Mathematics

Much of our everyday lives and work has mathematics at its heart. It encompasses applying mathematical techniques to routine procedures, problem solving, presenting arguments which may be justified by proofs alongside interpreting solutions in the context of the problem at hand. At St Mary’s we aim to provide an expertly devised varied curriculum which teaches techniques whilst engaging and inspiring students to apply these skills to real life problems which extend to other subject areas. Additionally we offer chances for enrichment through lunchtime clubs, external group competitions as well as individual challenges which are conducted internationally. We offer a regular lunchtime help club where students of all ages and abilities are encouraged to seek any support or help with individual questions or topic areas.

Key Stage 3

In Key Stage 3 pupils follow the programs of study prescribed by the National Curriculum. They learn new techniques in each of the set areas of Number & Measure, Geometry, Algebra, Statistics, Probability, Ratio and proportion and Rates of Change and apply these to problems. We challenge and extend their thinking often going beyond that set out below. The pupils are encouraged to explain their thinking and to set this down on paper. They meet simple proofs and are encouraged to develop their talents of reasoning, interpretation and problem solving in the context of real life problems. More detail as to the content is set out below.

Year 7 Secure Skills Include
Number & Measure:
• Know and use the priority of operations and laws of arithmetic.
• Recall multiplication facts up to 10 × 10
• Multiply and divide by 10, 100, 1000
• Round whole numbers to the nearest 10, 100, 1000
• Check answers using estimation.
• Add and subtract whole numbers using written methods.
• Multiply whole numbers using a written method.
• Divide whole numbers using a written method.
• Check answers using inverse operations.
• Round decimals to the nearest whole number.
• Interpret a calculator display.
• Solve problems involving time and money using a calculator.
• Order positive and negative numbers.
• Add and subtract positive and negative numbers.
• Begin to multiply with negative numbers.
• Identifying and understanding factors, multiples and prime numbers.
• Recognise and use square numbers, square roots and triangle numbers.
• Measure and draw lines to the nearest millimetre.
• Write decimals in order of size.
• Round decimals to the nearest whole number and to one decimal place.
• Round decimals to make estimates and approximations of calculations.
• Compare measurements by converting them into the same units.
• Solve simple problems involving units of measurement in the context of length.Convert between metric units of length, mass and capacity.
• Read scales on a range of measuring equipment.
• Interpret the display of a calculator in different contexts.
• Interpret metric measures displayed on a calculator.
• Multiply decimals mentally.
• Check a result by considering whether it is of the right order of magnitude.
• Understand where to position the decimal point by considering equivalent calculations.
• Add and subtract decimals.
• Multiply and divide decimals by single-digit whole numbers.
• Use fraction notation to describe parts of a shape.
• Compare simple fractions.
• Use a diagram to compare two or more simple fractions.
• Change an improper fraction to a mixed number.
• Identify equivalent fractions.
• Simplify fractions by cancelling common factors.
• Add and subtract simple fractions.
• Calculate simple fractions of quantities.
• Work with equivalent fractions and decimals.
• Write one number as a fraction of another.
• Understand percentage as ‘the number of parts per 100’.
• Convert a percentage to a number of hundredths or tenths.
• Work with equivalent percentages, fractions and decimals.
• Use different strategies to calculate with percentages.
• Express one number as a percentage of another.
Year 8 Secure Skills Include
Number & Measure:
• Use written methods to add and subtract with decimals.
• Calculate mentally.
• Calculate with money.
• Estimate answers to calculations.
• Add, subtract, multiply and divide positive and negative numbers.
• Calculate using squares, square roots, cubes and cube roots.
• Use index notation for powers of numbers.
• Estimate the square root of a number.
• Use mental methods to calculate combinations of powers roots and brackets.
