Mathematics

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Students will be able to independently use the following skills: 

• Probability 

• Sample Space Diagram for listing outcomes 

• Use Venn Diagrams  

• Understand the probability of all events sum to 1. 

• Multiplication of decimals & fractions. 
• Number 

• Place Value 

• Rounding to given number of significant figures 

• Rounding to a given number of decimal places 

• Negative numbers 

• Long multiplication by using grid method. 

• Division using bus stop method. 

• Prime factor decomposition (factor trees) 

• Identify square numbers up to 12 

• Calculating Highest Common Factor & Lowest Common Multiple of two numbers. Applying this skill to problem solving. 

• Four operations with decimals & fractions. 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can….Use the core knowledge to access KS3 Mathematics. 

What should they be able to know?

• Understand place value. 

• How to round to given number of significant figures and decimal places 

• What is a factor 

• What is a multiple 

• What is a prime number 

• What is an event 

• Four operations with fractions, decimals, integers and negative numbers. 

What should they be able to do?

To use these skills to answer questions & solve problems. 

Learning checkpoints and assessment:

Mini-whiteboard quizzes, exit tickets, traffic lights from planner, homework, end of term assessment. . 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Algebra as BIDMAS with placeholders for numbers e.g. x y etc 

• What are like terms and how to collect/simplify 

• Multiplying out brackets 

• Using the laws of indices 

• Extensions include negative powers, working with quadratic brackets 

Yr8-9 

• Multiplying out double brackets  

• Factorising both single brackets and quadratics 

• Working with negative indices 

Yr10 

• Fractional and negative indices 

• Factorising quadratics the have a coefficient of

  x2�2

  other than 1. 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Know the difference between

  x3 �3 

  and

  3x

• Collect like terms including situations with powers and multiple variables e.g.

  4xy+2xy4��+2��

• Multiply out various sizes of single brackets and collections of single brackets e.g.

  4(3x+2y+10)−5(7x−y−3)43�+2�+10−5(7�−�−3)

• Apply laws of indices for multiplication of terms e.g.

  5y×3y25�×3�2

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Substitute numbers into expressions 

• Include negative numbers 

• Include fractional values and decimals 

• EXTENSION: Substitute one expression into another (to help with functions later) 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Students setup the calculation by rewriting with values substituted  

• Years 7-8 might deal mainly with integers and negatives. 

• Students calculate effectively with integers, fractions and negative values  

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Describe the four transforms using technical language 

• Apply the transforms from technical information 

•  

  Depth added by: 

• Naming equations of lines Y8 and up 

• Including fractional enlargements  

• Combining transforms 

• Including negative SF for enlargement Y9 top set and Y10 

•  

   

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Describe transforms in clear mathematical terms. 

  Describe in only single transforms 

  Carry out transforms correctly (inc fractional and negative where appropriate) 

What?

What are we learning? 

• Number - Four Operations and Place Value; Fractions, Decimal and Percentages, Mixed Number and Standard Form 

• Handling Data -Probability (Venn Diagrams, Two-way tables & the Product Rule) 

What’s interleaved?  

• Times tables 

• Division 

• Factors & multiples 

• Prime numbers 

• Converting between fractions, decimals & percentages 

• Order of operation 

• Place Value 

What’s challenging? 

• Student to appreciate the relationship between fractions, decimals and percentages & how they are used to represent probabilities. 

• Using Standard Form to write very large and very small numbers 

Why?

Why do we need to deliver this (vision statement)? Why now? 

To establish KS3 Mathematical skills required to access KS4 topics. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Students will be able to independently use the following skills: 

• Probability 

• Sample Space Diagram for listing outcomes 

• Two-way tables for listing outcomes 

• Use Venn Diagrams  

• Understand the probability of all events sum to 1 

• Multiplication of decimals & fractions 

• Use the product rule for finding the total number of possible outcomes 

• Number 

• Conversion between metric units of length, capacity and mass. 

