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Maths

Mathematics is a subject that all students need. In addition to the acquisition of vital numeracy skills needed for the future, it is also a field that should be enjoyed.

It is the aim of the Maths department that all students become fluent and confident with Mathematics. The study of Mathematics can provide answers to everyday questions that cannot be solved in any other way. More than just being a subject and qualification which is required at school, it is a subject of wonder and joy. Problems are used in lessons to provide enjoyment and foster creativity. 

At KS3 level there is a big focus in the lessons on becoming fluent with the basic skills before progressing on to reason answers, in slightly different context and then problem solving in an unfamiliar or unusual way.  

Problem solving now makes up a key role in the National curriculum and in exams at all levels. It is for this reason that we train the students to attempt questions in different ways and we build up the ability of the pupils to become resilient and persevere with the work, even when it seems difficult. 

The aims and objectives of the Mathematics GCSE are to enable students to: 

  • develop fluent knowledge, skills and understanding of mathematical methods and concepts 
  • acquire, select and apply mathematical techniques to solve problems
  • reason mathematically, make deductions and inferences, and draw conclusions
  • comprehend, interpret and communicate mathematical information in a variety of forms appropriate to the information and context. 

 

The study of the GCSE material begins in year 9 and during the three years the students cover the following six areas: 

1 Number 

2 Algebra 

3 Ratio, proportion and rates of change 

4 Geometry and measures 

5 Probability 

6 Statistics 

Courses in Maths

Key Stage 4

  • GCSE Mathematics (9-1) (Edexcel)  

 

Term By Term Schemes of Work

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Key Stage 3 Maths

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Key Stage 4 Maths Lower

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Key Stage 4 Maths Higher

 

Year 7 Curriculum Breakdown

Year 7

Half Term

Topic

Learning Outcomes

Assessment

Half term 1

Use the four operations with positive numbers

Grade 1: Students will be confident in using all basic operations with up to 5 digits numbers for addition and subtraction using formal column methods. Students will know times table facts to multiply and divide up to 12 x12. Students will have a clear understanding of place value.

Grade 2: Students will be able to add and subtract any decimal value. This will include decimal multiplication and division using formal methods and the multiplication and division of large numbers.

Grade 3: Students will be confident solving problems with money and long multiplication.

Grade 4: Students can perform calculations using a calculator with standard form. Students can covert between standard form and normal numbers, they can also perform basic operations.

Four operations and Negative numbers Mini assessments

Negative numbers

Grade 1: Students will be able to order and understand the meaning of positive and negative numbers. They will be able to perform all basic operations with positive and negative numbers.

Grade 2: Students will be confident using all rules of negatives with all 4 operations, this includes double negatives.

Indices and BIDMAS

Grade 1: Students can perform basic operations and know timetables up to and including 12x 12.

Grade 2: Students can calculate squares, cubes and square roots of numbers up to 12x12. For larger values a calculator can be used.

Grade 3: Students can confidently apply BIDMAS to any calculation, this should be considered when using a calculator. In addition they can calculate powers of 2,3,4 and 5.

Grade 4: Students can calculate integer powers and roots by using a calculator

Grade 5: Students can calculate negative and fractional indices with and without a calculator

Indices, factors, multiples, primes and

percentages mini assessments

Factors, multiples and primes

Grade 1: Students will know times tables up to 12 x12

Grade 2: Students will know the definition of factors, multiples and primes. They will be able to recognise these and state them in a logical order

Grade 3: Students will be able find the HCF and LCM of up to three numbers and can write a number as a product of prime factors

Grade 4: Students can use prime factors to find the HCF and LCM of two large numbers, for example 72 and 60.

Percentages

Grade 1: You can multiply and divide by a power of ten up to and including 1000.

Grade 2: Students can find a percentage, a multiple of 5, of an amount. This must include money problems.

Grade 3: Students can find any percentage of an amount, including the use of money. Students can calculate percentage increase and decreases, including the use of simple interest. They can express a number as a percentage of another. They can calculate percentage change.

Grade 4: Students can find original amounts from percentage problems

Grade 5: Students will be able to solve problems with compound interest


Half Term

Topic

Learning Outcomes

Assessment

Half term 2

Simplifying Expressions

Grade 1: Students will be able to simplify expressions using one operation, this could include,  y + y + y = 3y or a simple multiplier

5 x 3t = 15t.

