Mathematics

Mathematics at Bidbury Infant School

At Bidbury, we have high expectations for all of our children and believe that they can achieve highly and become confident and skilled mathematicians. We strive for all children to be curious about mathematics and to understand the importance of mathematics in their everyday lives. We are committed to ensuring that children are able to use their mathematical skills and knowledge confidently in their lives in a range of different contexts. Our programme of study is organised carefully so that children can build on their skills and knowledge.

Our mathematics curriculum aims for pupils to become fluent in the fundamentals of maths and provides children with rich mathematical experiences. It is built on the key aims of the National Curriculum which are to ensure that all learners:

• 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 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.

We encourage pupils to make significant links between mathematics as a discreet subject and using their mathematical knowledge in other subjects, as well as within real life problems. Bidbury Infant School works with the Solent Maths Hub and we currently follow the White Rose Mathematics scheme of work. This is followed from YR to Year 2 and aids transition as the children move on in their learning journey up to Bidbury Junior School. 

Our Maths Vision for Bidbury

In line with the aims of the National Curriculum for Mathematics, we aim to ensure that all children gain:

• a deep and sustainable learning in mathematics which they are able to apply to a range of contexts
• develop a wide mathematical vocabulary to justify and reason
• the ability to build on previous knowledge
• the ability to reason about a concept and make connections
• a sound procedural and conceptual understanding
• fluency with number
• an ability to solve complex problems by breaking them down into smaller steps and showing resilience

It is our intention that by the time the children leave Bidbury they will be naturally, confident and fluent mathematicians. They will be curious learners and eager to explore mathematical concepts and ask questions to find solutions to problems in both school and the wider world. We at Bidbury want to enable all children to develop an intrinsic love of maths that will support them through their life journey.

Early Years Foundation Stage

There are six main areas that collectively underpin children’s early mathematical learning, and which provide the firm foundations for the maths that children will encounter as they progress through 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.

National Curriculum subject content for key stage 1

• 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. 

National Curriculum Year 1 programme of study 

Number – number and place value

Pupils should be taught to:

• count to and across 100, forwards and backwards, beginning with 0 or 1, or from any given number
• count, read and write numbers to 100 in numerals; count in multiples of twos, fives and tens
• given a number, identify one more and one less
• identify and represent numbers using objects and pictorial representations including the number line, and use the language of: equal to, more than, less than (fewer), most, least
• read and write numbers from 1 to 20 in numerals and words.

Number – addition and subtraction

Pupils should be taught to:

• read, write and interpret mathematical statements involving addition (+), subtraction (–) and equals (=) signs
• represent and use number bonds and related subtraction facts within 20
• add and subtract one-digit and two-digit numbers to 20, including zero
• solve one-step problems that involve addition and subtraction, using concrete objects and pictorial representations, and missing number problems such as 7 =    – 9.

Number – multiplication and division

Pupils should be taught to:

• solve one-step problems involving multiplication and division, by calculating the answer using concrete objects, pictorial representations and arrays with the support of the teacher.

Number – fractions

Pupils should be taught to:

• recognise, find and name a half as one of two equal parts of an object, shape or quantity
• recognise, find and name a quarter as one of four equal parts of an object, shape or quantity.

Measurement

Pupils should be taught to:

• compare, describe and solve practical problems for:
  • lengths and heights [for example, long/short, longer/shorter, tall/short, double/half]
  • mass/weight [for example, heavy/light, heavier than, lighter than]
  • capacity and volume [for example, full/empty, more than, less than, half, half full, quarter]
  • time [for example, quicker, slower, earlier, later]
• measure and begin to record the following:
  • lengths and heights
  • mass/weight
  • capacity and volume
  • time (hours, minutes, seconds)
• recognise and know the value of different denominations of coins and notes
• sequence events in chronological order using language [for example, before and after, next, first, today, yesterday, tomorrow, morning, afternoon and evening]
• recognise and use language relating to dates, including days of the week, weeks, months and years
• tell the time to the hour and half past the hour and draw the hands on a clock face to show these times.

Geometry – properties of shapes

Pupils should be taught to:

• recognise and name common 2-D and 3-D shapes, including:
• 2-D shapes [for example, rectangles (including squares), circles and triangles]
• 3-D shapes [for example, cuboids (including cubes), pyramids and spheres].

Geometry – position and direction

Pupils should be taught to:

• describe position, direction and movement, including whole, half, quarter and three-quarter turns.