• Convert between decimals and percentages – more than 100 

• Solve problems involving time 

• Addition and subtraction laws for indices 

• Four operations with decimals, fraction & mixed numbers 

• Calculate percentage increase and decrease, including using a multiplier 

• Express one number as a fraction or a percentage of another with and without a calculator 

• Work with percentage change/profit. 

• Choose appropriate methods to solve percentage problems 

• To convert between ordinary numbers and standard form 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can….Use the core knowledge to access KS3 Mathematics. 

What should they be able to know? 

• Calculate 1%, 10%, 25%, 50% and 75% of an amount without using a calculator. 

• Calculate any percentage of an amount using a calculator. 

• To calculate percentage increase and decrease of an amount. 

• What is an index number? 

• To recognise and interpret standard form 

What should they be able to do? 

To use these skills to answer questions & solve problems. 

Learning checkpoints and assessment: 

Mini-whiteboard quizzes, exit tickets, traffic lights from planner, homework, end of term assessment. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Algebra as BIDMAS with placeholders for numbers e.g. x y etc 

• What are like terms and how to collect/simplify 

• Multiplying out brackets 

• Using the laws of indices 

• Extensions include negative powers, working with quadratic brackets 

Yr8-9 

• Multiplying out double brackets  

• Factorising both single brackets and quadratics 

• Working with negative indices 

Yr10 

• Fractional and negative indices 

• Factorising quadratics the have a coefficient of

  x2�2

  other than 1. 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Know the difference between

  x3 �3 

  and

  3x

• Collect like terms including situations with powers and multiple variables e.g.

  4xy+2xy4��+2��

• Multiply out various sizes of single brackets and collections of single brackets e.g.

  4(3x+2y+10)−5(7x−y−3)43�+2�+10−5(7�−�−3)

• Apply laws of indices for multiplication of terms e.g.

  5y×3y25�×3�2

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Substitute numbers into expressions 

• Include negative numbers 

• Include fractional values and decimals 

• EXTENSION: Substitute one expression into another (to help with functions later) 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Students setup the calculation by rewriting with values substituted  

• Years 7-8 might deal mainly with integers and negatives. 

• Students calculate effectively with integers, fractions and negative values  

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Describe the four transforms using technical language 

• Apply the transforms from technical information 

•  

  Depth added by: 

• Naming equations of lines Y8 and up 

• Including fractional enlargements  

• Combining transforms 

• Including negative SF for enlargement Y9 top set and Y10 

•  

   

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Describe transforms in clear mathematical terms. 

  Describe in only single transforms 

  Carry out transforms correctly (inc fractional and negative where appropriate) 

What?

What are we learning? 

• Number - Four Operations and Place Value; Fractions, Decimal and Percentages, Mixed Number, Standard Form & index laws 

• Handling Data -Probability (Venn Diagrams, Two-way tables, the Product Rule & tree diagrams) 

What’s interleaved?  

• Times tables 

• Division 

• Factors & multiples 

• Prime numbers 

• Converting between fractions, decimals & percentages 

• Order of operation 

• Place Value 

• Inequality symbols and when they are used 

​What’s challenging? 

• Student to appreciate the relationship between fractions, decimals and percentages & how they are used to represent probabilities. 

• Using Standard Form to write very large and very small numbers 

Why?

Why do we need to deliver this (vision statement)? Why now? 

To establish KS3 Mathematical skills required to access KS4 topics. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Students will be able to independently use the following skills: 

• Probability 

• Relative frequency 

• Expected Outcomes 

• Independent Events 

• Use tree diagrams to work out probabilities and solve 'with replacement' problem  

• Number 

• Negative index laws and Powers of powers. 

• use inequality notation to specify simple error intervals due to truncation or rounding 

•  add, subtract, multiply and divide numbers in standard form, including using a calculator to work with numbers in standard form. 

• Four operations with decimals, fraction & mixed numbers 

• Solve 'reverse' percentage problems 

• Recognise and solve percentage problems (calculator and non-calculator) including: money problems with simple and compound interest, problems with VAT, wages and taxes;    

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can….Use the core knowledge to access KS3 Mathematics. 

