UG010896 – Edexcel GCSE Mathematics – Teachers’ … department/maths... · Web view20...

GCSE Intermediate Scheme of Work

Module Stage TIMETarget Grades

Previous Module Homework SumBooks Sheet

1 Number 1 7 hours

E/D/C 1 Multiplication and Division2 Negative Numbers3 Use of the Calculator

2 Geometry 1 8 hours

E/D/C 33 Bearings34 Parallel Lines36 Triangles37 Regular Polygons38 Irregular Polygons

3 Numbers and Powers 1 5 hours

E/D 10 Prime Factors29 Trial and Improvement

4 Collecting and sorting data 1 3 hours

E 61 Questionnaires

5 Simplifying and substituting 1 4 hours

E/D/C 1, 3 21 Substitution22 Simplifying Expressions24 Multiplying Brackets Ex 1 and 225 Factorising

6 Transformations 1 5 hours

E/D/C/B 2 44 Reflections, Rotations and Translations 145 Reflections, Rotations and Translations 246 Reflections, Rotations and Translations 347 Reflections, Rotations and Translations 4

7 Fractions 1 5 hours

E/D/C/B 1, 3 5 Fractions, Decimals and Percentages 1 Ex 1 and 590 Recurring Decimals

8 Equations and inequalities 1 5 hours

E/D/C/B 5 26 Equations27 More Equations Ex 130 Inequalities

9 Percentages 1 5 hours

E/D/C/B 1, 7 5 Fractions, Decimals and Percentages 16 Fractions, Decimals and Percentages 27 Interest

10 Sequences 1 3 hours

E/D/C/B 5 11 Number Patterns and Sequences 112 Number Patterns and Sequences 2

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11 Circles 1/2 5 hours

D/C/B 2 54 Circumference of a Circle.

12 Probability 1/2 4 hours

E/D 75 Probability 176 Probability 277 Probability 3

13 Shape, volume and surface area 1/2 7 hours

E/D/C 11 55 Area and Perimeter56 Volume Ex 281 Constructions

14 Ratio and proportion 2 5 hours

E/D/C 1, 3, 7 8 Scale Drawings and Ratio57 Compound Measure - Speed and Density58 Compound Measure - Best Buy and a Mixed Exercise

15 Displaying data 2 6 hours

E/D/C 2, 4 62 Pie Charts63 Frequency Polygons 164 Frequency Polygons 291 Stem and Leaf Diagrams92 Box Plots

16 Approximation 2 4 hours

E/D/C 1 3 Use of the Calculator4 Estimation53 Degree of Accuracy

17 Average and spread 2 5 hours

E/D/C 65 Mean, Median, Mode and Range66 Mean 167 Mean 268 Mean 3 - diagrams69 Mean 4 - Frequency distributions with class intervals70 Mean 5 - Histograms89 Moving Averages

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18 Transformations 2 5 hours

C/B 6 8 Scale Drawings and Ratio48 Enlargements 149 Enlargements 250 Similar Shapes

19 Substitution and formulae 2 4 hours

C/B 3, 5, 8 29 Trial and Improvement32 Rearranging Formulae

20 Pythagoras’ Theorem 2 4 hours

C 2, 3, 5, 8, 19

39 Pythagoras' Theorem

21 Trigonometry 2 6 hours

C/B 2, 20 40 Trigonometry 141 Trigonometry 242 Trigonometry 343 Trigonometry 4

22 Scatter diagrams 2 3 hours

D 4, 15 73 Scatter Diagrams 174 Scatter Diagrams 2

23 Cumulative Frequency 2 4 hours

C/B 4, 15, 17 71 Cumulative Frequency 172 Cumulative Frequency 284 Using Quadratic Equation

24 Probability 2 4 hours

D/C/B 12 78 Tree diagrams79 Relative Frequency 180 Relative Frequency 2

25 Quadratics 2 4 hours

C/B 5, 8 24 Multiplying Brackets Ex 327 More Equations Ex 2

26 Algebraic graphs 2 7 hours

E/D/C/B 5, 8, 19, 25

13 Distance Time Diagrams 114 Distance Time Diagrams 215 Conversion Graphs 116 Conversion Graphs 217 Sketching and Recognising Graphs 118 Sketching and Recognising Graphs 219 Plotting Graphs 120 Plotting Graphs 228 Straight Line Graphs and Sim Eqns Ex 1

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27 Percentages 3 4 hours

C/B 1, 7, 9 HIGHER 6 Percentages

28 Constructions

3 5 hours

E/C/B 2 51 Locus Problems 152 Locus Problems 2

29 Indices and surds 3 7 hours

C/B 3 23 Indices56 Volume Ex 159 Formulae for Area, Volume and Perimeter 160 Formulae for Area, Volume and Perimeter 285 Surds

30 3D, volumes and surface areas 3 5 hours

D/C 11, 13 35 Nets and Isometric Drawing87 Plans and Elevations (1)88 Plans and Elevations (2)

31 Standard index form 3 3 hours

B 3, 16, 29 9 Standard Form

32 Angles in circles 3 4 hours

B 2, 13 HIGHER 37 Geometry of a Circle 1HIGHER 38 Geometry of a Circle 2

33 Algebra 3 8 hours

C/B 8, 25, 26 28 Straight Line Graphs and Simultaneous Equations Ex 231 Inequalities - Graphs82 Simultaneous Equations

34 Co-ordinates and transformations 3 4 hours

C/B 6, 18 HIGHER 89 3 Dimensional Co-ordinates 1HIGHER 90 3 Dimensional Co-ordinates 2

35 Data Handling 3 3 hours

C/B 4, 12, 15, 17, 22

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GCSE Intermediate Scheme of Work1387/1388 (STAGE ONE)

MODULE 1 NumberTIME: 7 hoursTARGET GRADE: E/D/CPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 Ruff Guide

DIFFERENTIATION / EXTENSION / HOMEWORK

The ability to order large numbers and appreciation of place value to at least thousands.

Knowledge of times tables would be particularly useful.

Knowledge of strategies for multiplying and dividing whole numbers by 10.

Understanding place value in whole numbers NA2a

22

Place value, multiplication and division of decimal numbers by powers of ten NA3a

168, 172

Draw tables to illustrate ×100, ÷10 of decimal numbers.Consideration of mental maths problems with negative powers of 10: 2.5 × 0.01, 0.001.

Multiplying and dividing by multiples of powers of ten NA3a

11, 18-19, 173, 174

Multiplying and dividing by a number between 0 and 1 NA3a

172, 173, 174

Writing assorted numbers in order of size NA2a

Order numbers of any size. 23, 24, 168,176

Write out a series of calculations (possibly as a flowchart) for placing a series of numbers in order of size

Long multiplication and long division without using a calculator NA3a

11-13, 17

Non-calculator maths: 3-digit numbers multiplied by 3-digit numbers. H/W SumBooks 1

Order of operations NA3b 20-21 Directed number work with two or more operations, or with decimals.