National Curriculum Year 2 programme of study 

Number – number and place value

Pupils should be taught to:

• count in steps of 2, 3, and 5 from 0, and in tens from any number, forward and backward
• recognise the place value of each digit in a two-digit number (tens, ones)
• identify, represent and estimate numbers using different representations, including the number line
• compare and order numbers from 0 up to 100; use <, > and = signs
• read and write numbers to at least 100 in numerals and in words
• use place value and number facts to solve problems. 

Number – addition and subtraction

Pupils should be taught to:

• solve problems with addition and subtraction:
  • using concrete objects and pictorial representations, including those involving numbers, quantities and measures
  • applying their increasing knowledge of mental and written methods
• recall and use addition and subtraction facts to 20 fluently, and derive and use related facts up to 100
• add and subtract numbers using concrete objects, pictorial representations, and mentally, including:
  • a two-digit number and ones
  • a two-digit number and tens
  • two two-digit numbers
  • adding three one-digit numbers
• show that addition of two numbers can be done in any order (commutative) and subtraction of one number from another cannot
• recognise and use the inverse relationship between addition and subtraction and use this to check calculations and solve missing number problems. 

Number – multiplication and division

Pupils should be taught to:

• recall and use multiplication and division facts for the 2, 5 and 10 multiplication tables, including recognising odd and even numbers
• calculate mathematical statements for multiplication and division within the multiplication tables and write them using the multiplication (×), division (÷) and equals (=) signs
• show that multiplication of two numbers can be done in any order (commutative) and division of one number by another cannot
• solve problems involving multiplication and division, using materials, arrays, repeated addition, mental methods, and multiplication and division facts, including problems in contexts. 

Number – fractions

Pupils should be taught to:

• recognise, find, name and write fractions 1/3, 1/4, 2/4 and 3/4of a length, shape, set of objects or quantity
• write simple fractions for example, 1/2 of 6 = 3 and recognise the equivalence of 2/4 and 1/2. 

Measurement

Pupils should be taught to:

• choose and use appropriate standard units to estimate and measure length/height in any direction (m/cm); mass (kg/g); temperature (°C); capacity (litres/ml) to the nearest appropriate unit, using rulers, scales, thermometers and measuring vessels
• compare and order lengths, mass, volume/capacity and record the results using >, < and =
• recognise and use symbols for pounds (£) and pence (p); combine amounts to make a particular value
• find different combinations of coins that equal the same amounts of money
• solve simple problems in a practical context involving addition and subtraction of money of the same unit, including giving change
• compare and sequence intervals of time
• tell and write the time to five minutes, including quarter past/to the hour and draw the hands on a clock face to show these times
• know the number of minutes in an hour and the number of hours in a day. 

Geometry – properties of shapes

Pupils should be taught to:

• identify and describe the properties of 2-D shapes, including the number of sides and line symmetry in a vertical line
• identify and describe the properties of 3-D shapes, including the number of edges, vertices and faces
• identify 2-D shapes on the surface of 3-D shapes, [for example, a circle on a cylinder and a triangle on a pyramid]
• compare and sort common 2-D and 3-D shapes and everyday objects.

Geometry – position and direction

Pupils should be taught to:

• order and arrange combinations of mathematical objects in patterns and sequences
• use mathematical vocabulary to describe position, direction and movement, including movement in a straight line and distinguishing between rotation as a turn and in terms of right angles for quarter, half and three-quarter turns (clockwise and anticlockwise). 

Statistics

Pupils should be taught to:

• interpret and construct simple pictograms, tally charts, block diagrams and simple tables
• ask and answer simple questions by counting the number of objects in each category and sorting the categories by quantity
• ask and answer questions about totalling and comparing categorical data.

White Rose Maths frameworks

White Rose teaches children mathematical concepts through pictorial, practical and written methods in order to develop a deep understanding, confidence and competence in Maths and improve fluency. Fluency in Maths is about developing number sense and being able to choose and use the most appropriate method for the task at hand and be able to apply a skill to multiple contexts. The scheme follows a teaching for mastery approach and uses Concrete, Pictorial and Abstract (CPA) to support the children with their learning. Our programme of study is taught in manageable steps which allows pupils to progress through the curriculum at the same pace and also allows, where possible, children to make accelerated progress. Children revisit previously learned knowledge, concepts and procedures to make sure that their mathematical knowledge becomes deeply embedded, increasing their maths confidence. Those pupils behind age-related expectations are provided with the opportunities to learn the mathematical knowledge and skills that are necessary to keep up with their peers.

The White Rose Maths resources and schemes of learning outline yearly frameworks that break down what children need to learn during each week of each term to master the learning objectives laid out by the National Curriculum and DFE statutory framework for the EYFS.

YR maths yearly overview