What should they be able to know? 

• Draw a tree diagram to represent an event. 

• Draw a venn diagram to represent an event. 

• Simplify indices – recognising you need the same base to be able to apply the index law. 

• Finding percentage change/profit. 

What should they be able to do? 

To use these skills to answer questions & solve problems. 

Learning checkpoints and assessment: 

Mini-whiteboard quizzes, exit tickets, traffic lights from planner, homework, end of term assessment. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Algebra as BIDMAS with placeholders for numbers e.g. x y etc 

• What are like terms and how to collect/simplify 

• Multiplying out brackets 

• Using the laws of indices 

• Extensions include negative powers, working with quadratic brackets 

Yr8-9 

• Multiplying out double brackets  

• Factorising both single brackets and quadratics 

• Working with negative indices 

Yr10 

• Fractional and negative indices 

• Factorising quadratics the have a coefficient of

  x2�2

  other than 1. 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Know the difference between

  x3 �3 

  and

  3x

• Collect like terms including situations with powers and multiple variables e.g.

  4xy+2xy4��+2��

• Multiply out various sizes of single brackets and collections of single brackets e.g.

  4(3x+2y+10)−5(7x−y−3)43�+2�+10−5(7�−�−3)

• Apply laws of indices for multiplication of terms e.g.

  5y×3y25�×3�2

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Substitute numbers into expressions 

• Include negative numbers 

• Include fractional values and decimals 

• EXTENSION: Substitute one expression into another (to help with functions later) 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Students setup the calculation by rewriting with values substituted  

• Years 7-8 might deal mainly with integers and negatives. 

• Students calculate effectively with integers, fractions and negative values  

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Describe the four transforms using technical language 

• Apply the transforms from technical information 

•  

  Depth added by: 

• Naming equations of lines Y8 and up 

• Including fractional enlargements  

• Combining transforms 

• Including negative SF for enlargement Y9 top set and Y10 

•  

   

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Describe transforms in clear mathematical terms. 

  Describe in only single transforms 

  Carry out transforms correctly (inc fractional and negative where appropriate) 

What?

What are we learning? 

• Number - Four Operations and Place Value; Fractions, Decimal and Percentages, Mixed Number, Standard Form & index laws 

• Handling Data -Probability (Venn Diagrams, Two-way tables, the Product Rule & tree diagrams) 

What’s interleaved?  

• Times tables 

• Division 

• Factors & multiples 

• Prime numbers 

• Converting between fractions, decimals & percentages 

• Order of operation 

• Place Value 

• Inequality symbols and when they are used 

• Ratio 

​What’s challenging? 

• Student to appreciate the relationship between fractions, decimals and percentages & how they are used to represent probabilities. 

• Using Standard Form to write very large and very small numbers

Why?

Why do we need to deliver this (vision statement)? Why now? 

To establish KS3 Mathematical skills required to access KS4 topics. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Probability

• Using experimental data to estimate probabilities 

• Find probabilities from tables, Venn diagrams and frequency trees 

• Use tree diagrams for dependent and independent events 

• Construct and interpret conditional probabilities for Venn diagrams, tree diagrams and two-way tables 

Number

• Calculate with surds including rationalising the denominator  

• Understand and use limits of accuracy (estimation - error intervals using inequality notation; upper and lower bounds) 

• Upper and lower bounds calculations 

• Fractional index laws. 

• Express one number as a percentage of another 

• Reverse percentages - Find the original value after a percentage change 

• Calculate simple and compound interest 

• Solve problems involving growth and decay  

• Solve problems involving percentages, ratios and fractions 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can….Use the core knowledge to access KS3 Mathematics. 

What should they be able to know? 

• Construct and interpret tree diagrams for dependent and independent events. 

• To know what a surd is. 

• To simplify surds. 

• To understand upper and lower bounds. 

• To calculate reverse percentages 

• To calculate simple and compound interest 

What should they be able to do? 

To use these skills to answer questions & solve problems. 