• Use a calculator to check answers.
• Substitute numbers into formulas involving power, roots and brackets.
• Use index notation.
• Write a number as a product of its prime factors.
• Use prime factor decomposition to find the HCF and LCM.
• Rounding whole numbers and decimals.
• Writing large numbers as a decimal number of millions.
• Ordering positive and negative decimals.
• Using the symbols > and < between two negative decimals.
• Multiplying larger numbers.
• Multiplying decimals with up to two decimal places.
• Multiplying any number by 0.1 and 0.01.
• Adding and subtracting decimals of any size.
• Multiplying and dividing by decimals.
• Dividing by 0.1 and 0.01.
• Adding and subtracting fractions with any size denominator.
• Multiply integers and fractions by a fraction
• Use appropriate methods for multiplying fractions.Convert fractions to decimals.
• Write one amount as a fraction of another.
• Find the reciprocal of a number.
• Divide integers and fractions by a fraction.
• Use strategies for dividing fractions.
• Use the four operations with mixed numbers.
• Recall equivalent fractions and decimals.
• Recognise recurring and terminating decimals.
• Order fractions by converting them to decimals or equivalent fractions.
• Recall equivalent fractions, decimals and percentages.
• Use different methods to find equivalent fractions, decimals and percentages.
• Use the equivalence of fractions, decimals and percentages to compare proportions.
• Working out one number as a percentage of another.
• Working out percentage increase and decrease.
• Use a multiplier to calculate percentage increase and decrease.
• Use the unitary method to solve percentage problems.
• Use strategies for calculating fractions and decimals of a given number.
• Use mental strategies of conversion and equivalence of fractions, decimals and percentages to solve word problems mentally.
Geometry:
• Work out the perimeters of shapes.
• Solve perimeter problems.
• Find areas by counting squares.
• Calculate the areas of squares and rectangles.
• Calculate the areas of shapes made from rectangles.
• Solve problems involving area.
• Choose suitable units to estimate length and area.
• Use units of measurement to solve problems.
• Use metric and imperial units.
• Describe and label lines, angles and triangles.• Identify angle, side and symmetry properties of triangles.
• Use a protractor to measure and draw angles.
• Estimate the size of angles.
• Solve problems involving angles.
• Use a ruler and protractor to draw triangles accurately.
• Solve problems involving angles and triangles.
• Use the rule for angles on a straight line, angles around a point and vertically opposite angles.
• Solve problems involving angles.
• Use the rule for the sum of angles in a triangle.
• Calculate interior and exterior angles.
• Solve angle problems involving triangles.
• Identify and name types of quadrilaterals.
• Use the rule for the sum of angles in a quadrilateral.
• Solve angle problems involving quadrilaterals.
• Identify congruent shapes.
• Use the language of enlargement.
• Enlarge shapes using given scale factors.
• Work out the scale factor given an object and its image.
• Recognise line and rotational symmetry in 2D shapes.
• Identify all the symmetries of 2D shapes.
• Identify reflection symmetry in 3D shapes.
• Recognise and carry out reflections in a mirror line.
• Reflect a shape on a coordinate grid.
• Describe a reflection on a coordinate grid.
• Describe and carry out rotations on a coordinate grid.
• Translate 2D shapes.
• Combine transformations.
Geometry:
• Derive and use the formula for the area of a triangle.
• Find areas of compound shapes.
• Calculate areas of parallelograms and trapezia.
• Calculate the volume of cubes and cuboids.
• Sketch nets of 3D solids.
• Calculate the surface area of cubes and cuboids.
• Calculate the volume of cubes and cuboids.
• Calculate the surface area of cubes and cuboids.
• Matching quadrilaterals to their descriptions.
• Using known facts about quadrilaterals to solve problems.
• Using alternate angles to find unknown angles.• Using reasoning to complete mathematical proofs.
• Solving geometrical problems using side and angle properties of triangles and quadrilaterals.
• Identifying corresponding angles.
• Solving problems using properties of angles in parallel and intersecting lines.
• Calculating the sum of the interior and exterior angles of a polygon.
• Calculating the interior and exterior angles of a polygon.
