# Mathematics

Welcome to Mathematics at OLSJ!

Developed over centuries, mathematics has provided solutions to some of the world’s most interesting problems. It is essential to everyday life, education and employment.

At Our Lady and St. Joseph, we aim to provide children with a solid foundation for understanding the world, the ability to reason mathematically, as well as fostering a sense of enjoyment and curiosity about the subject.

We recognise the National Curriculum as the benchmark for curriculum progression and learning in maths. Based on this, we use and adapt the White Rose Mathematics scheme to support our pupils' learning and progress in fluency and in problem solving and reasoning.

Mathematics Curriculum Statement of Intent

To develop every child's ability and understanding of calculation, reasoning and problem solving. These fundamentals of maths will give the children the skills they need to thrive in school and apply their learning successfully to real life. It will also aim to foster in our pupils a life long love and enjoyment of mathematics.

At OLSJ, we use concrete, pictorial and abstract methodology, as the children progress through the school and in an age appropriate way. This is a three-part strategy in which each part builds on the previous instruction, encouraging pupils to create meaningful connections between concrete, pictorial and abstract levels of thinking and understanding.

Concrete: In this stage, pupils are introduced to an idea, concept or skill. At OLSJ, teachers introduce new knowledge by modeling each mathematical concept with concrete materials. This is the “doing” stage in which concrete objects (real life objects or physical manipulatives such as numicon, dienes, cubes) are used to model problems. At first, should the problem be about adding a collection of apples and bananas, the teacher would use these exact objects. They would then move onto using unifix cubes, counters or numicon to represent the problem.

Pictorial: This stage involves drawing pictural represenations of the mathamatical problem. For example drawing circles, dots, bar models, part-part-whole models, ten frames, tallies, or using stamps to imprint pictures for counting.  This is the “seeing” stage, using representations of the previously used concrete objects to model problems.

Abstract: In this stage, the teacher models the mathematics concept at a symbolic level, using only numbers, mathematical symbols (+, –, x, /) and other mathematic notation. This is the “symbolic” stage, where students are able to use abstract symbols to model problems.

This three-step process provides students with a deeper understanding of mathematical concepts and is an essential foundational approach for future problem solving. It is important to remember this approach is not linear, each apporach does not need to be covered in one individual lesson. Moving back and forth between the different approaches can deepen understanding. It is vital to show concrete, pictoral and abtract representations side by side so that children can make links between them. The ultimate goal is for children to become confident in the abstract stage, and providing links will make this more achievable.

What skills does OLSJ’s Maths Curriculum develop?

We want pupils to become fluent in the fundamentals of mathematics, to be able to reason and to solve problems. Our curriculum embraces these National Curriculum aims, and provides guidance to help pupils to become:

Visualisers – we use the CPA approach to help pupils understand mathematics and to make connections between different representations.

Describers – we place great emphasis on mathematical language, vocabulary and questioning so pupils can discuss the mathematics they are doing, and so support them to take ideas further.

Experimenters – as well as being fluent mathematicians, we want pupils to love and learn more about mathematics.

## Why is our Maths curriculum ordered in the way it is?

To learn mathematics effectively, some things have to be learned before others, e.g. place value needs to be understood before working with addition and subtraction, addition needs to be learnt before looking at multiplication (as a model of repeated addition). You will see this emphasis on number skills first, carefully ordered, throughout our primary curriculum. For some other topics, the order isn’t as crucial, e.g. Shapes and Statistics need to come after number, but don’t depend on each other. We try to mix these so pupils have as wide a variety of mathematical experiences as possible in each term and year.

Curriculum Implementation Key Stages 1 & 2

Year 1

Number/Calculation

• Count to / across 100
• Count in 1s, 2s, 5s and 10s Identify ‘one more’ and ‘one less’
• Read & write numbers to 20
• Use language, e.g. ‘more than’, ‘most’ Use +, - and = symbols
• Know number bonds to 20
• Add and subtract one-digit and two-digit numbers to 20, includingzero
• Solve one-step problems, including simple arrays

Geometry & Measures

• Use common vocabulary for comparison, e.g. heavier, taller, full, longest, quickest
• Begin to measure length, capacity, weight
• Recognise coins & notes
• Use time & ordering vocabulary
• Tell the time to hour/half-hour
• Use language of days, weeks, months & years
• Recognise & name common 2-d and 3-d shapes
• Order & arrange objects
• Describe position & movement, including half and quarter turns