Learning checkpoints and assessment: 

Mini-whiteboard quizzes, exit tickets, traffic lights from planner, homework, end of term assessment. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Algebra as BIDMAS with placeholders for numbers e.g. x y etc 

• What are like terms and how to collect/simplify 

• Multiplying out brackets 

• Using the laws of indices 

• Extensions include negative powers, working with quadratic brackets 

Yr8-9 

• Multiplying out double brackets  

• Factorising both single brackets and quadratics 

• Working with negative indices 

Yr10 

• Fractional and negative indices 

• Factorising quadratics the have a coefficient of

  x2�2

  other than 1. 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Know the difference between

  x3 �3 

  and

  3x

• Collect like terms including situations with powers and multiple variables e.g.

  4xy+2xy4��+2��

• Multiply out various sizes of single brackets and collections of single brackets e.g.

  4(3x+2y+10)−5(7x−y−3)43�+2�+10−5(7�−�−3)

• Apply laws of indices for multiplication of terms e.g.

  5y×3y25�×3�2

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Substitute numbers into expressions 

• Include negative numbers 

• Include fractional values and decimals 

• EXTENSION: Substitute one expression into another (to help with functions later) 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Students setup the calculation by rewriting with values substituted  

• Years 7-8 might deal mainly with integers and negatives. 

• Students calculate effectively with integers, fractions and negative values  

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

• Working to various levels: 

• Describe the four transforms using technical language 

• Apply the transforms from technical information 

•  

  Depth added by: 

• Naming equations of lines Y8 and up 

• Including fractional enlargements  

• Combining transforms 

• Including negative SF for enlargement Y9 top set and Y10 

•  

   

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

• Describe transforms in clear mathematical terms. 

  Describe in only single transforms 

  Carry out transforms correctly (inc fractional and negative where appropriate) 

What?

What are we learning? 

• Cycle 1 of 4: 

• Number, Ratio and Algebra 

What’s interleaved?  

• Laws of indices and standard index form 

• Prime factors and HCF/LCM 

• Bar modelling(used with representing ratio problems) and solving equations including unknowns on both sides 

• Drawing straight line graphs and finding solutions to equations such as 3x – 1 =8 

• Using areas of rectangles to expand and factorise algebraic expressions including factorising quadratics 

What’s challenging? 

• Students appreciate that the value of a ratio isn’t affected by multiplying or dividing each term by the same number. However, the value of a ratio is affected by adding or subtracting the same number in each case. 

• When working with powers of powers remembering the addition law only applies to the powers – the integers still need to be multiplied. 

• Perform standard form calculations involving multiplication and division leaving final answer in standard form fully correct. 

• Factorise harder quadratics of the form  ax2 + bx + c 

Why?

Why do we need to deliver this (vision statement)? Why now? 

Students are taught ‘popular’ interleaved exam topics from earlier on prior to November PPE. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Students will be able to provide evidence of understanding the following skills: 

• Indices, powers and roots – use the laws of indices to simplify expressions 

• Standard Form – write large numbers in standard form and convert into ordinary numbers and I can write small numbers in standard form and convert into ordinary numbers 

• Standard Form Calculations –  multiply and divide numbers in standard form and add and subtract numbers in standard form 

• Prime Factors - find the HCF(or LCM) of a pair of numbers using prime factor decomposition to list the prime factors of a number 

• Ratio Problems – solve problems involving ratios and fractions (including with measures and shapes) 

• Sharing in a Ratio – divide a quantity into 2 and 3 parts in a given ratio and solve worded 

• problems 

• Compound Measures – solve problems involving Speed, Distance and Time and Density, Mass and Volume. 

• Exchange Rates –  calculate using exchange rates and decide which is better value 

• Best Buy Problems – calculate using the unitary method which item is best value in a ‘Best Buy’ problem 

• Expanding Brackets –  expand single & double brackets and apply to problem solving questions involving shapes 

• Factorising – factorise linear and quadratic expressions and use to simplify simple algebraic fractions 

• Solving Quadratics -  factorise to solve quadratic equations of the form x2 + bx + c = 0 

• Solving Equations – solve equations involving brackets, unknowns on both sides and fractions and I am confident leaving my answer as a fraction 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can….Use the core knowledge to access ‘interleaved’ exam questions.