4-rules using negative numbers NA3a Work with positive and negative temperatures.

25-31 H/W SumBooks 2

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GCSE Intermediate Scheme of Work Work confidently without the

aid of a calculator, including the four rules with negative numbers.

Rounding off to a given power of ten NA2a

37-39

Interpreting a calculator display NA3p Use a calculator to solve number problems and interpret the answers.

Investigate the largest/smallest numbers on a calculator. H/W SumBooks 3

NOTESAll working should be presented clearly.Non-calculator methods should show remainders & carries as evidence.

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MODULE 2 GeometryTIME: 8 hoursTARGET GRADE: E/D/CPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Knowledge of the names and properties of triangles, quadrilaterals and polygons.

Oral testing on a regular basis regarding the names and properties of the shapes covered.

The ability to use a protractor to measure angles.

Understanding of the concept of parallel lines.

Calculating angles on a straight line and at a point* SSM2a

Calculate angles at a point and on a straight line.

206

Recognising opposite angles at a vertex* SSM2a

206

Calculating angles in triangles SSM2b Use the angle sum for triangles and quadrilaterals to find other angles in the shapes.

207 H/W SumBooks 36Using angle properties of isosceles, equilateral and right-angled triangles SSM2b

207

Using parallel lines, alternate angles and corresponding angles SSM2a

Calculate angles on parallel lines, at a point and on a straight line.


Understanding the proof that the angle sum of a triangle is 180 degrees SSM2a

Understand the two proofs relating to angles in a triangle.

211

Understanding the proof regarding exterior angles of triangles SSM2a

211

Recalling names and recognising properties of special quadrilaterals SSM2c

212-3

Explaining why the angle sum of a quadrilateral is 360 degrees SSM2b

211

Calculating angles in quadrilaterals SSM2b

Use the angle sum for triangles and quadrilaterals to find other angles in the shapes.

214

Interior and Exterior angles of quadrilaterals, pentagons, hexagons and regular polygons SSM2d

Know how to work out the angle sum for any given polygon, use the to find other angles relating to polygons and understand which shapes tessellate.


Tessellation SSM2d 224 Investigate which regular polygons will tessellate alone, or with each other.

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GCSE Intermediate Scheme of WorkUsing the angle properties of parallelograms SSM2aDrawing and measuring bearings SSM4a Draw and measure three figure

bearings accurately.139 H/W SumBooks 33

Converting between measurements** SSM4a

117-119

RESOURCESChannel 4 – Shape, space and Handling data programme 3

NOTESPupils are often confused about the position from where a bearing is measured.*Not specifically mentioned in Intermediate specification.**For 1387 this fits more appropriately into module 14.

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MODULE 3 Numbers and PowersTIME: 5 hoursTARGET GRADE: E/DPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Basic number bonds and multiplication/division facts.

Awareness of position of numbers on number lines.

Ability to recognise basic number patterns.

Mental test to check knowledge of squares and cubes.

Square and cube numbers NA2b Calculate square and cube numbers.

Recognise the different types of numbers.

32-33

Squares and square roots NA2bCubes and cube roots NA2b

Find square and cube roots of numbers including decimals by trial and improvement and by calculator methods.

34-36

Trial and improvement methods NA2b (to find square and cube roots of numbers including decimals)

H/W SumBooks 29

Factors and multiples NA2aFinding Highest Common Factor and Lowest Common Multiple NA2a

Use lists of multiples to find the lowest common multiple.

Write numbers in terms of their factors/prime factors and use prime factors to find the HCF.

44-45 Use prime factors to find LCM.

H/W SumBooks 10

Powers of numbers* NA2b Calculate powers of whole numbers including negative numbers.

308-309

Further work on indices to include negative and/or fractional indices.

Investigational tasks leading to number patterns involving powers of numbers.

NOTESAll of the work in this unit is easily reinforced by starter and end activities.*Note that in 1388 the rules of indices are not tested until stage 3.

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MODULE 4 Collecting and sorting dataTIME: 3 hoursTARGET GRADE: EPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 TEXT


An understanding of why data needs to be collected and some idea about different types of graphs.

Different ways of collecting data HD1a Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data.

Use a spreadsheet to collect data in tables and draw different types of graphs

H/W SumBooks 61 Questionnaires

Designing questions to collect data HD3a & HD1g

Design a simple questionnaire, and appreciate deficiencies in a question.

Collecting data by sampling HD3a & HD1g

Understand the concept of sampling a population, what makes a fair sample, and explain deficiencies of sampling techniques.

Collecting data by observation HD3a Collect data from a variety of sources.Collecting data by experiment HD3a

Obtaining data from a database, tables and lists HD3bSorting and presenting data HD3a & HD1c

Sort and collect data in a tally table and grouped frequency table.

Designing and using two-way tables HD3c

Design and use two-way tables.

Dealing with practical problems when collecting data HD3d

NOTESClearly label all axes on graphs and use a ruler to draw straight lines.

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MODULE 5 Simplifying and substituting TIME: 4 hoursTARGET GRADE: E/D/C

PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 1, 3. Experience of using a

letter to represent a number.

Ability to use negative numbers with the four rules.

Using letters to represent numbers NA5aUsing negative numbers NA5d STAGE TWOUsing word formulae NA5g

Substitute positive and negative numbers into word formulae and algebraic formulae.


Using algebraic formulae NA5g 91Collecting like terms NA5b Simplify algebra by collecting

like terms – answers may involve negative coefficients.

99 H/W SumBooks 22

Multiplying with letters and numbers NA5bRemoving a single pair of brackets NA5b Remove and factorise a single

pair of brackets – including cases where a variable is removed as a factor.

100 H/W SumBooks 24 Ex 1 & 2

Factorising with a single pair of brackets NA5b

102 H/W SumBooks 25

Factorising where the factor may involve more than one variable.

NOTESEmphasise correct use of symbolic notation (e.g. 3x rather than 3 × x).

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MODULE 6 TransformationsTIME: 5 hoursTARGET GRADE: E/D/C/B


CONTENT MAIN OBJECTIVES Y10 Text


Module 2. Some experience of

plotting points. Knowledge of the

range of 2-D shapes, and parallel lines.

The ability to recognise that a shape has symmetrical properties.

Testing of the ability to draw shapes to a specified number of lines of symmetry, or order of rotational symmetry.

Co-ordinates in first quadrant SSM3e/NA6bCo-ordinates in four quadrants SSM3e/NA6b

Plot and read co-ordinates in four quadrants.

189-190

Congruent shapes* SSM2d Recognise congruency Given a shape on squared paper, produce as many other different congruent shapes as possible.

Line symmetry* SSM3bPlanes of symmetry SSM3b

Sketch planes of symmetry on simple shapes.

State the properties of each 2-D shape and classify a shape according to its symmetrical properties.

