Curriculum Intent

The Mathematics Department aims to provide all students with a rewarding and enjoyable experience of mathematics. We will prepare students to become confident, numerate individuals who are able to deal with all aspects of mathematics in their chosen career and in all aspects of their adult life.

This will be accomplished through our commitment to excellent teaching, a well-designed curriculum with an interesting variety of lessons to motivate and engage all students. We have high expectations of all students so that they will recognise and achieve their full potential. We hope that students will develop their own skills in analysis, reasoning, creativity, collaboration and self-evaluation so that they can meet the mathematical problems they face with thoughtfulness and enthusiasm.

 

Mathematics at Werneth School is an exciting and interesting subject which is related to the world around us. We have adopted a ‘mastery approach’, which means that when a concept has been mastered students will then solve complex problems and apply to real life scenarios to develop depth of understanding. A 5 year scheme builds skills, year on year, to enable students to become fluent in maths and have the ability to apply what they know to unfamiliar areas of the curriculum; an essential life skill. Units are taught in six week blocks where students' knowledge is regularly evaluated. There is a final summative assessment at the end of the unit.

In our classrooms, students experience a variety of activities including problem solving, group work and investigations, alongside more traditional consolidation, and practice. We are a well-resourced department of 10 specialist teachers with access to many dedicated resources such as Sparx maths.  All of these are available to support the student’s independent learning outside the classroom.

 

Curricular Features

  • To become fluent in numerate techniques that support good progress in mathematics and are essential life skills for be prepared for further education and working life
  • To develop the oracy skills and use of technical language in the subject so that students can articulate their thoughts and provide reasoning for their work
  • To provide deep learning of mathematical concepts through mastery learning activities throughout the five year curriculum
  • To enhance students knowledge of mathematics in the real world by providing contextual learning experiences such as learning compound percentages by studying mortgages
  • To provide learners the opportunity to study mathematics further through additional curricular opportunities in statistics and further mathematics.
  • To build mathematical resilience to support problem solving throughout the curriculum and develop that as a skill which can be used cross curriculum
  • A curriculum that is designed for students to learn to their ability as well as aspiring to improve throughout

Curriculum overview:

Y7:

 

Autumn

Spring

Summer

Area of study:

Addition and its applications

Subtraction and its applications

Multiplication and its applications

Division and its applications

Fractions, decimals and percentages

Angles and measuring

What should they know?

How to add numbers including decimals, negatives and fractions

 

How to  use place value as a tool to manipulate and identify numbers

How to subtract numbers including decimals, negatives and fractions

 

Can use place value as a tool to manipulate and identify numbers

How to subtract multiply numbers including decimals, negatives and fractions

 

Can combine previous skills alongside applications of multiplication

How to subtract division numbers including decimals, negatives and fractions

 

Can combine previous skills alongside applications of multiplication

Can confidently work with numbers presented in either fractional, decimal or percentage form as well as changing between forms

The importance of angles and their uses including the rules that govern them and where those rules were postulated from

 

The importance of units of measure and how and why we convert between different systems

What should they be able to do?

Be able to apply the above skills to functional questions including applications such as working with money, timetables and algebraic expressions

 

To utilise these skills for geometrical purposes such as perimeter and angles

Be able to apply the above skills to functional questions including applications such as working with temperatures and understanding debt

 

To utilise these skills for geometrical and working with inverse operations

Be able to apply the skills of multiplication to a variety of topics such as solving equations

 

To apply the knowledge of multiplication to real world scenarios such as finding areas

Be able to apply the skills of division  to a variety of topics such as sharing into quantities

 

To apply the knowledge of division to real world scenarios such as sequences that occur in nature

Confidently work with numbers presented in either fractional, decimal or percentage form as well as changing between forms

 

Can manipulate the forms of FDP to perform calculations including percentage changes

Can confidently draw and measure angles

 

Can use the rules of angles to find missing angles around points, on lines and within triangles

 

Can confidently convert between units and have an understanding of the parameters of units for measures

Key vocabulary

Sum

Fraction

Decimal

Value

Negative

Perimeter

Difference

Fraction

Decimals

Value

Negative

Debt

Product

Area

Simplify

Expressions

Estimate

Geometric

Arithmetic

Sequence

 

Percentage

Fraction

Decimal

Increase

Decrease

Change

Obtuse

Reflex

Acute

convert

Assessment

To ensure consistency of assessment across the year for students we use the following model

  • In each of the above units students will have the opportunity to complete a series of progress checks. These are aimed at checking students' understanding and they will complete a relevant piece of improvement work based on teacher feedback - These assessments are based on student learning so carry no score. An example can be seen in the attached powerpoint
  • In the first terms in Autumn, Spring and Summer students will sit an end of unit examination which is based on their current learning
  • In the second terms in Autumn and Spring students will sit a progress check, this assessment is based on current and previous learning. The results of these and the above assessments are then used to provide you with a grade that your son/daughter will have on their report home
  • In the last summer term students will sit their end of year exam which is a more extensive assessment consisting of a non-calculator and a calculator exam as above these are graded using GCSE requirements and the results reported home

 

Y8:

 

 

Autumn

Spring

Summer

Area of study:

Sequences and Equations

Indices

Constructions

Ratio and Scale

2D shapes

Data handling

What should they know?

