UG010896 – Edexcel GCSE Mathematics – Teachers’ …
GCSE Intermediate Scheme of Work
Target Previous
Module Stage TIME Grades Module Homework SumBooks Sheet 1 Number 1 7 E/D/C 1 Multiplication and Division
hours 2 Negative Numbers
3 Use of the Calculator 2 Geometry 1 8 E/D/C 33 Bearings
hours 34 Parallel Lines
36 Triangles
37 Regular Polygons
38 Irregular Polygons 3 Numbers and Powers 1 5 E/D 10 Prime Factors
hours 29 Trial and Improvement 4 Collecting and sorting data 1 3 E 61 Questionnaires
hours
5 Simplifying and substituting 1 4 E/D/C 1, 3 21 Substitution
hours 22 Simplifying Expressions
24 Multiplying Brackets Ex 1 and 2
25 Factorising
6 Transformations 1 5 E/D/C/B 2 44 Reflections, Rotations and Translations 1
hours 45 Reflections, Rotations and Translations 2
46 Reflections, Rotations and Translations 3
47 Reflections, Rotations and Translations 4 7 Fractions 1 5 E/D/C/B 1, 3 5 Fractions, Decimals and Percentages 1 Ex 1
hours and 5
90 Recurring Decimals 8 Equations and inequalities 1 5 E/D/C/B 5 26 Equations
hours 27 More Equations Ex 1
30 Inequalities
9 Percentages 1 5 E/D/C/B 1, 7 5 Fractions, Decimals and Percentages 1
hours 6 Fractions, Decimals and Percentages 2
7 Interest
10 Sequences 1 3 E/D/C/B 5 11 Number Patterns and Sequences 1
hours 12 Number Patterns and Sequences 2 1 of 44
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GCSE Intermediate Scheme of Work
Target Previous
Module Stage TIME Grades Module Homework SumBooks Sheet 11 Circles 1/2 5 D/C/B 2 54 Circumference of a Circle.
hours
12 Probability 1/2 4 E/D 75 Probability 1
hours 76 Probability 2
77 Probability 3 13 Shape, volume and surface area 1/2 7 E/D/C 11 55 Area and Perimeter
hours 56 Volume Ex 2
81 Constructions 14 Ratio and proportion 2 5 E/D/C 1, 3, 7 8 Scale Drawings and Ratio
hours 57 Compound Measure - Speed and Density
58 Compound Measure - Best Buy and a Mixed
Exercise
15 Displaying data 2 6 E/D/C 2, 4 62 Pie Charts
hours 63 Frequency Polygons 1
64 Frequency Polygons 2
91 Stem and Leaf Diagrams
92 Box Plots 16 Approximation 2 4 E/D/C 1 3 Use of the Calculator
hours 4 Estimation
53 Degree of Accuracy 17 Average and spread 2 5 E/D/C 65 Mean, Median, Mode and Range
hours 66 Mean 1
67 Mean 2
68 Mean 3 - diagrams
69 Mean 4 - Frequency distributions with class
intervals
70 Mean 5 - Histograms
89 Moving Averages 2 of 44
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GCSE Intermediate Scheme of Work
Target Previous Module Stage TIME Grades Module Homework SumBooks Sheet 18 Transformations 2 5 C/B 6 8 Scale Drawings and Ratio
hours 48 Enlargements 1
49 Enlargements 2
50 Similar Shapes 19 Substitution and formulae 2 4 C/B 3, 5, 8 29 Trial and Improvement
hours 32 Rearranging Formulae 20 Pythagoras’ Theorem 2 4 C 2, 3, 5, 8, 39 Pythagoras' Theorem
hours 19
21 Trigonometry 2 6 C/B 2, 20 40 Trigonometry 1
hours 41 Trigonometry 2
42 Trigonometry 3
43 Trigonometry 4 22 Scatter diagrams 2 3 D 4, 15 73 Scatter Diagrams 1
hours 74 Scatter Diagrams 2 23 Cumulative Frequency 2 4 C/B 4, 15, 17 71 Cumulative Frequency 1
hours 72 Cumulative Frequency 2
84 Using Quadratic Equation 24 Probability 2 4 D/C/B 12 78 Tree diagrams