Identify lines of symmetry or the order of rotational symmetry in 2-D shapes.

191-3 An attempt to draw up to 3 shapes each which have exactly 1, 2, 3, … 8 lines of symmetry, and investigate

whether a rule exists between the number of vertices and the number of lines of symmetry.

Sketch all the planes of symmetry of a cube on 9 diagrams.

Rotational symmetry* SSM3b 194-6Transforming 2D shapes by reflection SSM3b

Reflect a 2D shape in a vertical, horizontal or diagonal line and

197-203

H/W SumBooks 44, 45

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GCSE Intermediate Scheme of WorkSpecify a mirror line parallel to axes SSM3a

state the equation of the line.

Rotating shapes SSM3bTransforming 2D shapes by rotation SSM3bDescribing transformations in full (rotations, reflections and translations) SSM3a

Rotate a 2D shape about the origin or a point other than the origin, stating the angle, direction and centre of

rotation.

197, 204-5

H/W SumBooks 46, 47

Translations SSM3b Translate a 2D shape and describe the translation in words.

197

* Not specifically mentioned in Intermediate specification.

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MODULE 7 FractionsTIME: 5 hoursTARGET GRADE: E/D/C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 1, 3. A basic

understanding of fractions as being ‘parts of a whole unit’.

Use of a calculator with fractions.

Interchanging improper fractions and mixed numbers. NA3d

Understand and change between improper fractions and mixed numbers.

151-2

Calculating a fraction of a quantity. NA3c

Calculate a fraction of a quantity.

153 H/W SumBooks 5 Ex 5

Using diagrams to find equivalent fractions. NA2c

Equate one fraction with another, and simplify fractions to their lowest terms

Write one number as a fraction of another.

154

Cancelling fractions. NA2cWriting a given number as a fraction of another. NA3c

155-156 For very able students cancelling down of algebraic expressions could be considered.

Interchanging fractions and decimals and using recurring decimals. NA2d & NA3c

Understand the concept of a recurring decimal.

Convert fractions into decimals and vice versa, including recurring decimals.

169, 175-178??179-180,

Relating the basic fractions to readily remembered percentages and vice-versa.

H/W SumBooks 5 Ex1

H/W SumBooks 90

Ordering fractions using common denominators. NA2c

Order fractions using common denominators or decimal conversions.

161

Adding and subtracting fractions using common denominators. NA3c

Perform the four basic operations with fractions.

157-160

Multiplying and dividing fractions. NA3d 162-165Using fractions in problems involving multiplication and division. NA3d

Solve problems involving fractions.

166-167

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GCSE Intermediate Scheme of WorkNOTESConstant revision of this aspect is needed. All work needs to be presented clearly with the relevant stages of working shown. Non-calculator work with fractions is generally poorly attempted at GCSE.

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MODULE 8 Equations and inequalities TIME: 5 hoursTARGET GRADE: E/D/C/BPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Module 5. Experience of finding

missing numbers. The idea that some

operations are ‘opposite’ to each other.

An understanding of balancing methods.

Inverse operations NA5f Solve problems requiring inverse operations.

Use of inverse operations and rounding to 1 sig. fig. could be applied to more complex calculations.

Reverse rate problems NA4a STAGE THREESimple linear equations NA5e Solve linear equations including

those with an unknown on both sides, those that require prior simplification (e.g. brackets), fractional equations, and those where the answers are either negative or a fraction.

94 Derive equations from practical situations (such as angle calculations).

Solve equations or inequalities where more manipulation of fractions is required.

H/W SumBooks 26

H/W SumBooks 27 Ex1 with fractions.

H/W SumBooks 30

Equations combining operations NA5e 96-97Solving equations with the unknown on both sides NA5f

97-98

Solving equations using brackets and negative solutions NA5f

103-105

Set up simple equations NA5e 106Using algebraic equations to solve problems NA5e

Derive algebraic expressions from information given and extend this to derive equations.

107

Solving simple inequalities* NA5j Solve linear inequalities through both algebraic methods and listing possible integer values.

Y11 pg 168-170

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GCSE Intermediate Scheme of WorkPupils need to realise that not all linear equations can easily be solved by either observation or trial and improvement, and hence the use of a formal method is vital.Pupils can leave their answers in fractional form where appropriate.*For 1388 this is not assessed until Stage 2.

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MODULE 9 PercentagesTIME: 5 hoursTARGET GRADE: E/D/C/BPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 ??? DIFFERENTIATION / EXTENSION / HOMEWORK

Modules 1, 7. A basic understanding

of the concept of a percentage.

An understanding of the ideas behind VAT, and interest.

Mental methods of calculating common percentages (e.g. 17½% using 10%, 5%, 2½%).

Understanding percentages NA2e The inclusion of percentages which lead to recurring decimals (e.g. 33 1/3%), and situations which lead to percentages of more than 100%.

Problems which lead to the necessity of rounding to the nearest penny (e.g. real-life contexts).

Independent research into the many uses made of percentages, particularly in the media.

The construction of a VAT ready-reckoner table.

H/W SumBooks 5, 6

Interchanging between percentages, fractions and decimals NA3e

Change between percentages, fractions and decimals.

181-5

Finding percentages, and percentage changes NA3j

Find percentages of quantities, by both mental mathematics and calculator methods as appropriate.

Increase and decrease quantities by a percentage, including within contexts of VAT, profit and loss.

Find one quantity as a percentage of another, and calculate the percentage when an actual profit or loss is given.

Solve problems using percentages e.g. taxation, bills.

313-317

Finding VAT, a percentage profit or loss NA3j

319-321, R3 38-9

Finding the added cost of buying goods on credit terms NA3j

R3 108-9

Using simple interest NA3j Calculate simple and compound interest.

Comparisons between simple and compound interest

Using compound interest* NA3k 316

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GCSE Intermediate Scheme of Workcalculations, leading to the use of fractions or formulae in compound interest methods.

H/W SumBooks 7

RESOURCESChannel 4 – Number and Algebra programme 1

*In 1388 this is not tested until Stage 3.

NOTESAmounts of money should always be rounded to the nearest penny where necessary, except where such rounding is premature (e.g. in successive calculations like in compound interest).All working should always be shown.

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MODULE 10 SequencesTIME: 3 hoursTARGET GRADE: E/D/C/B




Module 5. The ability to follow a

series of instructions and appreciate that symbols can represent numbers.

Use of mental maths in the substitution of simple numbers into expressions.

Extending diagrammatic sequences NA6a

Continue sequences of diagrams.

49-51 Match stick problems Fibonacci

sequence, Pascal’s triangle.

Uses of algebra to describe real situation e.g. n quadrilaterals have 4n sides.

H/W SumBooks 11

Extending number sequences NA6a Continue linear and non-linear sequences of numbers.

Linear E8.2 pg 73?? Non-Linear D5.1 pg 63

Generating common number sequences NA6aGenerating number sequences using term-to-term and position-to-term definitions NA6a

Generate sequences from given information.

