### 19 Sep # Getting To Grips With The New Primary Maths Curriculum

In the New Primary Maths Curriculum there are many changes, perhaps though the most significant is the expectation of how maths must now be taught to greater depth for greater understanding.  The teaching and learning must now aim to develop the following three strands, fluency, mathematical reasoning and problem solving.

“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”

Statutory guidance: National curriculum in England: mathematics programmes of study 16 July 2014

Ofsted, too, have recently updated their subject specific criteria for mathematics. When inspectors observe maths lessons now, they will look for:

• Teaching for conceptual understanding
• Problem solving and mathematical reasoning
• Assessment
• Teacher attitudes and knowledge

These aims and expectations, of both Ofsted and the New Curriculum, create a very different landscape for how teaching now needs to happen in order for expected learning to take place. These aims present a wonderful opportunity to develop students’ understanding of mathematics, enabling them to become successful in the subject.  However it also may present teachers with many challenges as it demands a lot of teachers’ own knowledge, fluency, ability to reason mathematically and problem solve. This is something they themselves may not have been taught.
Sometimes, in our opinion, that which appears to be the easiest of maths can be the most difficult to teach.

## Mathematics: How to teach fractions at KS2 for mastery

There is an earlier and challenging requirement for fractions and decimals. Understanding fractions can be a difficult journey from understanding the concept of whole number to understanding parts of whole numbers. It has been shown however, that primary-age pupils’ knowledge of fractions and division can predict the success in mathematics in later stages of their schooling. (Siegler et al, 2012). It follows therefore, that it is important to get the teaching right in primary schools. It is essential that teachers in KS1 are aware and understand how what they teach, is built upon in KS2 and likewise it is essential that teachers in KS2 have an awareness and understanding of what conceptual understanding they are building upon, and will be built upon at KS3.
The term fraction is to now be introduced to pupils in Yr1 where they will be expected to be able to recognise, find and name a half as one of two equal parts of an object, shape or quantity and similarly a quarter. Following on from this the major change is the expectation that the teaching will be done in earlier years than previously. For example some of the teaching and learning at KS2 will be some of that which previously took place at KS3.

“Number – fractions (including decimals and percentages) Statutory requirements Year 6
Pupils should be taught to:

• use common factors to simplify fractions; use common multiples to express fractions in the same denomination
• compare and order fractions, including fractions >
• 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
• divide proper fractions by whole numbers
• associate a fraction with division and calculate decimal fraction equivalents
• 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”

Statutory guidance: National curriculum in England: mathematics programmes of study 16 July 2014

Our Fraction course covers these changes and develops the teachers own skills and fluency.

## Mathematics: Teaching for Mastery: How to teach from concrete beginnings to abstract calculations

In Key Stage 1 and Key Stage 2 there is an increased emphasis on teaching number skills; balancing conceptual understanding with arithmetic proficiency is essential. Conceptual development of number is addressed in detail in the new curriculum, it is this understanding of number that influences anyone’s ability to calculate and manipulate number. This understanding is crucial to building resilience and fluency in mathematics. A firm understanding of place value is vital for any work with number. Fluency is much more than memorisation of procedures and facts and the new curriculum aims to address this.
There is now a requirement that students are able to do long multiplication and division using the formal written method. Ensuring strong foundations in number is essential before making the move from concrete to abstract understanding, which in turn may present some teachers with potential problems, as their own confidence and understanding may not be as strong as they would like.

Our course aids teachers develop their own sense of number and strategies for developing their students’ subject knowledge in number and place value, addition subtraction multiplication and division.

## Let’s Not Forget The Importance Of Mental Maths

In the New Curriculum a strong emphasis has been placed on mental and written calculation of whole numbers, decimals and fractions

“The principal focus of mathematics teaching in upper key stage 2 is to ensure that pupils extend their understanding of the number system and place value to include larger integers. This should develop the connections that pupils make between multiplication and division with fractions, decimals, percentages and ratio.

At this stage, pupils should develop their ability to solve a wider range of problems, including increasingly complex properties of numbers and arithmetic, and problems demanding efficient written and mental methods of calculation.

National curriculum in England: mathematics programmes of study 16 July 2014

The important word here is efficient.
A year 5 child knows all of their multiplication tables up to 12×12. When asked what is 13×4 he looked blank. Does this show understanding, reasoning , problem solving and is it efficient?
To facilitate this, our course aims for teachers to learn practical tips and systems to support them in teaching their pupils effective methods of mental calculation. Teachers will learn practical tips, systems and suggestions, to take back to their classrooms to promote mental recall of maths fact, particularly in problem solving in all areas of the new KS2 curriculum.

## Algebra –  The A-Z of It

The teaching and learning of Algebra is only specified for Year 6, however algebraic thinking should be happening across the school. Many teachers are probably already teaching it, without realising that is what they are doing. Indeed for many Primary teachers this may be one of those areas of maths they feel they have not used since leaving school and are a little wary of teaching.

“Statutory requirements Year 6 Algebra
Pupils should be taught to:
•    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 variable”

National curriculum in England: mathematics programmes of study 16 July 2014

Our course addresses the demands of the New Curriculum to introduce formal algebra into KS2 but importantly looks at what algebra actually is, why it is important and will show how the hidden algebra in the curriculum can be taught to benefit reasoning and fluency. This means exploring numbers and how they combine together, and becoming familiar with ideas such as the inverse. As with any strand of maths, formal algebra cannot be introduced without a strong foundation in concrete methods having been laid down in previous years.

## Covering all angles: Teaching measurement and geometry in line with the new national primary maths curriculum

Arithmetic may be greatly emphasised in the New Curriculum but there are still other programmes of study that will ensure the delivery of a broad and balanced curriculum. Previously known as Shape and Space this strand is now known as Geometry throughout KS1 and 2.
As with other strands of maths, KS1 teachers must be confident in their own geometric subject knowledge; not just for KS1 but also for KS2 in order to understand how the subject progresses, and to ensure that the foundations being laid in KS1 enable a seamless journey through the geometry curriculum, and are not building any misconceptions that will cause difficulties later in KS2. Likewise KS2 teachers need to be aware of the progression for KS3 in order to lessen any later difficulties that might be caused by misconceptions at KS2. In order for pupils to be fluent in geometry they will need to become increasingly familiar with, and confident in, using accurate vocabulary.

Mathematics year 6: Geometry – position and direction
Pupils should be taught to:

• describe positions on the full coordinate grid (all 4 quadrants)
• draw and translate simple shapes on the coordinate plane, and reflect them in the axes”

National curriculum in England: mathematics programmes of study 16 July 2014
“Geometry – properties of shapes
Pupils should be taught to:

• 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”

National curriculum in England: mathematics programmes of study 16 July 2014

The aims of this course are to consider the requirements in upper key stage 2 of measurement and geometry and how they can be linked to calculations and to consider the extra mathematical content at this level and how to plan for its delivery.