hours 79 Relative Frequency 1
80 Relative Frequency 2 25 Quadratics 2 4 C/B 5, 8 24 Multiplying Brackets Ex 3
hours 27 More Equations Ex 2 26 Algebraic graphs 2 7 E/D/C/B 5, 8, 19, 13 Distance Time Diagrams 1
hours 25 14 Distance Time Diagrams 2
15 Conversion Graphs 1
16 Conversion Graphs 2
17 Sketching and Recognising Graphs 1
18 Sketching and Recognising Graphs 2
19 Plotting Graphs 1
20 Plotting Graphs 2 3 of 44
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GCSE Intermediate Scheme of Work
28 Straight Line Graphs and Sim Eqns Ex 1
Target Previous
Module Stage TIME Grades Module Homework SumBooks Sheet 27 Percentages HIGHER 6 Percentages 3 4 C/B 1, 7, 9
hours
28 Constructions 3 5 E/C/B 2 51 Locus Problems 1
hours 52 Locus Problems 2 29 Indices and surds 3 7 C/B 3 23 Indices
hours 56 Volume Ex 1
59 Formulae for Area, Volume and Perimeter 1
60 Formulae for Area, Volume and Perimeter 2
85 Surds
30 3D, volumes and surface areas 3 5 D/C 11, 13 35 Nets and Isometric Drawing
hours 87 Plans and Elevations (1)
88 Plans and Elevations (2) 31 Standard index form 3 3 B 3, 16, 29 9 Standard Form
hours
32 Angles in circles HIGHER 37 Geometry of a Circle 1 3 4 B 2, 13
HIGHER 38 Geometry of a Circle 2 hours
33 Algebra 3 8 C/B 8, 25, 26 28 Straight Line Graphs and Simultaneous
hours Equations Ex 2
31 Inequalities - Graphs
82 Simultaneous Equations 34 Co-ordinates and transformations HIGHER 89 3 Dimensional Co-ordinates 1 3 4 C/B 6, 18
HIGHER 90 3 Dimensional Co-ordinates 2 hours
35 Data Handling 3 3 C/B 4, 12, 15,
hours 17, 22
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE)
MODULE 1 Number
TIME: 7 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Ruff DIFFERENTIATION /
STARTER OBJECTIVES Guide EXTENSION / HOMEWORK
Understanding place value in whole numbers 22 , The ability to order large
NA2a numbers and appreciation
of place value to at least Place value, multiplication and division of decimal 168, 172 Draw tables to illustrate ×100, thousands. numbers by powers of ten NA3a ?10 of decimal numbers.
Consideration of mental maths , Knowledge of times tables
problems with negative would be particularly
useful. powers of 10: 2.5 × 0.01,
0.001. , Knowledge of strategies for
Multiplying and dividing by multiples of powers of 11, 18- multiplying and dividing
ten NA3a 19, 173, whole numbers by 10.
174
Multiplying and dividing by a number between 0 172, 173,
and 1 NA3a 174
Writing assorted numbers in order of size NA2a 23, 24, Write out a series of calculations , Order numbers of any size.
168,176 (possibly as a flowchart) for
placing a series of numbers in
order of size
Long multiplication and long division without 11-13, 17 Non-calculator maths: 3-digit
using a calculator NA3a 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 25-31 , Work with positive and negative , H/W SumBooks 2
temperatures.
, 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 Investigate the largest/smallest , Use a calculator to solve number
numbers on a calculator. problems and interpret the answers.
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GCSE Intermediate Scheme of Work
, H/W SumBooks 3
NOTES
All working should be presented clearly.