The use of sequences and the rules that differing sequences use

 

How algebra can be applied to questions to find unknowns in a variety of contexts

To connect the idea of multiplication to the use of index notation

 

To apply index notation to simplify algebra of increasing complexity

How to create accurate diagrams including the use of angles to identify locations

 

To develop angles knowledge into polygons

The use of ratio to share amounts into unequal parts

 

Using ratio and scales to create diagrams and using maps

To explore the properties of 2D shapes including finding the area of shapes such as trapeziums and compound shapes

 

To understand the use of surface area in real life contexts

The different statistical diagrams that can be used in maths including their uses and limitations

 

How different statistical procedures can be applied to a data set to provide conclusions and which are most appropriate

What should they be able to do?

To find the nth term of a sequence and to use this to find terms in a sequence or whether a number is in a sequence

 

To solve equations with up to three operations including basic applications of this skill with perimeter and angles

To be able to explain why the rules of indices work and then use said rules in a variety of algebraic simplifications

 

To use the above rules to expand and factorise single brackets as a key algebraic skill

To be able to draw a triangle accurately using a compass and protractor and then to use this skills to identify regions using Loci

 

To understand the rules of internal and external polygon angles and apply these to complex shape problems

Able to take a ratio and simplify it into its simplest form.

 

Share a given amount into a ratio or find that total given a part amount

 

To use a scale on a map or diagram to find real life dimensions

To be able to find the area of two dimensional shapes including circles

 

To be able to calculate a surface area and then use this in a functional context to find required amount of materials and or cost 

To be able to draw and interpret a range of statistical diagrams including pie charts and various graphs

 

To be able to find averages of data and choose a correct average for the data set including reasoning

Key vocabulary

Sequence

Rule

Reverse

Operation

Index

Indices

Simplification

Evaluate

Bisector

Loci

External

Internal

Scale

Ratio

Share

 

Area

Trapezium

parallelogram

Compound

Surface area

Pie chart

Mode

Mean

Range

Median

Assessment

To ensure consistency of assessment across the year for students we use the following model

  • In each of the above units students will have the opportunity to complete a series of progress checks. These are aimed at checking students' understanding and they will complete a relevant piece of improvement work based on teacher feedback - These assessments are based on student learning so carry no score. An example can be seen in the attached powerpoint
  • In the first terms in Autumn, Spring and Summer students will sit an end of unit examination which is based on their current learning
  • In the second terms in Autumn and Spring students will sit a progress check, this assessment is based on current and previous learning. The results of these and the above assessments are then used to provide you with a grade that your son/daughter will have on their report home
  • In the last summer term students will sit their end of year exam which is a more extensive assessment consisting of a non-calculator and a calculator exam as above these are graded using GCSE requirements and the results reported home

 

Y9:

 

 

Autumn

Spring

Summer

Area of study:

Principles of algebra

Graphs and coordinates

Proportional reasoning

Reasoning with number

probability

Transformations

What should they know?

Complex algebraic techniques involving binomials

 

Solving more complex equations such as those with multiple unknowns of either the same or different variables

Exploring the principles of graphs including how coordinates work and finding missing vertices

 

using graphs of real life contexts to find rates of change 

Exploring proportional relationships and how changing operations effect results

 

Working with compound units in a variety of contexts

Students expand on knowledge of percentages and how to use them in different contexts such as bank accounts

 

Exploration of standard form and how it used to identify large and small numbers

Students explore the use of probability and how it is calculated in theory and then its limitations in real world scenarios

 

Students study the use of Venn diagrams and how they are used to display information

Students explore the use of transformations to move shapes around a coordinate grid.

 

Similar shapes and their properties including the connection to enlargement

What should they be able to do?