• Finding unknown angles by forming and solving equations.
• Solving geometrical problems showing reasoning.
Algebra:
• Find outputs of simple functions written in words and using symbols.
• Describe simple functions in words.
• Simplify simple algebraic expressions by collecting like terms.
• Use arithmetic operations with algebra.
• Use brackets with numbers and letters.
• Simplify more complicated expressions by collecting like terms.
• Write expressions from word descriptions using addition, subtraction and multiplication.
• Write expressions to represent function machines.
• Substitute positive integers into simple formulae written in words.• Substitute integers into formulae written in letter symbols.
• Identify variables and use letter symbols.
• Write simple formulae using letter symbols.
• Identify formulae and functions.
• Identify the unknowns in a formula and a function.
• Plot and read coordinates in all four quadrants.
• Revisit sequences including term-to-term rules.
• Develop the use of mathematical language to describe sequences.
• Demonstrate how sequences can be used as a mathematical model to describe patterns.
• Generate sequences from practical sequences, describing how patterns grow.
• Continue sequences arising from practical contexts and use them to answer questions.
• Read, generate and plot coordinates.
• Recognise geometric shapes drawn on coordinate grids and find coordinates of points using geometric information.
• Find and calculate the midpoints of a line segment.
• Continue and describe special sequences.
• Generate sequences using more complex (two-step) term-to-term rules.
• Continue sequences arising from practical contexts.
• Begin to identify and use position-to-term rules.
• Recognise an arithmetic sequence and find the starting number and common difference.
• Recognise, name and plot straight line graphs parallel to the x- or y-axis.
• Generate coordinates that satisfy a simple linear rule and plot the graph in the first quadrant.
• Read values from a graph.
• Recognise, name and plot the graphs of y = x and y = –x.
• Identify and use position-to-term rules.
• Write the nth term of a sequence using algebra.
• Recognise the relationships between term-to-term rules, position-to-term rules and nth terms.
Algebra:
• Substitute into algebraic expressions involving powers.
• Write expressions and formulae.
• Change the subject of a formula.
• Simplify expressions involving brackets, use rules for indices and factorise expressions.
• Multiply out double brackets and collect like terms.
• Understand and simplify algebraic powers.
• Substitute values into formulas involving powers.
• Expand brackets.
• Make and simplify algebraic expressions.
• Substitute into algebraic expressions involving powers.
• Write expressions and formulae.
• Change the subject of a formula.• Simplify expressions involving brackets, use rules for indices and factorise expressions.
• Multiply out double brackets and collect like terms.
• Factorise expressions.
• Find the inverse of a function.
• Solve simple equations using function machines.
• Solve real life problems using equations.
• Solve two-step equations using function machines.
• Solve real life problems using equations.
• Solve equations using the balancing method.
• Solve equations with the unknown number on both sides.
• Reading values from conversion graphs.
• Plotting conversion graphs from a table of data.
• Interpreting distance-time graphs.
• Plotting distance-time graphs from descriptive text.
• Using distance-time graphs to solve problems.
• Plotting line graphs from tables of data.
• Interpreting line graphs.
• Reading values from real-life graphs.
• Describing trends and making predictions based on information presented graphically.
• Working out percentages.
• Draw, use and interpret conversion graphs.
• Draw, use and interpret distance-time graphs.
• Draw and interpret line graphs.
• Draw, use and interpret real-life graphs.
• Discuss and interpret linear and non-linear graphs.
• Interpreting graphs.
• Drawing and using real-life graphs.
• Using graphs to solve problems and make predictions.
• Plotting graphs and reading values to solve problems.
• Plot a straight-line graph and work out its gradient.
• Plot the graphs of linear functions.
• Find midpoints of line segments.
• Write the equations of straight line graphs in the form y = mx + c
Statistics:
• Find the mode of a set of data, numerical and non-numerical.