Non-calculator methods should show remainders & carries as evidence. 6 of 44
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 2 Geometry
TIME: 8 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Ruff DIFFERENTIATION / STARTER OBJECTIVES Guide EXTENSION / HOMEWORK
Calculating angles on a straight line and at a 206 , Knowledge of the names , Calculate angles at a point and on a
point* SSM2a and properties of triangles, straight line.
quadrilaterals and polygons. Recognising opposite angles at a vertex* SSM2a 206
, Oral testing on a regular Calculating angles in triangles SSM2b 207 H/W SumBooks 36 , Use the angle sum for triangles and ,
basis regarding the names Using angle properties of isosceles, equilateral and 207 quadrilaterals to find other angles in the
and properties of the shapes right-angled triangles SSM2b shapes.
covered.
, The ability to use a Using parallel lines, alternate angles and 208-9 , Calculate angles on parallel lines, at a , H/W SumBooks 34 protractor to measure corresponding angles SSM2a point and on a straight line.
angles.
, Understanding of the Understanding the proof that the angle sum of a 211 , Understand the two proofs relating to concept of parallel lines. triangle is 180 degrees SSM2a angles in a triangle. Understanding the proof regarding exterior angles 211
of triangles SSM2a
Recalling names and recognising properties of 212-3
special quadrilaterals SSM2c
Explaining why the angle sum of a quadrilateral is 211
360 degrees SSM2b
Calculating angles in quadrilaterals SSM2b 214 , Use the angle sum for triangles and
quadrilaterals to find other angles in the
shapes.
Interior and Exterior angles of quadrilaterals, 220-1 , Know how to work out the angle sum , H/W SumBooks 37
pentagons, hexagons and regular polygons SSM2d for any given polygon, use the to find
Tessellation SSM2d other angles relating to polygons and 224 , Investigate which regular
understand which shapes tessellate. polygons will tessellate
alone, or with each other.
Using the angle properties of parallelograms
SSM2a
Drawing and measuring bearings SSM4a 139 , Draw and measure three figure bearings , H/W SumBooks 33
accurately.
Converting between measurements** SSM4a 117-119
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GCSE Intermediate Scheme of Work RESOURCES
Channel 4 – Shape, space and Handling data programme 3
NOTES
Pupils 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 3 Numbers and Powers
TIME: 5 hours
TARGET GRADE: E/D
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Ruff DIFFERENTIATION / STARTER OBJECTIVES Guide EXTENSION / HOMEWORK , Basic number bonds and Square and cube numbers NA2b 32-33 , Calculate square and cube numbers.
, Recognise the different types of numbers. multiplication/division
facts. Squares and square roots NA2b 34-36 , Find square and cube roots of numbers
Cubes and cube roots NA2b including decimals by trial and , Awareness of position of Trial and improvement methods NA2b (to find improvement and by calculator methods. , H/W SumBooks 29 numbers on number lines. square and cube roots of numbers including
decimals) , Ability to recognise basic Factors and multiples NA2a 44-45 , Use lists of multiples to find the lowest , Use prime factors to number patterns. Finding Highest Common Factor and Lowest common multiple. find LCM.
Common Multiple NA2a , Write numbers in terms of their , H/W SumBooks 10 , Mental test to check factors/prime factors and use prime knowledge of squares and factors to find the HCF.
Powers of numbers* NA2b 308-309 , Calculate powers of whole numbers , Further work on cubes. including negative numbers. indices to include negative and/or
fractional indices.
, Investigational tasks
leading to number
patterns involving
powers of numbers.
NOTES
All 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE)MODULE 4 Collecting and sorting data
TIME: 3 hours
TARGET GRADE: E
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , An understanding of why Different ways of collecting data HD1a , Carry out a statistical
investigation of their Designing questions to collect data HD3a & HD1g , Design a simple questionnaire, and data needs to be collected own including; appreciate deficiencies in a question.
and some idea about designing an Collecting data by sampling HD3a & HD1g , Understand the concept of sampling a appropriate means of population, what makes a fair sample, different types of graphs. gathering the data. and explain deficiencies of sampling
, Use a spreadsheet to techniques.
collect data in tables Collecting data by observation HD3a , Collect data from a variety of sources. and draw different Collecting data by experiment HD3a types of graphs Obtaining data from a database, tables and lists , H/W SumBooks 61 HD3b
Questionnaires Sorting 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
NOTES
Clearly label all axes on graphs and use a ruler to draw straight lines. 10 of 44
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 5 Simplifying and substituting
TIME: 4 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 1, 3. Using letters to represent numbers NA5a 82-87 H/W SumBooks 21 , Substitute positive and negative numbers ,
Using negative numbers NA5d STAGE TWO into word formulae and algebraic , Experience of using a letter Using word formulae NA5g formulae.