Grade 2: Students will      be able to simplify expressions a x b = ab, 3 x y = 3y, a2 = a x a, a ÷ b = a/b 3y + 6y = 9y (must have coefficients as fractions not decimals i.e. ½a no + 0.5a)

Grade 3: Students will be able to simplify expressions using all four operations, this will include the three index laws. This should include D3 x D5, T3 ÷ T5, (F4)3

Grade 4: Students will be comfortable using all four operations including index laws with coefficients, this should include (4x3)2.

Grade 5: Students should be extended by evaluating powers with algebraic expressions. This can include negative and fractional rules, (25t6y10)1/2.

Mini assessment; simplifying and expanding brackets

Expanding brackets

Grade 1: Students will be able to apply times tables and simplify basic expressions, this could include,  y + y + y = 3y or a simple multiplier 5 x 3t = 15t.

Grade 2: Students will be able to expand single brackets including co-efficients. This should range from 2(x + 4) up to and including 3x(x - 4)

Grade 3: Students will be able to expand double brackets with positive and negative values.

Grade 4: Students will be able to expand double brackets with different co-efficients. This should include both terms being letters and double negatives.

Grade 5:

Grade 6:

Grade 7: Students will be able to expand cubic functions including with co-efficients.

 

Factorising Expressions

Grade 1: Students will be able to apply times tables and simplify basic expressions, this could include,  y + y + y = 3y or a simple multiplier 5 x 3t = 15t

Grade 2: Students will know and define prime numbers, multiples and factors in a logical order. Simplify expressions a x b = ab, 3 x y = 3y, a2 = a x a, a ÷ b = a/b 3y + 6y = 9y (must have coefficients as fractions not decimals i.e. ½a no + 0.5a)

Grade 3: Students will be able to factorise into single brackets with one co-efficient, this should include numbers and letters, such as, 2x +10 and t2 -4t.

Grade 4: Students will be able to factorise expressions into single brackets with more than one co-efficient, this should include numbers and letters.

Grade 5: Students will be able to factorise quadratic expressions with positive and negative numbers.

Grade 6:

Grade 7: Students will be able to factorise quadratic expressions with a coefficient ˃1. They should also begin to factorise simple cubic expressions such as x3 -4x2.

Substitution

Grade 1: Students will be able to substitute positive values into simple two step function machines.

Grade 2: Students will know how to Substitute positive numbers into expressions and linear formulae. Students will also be confident in the use of a formula written in words, such as cost = 20 x distance travelled

Grade 3: Students will be able to substitute into expressions with negative numbers, including the use of quadratic formulae. This should include the drawing of linear graphs

Grade 4: Students will be able to draw quadratic and cubic graphs by completing a table of values with a calculator.

Grade 5: Students will be able to draw cubic graphs and interpret the graphs (reading off values). In addition students will be able to draw reciprocal graphs.

Grade 6: Students will be able to use the quadratic formula.

Grade 7:

Factorising, substitution and solving equations mini assessments

Solving Equations

Grade 1: Students will be able to use function machines as simple equations. 

Grade 2: Students will be able to solve simple equations such as 4x = 24 and x - 3 = 7

Grade 3: Students will be able to solve linear equations and generate expressions for facts such as perimeter and angles in a triangle.

Grade 4: Students will be able to solve equations with unknowns on both sides, this should include the use of brackets. Students should be confident dealing with fractional answers.

Grade 5: Students will be able to solve quadratic equations by factoring first. They should also be able to solve equations using cross multiplication to remove denominators.

Students can also solve simultaneous equations including the use of manipulation, this should include the formation of equations from worded problems.

Grade 6: Students will be able to solve quadratic equations using the quadratic formula.

Grade 7:

Grade 8: Students can solve quadratic simultaneous equations by substitution. 


Half Term

Topic

Learning Outcomes

Assessment

Half term 3

Notation and Shape Properties

Grade 1: Students can measure lines to the nearest mm and angle to the nearest degrees. They can recognise and name triangles, quadrilaterals and regular polygons. Students can also use faces, vertex and vertices to name 3D shapes. In addition they can name the parts of a circle

Grade 2: Students can draw angles to the nearest degrees, they can name angles and label sides and angles in shapes using mathematical notation.

