Maths

Checking understanding of place value in integers

Securing understanding of place value in integers

Deepening understanding of place value in integers

Exponential and fractional column headings

Place value in decimals

Checking understanding of place value in metric units

Securing understanding of place value in metric units

Place value in imperial units

Checking understanding of ordering and comparing numbers

Securing understanding of ordering and comparing numbers

Problem solving with place value

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

Checking understanding of factors, multiples, squares and cubes

Securing understanding of factors, multiples, squares and cubes

Listing multiples

Divisibility tests for 2 and 3

Divisibility tests for 6 and 9

Divisibility tests for 5 and 10

Divisibility tests for 4 and 8

Square and cube numbers

Square and cube roots

Power notation

Powers and roots using a calculator

Listing factors

Checking understanding of prime numbers

Expressing an integer as a product of its prime factors

Calculating integers from their prime factor expressions

Highest common factor

Lowest common multiple

HCF or LCM

Problem solving with factors, multiples, squares and cubes

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

Checking understanding of arithmetic procedures with integers and decimals

Securing understanding of arithmetic procedures with integers and decimals

Checking and securing understanding of negative numbers in context

Addition of positive and negative integers

Subtraction of positive and negative integers

Checking and securing understanding of written addition and subtraction strategies

Checking and securing understanding of multiplication and division

Multiplication and division where only one value is negative

Multiplication and division where two or more values are negative

Simplifying multiplication and division using multiples of 10

Multiplying with decimals

Dividing with decimals

Checking and securing understanding of the commutative and associative laws

Checking and securing understanding of the distributive law

Priority of operations with positive integers

Priority of operations with positive and negative integers and decimals

Using the associative, commutative and distributive laws together

Using your calculator efficiently

Problem solving with integers and decimals

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

Checking understanding of expressions and equations

Securing understanding of expressions and equations

Representing a generalised number

Algebraic notation

Algebraic terminology

Representing an unknown or variable

Generalised algebraic statements

Substituting particular values

Like terms

Simplifying by collecting like terms

Multiplying an expression by a constant

Multiplying an expression by a term

Multiplying and simplifying with multiple expressions

Simplifying before multiplying with multiple expressions

Highest common factor with algebraic terms

Factorising expressions

Problem solving with expressions and equations

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

Checking understanding of plotting coordinates

Securing understanding of plotting coordinates

Plotting non-integer coordinates

Plotting coordinates generated from a rule

Plotting coordinates generated from a rule using technology

Plotting a relationship

Problem solving with plotting coordinates

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

Checking understanding of perimeter and area

Securing understanding of perimeter and area

Finding the perimeter of polygons

Calculating missing lengths with perimeter of polygons

Perimeter with composite rectilinear shapes

Area of a triangle

Using the formula for the area of a triangle

Area of composite rectilinear shapes

Calculating missing side lengths from the area of composite rectilinear shapes

Area of a trapezium

Calculating missing side lengths from the area of a trapezium

Problem solving with perimeter and area

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

Checking and securing understanding of fractions

The identity property of multiplication and division

Checking and securing converting improper fractions to mixed numbers

Checking and securing converting mixed numbers to improper fractions

Converting fractions to terminating decimals

Converting fractions to recurring decimals

Converting terminating decimals to fractions

Simplifying fractions

Converting fractions with technology

Limitations of technology in calculations

Ordering negative integers

Ordering decimals

Ordering fractions by converting

Ordering fractions by way of a common denominator

Ordering fractions in different ways

Ordering positive and negative fractions and decimals

Between numbers

Problem solving with fractions and decimals

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)

Checking understanding of addition and subtraction with fractions

Securing understanding of addition and subtraction with fractions

Checking understanding of multiplication with fractions

Securing understanding of multiplication with fractions

Deepening understanding of multiplication with fractions

Checking and securing dividing a fraction by a whole number

Dividing a whole number by a fraction

Dividing a fraction by a fraction

Priority of operations with positive and negative integers, decimals and fractions

Problem solving with arithmetic procedures involving fractions

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

Checking understanding of multiplicative relationships

Securing understanding of ratio as a multiplicative relationship

Multiplicative relationships in context

Expressing multiplicative relationships as ratios and fractions

Multiplicative relationships

Equivalent multiplicative relationships

Representing a multiplicative relationship

Ratio language and notation

Checking and securing finding a fraction of a given amount

Deepening understanding with fractions of a given amount

Expressing one number as a fraction of another

Dividing a quantity into a given ratio

Determining the whole

Determining the part

Describing exchange rates with ratio

Describing more conversions with ratio

Problem solving with fractions and ratios

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

Checking understanding of basic transformations

Introduction to translation

Describing a translation

Translating objects

Introduction to rotations

Describing a rotation's direction and size

Understanding the centre of rotation

Rotating objects

Introduction to reflections

Describing a reflection

Reflecting objects

Introduction to enlargements

Describing an enlargement

Enlarging objects

Transformed objects

Investigating transformations with Desmos

Investigating transformations with GeoGebra

Problem solving with transformations

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.

Transformations

Maths

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