Using algebraic formulae NA5g 91 to represent a number.
Collecting like terms NA5b 99 , Simplify algebra by collecting like terms , H/W SumBooks 22 , Ability to use negative – answers may involve negative
coefficients. numbers with the four
Multiplying with letters and numbers NA5b rules. Removing a single pair of brackets NA5b 100 , Remove and factorise a single pair of , H/W SumBooks 24 Ex
brackets – including cases where a 1 & 2
variable is removed as a factor. Factorising with a single pair of brackets NA5b 102 , H/W SumBooks 25 , Factorising where the
factor may involve
more than one variable.
NOTES
Emphasise correct use of symbolic notation (e.g. 3x rather than 3 × x).
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 6 Transformations
TIME: 5 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Text DIFFERENTIATION / STARTER OBJECTIVES EXTENSION / HOMEWORK , Module 2. Co-ordinates in first quadrant SSM3e/NA6b 189-190 , Plot and read co-ordinates in four
Co-ordinates in four quadrants SSM3e/NA6b quadrants. , Some experience of Congruent shapes* SSM2d , Recognise congruency , Given a shape on
plotting points. squared paper, produce
as many other different , Knowledge of the range of congruent shapes as
2-D shapes, and parallel possible.
Line symmetry* SSM3b 191-3 , Sketch planes of symmetry on simple , An attempt to draw up lines. Planes of symmetry SSM3b shapes. to 3 shapes each which , The ability to recognise have exactly 1, 2, 3, … , State the properties of each 2-D shape
8 lines of symmetry, and classify a shape according to its that a shape has and investigate symmetrical properties. symmetrical properties. , whether a rule exists , Identify lines of symmetry or the order
between the number of of rotational symmetry in 2-D shapes. , Testing of the ability to vertices and the number of
draw shapes to a specified lines of symmetry.
, Sketch all the planes of number of lines of symmetry of a cube on symmetry, or order of 9 diagrams.
Rotational symmetry* SSM3b 194-6 rotational symmetry. Transforming 2D shapes by reflection SSM3b 197-203 H/W SumBooks 44, , Reflect a 2D shape in a vertical, , Specify a mirror line parallel to axes SSM3a horizontal or diagonal line and state the 45 equation of the line.
Rotating shapes SSM3b 197, 204-, Rotate a 2D shape about the origin or a , H/W SumBooks 46,
Transforming 2D shapes by rotation SSM3b 5 point other than the origin, stating the 47 Describing transformations in full (rotations, angle, direction and centre of
reflections and translations) SSM3a , rotation.
Translations SSM3b 197 , Translate a 2D shape and describe the
translation in words.
* Not specifically mentioned in Intermediate specification.
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 7 Fractions
TIME: 5 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 TEXT DIFFERENTIATION / STARTER OBJECTIVES EXTENSION / HOMEWORK , Modules 1, 3. Interchanging improper fractions and mixed 151-2 , Understand and change between
numbers. NA3d improper fractions and mixed numbers. , A basic understanding of Calculating a fraction of a quantity. NA3c 153 , Calculate a fraction of a quantity. , H/W SumBooks 5 Ex
fractions as being „parts of 5
Using diagrams to find equivalent fractions. NA2c 154 , Equate one fraction with another, and a whole unit?. Cancelling fractions. NA2c simplify fractions to their lowest terms 155-156 , For very able students , Use of a calculator with Writing a given number as a fraction of another. , Write one number as a fraction of cancelling down of
NA3c another. algebraic expressions fractions. could be considered. Interchanging fractions and decimals and using 169, 175-, Understand the concept of a recurring , Relating the basic
recurring decimals. NA2d & NA3c 178??179-decimal. fractions to readily
180, remembered , Convert fractions into decimals and vice
percentages and vice-versa, including recurring decimals.
versa.
