# Maths

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.

By the end of EYFS, pupils meeting age related expectations will be able to:

• Count reliably to 20
• Count a number of objects by pointing to/moving each one as they count
• Recognise numbers to 20
• Order numbers 1 – 20
• Say 1 more and1 less than numbers to 20
• Add and subtract two single digit numbers
• Form all digits 0-9 correctly
• Know the names of the days of the week in order
• Begin to recognise and name common 2D shapes, e.g. square, rectangle, circle and triangle
• Begin to recognise and name some 3D shapes, e.g. cube, sphere, cylinder, cone

By the end of KS1, pupils meeting age related expectations will be able to:

• read scales in divisions of ones, twos, fives and tens
• partition any two-digit number into different combinations of tens and ones, explaining their thinking verbally, in pictures or using apparatus
• add and subtract any 2 two-digit numbers using an efficient strategy, explaining their method verbally, in pictures or using apparatus (e.g. 48 + 35; 72 – 17)
• recall all number bonds to and within 10 and use these to reason with and calculate bonds to and within 20, recognising other associated additive relationships (e.g. If 7 + 3 = 10, then 17 + 3 = 20; if 7 – 3 = 4, then 17 – 3 = 14; leading to if 14 + 3 = 17, then 3 + 14 = 17, 17 – 14 = 3 and 17 – 3 = 14)
• recall multiplication and division facts for 2, 5 and 10 and use them to solve simple problems, demonstrating an understanding of commutativity as necessary
• identify 14, 13, 12, 24, 34, of a number or shape, and know that all parts must be equal parts of the whole
• use different coins to make the same amount
• read the time on a clock to the nearest 15 minutes
• name and describe properties of 2-D and 3-D shapes, including number of sides, vertices, edges, faces and lines of symmetry.

By the end of KS2, pupils meeting age related expectations will be able to:

• order and compare numbers up to 10 000 000
• read and write numbers up to 10 000 000 and determine the value of each digit
• round any whole number to a required degree of accuracy
• use negative numbers in context
• calculate intervals across zero
• solve number and practical problems that involve all of the above
• multiply numbers up to 4 digits by a two-digit whole number using formal written method
• divide numbers up to 4 digits by a two-digit whole number using formal written method
• interpret remainders as whole number remainders, fractions, or by rounding, as appropriate for the context
• divide numbers up to 4 digits by a two-digit number using the formal written method of short division where appropriate
• perform mental calculations, including with mixed operations and large numbers
• identify common factors, common multiples and prime numbers
• use their knowledge of the order of operations to carry out calculations involving the four operations
• solve addition and subtraction multi-step problems in contexts, deciding which operations and methods to use and why
• solve problems involving addition, subtraction, multiplication and division
• use estimation to check answers to calculations and determine, in the context of a problem, an appropriate degree of accuracy
• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions > 1
• add and subtract fractions with different denominators and mixed numbers, using equivalent fractions
• multiply simple pairs of proper fractions, writing the answer in its simplest form
• divide proper fractions by whole numbers
• associate a fraction with division
• calculate decimal fraction equivalents for a simple fraction
• identify the value of each digit in numbers given to three decimal places and multiply and divide numbers by 10, 100 and 1000 giving answers up to three decimal places
• multiply one-digit numbers with up to two decimal places by whole numbers
• use written division methods in cases where the answer has up to two decimal places
• solve problems which require answers to be rounded to specified degrees of accuracy
• recall and use equivalences between simple fractions, decimals and percentages, in different contexts
• solve problems involving the relative sizes of two quantities where missing values can be found by using integer multiplication and division facts
• solve problems involving the calculation of percentages [eg, of measures, and such as 15% of 360] and the use of percentages for comparison
• solve problems involving similar shapes where the scale factor is known or can be found
• solve problems involving unequal sharing and grouping using knowledge of fractions and multiples
• use simple formulae
• generate and describe linear number sequences
• express missing number problems algebraically
• find pairs of numbers that satisfy an equation with two unknowns
• enumerate possibilities of combinations of 2 variable

Implementation at our school

The pupil in most year groups will be taught maths daily for about an hour. This may vary depending on the age and abilities of year groups or individual children. We use the National Curriculum, the White Rose Maths Programmes of Study and the Maths – No Problem! Scheme to support planning and teaching. Our teaching is based on the principle that children should experience all aspects of the maths curriculum and that they are all capable of achieving high standards in the subject.

• The large majority of children progress through the curriculum content at the same pace.
• Differentiation is achieved by emphasising deep knowledge and through individual support and intervention.
• Practice and consolidation play a central role. Carefully designed variation within this builds fluency and understanding of underlying mathematical concepts.
• Teachers use precise questioning in class to test conceptual and procedural knowledge and assess children regularly to identify those requiring intervention, so that all children keep up and next steps can be planned.

Problem solving and reasoning are at the heart of our approach to learning in maths so that the children learn to apply new concepts in appropriate, real life contexts.

It is a common characteristic of our maths lessons that children in all year groups and all at levels of attainment will show their understanding using practical equipment, as appropriate.

Impact

The school has a supportive ethos and our approaches support the children in developing their collaborative and independent skills, as well as empathy and the need to recognise the achievement of others. Regular and ongoing assessment informs teaching, as well as intervention, to support and enable the success of each child.

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