Mathematics

Maths at St. Peter’s

At St. Peter’s, our aims, vision and values are at the core of everything we do.

We are guided by the key message of our Mission Statement,

'If we follow Jesus, the world will follow us.'

They define our teaching and learning, and provide an environment which prepares our pupils as confident, capable, resilient and responsible citizens able to enjoy a healthy life to the full.

Our inclusive school community works in partnership to meet the responsibility of developing each child in every way – spiritually, emotionally, academically, physically and socially because each child who is a unique creation of God and loved by God, deserves this.

We deliver the Maths curriculum through the unique approach of the St. Peter’s Family and our St. Peter’s five key driver words: Faithful, Confident, Responsible, Resilient and Healthy.

Why is Maths important at St. Peter’s?

• Mathematics is essential to everyday life.  Therefore, Mathematics at St Peter’s Catholic Primary School teaches children how to make sense of the world around them through developing their ability to calculate, investigate, reason and solve problems.
• Through their growing knowledge and understanding, children develop fluency within the subject, as well as a deeper understanding of the mathematical processes they use on a daily basis and why they use them. 
• Through a strong problem solving and reasoning approach to Maths at St. Peter’s, all children develop their mathematical reasoning, encouraging children to think about the mathematical processes that they are using and find explanations as to how they came to their answers.
• Pupils develop an enjoyment of learning through practical activity and regular problem solving, investigation, exploration and discussion;
• Children develop fluency and flexibility within Mathematics, enabling children to make links between ideas, methods, strategies and concepts, therefore developing transferable mathematical skills;
• Maths at St. Peter’s allows children to regularly engage in real problems, enabling them to actually make sense of maths;
• Pupils develop curiosity in seeking solutions and exploring patterns.
• Children develop confidence, responsibility and resilience when seeking solutions, working through problems and following a line of enquiry.
• Maths promote confidence and competence with numbers and the number system;
• Children learn to understand relationships and patterns in both number and geometry in their everyday lives.
• Children learn to appreciate the contribution made by many cultures to the development and application of Mathematics.
• Pupils develop a practical understanding - in relation to statistics, ratio, proportion and algebra - of the ways in which information is gathered and presented.
• Pupils explore features of geometry (shape and position), and develop measuring skills in a range of contexts.
• Children see Maths as an important part of everyday life, understand that we use Maths in everything that we do, which aids the development of the cross-curricular use of mathematics in other subjects.

What are the key knowledge concepts in Maths at St. Peter’s?

What are the key Maths subject discipline skills?

• become FLUENT in 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 in all areas of the subject, developing their reasoning skills: analyse, justify, explain, decision make, evaluate, deduce, prove and predict.  
• SOLVE PROBLEMS by applying their mathematics to a variety of problems with increasing sophistication, including breaking down problems into a series of simpler steps and persevering in seeking solutions. Children develop their problem solving skills: working backwards, systematic recording, conjecturing and hypothesising, trial and improvement, spotting patterns and relationships, organising a list or table, visualising and logical reasoning.
• Develop RESILIENCE when solving problems, seeking solutions and following a line of enquiry.
• Build and develop CONFIDENCE in using and applying the number system, with regards to place value, the four operations and number sense.

How does St. Peter’s ensure progression in our key knowledge and concepts in Maths?

• The St. Peter’s Calculation Policy outlines progression in teaching and learning of the four operations, from mental strategies through to formal written methods.
• All children experience a Problem Solving and Reasoning led Maths curriculum, allowing for the various problem solving and reasoning skills to be developed and progressed, throughout their time at St. Peter’s.
• Pupil’s attainment assessed against Year group expectations throughout each academic year.
• Pupil’s individual progress assessed against prior attainment throughout each academic year.
• Increasing complexity of activities expected.
• Emphasis placed on the importance of Mathematical vocabulary and increasingly complex language.
• Children experience learning mathematical concepts through a variety of teaching and learning approaches, eg, practical, active sessions, mental, written, etc.
• Constant recapping and consolidation of Mathematical topics, strategies, units of work.
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How do we know our children have made progress?

End points

FS children can:

• count reliably with numbers from one to 20
• place them in order and say which number is one more or one less than a given number
• using quantities and objects, add and subtract two single-digit numbers and count on or back to find the answer
• solve problems, including doubling, halving and sharing.
• use everyday language to talk about size, weight, capacity, position, distance, time and money to compare quantities and objects and to solve problems
• recognise, create and describe patterns
• explore characteristics of everyday objects and shapes and use mathematical language to describe them.

End points

KS1 children can:

• 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.
• solve problems with addition and subtraction: using concrete objects and pictorial representations, including those involving numbers, quantities and measures. Whilst 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 and 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
• 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.
• recognise, find, name and write fractions 1/3 , 1/4 , 2/4 and 3/4 of 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 .
• 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.
• 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.
• 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).
• 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.