, H/W SumBooks 5
Ex1
, H/W SumBooks 90
Ordering fractions using common denominators. 161 , Order fractions using common
NA2c denominators or decimal conversions.
Adding and subtracting fractions using common 157-160 , Perform the four basic operations with
denominators. NA3c fractions.
Multiplying and dividing fractions. NA3d 162-165
Using fractions in problems involving 166-167 , Solve problems involving fractions.
multiplication and division. NA3d
NOTES
Constant 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. 13 of 44
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 8 Equations and inequalities
TIME: 5 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Text DIFFERENTIATION / STARTER OBJECTIVES EXTENSION / HOMEWORK , Module 5. Inverse operations NA5f , Solve problems requiring inverse , Use of inverse
operations. operations and , Experience of finding rounding to 1 sig. fig.
missing numbers. could be applied to
more complex , The idea that some calculations.
operations are „opposite? to Reverse rate problems NA4a STAGE THREE
Simple linear equations NA5e 94 , Solve linear equations including those , Derive equations from each other. Equations combining operations NA5e with an unknown on both sides, those 96-97 practical situations , An understanding of that require prior simplification (e.g. (such as angle Solving equations with the unknown on both sides 97-98
NA5f brackets), fractional equations, and those calculations). balancing methods. where the answers are either negative or Solving equations using brackets and negative 103-105 , Solve equations or
a fraction. solutions NA5f inequalities where
Set up simple equations NA5e 106 more manipulation of
fractions is required. Using algebraic equations to solve problems NA5e 107 , Derive algebraic expressions from
, H/W SumBooks 26 information given and extend this to
derive equations. , H/W SumBooks 27
Solving simple inequalities* NA5j Y11 pg Ex1 with fractions. , Solve linear inequalities through both
168-170 algebraic methods and listing possible , H/W SumBooks 30
integer values.
NOTES
Pupils 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 9 Percentages
TIME: 5 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 ??? DIFFERENTIATION / STARTER OBJECTIVES EXTENSION / HOMEWORK , Modules 1, 7. Understanding percentages NA2e , The inclusion of
Interchanging between percentages, fractions and 181-5 percentages which lead , Change between percentages, fractions , A basic understanding of decimals NA3e and decimals. to recurring decimals
the concept of a percentage. (e.g. 33 1/3%), and Finding percentages, and percentage changes NA3j 313-317 , Find percentages of quantities, by both situations which lead to Finding VAT, a percentage profit or loss NA3j mental mathematics and calculator 319-321, , An understanding of the percentages of more methods as appropriate. R3 38-9 than 100%. ideas behind VAT, and Finding the added cost of buying goods on credit , Increase and decrease quantities by a R3 108-9 , Problems which lead to terms NA3j percentage, including within contexts of interest. the necessity of VAT, profit and loss. rounding to the nearest , Mental methods of , Find one quantity as a percentage of penny (e.g. real-life another, and calculate the percentage calculating common contexts). when an actual profit or loss is given. percentages (e.g. 17?% , Independent research , Solve problems using percentages e.g. into the many uses taxation, bills. using 10%, 5%, 2?%). made of percentages,
particularly in the
media.
, The construction of a
VAT ready-reckoner
table.
H/W SumBooks 5, 6 ,
Using simple interest NA3j , Calculate simple and compound interest. , Comparisons between
simple and compound Using compound interest* NA3k 316
interest calculations,
leading to the use of
fractions or formulae in
compound interest
methods.
, H/W SumBooks 7 RESOURCES
Channel 4 – Number and Algebra programme 1 *In 1388 this is not tested until Stage 3. 15 of 44
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GCSE Intermediate Scheme of Work
Amounts of money should always be rounded to the nearest penny where necessary, NOTES 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE) MODULE 10 Sequences
TIME: 3 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Module 5. Extending diagrammatic sequences NA6a 49-51 , Continue sequences of diagrams. , Match stick problems
Extending number sequences NA6a Linear , Fibonacci sequence, , Continue linear and non-linear , The ability to follow a E8.2 pg Pascal?s triangle. sequences of numbers.
series of instructions and 73?? , Uses of algebra to
Non-describe real situation appreciate that symbols can Linear e.g. n quadrilaterals
represent numbers. D5.1 pg have 4n sides.