What should they be able to know?

How to apply the core skills of number, ratio and algebra 

What should they be able to do?

To interleave the skills and successfully respond the related GCSE past exam questions 

Learning checkpoints and assessment:

• Mini-whiteboard – show step by step solutions 

• Sparx ‘book’ homework 

•  End of cycle mini- past paper compilation assessment 

What?

What are we learning? 

• Cycle 2 of 4: 

• Shape and Data

What’s interleaved?  

• Trigonometry and Pythagoras’ theorem – look out for radius of the cone forming the base of a right angled triangle – look out for use of Pythagoras’ theorem to calculate the slant length of the cone. 

• Circumference of a circle and length of an arc 

• Area of a circle and area of a sector 

• Simplifying fractions when finding areas of sectors and length of arcs without a calculator. 

• Frequency diagrams with frequency polygons – showing a frequency polygon can be constructed from the frequency diagram. 

• Link Cumulative Frequency graphs and box plots 

What's Challenging?

• Learning  π (pi) is the relationship between the circumference and the diameter of the circle(might not have been emphasized in KS3) 

• Looking out for hemispheres being placed on top of other 3D shapes 

• Understanding a cone is a pyramid with a circular base 

• Remembering how to derive the formula for the surface area of a cylinder and the curved surface area of a cone 

• Compare 2 box plots – ensuring comparative statements are comparing the median(easily identifiable average) and best measure of spread(the interquartile range – size of the box) 

Why?

Why do we need to deliver this (vision statement)? Why now? 

Students are taught ‘popular’ interleaved exam topics from earlier on prior to November PPE – clear up early misconceptions such as recognising a negative scalar causes the vector to change direction. 

How?  

How will they achieve this? How will all access this (inclusion for all/ SEND)?

Core knowledge:  

Students will be able to provide evidence of understanding the following skills: 

• Circles 1 –  find the area and circumference of a circle, semi-circle and quarter circle and solve real problems involving circles 

• Circles 2 -  solve problems involving circles with and without a calculator (leaving my answer in terms of π if needed) 

• Volume –  work out the volume of a cube, cuboids and prisms and apply to real problems 

• Volume of a Cylinder – work out the volume of a cylinder and apply to real problems 

• Cones & Spheres – work out the volume and surface area of a cone and sphere, given the formula 

• 3D Shapes – recognise 3D shapes and their properties and describe them using the correct mathematical language and understand the 2D shapes that make up the 3D objects 

• Plans & Elevations –  identify and sketch planes of symmetry of 3D shapes and draw 

• plans and elevations of 3D shapes 

• Vectors 1 – add and subtract vectors both in a column and on a grid (write and draw) 

• Vectors 2 - find the resultant of two vectors and find multiples of a vector and represent both in a column vector and drawn on a grid 

• Vector Problem Solving – solve geometric problems in 2D using vector methods and 

• apply to simple geometric proofs 

• Frequency Polygons –construct and use frequency polygons 

• Scatter Graphs – plot and interpret scatter graphs and determine if there is a relationship between two variables AND use a line of best fit to estimate values 

• Cumulative Frequency – draw and interpret cumulative frequency tables and diagrams and work out the median, quartiles and interquartile range 

• Box Plots – draw and interpret box plots and make comparisons by commenting on the median and spread of data of two box plots 

How well?

What should they be able to know? What should they be able to do? How do they know they have done this well?

Because they can…. Use the core knowledge to access exam questions. 

What should they be able to know? 

How to apply the core skills of shape and data 

What should they be able to do?  

• To practise the core knowledge and successfully respond the related GCSE past exam questions – end of cycle assessment or November PPE. 

Learning checkpoints and assessment: 

• Mini-whiteboard – show step by step solutions 

• Sparx ‘book’ homework 

•  End of cycle mini- past paper compilation assessment 

• November PPE