 the number bonds to 20 and be precise in using and understanding place value. An emphasis on practice at this early stage will aid fluency.
Pupils should read and spell mathematical vocabulary, at a level consistent with their increasing word reading and spelling knowledge at key stage 1.
Lower Key Stage 2- 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.
Pupils should read and spell mathematical vocabulary correctly and confidently, using their growing word reading knowledge and their knowledge of spelling.
Upper Key Stage 2- 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 link below will take you to the National Curriculum for mathematics and within this you will find the programmes of study for each year group.
Mathletics is a targeted, rewarding and captivating online learning resource, which is aligned to curriculum standards. Children have take-home access to Mathletics – they simply sign in with their school username and password (see below) using any compatible computer or mobile device.
We recommend that you spend time looking at the program with your child to explore how Mathletics will benefit their learning. As a parent or carer, you can sign up to the Mathletics Family Centre. This will give you access to the learning content your child is following, and information regarding his or her progress within Mathletics.
- Visit www.mathletics.com/parents
- Complete the fields and click Register
- Record your new username and password
To access the Mathletics Family Centre:
- Visit www.mathletics.com
- Sign in using your own username and password
The extra Mathletics practice at home can make all the difference to your child’s progress. Encourage them to achieve a weekly target of 1000 points to earn a certificate, building through bronze, silver and gold across the school year. Go for gold! Further information and guides on Mathletics can be found under ‘Help’ in the Mathletics Family Centre.
Each year, from year 2 through to year 6 have specific times tables they must learn:
- Year 2: x2, x5, x10
- Year 3: x3, x4, x6
- Year 4: x7, x8, x9, x11, x12
- Year 5 & 6 : further consolidation of all tables including ‘mega’ facts (6 x 80; 7 x 900; 400 x 6) and ‘mini’ facts (0.5 x 8; 3 x 0.03; 0.009 x 8)
For times tables I would advise you, as parents/ carers, spend a few weeks exploring one particular times table; look into any patterns; find things that are grouped by that amount (for example traffic lights in 3s; boxes of eggs in 6s; colours in a rainbow in 7s); practice the related division facts; depending on year group expectations, practice the ‘mini’ and ‘mega’ facts (7 x 4 and 0.7 x 4 (mini) and 70 x 4 (mega).
Multiplication Tables Check (MTC)
The multiplication tables check (MTC) is a digital assessment intended to support teachers in ensuring that all pupils know their multiplication tables by the end of primary school. It will enable schools to identify those pupils who may need more support with their times tables.
This academic year (2020/21) the optional MTC will be administered to year 4 pupils, between the official dates of Monday 7 June and Friday 25 June– the check will take most pupils no longer than 5 minutes to complete.
This is an opportunity for schools to become familiar with the nature of the check before its planned introduction as a statutory assessment in the 2021/22 academic year. Further information will be available in the MTC administration guidance, which is published for schools at the start of the summer term, this will include how to access the MTC service.
The Government have published a Multiplication tables check information video, which demonstrates which pupils and schools can expect. They have also published a leaflet for schools to share with parents.