Students can expand and factorise quadratic expressions

 

Students can solve equations and inequalities that involve multiple operations

 

Students can solve a simultaneous equation to find two unknowns in a variety of ways

Students can plot and calculate coordinates in two and three dimensions

 

Students can utilise skills with linear graphs including plotting, finding the equation of and interpreting those that have context

Able to find missing amounts using both direct and inverse proportional reasoning

 

Can apply the above skills to working out best buys, currency conversions and recipe scaling

 

Can calculate speed, density and pressure

Students can expand their knowledge of percentages to using multipliers and then utilise this to find compound percentages and reverse percentages

 

Students can put numbers into and out of standard form including performing four operations on numbers in standard form

Able to calculate a probability from a variety of scenarios

 

Can calculate a relative frequency and then relate this to what would happen in reality

 

Can calculate the probability of multiple events happening

Can populate a venn diagram and calculate a given probability

Students are able to perform reflections, rotations and translations as well as being able to describe an already given transformations

 

Students will be able to enlarge a shape on a coordinate grid including from a given point

 

Students will be able to give the conditions under which shapes are similar and find missing sides in said shapes

Key vocabulary

Factorise

Solve

Binomial

Quadratic

Coordinate

Axis

Gradient

Intercept

Speed

Density

Pressure

Conversion

Standard form

Multiplier

Compound

Interest

Probability

Exclusive

Mutually

Independent

Union

Interception

Reflect

Rotate

Translate

Enlarge

Similar

Scale Factor

Congruent

Assessment

To ensure consistency of assessment across the year for students we use the following model

  • In each of the above units students will have the opportunity to complete a series of progress checks. These are aimed at checking students' understanding and they will complete a relevant piece of improvement work based on teacher feedback - These assessments are based on student learning so carry no score. An example can be seen in the attached powerpoint
  • In the first terms in Autumn, Spring and Summer students will sit an end of unit examination which is based on their current learning
  • In the second terms in Autumn and Spring students will sit a progress check, this assessment is based on current and previous learning. The results of these and the above assessments are then used to provide you with a grade that your son/daughter will have on their report home
  • In the last summer term students will sit their end of year exam which is a more extensive assessment consisting of a non-calculator and a calculator exam as above these are graded using GCSE requirements and the results reported home
  •  

 

Y10:

Higher and Foundation tier students will study the same content but will vary in their starting and end point depending on ability

 

Autumn

Spring

Summer

Area of study:

Non Calculator methods

Similarity and congruence

Proportions and proportional change

Delving into Data

Applications of algebra

What should they know?

Students should be able to confidently work without a calculator in a variety of contexts

 

Be able to work through sequences, fractions, limits of accuracy and the use of powers

Students should be able to make the connection between similar shapes and state the conditions of congruency

 

Students should be able to extend work on trigonometry into 3D and non right angled triangles

Students should extent their knowledge of ratio to include combining ratios

 

Students discover how to use a compound percentage and how this relates to bank accounts and mortgages

Students will explore data presentation in more abstract ways

 

Calculating both dependent and independent probabilities from tree diagrams and venn diagrams

Students continue to develop their algebraic skills into ever more complex scenarios

 

Learning to solve questions that have more than one root and the different methods through which this can be accomplished

 

Solving inequalities with more than one interval or answer

What should they be able to do?

Students should be able to find the rules governing both linear and quadratic sequences

 

Find and use the limits of accuracy to calculate quantities to a suitable degree of accuracy

 

Be able to state and then use the rule of indices including use of fractional and negative powers including applications such as standard form

Find the missing sizes in similar shapes including area and volume

 

Use chains of reasoning to detail if two shapes are congruent and under what conditions

Use pythagoras and trigonometry in three dimensions

 

Find and use standard trigonometric values including using both sine and cosine rules 

Students should be able to work with ratio to find missing amounts including connecting ratios together

 

Students should be able to work with percentages efficiently including

Working algebraically with proportions to find missing amounts in relationships

Students will learn how to create cumulative frequency graphs and histograms and how to interpret these diagrams and draw further ones such as box plots

 

Students will learn the relationships between successive outcomes in probability and how to display these.

 

Learning how to calculate a probability from a situation which is conditional

Students will learn to develop their algebraic techniques into solving more complex equations with fractional components

 

Students should be able to solve quadratic equations through a variety of means such as factorising, graphical or quadratic formula

 

Students will be able to solve inequalities that have more than one interval or that are quadratic

 

Solving simultaneous equations when one equation is linear and the other is quadratic

Key vocabulary

fractional

negative

limit

accuracy

bound

quadratic

Similar

Congruent

Pythagoras

Trigonometry

Sine

Cosine

 

Direct

Inverse

Compound

Annum

Cumulative

Frequency

Histogram

Interquartile

Range

Conditional

 

Interval

Quadratic

Solve

Inequality

Assessment

To ensure consistency of assessment across the year for students we use the following model

  • In each of the above units students will have the opportunity to complete a series of progress checks. These are aimed at checking students' understanding and they will complete a relevant piece of improvement work based on teacher feedback - These assessments are based on student learning so carry no score. An example can be seen in the attached powerpoint
  • In the second terms in Autumn, Spring and Summer students will sit an end of unit examination which is based on their current learning
  • In the first terms in Autumn and Spring students will sit a progress check, this assessment is based on current and previous learning. The results of these and the above assessments are then used to provide you with a grade that your son/daughter will have on their report home
  • In the second spring term students will sit their end of year examination this is allows us time to provide feedback and intervention to students prior to the commencement of year 11

 

Y11:

 

 

Autumn

Spring

Summer

Area of study:

2D and 3D shapes

Applications of algebra 2

Multiplicative and geometric reasoning

Students will spend the remainder of the curriculum time reviewing learning from the GCSE specification 

 

Once students have completed diagnostic assessment detailed below revision schedule both individually and for the class as a whole is planned to cover gaps in learning

What should they know?

Find the length and areas of arcs and sectors including circular segment areas 

 

How to calculate the volumes of complex three dimensional shapes 

 

How to answer contextual questions on both surface area and volume with complex three dimensional shapes

 

How to use a vector to describe a journey both algebraically and numerically 

Students study the complexity of algebra and advanced techniques and their application to Maths

 

Students will study the use of functions and how they can alter a algebraic outcome

 

Students will study iteration and its uses and how an iterative method can provide an estimate of outcome 

Students will look to create chains of reasoning from first principles to proof or disprove a statement or scenario

 

Study of more complex graphs such as cubics and exponentials

 

Can create a resonated response to find a missing angle in a circle theorem

GCSE specification should be known confidently and secure knowledge of the skills required to answer a GCSE paper confidently 

What should they be able to do?

Can modify calculations for area and circumference of circle to find arcs and sectors

 

Calculate the volume of cylinders, cones and spheres and modify techniques on these to calculate a preserved volume of a frustum 

 

Calculate a numerical vector or combination of vectors. Can use a vector technique to proof a journey including a ratio

Can use learnt algebraic techniques to simplify and solve algebraic fractions

 

Can find the outcome of a function provided the input and then use this to calculate expressions for both inverse and compound functions 

 

Can perform an iteration or an iterative process to find a likely outcome 

Can construct an algebraic proof to prove a given statement

 

Can use reasoning and angle rules to find missing angles including those in a circle theorem question

 

Can plot and interpret real life graphs such as exponentials

 

Can find missing values in an exponential expression 

Answer GCSE questions confidently in line with and exceeding their target grade

Key vocabulary

Sector

Arc

Frustum 

Preserved

Simplify

Iterative

Inverse

Compound 

Root

Parallel

Perpendicular 

 

Glossary of Mathematical terms

Assessment

To ensure consistency of assessment across the year for students we use the following model 

  • In each of the above units students will have the opportunity to complete a series of progress checks. These are aimed at checking students' understanding and they will complete a relevant piece of improvement work based on teacher feedback - These assessments are based on student learning so carry no score. An example can be seen in the attached powerpoint 

  • In each term students will sit an examination to ascertain their current grade and provide feedback which will help them to improve their outcome at GCSE 

  • In Autumn 2 term students will sit their formal mock examination where they will complete a full suite of exam paper and be given a grade using the grade boundaries applied at GCSE 

  • In Spring 2 students will sit a final diagnostic assessment which will identify where their gaps in learning are so that revision for final examination can be individualised for each students 

GCSE Exam Information:

  • GCSE examination in Maths follows the Edexcel 9-1 specification
  • Students will sit three exam papers (1 non calculator and 2 calculator papers) each are weighted equally at 80 marks and have equal time lengths of 90 minutes
  • Students will be assigned to a tier based on their academic performance throughout school with foundation tier covering grades U-5 and the higher tier grades 3-9. Students will only sit the higher tier if their assessment results consistently show they are able to achieve a strong pass
As a department we recommend the following revision book , this is available to buy from school at a discounted price from regular retailers

Useful links:

  • Maths department utilises the SPARX maths program for all homework and revision purposes. A support video on how to use this and its purpose can be found in the subject powerpoint below. Link to Sparx
  • There are numerous GCSE websites available for Mathematics support and revision, as a department we advocate the use of the following sites which contain GCSE support videos and exam questions that students can download and answer

Maths Genie

Corbett Maths

MME revise

Third Space learning

The GCSE maths tutor

 

Any enquiries about Mathematics can be made by emailing the address below...

maths.enquiries@wernethschool.com