End points

Year 4 Children can:

• count in multiples of 6, 7, 9, 25 and 1000
• find 1000 more or less than a given number
• count backwards through zero to include negative numbers
• recognise the place value of each digit in a four-digit number (thousands, hundreds, tens, and ones)
• order and compare numbers beyond 1000
• identify, represent and estimate numbers using different representations
• round any number to the nearest 10, 100 or 1000
• resolve number and practical problems that involve all of the above and with increasingly large positive numbers
• read Roman numerals to 100 (I to C) and know that over time, the numeral system changed to include the concept of zero and place value.
• add and subtract numbers with up to 4 digits using the formal written methods of columnar addition and subtraction where appropriate
• estimate and use inverse operations to check answers to a calculation
• solve addition and subtraction two-step problems in contexts, deciding which operations and methods to use and why
• recall multiplication and division facts for multiplication tables up to 12 × 12
• use place value, known and derived facts to multiply and divide mentally, including: multiplying by 0 and 1; dividing by 1; multiplying together three numbers
• recognise and use factor pairs and commutativity in mental calculations
• multiply two-digit and three-digit numbers by a one-digit number using formal written layout
• solve problems involving multiplying and adding, including using the distributive law to multiply two digit numbers by one digit, integer scaling problems and harder correspondence problems such as n objects are connected to m objects.
• recognise and show, using diagrams, families of common equivalent fractions
• count up and down in hundredths; recognise that hundredths arise when dividing an object by one hundred and dividing tenths by ten.
• solve problems involving increasingly harder fractions to calculate quantities, and fractions to divide quantities, including non-unit fractions where the answer is a whole number
• add and subtract fractions with the same denominator
• recognise and write decimal equivalents of any number of tenths or hundredths
• recognise and write decimal equivalents to 4 1 , 2 1 , 4 3
• find the effect of dividing a one- or two-digit number by 10 and 100, identifying the value of the digits in the answer as ones, tenths and hundredths
• round decimals with one decimal place to the nearest whole number
• compare numbers with the same number of decimal places up to two decimal places
• solve simple measure and money problems involving fractions and decimals to two decimal places.
• Convert between different units of measure [for example, kilometre to metre; hour to minute]
• measure and calculate the perimeter of a rectilinear figure (including squares) in centimetres and metres
• find the area of rectilinear shapes by counting squares
• estimate, compare and calculate different measures, including money in pounds and pence
• compare and classify geometric shapes, including quadrilaterals and triangles, based on their properties and sizes
• identify acute and obtuse angles and compare and order angles up to two right angles by size
• identify lines of symmetry in 2-D shapes presented in different orientations
• complete a simple symmetric figure with respect to a specific line of symmetry.
• describe positions on a 2-D grid as coordinates in the first quadrant
• describe movements between positions as translations of a given unit to the left/right and up/down
• plot specified points and draw sides to complete a given polygon.
• interpret and present discrete and continuous data using appropriate graphical methods, including bar charts and time graphs.
• solve comparison, sum and difference problems using information presented in bar charts, pictograms, tables and other graphs.

End points

Year 6 Children can:

• read, write, order and compare 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, and calculate intervals across zero
• solve number and practical problems that involve all of the above.
• multiply multi-digit numbers up to 4 digits by a two-digit whole number using the

formal written method of long multiplication

• divide numbers up to 4 digits by a two-digit whole number using the formal written

method of long division, and 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, interpreting remainders according to the context

• 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 the concept of equivalent fractions
•  multiply simple pairs of proper fractions, writing the answer in its simplest form [for example, 4 1 × 2 1 = 8 1 ]
• divide proper fractions by whole numbers [for example, 3 1 ÷ 2 = 6 1 ]
• associate a fraction with division and calculate decimal fraction equivalents [for example, 0.375] for a simple fraction [for example, 8 3 ]
• 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, including 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 [for example, 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 two variables.
• solve problems involving the calculation and conversion of units of measure, using decimal notation up to three decimal places where appropriate
• use, read, write and convert between standard units, converting measurements of length, mass, volume and time from a smaller unit of measure to a larger unit, and vice versa, using decimal notation to up to three decimal places
• convert between miles and kilometres
• recognise that shapes with the same areas can have different perimeters and vice versa
• recognise when it is possible to use formulae for area and volume of shapes
• calculate the area of parallelograms and triangles
• calculate, estimate and compare volume of cubes and cuboids using standard units, including cubic centimetres (cm3 ) and cubic metres (m3 ), and extending to other units [for example, mm3 and km3 ].
• draw 2-D shapes using given dimensions and angles
• recognise, describe and build simple 3-D shapes, including making nets
• compare and classify geometric shapes based on their properties and sizes and find unknown angles in any triangles, quadrilaterals, and regular polygons
• illustrate and name parts of circles, including radius, diameter and circumference and know that the diameter is twice the radius
• recognise angles where they meet at a point, are on a straight line, or are vertically opposite, and find missing angles.
• describe positions on the full coordinate grid (all four quadrants)
• draw and translate simple shapes on the coordinate plane, and reflect them in the axes.
• interpret and construct pie charts and line graphs and use these to solve problems
• calculate and interpret the mean as an average.

In Maths lessons, as in all aspects of the curriculum, children are true to their faith. This can be summarised through one line taken from our Mission Statement: ‘We are happy when we do our best in our work and play’.