Grade 3: Students can identify when two shapes are congruent and state reasons using mathematical notation.

Notation and shape properties and Angle rules mini test.

Angle Rules

Grade 1:  Students can recognise and name triangles, quadrilaterals and regular polygons.

Grade 2: Students can find angles on a straight line, in a triangle, in an isosceles triangle and vertically opposite angles by calculation.

Grade 3: Students can recognise and use alternate and corresponding angles in addition to angle around a point and angles in a quadrilateral.

Grade 4: Students can work out exterior and interior angles of regular and irregular polygons. In addition they should be able to calculate the total degrees in a polygon using both formula and drawing method.

Grade 5:

Grade 6: Students can apply basic Circle Theorems and reasons to support these judgements.

Grade 7: Students can apply to alternate segment theorem and make statements to support simple proofs.

Area and Perimeter

Grade 1: Students can find area and perimeter by counting cm squares, this should include half squares. They can also use the area formula for squares and rectangles.

Grade 2: Students can convert between simple units, cm to m. They can use a formula to find the area of triangles and parallelograms.

Grade 3: Students can find the area and perimeter of compound shapes. They can find the area and circumference of circles.

Grade 4:

Grade 5: Students can find arc lengths and sector areas.

Grade 6: Students can apply the sine rule to find the area of a triangle.

Area and perimeter and volume and surface area mini test

Volume and Surface Area

Grade 1: Students will know times tables up to 12 x12

Grade 2: Students will be able to calculate the volume and surface area of cubes. They will also be able to draw simple nets of 3D shapes

Grade 3: Students will be to find volume and surface area of cuboids. They should be able to manipulate this formula to find a missing value.

Grade 4: Students can find the volume and surface area of any prism. 

Grade 5: Students are able to find the volume and surface area of cones, pyramids and spheres.

Grade 6:

Grade 7: Students can use ratios of similarity to find surface area and volume. 


Half Term

Topic

Learning Outcomes

Assessment

Half term 4

Representing and interpreting data

Grade 1: Students will be confident in drawing and interpreting pictograms and bar charts. They will also be comfortable designing a question and collecting data in a tally chart.

Grade 2: Students will be able to form frequency tables and use appropriate diagrams to display this, vertical line, frequency polygons, dual bar charts etc.

Grade 3: Students will be able to draw and interpret pie charts, two way tables and stem and leaf diagrams. They will also be able to recognise outliers.

Grade 4: Students will be confident in drawing and interpreting scatter diagrams including the use of a line of best fit. Students will be able to classify data and name the types of data.

Grade 5:

Grade 6: Students can draw and interpret box plots and cumulative frequency diagrams.

Grade 7: Students can draw and interpret Histograms.

Representing and interpreting data mini assessment

Averages

Grade 1: Students can calculate mode, median and range from a data set both with and without a calculator from an odd set of values.

Grade 2: Students can calculate mean, mode, median and range from a data set both with and without a calculator from any set of values. This must include graphical data.

Grade 3: Students can compare data using the mean, median, mode and range. In addition they can find a modal interval and mean from a frequency table.

Grade 4: Students can find all averages form a grouped frequency table

Averages and probability mini assessments

Probability

Grade 1: Students can record the outcomes of experiments and understand the probability scale and associated vocabulary.

Grade 2: Students can find the probability of an event occurring using both fractions and decimals. They should understand that probabilities total one and use this to find a probability of an event not occurring.

Grade 3: Students can use relative frequency to estimate probability and find expected outcomes from a given context. In addition students can draw Venn diagrams, with two circles, to explain possible outcomes, sample space diagrams and frequency trees.


Half Term

Topic

Learning Outcomes

Assessment

Half term 5

Equivalent Fractions

Grade 1: Students can order numbers and use times tables up to 12 x 12.

Grade 2: Students can order fractions with the same denominators, cancel fractions to their lowest form and find equivalent fractions.

Grade 3: Students can order fractions with different denominators by using LCM to find equivalence.

Fractions mini assessments

Four operations with fractions

Grade 1: Students can order numbers and use times tables up to 12 x 12.

Grade 2: Students can find equivalence and change between improper fractions and mixed numbers.

Grade 3: Students can use all operations with fractions including the use of mixed numbers. They can also find HCF and LCM.

Grade 7: Students can perform all operations with algebraic fractions

 

Fractions of amounts

Grade 1: Students can find simple fractions such as half, quarter, tenth and fifth.

Grade 2:  Students can find simple fractions of an amount, such as 4/5 of £65.

Grade 3: Students can confidently apply BIDMAS to any calculation, this should be considered when using a calculator. In addition they can calculate powers of 2,3,4 and 5. Students will be able to problem solve using fractions of quantities.

Grade 4: Students can calculate integer powers and roots by using a calculator

Grade 5: Students can calculate negative and fractional indices with and without a calculator.

Fractions, decimals and percentages

Grade 1: Students understand place value and can express percentage as part of 100

Grade 2: Students can perform basic conversions from fractions to percentages without the use of a calculator by using equivalence to 100.

Grade 3: Students can convert any fraction, decimal to percentage with the use of a calculator. This should include ordering a range of all three from smallest to largest.

Grade 7: Students can write recurring decimals as fractions using algebra to generalise.

Using a calculator and estimation

Grade 1:.Students can make simple estimations to calculations based on times tables.

Grade 2:Students can calculate squares and roots using the functions of a calculator. They can round solutions to the nearest 1, 10, 100 and any stated decimal place.

Grade 3: Students can perform complex calculations on a calculator and can round to significant figures. This includes calculations in standard form.

Grade 4: Students can round to decimal places, significant figures and understand truncation. Students can make estimates for large calculations that involve division by decimals.

Grade 5: Students can explain if estimate are under or over estimates based on a given calculation.

Factors, multiples and primes; using a calculator and estimation mini assessments 


Half Term

Topic

Learning Outcomes

Assessment

Half term 6

Ratio

Grade 1: Students can write a ratio for two or three given amounts.

Grade 2: Students can simplify ratios and express ratio as fractions.

Grade 3: Students can share a quantity into a given ratio and use a find totals given one part of a ratio.

Grade 4: Students can solve problems combining ratio, percentages and fractions of amounts.

Ratio Mini

Assessment

Proportion

Grade 1: Students understand times tables up to 12x 12 and can use division.

Grade 2: Students can solve problems with direct proportion, they can find the value of 1 and use this to scale up.

Grade 3: Students can solve problems by using multiples without a calculator and using the unitary method with a calculator.

Grade 4: Students understand proportional change and can use a multiplier, this is exemplified by currency conversion or changes from litres to gallons.

Grade 5: Students can use compound measures such as speed, distance and time or mass density and volume.

Grade 6: Students can form equations of proportionality in respect to both direct and indirect proportion.

Grade 7: Students can form and use equations in respect to both direct and indirect proportion.

Conversion Graphs

Grade 1: Students can write and plot coordinates in the first quadrant.

Grade 2: Students can use word formulas to generate points. They can also read values form a conversion graph with a simple scale.

Grade 3: Students can substitute values into formal to generate points. They can plot conversion graphs in relation to real life problems such as currency, speed conversions and cost of items/mileage.

Grade 4: Students can plot and use direct and inverse proportion graphs for real life situations. In addition they can make estimations from values that are not on the graph.

Grade 5:

Grade 6:

Grade 7:

Grade 8: Students can draw graphs to represent decay over time.

Proportion and Conversion Graphs Mini Assessments

  

Year 8 Curriculum Breakdown

 

 

 Key Stage 4 - Lower Curriculum Breakdown

Year 9

Half term

Topic

Lesson Outcomes

Assessment

Half term 1

ALGEBRA: BASICS

Collecting like terms

Algebra #1

Collecting like terms

Multiply and divide simple algebraic expressions

Use index notation when multiply and dividing algebraic terms

Write an expression / equation / formula / identity

EXPRESSIONS AND SUBSTITUTION INTO FORMULA

expand brackets

factorise into brackets

write expressions involving powers

substitute numbers into algebraic expressions

SEQUENCES

continue a sequence and find the next term

Algebra #2

Use function machines to find the next term in a sequence

find the next term in a sequence including Fibonacci, squares and cubes and diagrams

generate sequences using nth term

find the nth term and use to find any term

find the nth term and use to find any term

determine if a term is in the sequence

determine if a term is in the sequence

continue a geometric sequence

continue a quadratic sequence

 

