Maths

Numbers and numerals

Axioms and arrays

Factors and multiples

Order of operations

Positive and negative numbers

Expressions, equations and inequalities

Angles

Classifying 2-D shapes

Constructing triangles and quadrilaterals

Coordinates

Area of 2-D shapes

Transforming 2-D figures

Prime factor decomposition

Conceptualising and comparing fractions

Manipulating and calculating with fractions

Ratio

Percentages

Different number systems

This unit on place value allows pupils to develop the skills needed to estimate and round values. By understanding the value of each digit, pupils can determine what other values are close to the original value. It continues the exploration of the infinite nature of sets of numbers.

This unit looked at the composition of numbers containing up to 7 digits and how to read these numbers 

In this unit pupils revisit, secure and develop their understanding of place value with integers, decimals, fractions, metric and imperial units. This knowledge is then extended to order and compare numbers of increasing complexity.

Place value

This unit on factors, multiples, squares and cubes helps pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used in the next unit to explore multiplying and dividing with decimals.

In this unit, pupils learnt how to identify common factors and common multiples. in this unit, pupils build on this understanding to find the LCM and HCF

In this unit pupils develop their understanding of factors and multiples, then extend this knowledge to learn general divisibility tests for integers and develop strategies to determine the highest common factor and lowest common multiple of two or more integers.

Properties of number: factors, multiples, squares and cubes

Pupils use their understanding of place value and fluency with decimals from this unit in order to extend this understanding to fractions.  In the future unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required.

The prior unit on factors, multiples, squares and cubes helped pupils build on their understanding that any positive integer can be expressed as a product of its factors. This skill is used here to explore multiplying and dividing with decimals.

In this unit pupils develop their ability and efficacy with the four operations including more complicated and challenging calculations involving fractions, decimals and negative numbers. This leads into an exploration of the priority order of operations.

Arithmetic procedures with integers and decimals

In this unit, pupils formalise algebraic notation and terms and begin to formulate an understanding of basic algebraic manipulation. This understanding is built upon in the future unit where pupils learn how to solve linear equations

In this unit, pupils learnt how to represent the structure of a problem with two unknowns using a diagram. This understanding is built upon in this unit and formalised

In this unit, pupils learn about generalisation and formal algebraic manipulation techniques such as substitution, collecting like terms and factorising.

Expressions and equations

In this unit, pupils extend their knowledge of plotting coordinates from KS2 by now plotting non-integer values. Pupils learn that a set of points can satisfy a relationship and this understanding is built on in the sequences unit

In this unit, pupils learnt how to plot coordinates in all four quadrants via plotting positions and then shapes

In this unit pupils revisit and further develop their understanding of the coordinate plane, and learn how to plot non-integer coordinates. Pupils then plot from an equation both by hand and by using technology.

Plotting coordinates

In this unit pupils learn how to derive and use the formula for the area of a triangle and trapezium. In the future unit, this knowledge is called upon to find the volume of different prisms and area of composite shapes

In this unit, pupils explored the relationship between perimeter and area. In particular, they considered whether a shape can have the same area and perimeter value

In this unit pupils investigate how to calculate the area and perimeter of rectilinear shapes, and composite shapes using rectangles and triangles. They will also derive simple area formulae.

Perimeter and area

In this unit, pupils have explored the structure of fractions and their relationship with decimals and integers. This is built on in the future unit where pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

In this unit, pupils will be asked to compare and order both fractions and decimals and will assess when conversion is required. Fluency in working with decimals and integers is an important skill which is developed in the prior unit.

This unit develops understanding and manipulation of fractions, including conversion between fractions to terminating and recurring decimals. Pupils then learn strategies to order fractions of increasing complexity.

Comparing and ordering fractions and decimals (positive and negative)

In this unit, pupils generalised and developed their fluency of multiplying with fractions. In the future unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

In the prior unit, pupils explored the structure of fractions and their relationship with decimals and integers. In this unit, pupils deepen their understanding of the arithmetic procedures involving fractions and integers.

This unit revisits and secures fraction operations and extends pupil understanding to division of whole numbers by fractions and division of fractions by fractions.

Arithmetic procedures with fractions

The multiplicative relationship is extended in the future unit by considering percentages and the connections between multiplicative relationships and direct proportion. By building on a secure understanding of fractions and ratio, pupils can see their understanding of multiplicative relationships being extended.

In the prior unit, pupils generalised and developed their fluency of multiplying with fractions. In this unit, this understanding is extended to ratio and connections between ratios and fractions are explored.

This unit introduces the concept of multiplicative relationsihps, and connects fractions to the idea of ratios. Ratios are then explored in depth and used to solve contextual problems such as those involving exchange rates and general conversions.

Understanding multiplicative relationships: fractions and ratio

In this unit, pupils explore the effects of different transformations and whether the transformed shape is congruent or similar to the original shape. This is built on in the future unit where pupils formalise the criteria for determining congruence in triangles and study rotational symmetry

In this unit, pupils translated and reflected simple shapes on the full coordinate grid. In this unit, these processes are formalised and rotation and enlargement are introduced

This unit introduces pupils to shape tranformations: enlargements, rotations, reflections and translations both by hand and with technology.

Maths

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