63 H/W SumBooks 11 , , Use of mental maths in the Generating common number sequences NA6a 57-58 , Generate sequences from given Generating number sequences using term-to-term substitution of simple information.
and position-to-term definitions NA6a numbers into expressions. Finding the nth term (linear expressions) NA6a 52-56, , Investigate number patterns, describing
59-62 them in words and using the nth term for
linear expressions.
NOTES
Emphasis 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, the
difference between the terms and the algebraic description of the nth term.
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE /TWO) MODULE 13 Shape, volume and surface area
TIME: 7 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10/11 DIFFERENTIATION / STARTER OBJECTIVES Text EXTENSION / HOMEWORK , Module 11 – area and Constructing triangles SSM4b 132-134
Constructing 2-D shapes SSM4b 135-137 , Construct 2D shapes using ruler, pencil, , H/W SumBooks 81 circumference of circles. protractor and compasses.
, Names of triangles, Finding areas of plane shapes using formulae** Y11 text , Find the perimeter and area of simple , Simple fencing problems.
SSM4d pg 97-shapes, such as rectangles squares, , H/W SumBooks 55 quadrilaterals and 108 triangles, parallelograms, trapezia, kites, polygons. and composites of rectangles and
triangles. , Nets of simple solids. , Know the formulae for area and volume , Concept of area and of the shapes mentioned.
Using the language of 3D shapes* SSM2i 144-8 , Construct 3D shapes using ruler, pencil, , Find all possible nets volume. Constructing 3-D shapes SSM4b protractor and compasses. of a cube. , Ability to give answers to a Nets of simple solids SSM2i STAGE THREE , Investigate the different
nets that can be used to degree of accuracy. make certain 3-D shapes , Oral testing on a regular Developing, knowing and using the formula for the Y11 text , Work confidently with 3-D shapes and , Additional work using
volume of a cuboid** SSM4d pg 117-be able to calculate the volume of symbolic expressions. basis regarding the method Finding volume of solids made from cuboids** 118 cuboids, prisms, solids made from , H/W SumBooks 56 of calculating the SSM4d cuboids Ex 1 Using the formula for the volume of a cuboid to , Find how many boxes of a given size fit areas/volumes of shapes. solve problems** SSM4d into a larger box.
Finding volume of prisms** SSM4d Y11 text
pg 120-
121
Finding surface area of solids with triangular and Y11 text , Be able to calculate the surface area of
rectangular faces** SSM4d cuboids solids with triangular and rectangular
pg 119 faces.
*Not specifically mentioned in Intermediate specification. NOTES
**For 1388 this is not assessed until Stage 2. Need to constantly revise the expressions for area/volume of shapes.
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE /TWO) MODULE 12 Probability
TIME: 4 hours
TARGET GRADE: E/D
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 Text DIFFERENTIATION / STARTER OBJECTIVES EXTENSION / HOMEWORK , Experience of using the Writing probability as numbers HD4c, d , Write down theoretical probabilities of a , The work can be
single event happening. extended to include language of likelihood. that of the Higher , Knowledge of a probability syllabus.
scale from 0 to 1, including Equally likely events HD4d 331-334, , , H/W SumBooks 75
impossible and certain The probability of an event not happening HD4d 335 , Find the probability of an event not
Using the sum of probabilities equalling 1 HD4d happening given the probability of an events. event happening. , Ability to read from a two-
Predicting outcomes using simple probabilities* , Predict how many times an event may way table. HD4b happen given the probability. Estimating probability by experimenting* HD4b 336,343- , Establish the estimated probability of an
346 event happening.
Listing systematically outcomes for single events 337-342 , List outcomes of one or two events. , H/W SumBooks 76
or two successive events HD4c
Sample spaces and theoretical probabilities*
HD4b
Design and use two-way tables HD3c
Mutually exclusive events 350-1 , Understand the concepts of exclusivity , H/W SumBooks 77
and independence.
NOTES
Students can be unsure of the relationship P(not n) = 1 – P(n).
Only fractions, decimals or percentages should be used for probability. *For 1388 this is not assessed until Stage 2
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE ONE /TWO) MODULE 11 Circles
TIME: 5 hours
TARGET GRADE: D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 & DIFFERENTIATION / STARTER OBJECTIVES 11 TEXT EXTENSION / HOMEWORK , Modules 2. Recalling terms relating to a circle SSM2h Y10 187- , Use the vocabulary of a circle
8 (circumference, radius, diameter, sector, , Knowledge of basic circle segment, chord, tangent)
vocabulary, and ability to Understanding and using right angles between Y11 208 , Calculate angles within circles using
tangent and radius** SSM2h rules relating to tangents and radii. construct a circle. Understanding and using tangents of equal
length** SSM2h
Inscribing regular polygons in circles* SSM2h Y10
217??
Calculating circumferences* SSM4d Y11 109-, Recall and apply the formulae for the , Find area or perimeter
Using pi in exact calculations*** NA3n 112 area and circumference of a circle given of parts of a circle
Calculating areas of circles* SSM4d either the radius or diameter, using Y11 113-(halves, quarters or
Recalling formulae for areas of circles* SSM4d 5 various approximations to pi or leaving simple sectors).
Using pi in exact calculations*** NA3n pi as part of an irrational answer. , H/W SumBooks 54
, Recognise that units of volume or area Circumference of
cannot be converted using linear Circles conversion factors.
NOTES
Pi 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 Work
1387/1388 (STAGE TWO) MODULE 14 Ratio and proportion
TIME: 5 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION /
HOMEWORK , Modules 1, 3, 7. Basic ideas of ratio NA2f Y10 pg280-1 , Recognise a ratio as a way of showing
Y11 6-7 the relationship between two numbers. , Basic number skills and Simplifying ratios NA2f Y10 pg282 , Simplify a ratio by dividing both its , Similar triangles. ability to recognise Y11 8 numbers by a common factor.
, Recognise when a ratio is in its lowest common factors. terms. , Calculator skills. , Recognise that two numbers are in
proportion if their ratios stay the same as the quantities get larger or smaller.
Relating ratio form to fractions NA2f Y10 pg283 ,
Y11 9
Dividing in a given ratio NA3f Y10 pg 283-H/W SumBooks 8 , Divide a quantity into a given ratio (in ,
4 Y11 9-10 two or three parts).
Unitary method NA4a , Use the unitary method as a way of , H/W SumBooks
solving ratio and proportion problems 58
(e.g. recipes).
Using direct proportion** NA3l Y10 pg 307 ,
Y11 33
Converting between units given conversion Y11 250-1 , Convert between a variety of units and , Currency
factors* NA4a currencies where conversion factors are calculations using
given. current exchange
rates.
Knowing and using metric equivalents of common Y10 pg 126- , Convert between a variety of units using
imperial units* SSM4a knowledge of metric equivalents of 7
common imperial units.
Calculate speed and other compound measures Y10 pg 322-, Calculate speed and other compound , H/W SumBooks
SSM4a 4 Y11 48-50 measures. 57 Y11 218-222
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*For 1388 this is assessed in Stage 1. ** For 1388 this is not assessed until Stage 3. 22 of 44
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1387/1388 (STAGE TWO) MODULE 15 Displaying data
TIME: 6 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 2, 4. Grouping data in tally tables and grouped Y10 252-, Sort and collect data in a tally table and , Carry out a statistical
frequency tables HD3a 3 grouped frequency table. investigation of their , Measuring and drawing own including; Interpreting frequency diagrams HD5b Y10 227-
angles. designing an 9
appropriate means of Line graphs for discrete and continuous data, Y10 270-, Construct and interpret line graphs for , Fractions of simple gathering the data, and including time series* HD4a 1 all types of data. an appropriate means quantities. Constructing and interpreting stem and leaf Y10 244-, Construct and interpret ordered and of displaying the diagrams HD4a 5 unordered stem and leaf diagrams. , Plotting co-ordinates. results. Box plots HD4a Y10 277 , Construct box plots. , Use a spreadsheet to collect data in tables Calculating the angles to draw a pie chart HD4a Y10 230-, Use a pie chart to display data as and draw different Drawing Pie Charts HD4a 3 appropriate. types of graphs. Calculating using pie charts HD5b , Interpret given pie charts. , 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
NOTES
Clearly label all axes on graphs and use a ruler to draw straight lines. Angles should be within 2 degrees.