• Find the median of a set of data (odd and even number of values).
• Find the range of a set of data.
• Read and draw pictograms, bar charts and bar-line charts.• Read and construct tally charts and frequency tables.
• Find the mode and range from a chart or table.
• Read and construct grouped tally charts and frequency tables.
• Read and construct grouped bar charts for discrete and continuous data.
• Find the modal class from a bar chart or frequency table.
• Calculate the mode, median, mean and range of a set of values.
• Compare two sets of data using an average and the range.
• Read and draw a line graph.
• Read and draw a dual bar chart.
• Read and draw a compound bar chart.
• Enter data into a spreadsheet program.
• Use a spreadsheet to calculate the mode, median, mean and range.
• Use a spreadsheet to draw bar charts, dual bar charts, compound bar charts, grouped bar charts and line graphs.
Statistics:
• Identify sources of primary and secondary data.
• Choose a suitable sample size and what data to collect.
• Identify factors that may affect data collection and plan to reduce bias.
• Design a good questionnaire.• Design and use data collection sheets and tables.
• Interpret simple pie charts.
• Calculate angles and draw pie charts.
• Drawing and interpreting two-way tables.
• Calculating the mean from a simple frequency table.
• Tallying data into a grouped frequency table, designing a grouped frequency table, using a ≤ x < b notation, finding modal class and estimating range.
• Drawing and interpreting stem and leaf diagrams with different stem values.
• Finding mode, median and range from stem and leaf diagrams, and comparing them for different data sets.
• Compare data using averages and range, including mean calculated from frequency table.
• Compare data using the shape of a line graph or pie chart.
• Draw line graphs to compare sets of data.
• Decide on the most appropriate average to use.
• Draw scatter graphs.
• Describe types of correlation.
• Draw a line of best fit by eye on a scatter graph.
• Identify graphs and charts that are misleading because of the scales used and missing axis labels, mainly in financial contexts.
Ratio, Proportion and Rates of Change:
• Use direct proportion in simple contexts.
• Solve simple problems involving direct proportion.
• Use the unitary method to solve simple word problems involving direct proportion.
• Use ratio notation.
• Reduce a ratio to its simplest form.
• Reduce a three-part ratio to its simplest form by cancelling.
• Divide a quantity into two parts in a ratio given in words.
• Divide a quantity into two parts in a given ratio.
• Solve word problems involving ratio.
• Use ratios and measures.
• Use fractions to describe and compare proportions.
• Understand and use the relationship between ratio and proportion.
• Use percentages to describe proportions.
• Use percentages to compare simple proportions.
• Understand and use the relationship between ratio and proportion.
Ratio, Proportion and Rates of Change:
• Using ratios involving decimals.
• Solving proportion problems involving decimals.
• Solving engineering problems using ratio and proportion.
• Using unit ratios.
• Recognising when values are in direct proportion.
• Identify and describe practical examples of direct proportion.
• Solve problems involving direct proportion with or without a graph.
Probability:
• Use the language of probability.
• Use a probability scale with words.
• Understand the probability scale from 0 to 1.
• List and count outcomes.
• Calculate probability based on equally likely outcomes.
• Compare probabilities.
• Calculate probability of A or B happening by counting outcomes.
• Calculate the probability of an event not happening.
• Record data from a simple experiment.
• Estimate probability based on experimental data.
• Make conclusions based on the results of an experiment.
• Use probability to estimate the number of expected wins in a game.
• Apply probabilities from experimental data in simple situations.
Key Stage 4
In Key Stage 4 students follow the prescribed National Curriculum which is assessed by Edexcel Examination Board. Students are entered for either Higher Level leading to grades 4 – 9 or Foundation level leading to grades 1 – 5. The vast majority of the course builds upon and extends the skills learned at KS3, but students do encounter and develop new areas of mathematics. Particular emphasis is to be able to confidently:

·         Accurately recall facts and carry out routine procedures or set tasks requiring multi-step solutions.

·         Present arguments and proofs.

·         Make deductions, inferences and draw conclusions from mathematical information from mathematical information.

·         Interpret and communicate information accurately in the context of the given problem.

·         Evaluate methods used and results obtained.

·         Evaluate solutions to identify how they may have been affected by assumptions made.

Assessment is by three separate 1 ½ hour written examinations at the end of the course. Paper 1 is non-calculator and Papers 2 & 3 require the use of a scientific calculator. The three papers are equally weighted.

Those topic areas which are totally new to the tiers of entry are:

Foundation
Vectors
• Vectors in 2D, writing as column vectors.
• Simple vector journeys.
Trigonometry
• Use of Sine, cosine and tangent in right-angled triangles.
• Learning values of the trigonometrical functions of the special angles.
Congruent and Similar Triangles.
Compound Interest.
Solving Quadratic and Simultaneous Equations.
Indices and Standard Form.
Upper and Lower Bounds.
Graphs.
Set notation and its application to probability.
Direct and Inverse Proportion.Compound measures.
Higher
All the new Foundation content.
Vectors
• Vectors in 2D, magnitude and direction.
• Vector journeys.
• Collinear points and parallel vectors.
Circle Theorems
More involved area, perimeter and volume work extending to 3d solids and parts of circles.
Upper and Lower Bounds and calculations with these.
Trigonometry
• Use of Sine, cosine and tangent in right-angled triangles.
• Learning values of the trigonometrical functions of the special angles.
• Sine rule and cosine rule.
• Extend to 3D problems.Systematic listing strategies
• Use of factorial notation.
Functions
• Input, output and composite functions.
• Inverse functions.
• Transforming graphs of functions.
Growth and Decay
Set Theory and its applications to probability.
Numerical Methods
Pre-calculus methods for finding gradient of a curve and the area between a curve and the x axis.
• Applications of this to velocity-time and distance-time graphs.
Time series and moving averages.

 

Exam Board: Edexcel ( Specification 1MA1)

For further details on the syllabus content please visit:http://qualifications.pearson.com/en/qualifications/edexcel-gcses/mathematics-2015.html

Good websites for support

Mymaths

CorbettMaths

Mr Barton Maths which includes short videos of each topic.

Key Stage 5
Students who opt to study either Mathematics or Further Mathematics follow the Edexcel syllabus for both. These exciting subjects extend the knowledge and reasoning acquired thus far and challenge the students’ application and evaluation to a greater and much deeper level.

The A level Mathematics course builds upon the three areas of Pure Mathematics, Statistics and Mechanics. The students will expand their knowledge of

Proof
Algebra and functions
Coordinate geometry in the (x,y) plane
Sequences and Series
Trigonometry
Exponentials and Logarithms
Differentiation
Integration
Vectors
Quantities and units in mechanics
Kinematics
Forces and Newton’s laws
Moments
Statistical Sampling
Data presentation and interpretation
Probability
Statistical Distributions
Statistical Hypotheses Testing
Assessment is by three 2hour examination papers at the end of the course.

 In Further Mathematics the students will delve into fewer topic areas but far more deeply. They will meet

Proof
Matrices
Further Algebra and Functions
Further Calculus
Further Vectors
Polar Coordinates
Hyperbolic Functions
Differential Equations
Further Trigonometry
Coordinate Systems
Numerical Methods
Inequalities
Algorithms and Graph Theory
Algorithms on Graphs
Critical Path Analysis
Linear Programming
Assessment is by four 1 ½ hour examination papers at the end of the course.

Exam Board: For A level Mathematics the Exam board is Edexcel. The subject code is 9MA0.

                       For A level Further Mathematics the exam board is also Edexcel. The subject code is 9FM0.

For further details please visit: https://qualifications.pearson.com/en/qualifications/edexcel-a-levels/mathematics-2017.html

 

Good Websites for support

My Maths

Dr Frost

furthermaths.org.uk

 


For further information about the Mathematics curriculum please contact:

Mr Kieren O’ Sullivan
Head of Maths Department