57-58

Finding the nth term (linear expressions) NA6a

Investigate number patterns, describing them in words and using the nth term for linear expressions.

52-56, 59-62

NOTESEmphasis on good use of notation 3ab means 3 × a × b.When investigating linear sequences, students should be clear on the description of the pattern in words, thedifference between the terms and the algebraic description of the nth term.

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GCSE Intermediate Scheme of Work1387/1388 (STAGE ONE /TWO)

MODULE 13 Shape, volume and surface areaTIME: 7 hoursTARGET GRADE: E/D/C


CONTENT MAIN OBJECTIVES Y10/11 Text


Module 11 – area and circumference of circles.

Names of triangles, quadrilaterals and polygons.

Nets of simple solids. Concept of area and

volume. Ability to give

answers to a degree of accuracy.

Oral testing on a regular basis regarding the method of calculating the areas/volumes of shapes.

Constructing triangles SSM4b 132-134

Constructing 2-D shapes SSM4b Construct 2D shapes using ruler, pencil, protractor and compasses.

135-137

H/W SumBooks 81

Finding areas of plane shapes using formulae** SSM4d

Find the perimeter and area of simple shapes, such as rectangles squares, triangles, parallelograms, trapezia, kites, and composites of rectangles and triangles.

Know the formulae for area and volume of the shapes mentioned.

Y11 text pg 97-108

Simple fencing problems.

H/W SumBooks 55

Using the language of 3D shapes* SSM2iConstructing 3-D shapes SSM4bNets of simple solids SSM2i STAGE THREE

Construct 3D shapes using ruler, pencil, protractor and compasses.

144-8 Find all possible nets of a cube.

Investigate the different nets that can be used to make certain 3-D shapes

Developing, knowing and using the formula for the volume of a cuboid** SSM4dFinding volume of solids made from cuboids** SSM4d

Work confidently with 3-D shapes and be able to calculate the volume of cuboids, prisms, solids made from cuboids

Find how many boxes of a given size fit into a larger box.

Y11 text pg 117-118

Additional work using symbolic expressions.

H/W SumBooks 56 Ex 1

Using the formula for the volume of a cuboid to solve problems** SSM4d

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GCSE Intermediate Scheme of WorkFinding volume of prisms** SSM4d Y11

text pg 120-121

Finding surface area of solids with triangular and rectangular faces** SSM4d

Be able to calculate the surface area of solids with triangular and rectangular faces.

Y11 text cuboids pg 119

*Not specifically mentioned in Intermediate specification.**For 1388 this is not assessed until Stage 2.NOTES

Need to constantly revise the expressions for area/volume of shapes.

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MODULE 12 ProbabilityTIME: 4 hoursTARGET GRADE: E/D




Experience of using the language of likelihood.

Knowledge of a probability scale from 0 to 1, including impossible and certain events.

Ability to read from a two-way table.

Writing probability as numbers HD4c, d Write down theoretical probabilities of a single event happening.

The work can be extended to include that of the Higher syllabus.

Equally likely events HD4d 331-334,

H/W SumBooks 75

The probability of an event not happening HD4dUsing the sum of probabilities equalling 1 HD4d

Find the probability of an event not happening given the probability of an event happening.

335

Predicting outcomes using simple probabilities* HD4b

Predict how many times an event may happen given the probability.

Estimating probability by experimenting* HD4b

Establish the estimated probability of an event happening.

336,343-346

Listing systematically outcomes for single events or two successive events HD4cSample spaces and theoretical probabilities* HD4bDesign and use two-way tables HD3c

List outcomes of one or two events.

337-342

H/W SumBooks 76

Mutually exclusive events Understand the concepts of exclusivity and independence.


NOTESStudents can be unsure of the relationship P(not n) = 1 – P(n).Only fractions, decimals or percentages should be used for probability. 23 of 53

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GCSE Intermediate Scheme of Work*For 1388 this is not assessed until Stage 2

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MODULE 11 CirclesTIME: 5 hoursTARGET GRADE: D/C/BPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 & 11 TEXT


Modules 2. Knowledge of basic

circle vocabulary, and ability to construct a circle.

Recalling terms relating to a circle SSM2h

Use the vocabulary of a circle (circumference, radius, diameter, sector, segment, chord, tangent)

Y10 187-8

Understanding and using right angles between tangent and radius** SSM2hUnderstanding and using tangents of equal length** SSM2h

Calculate angles within circles using rules relating to tangents and radii.

Y11 208

Inscribing regular polygons in circles* SSM2h

Y10 217??

Calculating circumferences* SSM4dUsing pi in exact calculations*** NA3n

Recall and apply the formulae for the area and circumference of a circle given either the radius or diameter, using various approximations to pi or leaving pi as part of an irrational answer.

Recognise that units of volume or area cannot be converted using linear conversion factors.

Y11 109-112

Find area or perimeter of parts of a circle (halves, quarters or simple sectors).

H/W SumBooks 54 Circumference of Circles

Calculating areas of circles* SSM4dRecalling formulae for areas of circles* SSM4dUsing pi in exact calculations*** NA3n

Y11 113-5

NOTESPi can be 3 or 3.14 or 22/7 depending on accuracy or style of answer required.*For 1388 this is not assessed until Stage 2.**For 1387 this may be best covered in module.***For 1388 this is not assessed until Stage 3.

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GCSE Intermediate Scheme of Work1387/1388 (STAGE TWO)

MODULE 14 Ratio and proportionTIME: 5 hoursTARGET GRADE: E/D/CPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 11 TEXT


Modules 1, 3, 7. Basic number skills

and ability to recognise common factors.

Calculator skills.

Basic ideas of ratio NA2f Recognise a ratio as a way of showing the relationship between two numbers.

Y10 pg280-1 Y11 6-7

Simplifying ratios NA2f Simplify a ratio by dividing both its numbers by a common factor.

Recognise when a ratio is in its lowest terms.

Recognise that two numbers are in proportion if their ratios stay the same as the quantities get larger or smaller.

Y10 pg282 Y11 8

Similar triangles.

Relating ratio form to fractions NA2f Y10 pg283 Y11 9

Dividing in a given ratio NA3f Divide a quantity into a given ratio (in two or three parts).

Y10 pg 283-4 Y11 9-10

H/W SumBooks 8

Unitary method NA4a Use the unitary method as a way of solving ratio and proportion problems (e.g. recipes).

H/W SumBooks 58

Using direct proportion** NA3l Y10 pg 307 Y11 33

Converting between units given conversion factors* NA4a

Convert between a variety of units and currencies where conversion factors are given.

Y11 250-1 Currency calculations using current exchange rates.

Knowing and using metric equivalents of common imperial units* SSM4a

Convert between a variety of units using knowledge of metric

Y10 pg 126-7

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GCSE Intermediate Scheme of Workequivalents of common imperial units.

Calculate speed and other compound measures SSM4a

Calculate speed and other compound measures.

Y10 pg 322-4 Y11 48-50Y11 218-222

H/W SumBooks 57

*For 1388 this is assessed in Stage 1. ** For 1388 this is not assessed until Stage 3.

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MODULE 15 Displaying dataTIME: 6 hoursTARGET GRADE: E/D/C PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 2, 4. Measuring and

drawing angles. Fractions of simple

quantities. Plotting co-ordinates.

Grouping data in tally tables and grouped frequency tables HD3a

Sort and collect data in a tally table and grouped frequency table.

Y10 252-3

Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an appropriate means of displaying the results.

Use a spreadsheet to collect data in tables and draw different types of graphs.

H/W SumBooks 63, 64 Frequency Polygons

H/W SumBooks 91 Stem and Leaf diagrams

H/W SumBooks 92 Box Plots

H/W SumBooks 62 Pie Charts

Interpreting frequency diagrams HD5b Y10 227-9

Line graphs for discrete and continuous data, including time series* HD4a

Construct and interpret line graphs for all types of data.

Y10 270-1

Constructing and interpreting stem and leaf diagrams HD4a

Construct and interpret ordered and unordered stem and leaf diagrams.

Y10 244-5

Box plots HD4a Construct box plots. Y10 277

Calculating the angles to draw a pie chart HD4aDrawing Pie Charts HD4aCalculating using pie charts HD5b

Use a pie chart to display data as appropriate.

Interpret given pie charts.

Y10 230-3

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NOTESClearly label all axes on graphs and use a ruler to draw straight lines.Angles should be within 2 degrees.

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MODULE 16 ApproximationTIME: 4 hoursTARGET GRADE: E/D/C PRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y10 or 11 TEXT


Module 1. BODMAS. Quick fire mental test

for rounding values to different degrees of accuracy.

Rounding to the nearest 10, 100, 1000 NA3hCarrying out appropriate rounding given the context NA4b

Round numbers of any size to the nearest 10, 100, and 1000 or to any specified number of significant figures or decimal places.

Use rounding methods to make estimates for simple and complex calculations.

Y10 285-6 Y11 11-12

Discuss appropriateness of types of rounding in particular contexts.

H/W SumBooks 4 Estimations

Approximation to decimal places and significant figures NA3hUse of rounding to one significant figure for checking answers NA4b

Y10 304-5 Y11 30-31

Maximum and minimum values for rounded measurements* NA4bRecognising limitations on the accuracy of measurements NA4b

Recognise the upper and lower bounds of rounded numbers.

Recognise the limitations of a measurement.

Y10 325-6 Y11 51-2

Upper and lower bounds for decimals.

H/W SumBooks 53

Reading a calculator display to appropriate accuracy NA3oUse a calculator efficiently for complex calculations NA3o

Use a calculator correctly and efficiently for complex calculations (possibly involving powers and roots) and round the answers appropriately.

Y10 293-303 Y11 19-29

H/W SumBooks 3

NOTESPupils should be encouraged to include more accurate answers in their working out before rounding to ensure marks for correct calculations even if rounding is correct.Pupils need to be aware that correct rounding will lead to a number of the same magnitude as the original answer.* For 1388 this is not assessed until Stage 3.

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MODULE 17 Average and spreadTIME: 5 hoursTARGET GRADE: E/D/C




Some idea of the concept of average.

Finding the mode, median, mean and range from simple data HD4b

Calculate mode, mean, median and range for simple data.

Y10 241-3

Collect data from class – children per family etc.

Collect data from newspapers.

H/W SumBooks 65, 66

Selecting the most appropriate average HD4b

Justify the choice of a particular average.

Compare distributions using averages and range.

Y10 268

Discuss occasions when one average is more appropriate, and the limitations of each average.

Finding the mode from a discrete frequency table HD5dCalculating the total frequency from a discrete frequency table HD1fCalculate the mean from a discrete frequency table HD4e

Calculate mean and modal class from a discrete or grouped frequency table.

Y10 246-7

Look at the median class and approximate the median.

H/W SumBooks 67, 68, 69, 70

Mean and median for continuous data HD4eModal class for continuous data HD5d

Y10 248-256

Calculating a moving average* HD4f Calculate and interpret the meaning of a moving average.

Y10 272

H/W SumBooks 89

NOTESPupils tend to select modal class but identify it by the frequency rather than the class description.Explain that the median of grouped data is not necessarily from the middle class.The choice of midpoints for finding the mean from a grouped frequency table can cause problems.31 of 53

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GCSE Intermediate Scheme of Work*For 1388 this is not tested until Stage 3.

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MODULE 18 Transformations TIME: 5 hoursTARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Module 6. Plotting co-ordinates. An understanding of

the concept of enlargement.

Enlarging assorted shapes using various centres of enlargement and integer scale factors SSM3cEnlarging assorted shapes using non-integer scale factors SSM3cEnlargement calculations SSM3d

Enlarge shapes using a variety of positive scale factors.

Understand which are the invariant properties of enlargements.

Y11 89-91

H/W SumBooks 48 and 49 Enlargements

H/W SumBooks 50 Similarity

The tasks set can be extended to include combinations of transformations, including those from other modules.

Investigation into different ways of transforming an object into a particular image.

Similar triangles* SSM2gSimilarity of standard shapes SSM2g

Use scale factors to solve problems involving similar shapes.

Y11 202-3Y11 92-3

Translations SSM3aUnderstanding and using vector notation* SSM3f

Recognise translations as sliding movements, and translate simple 2D shapes within a plane using words or vector notation.

Y11 85-86

Describing transformations in full (enlargements and translations) SSM3a

Work on tasks involving these transformations.

Y11 95-96

Using and interpreting maps and scale drawings SSM3d

Use scale to interpret maps and scale drawings.

Y10 120-124

Scale drawing of the classroom/bedroom.

H/W SumBooks 8

NOTESEmphasis needs to be placed on ensuring that students do describe the given transformation fully.*In 1388 this is not tested until Stage 3.

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MODULE 19 Substitution and formulaeTIME: 4 hoursTARGET GRADE: C/BPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 3, 5, 8. Ability to follow a

series of instructions. Experience of powers,

equations, and formulae.

Rearranging simple formulae NA5gRearranging formulae where the subject occurs twice or is raised to a power* NA5g

Change the subject of formulae. Rearrange simple and complex

formulae, including cases where the subject occurs more than once.

Y11 171-5

H/W SumBooks 32

Further practice in rearranging formulae involving powers, and several operations.

Formulae involving reciprocals of the subject.

More use of directed numbers with powers.

H/W SumBooks 29

Substituting into expressions involving squares or cubes NA5d

Undertake simple substitution and substitution involving squaring.

Y11 176-77

Generating a formula NA5g Generate algebraic formulae from information.

Y11 178

Using trial and improvement to find approximate solutions of equations NA5m

Use trial and improvement methods to solve non-trivial equations such as cubics, usually to 1 d.p.

Y11 183-184

NOTESWhen using trial and improvement, care should be taken to set the work out in a manner where each result of each trial is obvious, and the final trial is identified. If an answer accurate to 1 d.p. is to be identified correctly, then at least one value between the two choices should be shown.*For 1388 this is not assessed until Stage 3.

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MODULE 20 Pythagoras’ TheoremTIME: 4 hoursTARGET GRADE: C PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 2, 3, 5, 8, 19. Knowledge of

different types of triangle.

Ability to use a calculator sensibly, particularly to find squares and square roots.

Knowledge of simple bearings.

Using Pythagoras’ Theorem to find the Hypotenuse SSM2fUsing Pythagoras’ Theorem to find the shorter sides SSM2fUsing Pythagoras’ Theorem to solve problems SSM2fCalculating lengths of lines on a grid * SSM3e

Identify the hypotenuse of a right-angled triangle.

Recall Pythagoras’ theorem. Pick out right-angled triangles

from diagrams, (e.g. circles, isosceles triangles).

Use Pythagoras’ theorem to find the length of any side of a right angled triangle.

Use Pythagoras’ theorem to solve problems such as bearings, areas of triangles, diagonals of rectangles etc.

Y11 126-134

The orientation of the triangle should be varied.

Further work can be developed on applying Pythagoras, theorem in three-dimensional problems.

Find Pythagorean triples.

H/W SumBooks 39

RESOURCESChannel 4 – Shape, Space & Handling data programme 1Coursework task Beyond Pythagoras.

NOTESConsult GCSE papers for types of questions, depending on the orientation of the triangle and whether or not the hypotenuse or shorter side is required.*Not assessed until Stage 3.

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MODULE 21 TrigonometryTIME: 6 hoursTARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 2, 20. Knowledge of

Pythagoras’ theorem. Ability to use a

calculator to change fractions to decimals.

Knowledge of basic concepts of ratio.

Mental testing of ability to recall ratios of sine, cosine and tangent.

Tangent, sine and cosine ratios SSM2gUses of the three ratios SSM2gAngles of elevation and depression SSM2gBearings and trigonometry SSM2g

Identify appropriately the various sides of a right-angled triangle as the Hypotenuse, Opposite and Adjacent.

Recall the ratios for sine, cosine and tangent.

Identify which of sine, cosine and tangent are required to solve a problem.

Use information given to write down the sine, cosine and tangent of an angle.

Use information given to find angles using the appropriate ratio.

Use the appropriate ratio to find the lengths of sides in a right-angled triangle.

Find angles of elevation and depression using the appropriate ratio.

Apply trigonometric ratios and Pythagoras’ Theorem to solve assorted problems, including those involving bearings.

Y11 135-153

Further work can be developed on applying the ratios in three-dimensional problems.

Work on the sine and cosine rules could be developed (Higher syllabus).

Given two properties of a right-angled triangle find the others.

H/W SumBooks 40, 41, 42, 43

RESOURCESChannel 4 – Shape, Space & Handling data programme 2

NOTES36 of 53

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GCSE Intermediate Scheme of WorkFor some students this work is found difficult simply because they cannot identify which sides to use or which ratio can be used. The labelling of sides can be confused when both angles are labelled.*Not assessed until Stage 3.

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MODULE 22 Scatter diagramsTIME: 3 hoursTARGET GRADE: D PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 4, 15. Plotting co-ordinates

(Module 8). An understanding of

the concept of a variable.

Recognition that a change in one variable can affect another.

Plotting and interpreting scatter diagrams HD4a & HD5fDescribing correlation from a scatter graph HD5fDrawing and using a line of best fit HD4i & HD5f

Plot and use a scatter graph to describe correlation.

Describe a relationship between two variables as illustrated by a scatter diagram.

Describe correlation in terms of the two variables, and as positive, weak, negative, or strong.

Draw a line of best fit where possible “by eye”, and use this to make predictions.

Y10 262-4

Vary the axes required on a scatter graph to suit the ability of the class.

H/W SumBooks 73, 74

NOTESPupils should realise that lines of best fit should have the same gradient as the correlation of the data.*For 1388 this is not tested until Stage 3.

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MODULE 23 Cumulative FrequencyTIME: 4 hoursTARGET GRADE: C/B PRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 4, 15, 17. Experience of plotting

points. Experience of reading

from graphs. Some concept of a

‘running total’.

Completing cumulative frequency tables HD4aPlotting cumulative frequency diagrams HD4aUsing cumulative frequency to find the median HD4eUsing cumulative frequency to find quartiles and interquartile range HD4e

Design and complete a cumulative frequency table, identifying class boundaries where necessary.

Plot a cumulative frequency curve using upper class boundaries.

Solve problems using a cumulative frequency curve (e.g. How many____ were more than…).

Use a cumulative frequency curve to estimate the median, lower quartile, upper quartile, and interquartile range.

Y10 274-6

Compare two cumulative frequency diagrams, to comment on the differences between distributions.

Collect a set of continuous data e.g. weights of 2p coins, draw grouped frequency table, cumulative frequency graph and calculate mean, median, mode, range, quartiles.

H/W SumBooks 71, 72

NOTESPupils often find it difficult to decide where to plot points. Notice that they have been expected to plot against mid-points for a frequency polygon but against upper class boundaries for a cumulative frequency curve.

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MODULE 24 ProbabilityTIME: 4 hoursTARGET GRADE: D/C/B


CONTENT MAIN OBJECTIVES Year 11 Text


Module 12. Writing probabilities

as fractions, decimals or percentages.

Probability of an event happening or not happening.

Using relative frequency HD4bEstimating probability from theoretical models HD4bUsing probability estimates to compare results HD5hUnderstanding the effect of sample size on probability estimates HD5i

Estimate probabilities and use relative frequencies to make predictions or test for bias.

Appreciate that a larger sample size will give a more accurate estimate.

69-72 Use the fraction button of a calculator to work with harder fractions.

Use venn diagrams to solve probability questions.

Make predictions of outcomes for probability games and then test the predictions.

H/W SumBooks 79, 80 Relative Frequency

H/W SumBooks 77

H/W SumBooks 78 Tree Diagrams

Using the vocabulary of probability to interpret results HD5g

Recognising independent events HD4h STAGE THREE

Know when to use the P(A) + P(B) ‘OR’ rule, and the P(A) × (B) ‘AND’ rule.

73-75

Calculating with mutually exclusive events HD4h STAGE THREE

76-77

Use tree diagrams to represent outcomes of compound events HD4h STAGE THREE

Complete tree diagrams as a means of showing outcomes for two successive events and related probabilities.

78-82

NOTESPupils can often lose marks at probability due to inability to manipulate fractions.Pupils do not always appreciate that some descriptions of probabilities cover more than one outcome e.g. tossing 2 coins and obtaining ‘one of each’.