 

 

 

Half term 2

EQUATIONS AND INEQUALITIES

solve any two step equation

Algebra #3

solve any two step equation

write expressions and set up simple equations involving words and shape

write expressions and set up simple equations involving words and shape

Use inequality notation

Show inequalities on a number line

Solve inequalities

Use inequalities to show error intervals in rounding

Mini-assessment and Revision

Revision lesson Sequences

Problem solving and Exam question practice

STRAIGHT LINE GRAPHS

Draw horizontal and vertical straight lines

Algebra #4

Plot graphs of y=mx + c from tables and interpret

Plot graphs of y=mx + c from tables and interpret

Sketch a graph using the y intercept and gradient and interpret

Work with parallel lines

find equation of a line

find equation of a line

find equation of a line through one point when given a gradient

APPLYING GRAPHS

find co-ordinates including those of missing points on a shape

find midpoints from co-ordinates and from graph

distance time graphs

velocity time graphs

currency conversion graphs

fixed charge and cost per unit graphs

find gradient and interpret gradient as rate of change

Mini-assessment and Revision

Revision lesson Straight line and real life graphs

Problem solving and Exam question practice

 

Half term 3

INTEGERS PLACE VALUE

Order positive, negative, decimal numbers including using inequality symbols

Number #1

4 operations with negative numbers

multiply and divide by powers of 10

BIDMAS

inverse operations

INDICES, POWERS AND ROOTS

evaluate numerical powers up to power of 5

square and cube roots

laws of indices multiply and divide

laws of indices brackets

use of calculators

FACTORS, MULTIPLES AND PRIMES

factors including HCF

Number #2

multiples including LCM

prime numbers and product of prime

HCF and LCM from product of prime

INDICES AND STANDARD FORM

laws of indices

fractional and negative powers

write numbers in standard form

write numbers in standard form

4 operations with numbers in standard form

 

 

Half term 4

DECIMALS

4 operations with decimals

Number #3

calculations with money

round to nearest decimal place and 1 sf

estimation by rounding to 1 sig fig

FRACTIONS, DECIMALS, PERCENTAGES

Write fractions and cancel down

Equivalent fractions

Order fractions

Mixed numbers to improper fractions

4 operations with fractions

4 operations with fractions

convert fractions to decimals and percentages

convert fractions to decimals and percentages

PERCENTAGES

express one number as a percentage of another

Number #4

find any % of amount

percentage increase / decrease

Worded percentage increase / decrease

percentage increase / decrease using a multiplier

simple interest

compound interest

compound interest 


Half term 5

PROPERTIES OF SHAPES, LINES AND ANGLES

Identify parallel and perpendicular lines and use angle notation

Shape # 1

properties of triangles and quadrilaterals including using a co-ordinate grid

angles on a line and around a point

angles in triangles

angles in quadrilaterals

angles in parallel lines

angles in parallel lines

Mini-assessment and Revision

Revision lesson Properties of shapes lines and angles

Problem solving and Exam question practice

INTERIOR EXTERIOR ANGLES

Calculate interior angle in regular polygon

Shape # 2

Calculate interior angle in irregular polygon

Use exterior and interior angles in angle problems

Use exterior and interior angles in angle problems

Prove tessellation using angles

Mini-assessment and Revision

Revision lesson Fractions, Decimals, Percentages

Problem solving and Exam question practice

RIGHT ANGLED TRIANGLES

Pythagoras finding hypotenuse

Shape # 3

Pythagoras shorter side

problem solve Pythagoras

trigonometry finding side

trigonometry finding angle

exact trig vales

Half term 6

PERIEMTER, AREA AND VOLUME

Perimeter of regular and compound shapes

Shape # 4

Area of triangles of rectangles

Area of trapezium

Area of parallelogram

Area of compound shapes

Surface area

Volume of prism

Volume of prism

Volume of cylinders

Mini-assessment and Revision

Revision lesson Perimeter, Area, Volume

Problem solving and Exam question practice

TRANSFORMATIONS

reflect shapes in a mirror lines

Shape # 5

fully describe reflections

rotate shapes

fully describe rotations

enlarge shapes by a positive integer

enlarge shapes by a fraction or negative number

describe enlargement

perform a perform multiple transformations

describe multiple transformations

similar shapes and congruency

similar shapes and congruency

Compass directions and constructions

compass directions and use of scales on maps

Shape # 6

compass directions and use of scales on maps

Draw circles and arcs to a given radius or diameter

3d shapes - draw sketches, identify face, vertex, edge

accurately construct triangles

accurately construct triangles

 

