Mathematics
At Lapal, maths is challenging, enjoyable and achievable for all. We incorporate concrete manipulatives, pictorial representations, words, numbers and symbols to enable children to explore and demonstrate mathematical ideas. This also enriches learning experiences and deepens understanding. Together these elements cement knowledge so that pupils truly understand mathematical concepts and procedures. All children are regularly encouraged to recall and apply their knowledge, skills and understanding to solve problems and reason. We provide all children with a variety of opportunities which encourages them to make connections. Our goal is to equip the children with the skills of calculation, reasoning and problem solving that they need in life beyond school.
Early Maths
There are six main areas that collectively underpin children’s early mathematical learning, and which provide the foundations for the maths that children will encounter as they progress through the years in primary school.
They are:
Cardinality and Counting: understanding that the cardinal value of a number refers to the quantity, or ‘howmanyness’ of things it represents
Comparison: understanding that comparing numbers involves knowing which numbers are worth more or less than each other
Composition: understanding that one number can be made up from (composed from) two or more smaller numbers
Pattern: looking for and finding patterns helps children notice and understand mathematical relationships
Shape and Space: understanding what happens when shapes move, or combine with other shapes, helps develop wider mathematical thinking
Measures: comparing different aspects such as length, weight and volume, as a preliminary to using units to compare later
Children are encouraged to use mathematical language, problem solve and reason in a broad range of practical contexts and throughout their play.
Click here to view the Early Years Maths Curriculum Overview.
Early Maths Links & Websites:

The NCETM Early Years Area  The aim of this section is to help gain a clearer understanding of how children build early number sense and to provide tips on how best to support that learning.

Number Blocks  Number blocks first broadcast in January 2017. It is a preschool BBC television series aimed at introducing children to early number. Snappy animation and lovable characters combine with engaging story lines to gently introduce concepts of number to support early mathematical understanding.

NRICH  The NRICH Early Years resources aim to further develop young children’s natural problemsolving abilities in the context of mathematics.

Learning Trajectories  This is a webbased tool to support our understanding about how children think and learn about mathematics and how to teach mathematics to young children (birth to age 8).
Our Approach to Teaching Maths at Lapal
Aims of the National Curriculum
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.
At Lapal, we support the children’s understanding of mathematical concepts, operations and relationships. The children develop efficient recall of the basic number facts such as number bonds, times tables, doubling and halving through maths lessons as well as homework tasks.
In order to develop the children’s procedural fluency, we teach a range of procedures and spend a lot of time discussing and exploring the most efficient procedure to use so that when children come across a question in a different context, they can apply their knowledge and skills in the most efficient way possible. For example when teaching addition in year three, the children would apply their number bond knowledge to add three digit numbers and one digit numbers. Drawing upon their knowledge and understanding of place value, the children recognise that only the ones column is affected so they know that they can answer this question mentally and therefore do not need to carry out a written method. However later on in the unit, when the children are adding a three digit number and a two digit number, they begin to add numbers where there is an exchange from ones to tens. They then move on to exchanging tens to hundreds before adding numbers where there are exchanges in both columns. It is here that the children are taught how to use a written method and develop the understanding of when and why we used written methods. Our maths curriculum equips the children to apply procedures accurately, efficiently, and flexibly. This allows them to transfer procedures to different problems and contexts and to recognise when one strategy or procedure is more appropriate to apply than another.

Reason mathematically by following a line of enquiry, conjecturing relationships and generalisations, and developing an argument, justification or proof using mathematical language
We encourage children to work actively in small groups or with their talk partners wherever possible because we have found this to be one of the best ways to develop the children’s reasoning skills. Through discussions with their peers, the children naturally spot errors, explain their thinking and encourage each other to justify their answers. Some children also challenge themselves to prove that their answer is correct by demonstrating their mathematical thinking in another way or by using resources to illustrate the concept.

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
During our maths lessons, we aim to teach and develop maths skills in interesting and exciting ways. The children are regularly involved in many practical activities and investigations using equipment, which also help develop their skills of problem solving and logical thinking.
Our Maths Curriculum
We use the White Rose Scheme of Learning to inform our planning. Our Maths curriculum is planned and sequenced so that new knowledge and skills build on what has been taught before. We dedicate more time to teaching each area of mathematics so that we can ensure that the relevant knowledge, skills and understanding are embedded. Children’s chances of success are maximised if they develop deep and lasting understanding of mathematical procedures and concepts we therefore ensure that learning is deep and sustainable.
We also use a range of other materials to support the teaching and learning of mathematics. These include:

Maths No Problem

NCETM

NRich

Gareth Metcalfe’s ‘I See Reasoning’ and ‘I See Problem Solving.’

Mastery documents

Rising stars: Maths for the more able
We also have a wealth of practical resources in school to support the teaching and learning of maths.
Please click on the year group below to see the Maths curriculum coverage for the academic year:
Mastery Approach
Concrete, Pictorial, Abstract (CPA)
The mastery approach incorporates objects, pictures, words, numbers and symbols to help children to explore and demonstrate mathematical ideas. All pupils, when introduced to a new concept, should have the opportunity to build competency in this topic by using the CPA approach. Pupils are encouraged to physically represent mathematical concepts. Objects and pictures are used to demonstrate and visualise abstract ideas, alongside numbers and symbols.
Concrete: children have the opportunity to use concrete resources to help them to understand and explain what they are doing. Children might begin by handling real objects, such as apples, and then move on to using physical representations of those objects, for example counters.
Pictorial: children then build on this concrete approach by using pictorial representations, which can then be used to reason and solve problems. Drawings act as a bridge between the concrete objects that the children have been using and the abstract symbols that they must learn to use.
Abstract: With the foundations firmly laid, children can move to an abstract approach using numbers and key concepts with confidence.
Times Tables
When it comes to times tables, speed and accuracy are important. We teach times tables daily, as part of our maths lessons, in years one to five. We believe that the more times table facts that the children remember, the easier it is for them to answer more complex calculations.
The National Curriculum expectation for Primary Schools across the UK is that, by the end of Year 4, pupils can recall all 12 times tables up to 12x2. With this in mind, we ensure that by the end of year 2, children are able to recall multiplication facts for the 2, 3, 5 and 10 times table accurately and promptly. By the end of year 3, we expect children to build on their multiplication knowledge from year two and recall multiplication facts for the four and eight times tables as well as the 2, 3, 5 and 10 times table.
The children have access to Timestables RockStars. This is used to support children’s accuracy and prompt recall of multiplication facts. All of the children in year two, three, four, five and six have access to TT Rockstars and their username and password can be found in their planner. You can access TT Rockstars through the tile on our RM Unify platform. Year one children will receive their username and password in the Summer term. Children are encouraged to access this resource both inside and outside school. The children are awarded with certificates during assembly each week. There is a celebration display board in the school hall which shows the winning classes from the most recent tournament.
The children also enjoy playing Hit The Button to practise recalling multiplication and division facts as well as number bonds and doubling and halving.
Towards the end of the academic year, children in year four will complete the Multiplication Tables Check. The online check will test the children on their multiplication tables up to 12 x 12. There are twentyfive questions in total and the children will have six seconds to answer each question, there will be a three seconds between questions. This activity on Maths Frame mirrors the 'Multiplication Tables Check' that will be given to children. The questions are generated randomly using the same rules as the 'Multiplication Tables Check.’ For more information about the Multiplication Tables Check, please find information leaflet below.
Useful Information: