Mathematics
Intent
At Leighton Middle School we believe that it is our duty to inspire young people to see the true beauty of maths in the wider world by bringing maths alive, and making it interesting and accessible to all. Mathematics is at the core of everyday life- from science and technology, to financial literacy and to support independence in future ambitions by developing cognitive function. We believe a high quality mathematics education is the foundation to increasing fluency in number skills, confidence in problem solving skills and developing independent learners who have tenacity when faced with a challenge.
Our aims are to develop the ability to move with fluidity between mathematical concepts, build connections between the skills learnt and to recall and apply knowledge to problem solve and reason.
Students are supported in developing mathematical language to explain, justify and debate to follow a line of enquiry. Through modelling, we show clear links between worded questions and mathematical processes. By celebrating a Maths Word Wall, we use complex terminology to encourage ambition to understand and apply the terms. During reasoning questions, students are asked to give written responses, to ensure clear interpretation of the maths and the literacy, in tandem. This helps the development of literacy skills to apply across the curriculum.
The mathematics department is committed to progressing each student at a rate that is supportive and challenging, ensuring the self-confidence of each student is built upon to prepare them for some of the more pure mathematical concepts. Although the expectation is that students would move through the program of study at approximately the same rate, we recognise the importance of securing knowledge, facilitating opportunities to practice and solidify understanding before moving on.
Implementation
To achieve our intentions, we implement the following.
- Our program of study has been adapted from White Rose maths at KS2 and MyMaths at KS3. The program is bespoke to LMS to ensure a smooth transition from their lower schools and into their upper schools through regular communication with both. A little and often approach is employed to interleave core skills throughout the year, to increase that fluency in number skills, whilst also fine tuning these skills to move the topic knowledge on.
- Students are placed in class groups according to various criteria. This is a combination of teacher observations, assessment data, KS1 data and personality styles. By placing the students in groups, they are with students who work in a similar pace and style and so this personalises the teaching and learning experience for both teacher and student. Personalised teacher feedback is also increased as a result of smaller groups.
- Knowledge and skills are delivered through use of mathematical understanding and not by copying a process. Students are encouraged in lessons to justify their answers, analyse the validity of their response and to question the answers of those around them, in a polite and constructive manner.
- Class teaching includes modelling answers in various ways. This may be worded in steps, bullet points, correct calculations or in diagram form. This expands the students' understanding of a skill from various approaches and develops their depth of knowledge.
- Students are encouraged to take pride in their achievements and to ensure presentation of all work is of a high standard. Homework is set to increase this independence further. This prepares students to take ownership of their educational journey, through time management and recalling and applying knowledge outside of the classroom, supporting independent learning.
- Intervention is available for students who require additional support and this is personalised to build self-confidence as well as knowledge and skills.
- At LMS we provide a wide and rich set of experiences throughout the year groups to apply and improve numeracy outside of the classroom. This enrichment is in the form of games clubs, sporting links, investigation afternoons, day trips, maths challenges and timetables battles.
Impact
Students of all abilities show a great drive and determination to improve their mathematical skills, accepting and working with the support put in place to help them strive towards personal excellence. During their journey, students become more numerically fluent and are able to recall and apply knowledge when revisiting and moving topics on.
Students come to LMS below the national average, according to standardised scores and they leave ready to take the next step in their mathematical journey; the majority above the national average.
Teachers obtain an understanding of students’ strengths and areas to develop through accurate teacher assessment and formal assessment data. As a result, class time is focused on maximising the benefit to the student.
At Leighton Middle School mathematics is a well-liked subject. Students become more inquisitive during their time with us, developing skills beyond just number but also increased ambition to progress in a way that is personal to each individual student. Pupil panels report a love of the challenge in lessons and a willingness and understanding on how to work both autonomously and collaboratively- with both students and teachers.
Curriculum Overview
Year 5
Autumn Term: First Half Term |
Autumn Term: Second Half Term |
Spring Term: First Half Term |
Spring Term: Second Half Term |
Summer Term: First Half Term |
Summer Term: Second Half Term |
Knowledge: To state the magnitude of a digit according to place value. Rounding to show and increase understanding of magnitude. Increasing and decreasing magnitude by powers of ten. Understand the relationship and definitions of multiples and factors. Recognising and finding prime, square and cubed numbers. Addition and subtraction using formal methods. To plot and location coordinates in up to a 4 quadrant grid.
Skills: • To write and explain numbers up to 1 million. • To round numbers up to 1,000 • To add negative numbers on a number line. • To multiple, divide and work with multiples of 10, 100 and 1000 • To find and explain factors, multiples, primes, squared and cubed numbers. • To add and subtract using formal column method, including multi- step problems. • To use inverse operations and rounding to check answers. • To find a coordinate in the first quadrant • To reflect in a mirror line and give coordinates • To explain a translation and translate a shape with given coordinates.
Vocabulary: Estimate/ Approximate Multiple Factor Product Prime number Squared/cubed Evaluate Inverse Sum/ Total Exchange Quadrant Horizontal/vertical Reflection/ Translation |
Knowledge: Relationships between fractions and the whole discovered, presented pictorially and with abstract methods. Multiplication and division using formal abstract methods. To recognise and calculate perimeter and area of various shapes.
Skills: • To recognise and show equivalent fractions • Find equivalent fractions, convert improper to mixed, and add and subtract fractions in various forms • To compare and order fractions • Column multiplication up to 4 by 2 digits • Short and long division methods with and without a remainder. • Add and subtract fractions with the same denominator • To measure and calculate the perimeter of any shape • To calculate the area of rectangles, including compound shapes and irregular shapes
Vocabulary: Equivalent Improper fraction Unit fraction Mixed number Proportion Numerator/denominator Product ‘scrub scrub zero’ Perimeter/circumference Area Compound Regular/irregular shapes Sketch |
Knowledge: Autumn arithmetic skills reviewed, consolidated to increase fluency. To extend bar modelling to represent fractions of an amount. Representing data in a graph, understanding scale and intervals. Drawing conclusions from graphs, making statements about the data from graphs. Students will increase understanding of a timetable used for transport or to represent 2 interlinking variables. Being able to link the parts to the whole in both decimals and fractions. Making additional links with percentages being part of a whole.
Skills: • Recap of the 4 formal methods of calculations. • To find fractions of an amount using bar model • Read and interpret and draw line graphs to solve problems • Read and interpret timetables, 2 way tables • To read timetables • To order and compare decimals up to 2 DP • To write decimals as fractions • To round a decimal to a whole • Understand how percentages work and show as fractions and decimals • Find equivalent FDP
Vocabulary: Interpret Intervals/scale Raw/primary/secondary data Equivalent Proportional Percent |
Knowledge: Develop a knowledge of direction using a proportion of 360 degrees. Establishing links to shape properties and angles. Reviewing, consolidating and extending decimal knowledge through methods detailed below.
Skills: • To measure angles in degrees with a protractor including reflex angles • To draw lines and angles accurately • To calculate angles on a line, around a point and in shapes • To describe properties of polygons to calculate lengths and angles • To add and subtract decimals within 1 and greater than 1 • To find compliments to 1 • To add and subtract with the same and difference number of decimal places • Understand decimals in sequences
Vocabulary: Protractor/degrees Estimate Calculate Accurately Sketch Supplementary Regular/irregular polygons Difference Sequence |
Knowledge: Autumn and Spring arithmetic skills reviewed, consolidated to increase fluency. Unit conversion interleaved throughout the year but is here formally consolidated to increase understanding of size, distance and weight. Perimeter and area is extended into understanding of 3 dimensions using volume and capacity. Knowledge of the properties of 3D shapes used to support the students making links with volume.
Skills: • Recap of the 4 formal methods of calculations, including fractions. • To convert between units of measurement- metric, imperial and time. • To read timetables- revisited • To explain what volume is • To find volume by counting cubes • To compare volumes of different objects • To estimate volumes and capacity • To write roman numerals up to 3,000
Vocabulary: Conversion Metric/imperial units 2 way table Volume Capacity Numerals |
Knowledge: Year to date arithmetic skills reviewed, consolidated to increase fluency. Bar modelling skills revisited and extended to represent all 4 operations. Review, revisit and consolidate mathematical terminology using the 3 read protocol. Teacher Assessed topics personalised to each class. Skills: • Recap of the 4 formal methods of calculations, including fractions. • To represent a calculation using a bar model. • To understand and apply mathematical terminology. • To budget for an event
• Teacher Assessed topics highlighted as areas to develop.
Vocabulary: Budget All from previous half terms. |
Year 6
Knowledge: To apply knowledge of place value to multiply and divide by 10, 100 and 1000, including decimals. Addition, subtraction, multiplication and division using formal methods, including decimals. Interpreting roman numerals. To define, understand and apply knowledge of factors and multiples to state HCF and LCM. To add, subtract, multiply and divide fractions, and utilise bar modelling to find fractions of amounts.
Skills: • To multiply and divide by 10, 100 and 1000, including decimals. • To add/subtract/multiply and divide using formal methods including decimals. • To read and write roman numerals up to 3000. • To find factors, multiples and primes, including common factors and multiples. • To find equivalent fractions and their decimal equivalents • To add/multiply/divide and subtract unit and non unit fractions and mixed numbers. • To use bar models to find a fraction of a quantity.
Vocabulary: Multiples and factors Highest common factor Lowest common multiple Equivalent Unit fractions/non unit fractions Mixed numbers |
Knowledge: Interpreting graphs and charts, including calculating averages from them and raw data. Converting between units of metric measures, time and distance. Finding quantities, temperature and mass on scales. Interpreting time difference on bus /train timetables and 2 way tables. Accurate use of a protractor and ruler to read and construct angles and lengths. Understanding angle rules that sum 180 and 360 degrees. Using percentage knowledge and factors of 100 to shade % of a grid, bar and various shapes. Using % knowledge to calculate simple and complex percentages, including increases and decreases.
Skills: • To interpret graphs and charts • To calculate the mean average • To convert between units of measure and time. • To read various intervals on scales for length, mass, capacity, etc. • To read a range of timetables • To measure and draw angles using a protractor • To name and calculate angles on a straight line and at a point. • To use bar models to find a percentage of a quantity.
Vocabulary: Interpret Mean and average Convert Intervals Protractor and degrees To scale and not to scale measure/Calculate Accurately |
Knowledge: Stating the properties of polygons and circles. Naming parts and recognising parallel, perpendicular lines, including lines of symmetry. The understanding of perimeter and area, knowing how to calculate both in various shapes, including composite shapes. Introduction of algebra being the use of an unknown variable. Solving simple equations and substituting into expressions. Understanding of ratio and proportion through direct proportion situations and expressing ratio in words. Drawing pie charts, interleaving percentage and angle knowledge.
Skills: • To recap 4 operations including fractions • To recognise properties of polygons and non-polygons. • To use formal methods to calculate the perimeter of shapes. • To calculate the area of rectangles, triangles and parallelograms (including trapeziums) • To calculate the area of compound rectilinear shapes. • To find an unknown in a linear equation. • To substitute into formulae • To construct and simplify ratio from numerical and worded forms, using bar models. • To draw a pie chart.
Vocabulary: Polygon/regular and irregular Perimeter and area circumference radius and diameter Rectilinear Parallelogram Trapezium equation substitute formulae (Direct) proportion Parts Simplify |
Knowledge: To revisit, review and recap primes, factors, multiples and squares and all 4 operations. Increase application of fraction manipulation. Utilising previous knowledge of parts of a whole to convert between, compare and order fractions, decimals and percentages. Calculating according to BIDMAS. Understanding of integers, decimals and fractions to recognise and continue sequences. Applying knowledge of shapes, whole and part turns to calculating missing angles. Plotting and interpreting coordinates and translating and reflecting shapes in 4 quadrants.
Skills: • To multiply and divide fractions, recognising the mean of ‘of’ • To shape a fraction of a shape • To convert between fractions, decimals and percentages with increased fluency. • To calculate adhering to BIDMAS • To recognise and continue sequences • To calculate missing angles • To plot coordinates in 4 quadrants and state missing coordinates. • To reflect and translate a shape.
Vocabulary: Order of operations (BIDMAS) Term to term Axis Quadrants Reflect and translate |
Knowledge: Exploring capacity to understand volume by counting cubes and by calculation. Extension of the use of algebra. Advice and guidance through bespoke revision packages for each class prior to the SATs. Support in recall methods, revisiting key skills and use of CGP packs to further familiarise the students with the question style. Exploration of tesselating shapes. Investigations using mixed number skills.
Skills: • Revisit and consolidate unit conversion and reading scales • To find the volume of shapes by counting and calculation. • To simplify an expression • To find pairs of numbers to satisfy an equation. • Revision sessions based upon lesson, homework and assessment feedback. • Retention of knowledge through repetition and regular revisiting of core knowledge. • Fluency of number skills through questioning, procedural variation of the questions and use of SATs style questions. • To explore tesselating shapes and link to angle knowledge. • Mixed number investigations.
Vocabulary: All previous vocabulary. Mass, volume and capacity Simplify Tessellation Hypothesis Investigation Assumptions Conclusion |
Knowledge: To begin the transition into KS3 style questioning using units 1, 2 and 3 from the MyMaths scheme of work. Sequencing of numbers can be described in words and algebraically using the nth term. Understanding of algebraic form by collecting like terms and simplifying expressions. Solving equations to state the unknown and exploring constructing equations from worded problems. Substituting into an expression, including negative values. Money Matters Topic Skills: • To describe a term to term rule and state the nth term. • To construct a sequence from an nth term. • To simplify an expression. • To construct and solve an equation. • To substitute into an expression. • To explore money in the real world, how to save it, spend it and the various ways of managing it. • To recap 4 operations including fractions
Vocabulary: Sequence Term to term nth term term expression equation substitute |
Year 7
Knowledge: Understanding the magnitude of measurements and converting. Using a timeline to workout time changes. Defining the difference between area and perimeter and calculating both. Recognising and calculating surface area and volume of a 3D shape. Ordering and completing all 4 operations with fractions. Calculating a fraction or percentage of an amount. Interpret and calculate averages from raw data. Reading various forms of graphs and diagrams. Adhering to the rules of questionnaires.
Skills: • To convert between units of measure- metric and imperial • To calculate forward and backwards in time. • To find the area and perimeter of shapes • To calculate surface area and volume • To compare and order fractions • To add and subtract fractions • To find fractions of amounts • To find percentages of amounts • To organise raw data into a frequency table. • To calculate 3 types of average and range. • To read and interpret different types of graphs • To design a questionnaire
Vocabulary: Convert Metric and imperial units Perimeter and area Circumference Compound Ascending and descending Interpret Mean/median/mode The range/spread Axis Bias |
Knowledge: Manipulation of algebraic terms and integers, including constructing expressions. To plot linear functions on a 4 quadrant cartesian grid. Estimating by rounding up to 2 d.p. Use of the various functions on a calculator, including ensuring adherence to BIDMAS with and without a calculator. Applying knowledge of scale to use a protractor to measure and draw angles. Using prior knowledge of angles to calculate missing angles. Recognising and describing various 2D shapes.
Skills: • To collect like terms • To expand and simplify expression • To multiply and divide terms • To write algebraic expressions and substitute into formulae • To plot coordinates, substitute values, draw straight line graphs and find gradients • To round to estimate to 2 d.p. • To recap formal methods of the 4 operations. • To use a calculator for worded calculations. • To use BIDMAS within calculations • To measure and draw angles • To calculate internal and external angles • To calculate angles in various contexts(triangle/quadrilaterals/parallel lines) • To describe the qualities of quadrilaterals.
Vocabulary: Term Expressions Construction Formula Substitution Plot Linear Gradient Intercept BIDMAS Indices/index number External angles Supplementary angles Alternate and corresponding Quadrilateral |
Knowledge: To compare and list factors and multiples including HCF and LCM. Understanding square and square rooting and larger roots. To complete a prime factor decomposition. Gaining familiarity with the functions on a calculator. Increasing algebraic fluency by completing all 4 operations with terms and integers. To find the value of a variable by solving. To transform shapes and coordinates.
Skills: • To find factors and multiples of given numbers • To find squares and square roots • To use prime factors to find HCF and LCM • To use a calculator to solve calculations • To solve simple, two step and three step equations • To reflect in a given axis • To rotate and understand rotational symmetry • To translate • To tessellate • To enlarge from a point
Vocabulary: Roots- positive and negative Prime factors decomposition like terms Inverse operation Reflection Rotation Translation Enlargement Transformations Tessellation |
Knowledge: Utilising previous understanding of fractions, decimals and percentages to increase fluency converting between them. To increase dexterity and accuracy with a pencil, ruler, compass and protractor. Increased understanding of a 3D shape shown in 2D, listing properties. Understanding of the capacity of a container/object through a volume investigation..
Skills: • To convert between FDP • To apply functional skills using real life problems • To construct triangles, scale drawings and isometric drawings • To identify the properties of 3D shapes • To draw plans and elevations • To investigate volume in the project 24 town
Vocabulary: Equivalent Functional Construction Accurate To scale/not to scale Isometric drawings Plans Elevations Prism Explore Investigate |
Knowledge: To place events on a probability scale using words, decimals, fractions and percentages. Defining the difference between probability in theory and ‘real’ life outcomes. Representing a sequence using term to term or an algebraic expression: nth term. To recognise when 2 variables are in direct proportion and link to ratio and recipe amounts.
Skills: • To label correctly on a probability scale and use correct language • To use theoretical and experimental probability • To find term to term and nth term rules • To follow a rule for sequences • To find direct proportion • To solve ratio and proportion questions
Vocabulary: Probability Likely Certain Impossible Unlikely Theoretical Experimental term to term nth term Sequences direct proportion ratio |
Knowledge: To explore multiplying decimals using various methods. Applying multiplying decimal methods to worded KS3 style questioning. Exploring the use of a calculator including fraction, indices and application of BIDMAS. Comparing real world examples of best value to explore proportion. Money Matters Topic Skills: • To be able to multiply decimals • To recap and consolidate the use of calculators to solve problems • To explore money in the world, including ways of saving money, methods of investing and mediums of spending. • To calculate the best value deal and ways of researching for a good deal. • To allow the students to explore what type of spender they are.
Vocabulary: Accuracy Inverse S-D button |
Year 8
Knowledge: To utilise knowledge of number to categorise, manipulate and estimate. Use of basic algebra to manipulate, simplify and utilise expressions and formulae. Applying previous fraction knowledge in algebraic form.
Skills: • To complete a prime factor decomposition • To calculate the HCF and LCM of 2 or more integers • To estimate a calculation using rounding to tens, whole or decimal places • To use trial and improvement to square root integers to 1 decimal place • To understand, manipulate and simplify using rules of indices • To utilise index laws algebraically • To expanding brackets- single and double • To factorise an expression • To substitute into and rearrange formulae • To add and subtract algebraic fractions
Vocabulary: Decomposition Evaluate Indices Iteration Term Coefficient Equations/expression Expanding/factorising Substitution |
Knowledge: Using angle knowledge to calculate unknown angles, then utilising these skills to prove congruency. The ability to recall formulae to calculate area. The fluency of unit conversion applied to area conversion, taking into accord the additional dimension. Understanding of primary and secondary data, how to display and interpret data. Using knowledge of term to term rules to specify a sequence as an nth term.
Skills: • To calculate angles in parallel lines and in polygons • To recognise conditions of congruency • To calculate area and perimeter of various polygons and compound shapes including circles. • To convert units of area • To plan data collection and display in various forms • To plot a cumulative frequency graph, scatter graph and stem and leaf diagram • To calculate and interpret averages and spread. • To state the nth term rule
Vocabulary: Alternate/corresponding Supplementary Co-interior Polygon/compound shape Exterior angles Raw dara Frequency Cumulative Averages and spread (range) Term to term |
Knowledge: Using complex FDP knowledge to state magnitude. To calculate fractions and percentages of an amount and change. Increased fluency in mental skills to reduce limbic friction. Increased dexterity through construction methods with mathematical instruments.
Skills: • To order fraction, decimals and percentages • To complete all 4 operations with fractions • To find percentages and fractions of amounts • To develop mental calculation with all 4 operations • To use powers of ten (basic standard form) • To construct bisectors and perpendiculars, scale drawings and loci • To calculate a bearing
Vocabulary: Of (means X) Standard form Common denominator Bisectors (relate to dissect) Perpendicular Loci/Locus Scale Bearing Clockwise/anti-clockwise |
Knowledge: Discovery of the link between an equation, real life and graphs. Increasing fluency in written methods by increasing complexity of questioning. The ability to invert several steps to solve complex equations.
Skills: • To plot linear and quadratic equations and state the equation of a line • To interpret real life graphs • To revisit, review and consolidate written calculations, the application of BIDMAS and decimal calculations, with and without calculators. • To solve multi-step equations
Vocabulary: Plot Linear Quadratic/Cubic Axis (horizontal/vertical) BIDMAS Invert/inverse Solve |
Knowledge: To understand ratio as a way of sharing according to a specific proportion. To transform a shape in various ways ensuring the shape remains either congruent or similar. Increased understanding of possible outcomes by analysing the likelihood of an event occurring, and displaying this information.
Skills: • To divide by a ratio and find a total when given a part • To recognise amount in direct proportion and find unknowns • To utilise proportion knowledge with algebraic parts • To transform shapes through reflection, stating or being given a mirror line • To transform shapes by scale enlargements and find the centre of enlargement • To list outcomes and state probabilities- displaying them on a tree diagram and utilising venn diagrams • To compare experimental and theoretical probability
Vocabulary: Shared Proportion (direct/indirect) Transformations Reflection, rotation, translation Enlargement Probability- likely, unlikely, certain, impossible Experimental/theoretical |
Knowledge: Dexterity development through accurate or scale drawing. Increased lateral observation through the use of 3D shapes and nets. Interleave and consolidate KS3 algebraic manipulation skills. Understanding of financial matters to support students going onto the next step in their educational journey. Money Matters Topic. Skills: • To draw the plan and elevation of a shape and visa versa • To calculate the surface area of complex prisms • To calculate the volume of complex prisms including capacity conversion and problem solving • To revisit and consolidate algebraic manipulation • To develop reasoning, problem solving and fluency using functional investigations • To complete a MoneyMatters unit for functional skills
Vocabulary: Elevation Surface area Prism Cross-section Capacity/volume Mortgage ISA Variable/fixed Credit (limit/check) |
British Values
Democracy |
The Rule of Law |
Individual Liberty |
Mutual Respect |
Students listen and discuss each other’s ideas, working in learning partners and investigating in groups. We discuss the importance of opinion and the rules of questioning when designing questionnaires and collecting data. |
Students follow class rules safely during tasks and activities to benefit everyone, as well as understanding the consequences if rules are not adhered to. |
Students work within boundaries to make a safe and personal choice from a given selection during activities that require a self-reflection upon their own individual level of confidence in each topic area. |
Students behave appropriately, allowing everyone involved the opportunity to work to the best of their ability. They take turns, sharing equipment, reviewing each other’s work respectfully and working collaboratively on projects whilst helping others. They learn from and with each other. |
Careers
Year 5 |
Year 6 |
Year 7 |
Year 8 |
Autumn term |
Autumn term |
Autumn term |
Autumn term |
Spring term |
Spring term |
Spring term |
Spring term |
Summer term |
Summer term |
Summer term |
Summer term |
Spiritual, Moral, Social and Cultural Development (SMSC)
Spiritual |
Moral |
Social |
Cultural |
Students use 'frame it to claim it' to reflect on their learning and to celebrate their achievements, challenges and progress. Statistical data used in lessons is taken from a variety of sources and interests to explore various aspects of the world around us. |
Class and learning partner discussions are encouraged to explore ideas and debate possible outcomes, providing the students an opportunity to deal with disagreement constructively i.e. worded probability. |
Learning partners are utilised to discuss and explore ideas with the importance placed upon working, participating and cooperating with each other. Coaching opportunities are utilised to extend the application of a skill through peer-to-peer support. Listening and engaging with others are placed hand in hand with individual mind set and tenacity. |
Students are taught the origins of the imperial and metric systems and the use of different measuring systems. Area and perimeter is linked to the world around them through patterns and tessellation. Applying probability justification using understanding of the world around us without stereotyping Graphical data explores differences between areas of the world i.e. population, temperature, rain fall, etc. The origin of Roman numerals and its use in modern day life is discussed. |