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MODULE 25 QuadraticsTIME: 4 hoursTARGET GRADE: C/B




Modules 5, 8. Removing and

factorising with one pair of brackets.

An appreciation that if the product of two numbers is zero then one of the numbers must be zero.

Confidence with the four rules for directed numbers.

Mental testing of pairs of numbers with a specific sum and product.

Expanding brackets – the product of two linear expressions NA5bFactorising of quadratic expressions. NA5bSolving quadratic equations by factorising NA5k

Expand and simplify two pairs of linear brackets, e.g. (x + 2)(x – 4), (3x + 2y)(4x + y), (x + p)(a + g) etc.

Factorise a trinomial, e.g. x 2 – 5x + 6 = (x – 6)(x + 1).

Expand the square of a linear expression.

Use a factorised trinomial in one variable to solve a quadratic equation.

Make efficient use of techniques covering signs, products and sums.

Y11 157-160, Y11 179-181

Difference of two squares.

More difficult quadratics to factorise.

Using the quadratic equation formula (Higher level).

H/W SumBooks 24 Ex3 Multiplying out brackets

H/W SumBooks 27 Ex2 Solving equations

NOTESThere may be a need to remove the HCF (numerical) of a trinomial before factorising to make the factorisation more obvious.*For 1388 this is not assessed until Stage 3.

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MODULE 26 Algebraic graphsTIME: 7 hoursTARGET GRADE: E/D/C/B




Modules 5, 8, 19, 25. The ability to plot

points that follow a simple rule (in four quadrants).

The ability to substitute positive and negative values into a non-linear formula.

Plotting graphs of functions where y is expressed in terms of x, leading to a straight line NA6b

Plot a straight-line graph from a given set of values.

Y11 213-217

H/W SumBooks 13-20

H/W SumBooks 28 Ex1

More able students could extend to identifying regions relating to straight-line graphs.

Students performing below grade C will struggle with much of this module and examples should be set

accordingly. Having drawn the

graph of type y = ax 3 + bx 2 + cx, investigate how it can be used to solve equations of the

type ax 3 + bx 2 + cx + k = 0, where a, b, c and k are constants.

Find gradients of straight lines, and exploring gradients of parallel lines* NA6cRecognising the y-intercept of a straight line* NA6cExploring graphs of the form y = mx + c* NA6b

Realise that an equation of the type y = mx + c represents a straight line graph, and plot this graph.

Understand the relevance of m and c in the above equation.

From a given graph, find the gradient and y-intercept and hence the equation of the graph.

Draw a straight-line graph without plotting points.

Y11 223-230

Plotting the graph of a quadratic function NA6ePlotting graphs of simple cubic and reciprocal functions* NA6fRecognising characteristics of graphs* NA6f

Plot curves from given quadratic and cubic functions.

Y11 231-3

Plotting linear graphs from real-life problems NA6dInterpret graphs representing real-life situations NA6d

Interpret and plot real-life graphs such as conversion graphs and distance/time graphs.

Recognise graphs e.g. filling different shaped containers.

Y11 244-9

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GCSE Intermediate Scheme of Work Use of a graphic

calculator.

RESOURCES NOTESChannel 4 – Number and Algebra programmes 4, 5 Links with the Science department could yield many experiments that would give rise to *For 1388 this is not assessed until Stage 3 straight line relationships.

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GCSE Intermediate Scheme of Work1387/1388 (STAGE THREE)

MODULE 27 PercentagesTIME: 4 hoursTARGET GRADE: C/B




Modules 1, 7, 9. The concept of

percentage, and an understanding of the effects of increasing and decreasing by a percentage.

Understanding the multiplicative nature of percentages as operators NA3e

Recognise that an increase of e.g. 15% leads to 115% and a decrease of e.g. 15% leads to 85%.

Find the original amount e.g. price before a sale, price before VAT.

Write down a decimal multiplier which is equivalent to an increase or decrease in percentage.

Use multipliers to solve reverse percentage and compound interest problems.

HIGHER H/W SumBooks 6

Understanding the concept and use of a reciprocal NA3aFinding 100% when another amount is known NA3eSolving reverse percentage problems NA3e

Y10 318

Combine multipliers to simplify a series of percentage changes.

Solving percentage problems NA3eSolving problems involving compound interest NA3k

R3 88-89

Calculate original price before compound interest.

NOTESPupils typically answer compound interest questions incorrectly, either by using simple interest or bycalculating over the wrong number of years.

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MODULE 28 Constructions TIME: 5 hoursTARGET GRADE: E/C/BPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Module 2. An ability to use a

pair of compasses. Understanding of the

term’s perpendicular, bisecting, parallel.

Constructing triangles SSM4c Construct shapes from given information using only compasses and a ruler.

Constructing a perpendicular bisector and finding the mid-point of a line segment SSM4cConstructing perpendiculars to a line SSM4cBisecting an angle SSM4c

Construct perpendicular bisectors, and angle bisectors using only compasses and a ruler.

Y11 191-2

Finding Loci SSM4eConstructing graphs of simple loci NA6h (perhaps should be diagrams of simple loci??)

Construct LOCI in terms of distance from a point, equidistance from two points, distance from a line,

equidistance from two lines and line of sight.

Shade regions using LOCI to solve problems e.g. vicinity to lighthouse/ port.

Y11 193-7

Solve LOCI problems that require a combination of LOCI

H/W SumBooks 51, 52

NOTESAll working should be presented clearly, and accurately. Sturdy pair of compasses are essential.

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MODULE 29 Indices and surdsTIME: 7 hoursTARGET GRADE: C/B




Module 3. An understanding of

powers and roots. Experience of using

squared and cubed units for area and volume.

Experience of using formulae to find perimeter, area and volume.

Mental test to check knowledge of cubes and squares/roots.

Using indices in expressions NA5dUsing index laws for multiplication and division (integer powers) NA2bSimplifying expressions using the rules of indices NA5d

Know the rules of indices (adding, subtracting and multiplying indices), and simplify expressions.

Evaluate fractional and negative indices.

Y11 165-7

Use index manipulation in problems involving standard form.H/W SumBooks 23

Using index notation NA2bRecalling integer cubes, squares and corresponding square roots NA3g

Recall the cubes of 2, 3, 4, 5 and 10

Recall integer squares and corresponding square roots to 15 × 15.

Y11 167

Using surds and pi in exact calculations without a calculator NA3n

Calculate exact answers by manipulating simple surds without a calculator.

Y11 53 H/W SumBooks 85

Converting between units of area or volume SSM4d

Use powers of scale factors to convert between units of area and volume.

Combine enlargement/similar triangle problems with area and volume conversions.


Understanding the dimensions of formulae for perimeter, area and volume SSM3d

Recognise the purpose of a formula by considering its dimensions.