 Year 10

 

Half Term

Topic

Learning Outcomes

Assessment

Half term 1

QUADRATIC EQUATIONS

expand single brackets

Algebra #5

expand two brackets

square a linear expression

factorise single brackets

factorise quadratic

difference of two squares

solve quadratic expression by factorising

QUADRATIC GRAPHS

plot linear graphs

Algebra #6

generate and plot simple quadratic graphs

generate and plot simple quadratic graphs

interpret quadratic graphs

EQUATIONS
REVISION

solve any two step equation

Algebra #7

solve any equation

write expressions and set up simple equations involving words and shape


Half Term

Topic

Learning Outcomes

Assessment

Half term 2

REARRANGING EQUATIONS, CUBICS, RECIPROCAL AND SIMULTANEOUS EQUATIONS

change the subject of a formula

Algebra #8

Simultaneous equations

draw cubic and reciprocal graphs

VECTORS

Translate shapes by vector

Algebra #9

Use column notation

Use column notation graphically

Calculate sums of multiple vectors

Calculate sums of multiple vectors

Know (proof) if a vector is parallel

SEQUENCES
REVISION

find the next term in a sequence including Fibonacci, squares and cubes and diagrams

Algebra #10

generating a sequences given the nth term

find the nth term and use to find any term

determine if a term is in the sequence

continue a quadratic sequence


Half Term

Topic

Learning Outcomes

Assessment

Half term 3

RATIO

Simplify ratios and use equivalent ratios

Number #5

Share ratios into a given quantity

use ratio in the form 1:n

Reverse Ratios

Ratios in shape

Multiplicative relationships between two rates and fractions

Problems involving three ratios

PROPORTION

Double and half recipes

Number #6

Scale up or down recipes

Find limiting ingredients in recipes

solve best buy problems

solve proportion using unitary method

direct proportion

inverse proportion


Half Term

Topic

Learning Outcomes

Assessment

Half term 4

MULTIPLICATIVE REASONING

convert between metric units

Number #7

speed

density

pressure

convert compound units

compound interest

use a variety of measures in ratio and proportion problems

growth and decay problems

CONSTRUCTION, LOCI AND BEARINGS

construct and bisect angles and lines

Number #8

loci

bearings

loci and bearings combined


Half Term

Topic

Learning Outcomes

Assessment

Half term 5

PERIMETER, AREA, VOLUME 2: CIRCLES, CYLINDERS, CONES

Find the circumference of a circle including in terms of pi (calc)

Shape #4

Find the circumference of a circle including in terms of pi (non-calc)

Find the area of a circle including in terms of pi (calc)

Find the area of a circle including in terms of pi (non-calc)

Find perimeter and area of parts of a circles and composite shapes

Find arc lengths and sector areas

Surface area and volume of cylinder

Surface area and volume of pyramid, cone

SIMILARITY AND CONGRUENCY

basic criteria for congruency for triangles

Shape #5

solve angle problems involving congruency

use scale factors with similar shapes

find missing sides in similar shapes


Half Term

Topic

Learning Outcomes

Assessment

Half term 6

TABLES, CHARTS, GRAPHS

time calculations

Stats #1

construct and interpret a frequency table and bar charts

line graphs including interpret

two way tables and frequency trees

back to back stem and leaf

histograms

PIE CHARTS

Construct pie charts

Interpret pie charts

Compare pie charts with other charts

SCATTER GRAPHS

Draw and interpret scatter graph

Extrapolation / Interpolation

STATISTICS, SAMPLING AND AVERAGES

understand sample, population, types of data

Stats #2

all averages from data

all averages from graphs and charts

 

all 4 averages from frequency table

 

all 4 averages from frequency table

 

reverse averages

  

Key Stage 4 Higher Curriculum Breakdown

 

 

 

 

 

For further information on the curriculum offered please contact Mr Trevor Lester at Lester.T@Whiteroseacademies.org (Head of Maths)