Fractions

• Recognise & use 1⁄2 & 1

Year 2

Number/Calculation

• Know 2, 5, 10x tables
• Begin to use place value (T/U)
• Count in 2s, 3s, 5s & 10s
• Identify, represent & estimate numbers
• Compare / order numbers, inc. < > =
• Write numbers to 100
• Know number facts to 20 (+ related to 100)
• Use x and ÷ symbols
• Recognise commutative property of multiplication

Geometry & Measures

• Know and use standard measures
• Read scales to nearest whole unit
• Use symbols for £ and p and add/subtract simple sums of less than £1 or in pounds Tell time to the nearest 5 minutes
• Identify & sort 2-d & 3-d shapes
• Identify 2-d shapes on 3-d surfaces
• Order and arrange mathematical objects
• Use terminology of position and movement

Fractions

• Find and write simple fractions
• Understand equivalence of e.g. 2/4 = 1/2

Data

• Interpret simple tables & pictograms

Year 3

Number/Calculation

• Learn 3, 4 & 8x tables
• Secure place value to 100
• Mentally add & subtract units, tens or hundreds to numbers of up to 3
• digits
• Written column addition & subtraction
• Solve number problems, including multiplication & simple division and missing number problems
• Use commutativity to help calculations

Geometry & Measures

• Measure & calculate with metric measures
• Measure simple perimeter
• Add/subtract using money in context
• Use Roman numerals up to XII; tell time
• Calculate using simple time problems
• Draw 2-d / Make 3-d shapes
• Identify and use right angles
• Identify horizontal, vertical, perpendicular and parallel lines

Fractions & decimals

• Use & count in tenths
• Recognise, find & write fractions
• Recognise some equivalent fractions
• Add/subtract fractions up to <1
• Order fractions with common denominator

Data

• Interpret bar charts & pictograms

Year 4

Number/Calculation

• Know all tables to 12 x 12
• Secure place value to 1000
• Use negative whole numbers
• Round numbers to nearest 10, 100 or 1000
• Use Roman numerals to 100 (C)
• Column addition & subtraction upto 4 digits
• Multiply & divide mentally
• Use standard short multiplication

Geometry & Measures

• Compare 2-d shapes, including quadrilaterals & triangles
• Find area by counting squares
• Calculate rectangle perimeters
• Estimate & calculate measures
• Identify acute, obtuse & right angles
• Identify symmetry
• Introduce simple translations

Data

• Use bar charts, pictograms & line graphs

Fractions & decimals

• Recognise tenths & hundredths
• Identify equivalent fractions
• Add & subtract fractions with common denominators
• Recognise common equivalents
• Round decimals to whole numbers
• Solve money problems

Year 5

Number/Calculation

• Secure place value to 1,000,000
• Use negative whole numbers in context
• Use Roman numerals to 1000 (M)
• Use standard written methods for all four operations
• Confidently add & subtract mentally
• Use vocabulary of prime, factor & multiple
• Multiply & divide by powers of ten
• Use square and cube numbers

Geometry & Measures

• Convert between different units
• Calculate perimeter of composite shapes & area of rectangles
• Estimate volume & capacity
• Identify 3-d shapes
• Measure & identify angles
• Understand regular polygons Reflect & translate shapes

Data

• Interpret tables & line graphs
• Solve questions about line graphs

Fractions

• Compare & order fractions
• Add & subtract fractions with common denominators, with mixed numbers
• Multiply fractions by units
• Write decimals as fractions
• Order & round decimal numbers
• Link percentages to fractions & decimals

Year 6

Number/Calculation

• Secure place value & rounding to 10,000,000, including negatives
• All written methods, including long division
• Use order of operations (not indices)
• Identify factors, multiples & primes
• Solve multi-step number problems

Algebra

• Introduce simple use of unknowns

Geometry & Measures

• Confidently use a range of measures & conversions
• Calculate area of triangles / parallelograms
• Use area & volume formulas
• Classify shapes by properties
• Know and use angle rules
• Translate & reflect shapes, using all four quadrants

Data

• Use pie charts
• Calculate mean averages

Fractions, decimals & percentages

• Compare & simplify fractions
• Use equivalents to add fractions
• Multiply simple fractions
• Divide fractions by whole numbers
• Solve problems using decimals & percentages
• Use written division up to 2dp
• Introduce ratio & proportion