Y11 185-7

H/W SumBooks 59, 60

NOTESPupils should work with powers of both numbers and algebraic variables.

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MODULE 30 3D, volumes and surface areasTIME: 5 hoursTARGET GRADE: D/C




Modules 11, 13. Finding areas of plane

shapes, and volumes of cuboids and prisms.

Finding area and circumference of a circle.

2D representations of 3D objects SSM2i Draw 2D representations of 3D objects, including the use of isometric paper.

Y11 198-9

Draw shapes made from multi-link on isometric paper.

H/W SumBooks 35

Plans and elevations SSM2i Use plans and elevations to answer questions.

Y11 200-1

Make solids using equipment such as clixi or multi-link.

Sketch a plan view of your bedroom or an elevation of your house.

H/W SumBooks 87, 88

Finding surface area of solids with triangular and rectangular faces* SSM4d STAGE TWOSolving problems involving surface area SSM2iInvestigating the geometry of cubes, cuboids and shapes made from cuboids SSM2fSolving problems involving volumes of prisms SSM2i

Draw nets of simple solids and use these to calculate surface areas of prisms, cylinders and shapes with

rectangular and triangular faces. Solve problems involving

volumes of prisms, cylinders and solids made from cuboids.

Y11 117-124

Build shapes from cubes which are represented in 2D.

H/W SumBooks 35

NOTESAccurate drawing skills need to be reinforced.

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MODULE 31 Standard index formTIME: 3 hoursTARGET GRADE: BPRIOR KNOWLEDGE/ STARTER OBJECTIVES



Modules 3, 16, 29. An understanding of

the effect of multiplying and dividing by powers of 10.

An ability to round to significant figures.

Using standard index form* NA2b STAGE TWOConverting between ordinary and standard index form representations NA3hUsing standard index form to make estimates NA3hCalculating with standard index form NA3mUsing a calculator for standard index form NA3r

Recognise that some numbers are too large or too small to be represented normally on a calculator.

Represent standard form as a number between 1 and 10 multiplied by a positive or negative power of ten.

Convert between standard form and ‘normal’ numbers.

Solve problems involving standard form, using the correct calculator method where possible.

Interpret a calculator display showing a number in standard form.

Y11 13-18Y11 36-8

Round large or small numbers to 1 significant figure to make estimates in standard form.

BODMAS and standard form.

Distance of planets from the sun.

Research constants that are expressed in standard form e.g. the speed of light.

H/W SumBooks 9

RESOURCESChannel 4 – Number and Algebra programme 2

NOTESWhen transferring an answer from the calculator, pupils forget to write ‘× 10’ before the power of 10, andthis could exclude them from all the marks in a GCSE question.*For 1388 this is assessed in Stage 2.

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MODULE 32 Angles in circlesTIME: 4 hoursTARGET GRADE: BPRIOR KNOWLEDGE/ STARTER OBJECTIVES

CONTENT MAIN OBJECTIVES Y11 TEXT DIFFERENTIATION / EXTENSION / HOMEWORK

Modules 2, 13. The geometry of an

isosceles triangle.

Understanding and using circle theorems SSM2h

Understand and apply the geometry rules included in the module content.

Questions for which a combination of the above rules are needed.

H/W SumBooks HIGHER 37, 38

The angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumference SSM2h

Thereom 1 pg 205, 206

Angles in the same segment are equal SSM2h

Thereom 2 pg 205, 206

The angle subtended at the circumference by a semi-circle is a right angle. SSM2h

Thereom 4 pg 207

Opposite angles of a cyclic quadrilateral add up to 180 degrees SSM2h

Thereom 3 pg 207

Explain why the perpendicular from the centre of a chord bisects the chord SSM2h

Possibly: The line which bisects a chord at right angles is always a diameterBut this isn’t in the Edexcel text??

Have I lost it, or is this not obvious?? Any line thro the centre of the chord will bisect the chord (NO?)

NOTESPupils should be able to describe how they find each angle.

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MODULE 33 AlgebraTIME: 8 hoursTARGET GRADE: C/B




Modules 8, 25, 26 Factorising

quadratics. Drawing linear and

quadratic graphs. Mental test of simple

simultaneous equations.

Using the difference of two squares NA5b

Factorise using the difference of two squares and use this to solve problems.

180

Simplify expressions by cancelling common factors NA5b

Use factorising methods to simplify algebraic fractions.

182

Solving simultaneous equations using elimination NA5i

Solve simultaneous equations by eliminating a variable, using them to solve problems.

161-164

Simultaneous equations that need rearranging before one of the methods can be used.

H/W SumBooks 82

Finding approximate solutions to quadratics using graphs NA6e

Solve quadratics by constructing an appropriate graph.

Use terms like ‘minimum point’ ‘maximum point’ ‘quadratic function’‘.

Use graphical methods to find the maximum or minimum of a quadratic function.

Solve cubics where the graph is given

231-33 Use graphical calculators to enable pupils to get through examples more rapidly.

Solving simultaneous equations using a graphical method NA5i

Solve simultaneous equations by graphical methods, using them to solve problems.

234-238

Use gradient and intercept to draw lines.


Solving linear inequalities in two Use regions on a graph to solve 239- H/W SumBooks 50 of 53

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GCSE Intermediate Scheme of Workvariables NA5j inequality problems in two

variables.243 31

NOTESInaccurate graphs could lead to incorrect solutions.Could lead to investigations such as Car hire, Mobile Phones.

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MODULE 34 Co-ordinates and transformationsTIME: 4 hoursTARGET GRADE: C/B




Modules 6, 18. An understanding of

the four types of transformation.

Co-ordinates in 1, 2 and 3 dimensions SSM3e

Use co-ordinates in 3 dimensions and use these to solve problems such as mid-points of lines.

210-1 Pythagoras on a 3-D grid.

H/W SumBooks HIGHER 89,90

Finding midpoints of lines SSM3e 212

Understanding similarity of plane figures SSM2g

Solve problems involving similar polygons.

92-94

Transforming 2-D shapes by translation, rotation, enlargement and reflection SSM3bCombinations of transformations SSM3b

Use and describe fully the four types of transformations in a variety of combinations.

95-96

NOTESPupils can lose marks in their GCSE for neglecting to mention one part of a transformation, e.g. the name of a line of symmetry, or a centre of rotation.

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MODULE 35 Data HandlingTIME: 3 hoursTARGET GRADE: C/B




Modules 4, 12, 15, 17, 22.

Experience of collecting, interpreting, displaying and calculating with data.

Identifying trends in time series HD5b Understand the module content. Y10 270-3

Additional work on making predictions based on current trends, using time series and/or moving averages

Comparing shapes of distributions HD5d Y10 278

Comparing distributions using measures of range and spread HD5d

Y10 268

Using a calculator for statistical calculations HD4j

NOTESAll working should be presented clearly, with descriptions of trends expressed as clearly as possible.

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