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1387/1388 (STAGE TWO)MODULE 16 Approximation
TIME: 4 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 or DIFFERENTIATION / STARTER OBJECTIVES 11 TEXT EXTENSION / HOMEWORK , Module 1. Rounding to the nearest 10, 100, 1000 NA3h Y10 285-, Round numbers of any size to the , Discuss
Carrying out appropriate rounding given the 6 Y11 nearest 10, 100, and 1000 or to any appropriateness of , BODMAS. context NA4b 11-12 specified number of significant figures types of rounding in
or decimal places. particular contexts. , Quick fire mental test for Approximation to decimal places and significant Y10 304-, Use rounding methods to make estimates , H/W SumBooks 4 rounding values to different figures NA3h 5 Y11 for simple and complex calculations. Estimations Use of rounding to one significant figure for 30-31 degrees of accuracy. checking answers NA4b Maximum and minimum values for rounded Y10 325-, Recognise the upper and lower bounds , Upper and lower
measurements* NA4b 6 Y11 of rounded numbers. bounds for decimals.
Recognising limitations on the accuracy of 51-2 , Recognise the limitations of a , H/W SumBooks 53 measurements NA4b measurement.
Reading a calculator display to appropriate Y10 293-, Use a calculator correctly and efficiently , H/W SumBooks 3
accuracy NA3o 303 Y11 for complex calculations (possibly
Use a calculator efficiently for complex 19-29 involving powers and roots) and round
calculations NA3o the answers appropriately.
NOTES
Pupils 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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1387/1388 (STAGE TWO) MODULE 17 Average and spread
TIME: 5 hours
TARGET GRADE: E/D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Some idea of the concept of Finding the mode, median, mean and range from Y10 241-, Calculate mode, mean, median and , Collect data from class
simple data HD4b 3 range for simple data. – children per family average. etc.
, Collect data from
newspapers.
, H/W SumBooks 65,
66
Selecting the most appropriate average HD4b Y10 268 , Justify the choice of a particular average. , Discuss occasions
when one average is , Compare distributions using averages
more appropriate, and and range.
the limitations of each
average.
Finding the mode from a discrete frequency table Y10 246-, Calculate mean and modal class from a , Look at the median
HD5d discrete or grouped frequency table. 7 class and approximate
Calculating the total frequency from a discrete the median.
frequency table HD1f , H/W SumBooks Calculate the mean from a discrete frequency table 67, 68, 69, 70 HD4e Mean and median for continuous data HD4e Y10 248-
Modal class for continuous data HD5d 256
Calculating a moving average* HD4f Y10 272 , Calculate and interpret the meaning of a , H/W SumBooks 89
moving average.
NOTES
Pupils 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. *For 1388 this is not tested until Stage 3.
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1387/1388 (STAGE TWO) MODULE 18 Transformations
TIME: 5 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Module 6. Enlarging assorted shapes using various centres of Y11 89-H/W SumBooks 48 , Enlarge shapes using a variety of ,
enlargement and integer scale factors SSM3c 91 positive scale factors. and 49 , Plotting co-ordinates. Enlarging assorted shapes using non-integer scale , Understand which are the invariant Enlargements factors SSM3c , An understanding of the properties of enlargements. , H/W SumBooks 50 Enlargement calculations SSM3d Similarity concept of enlargement.
, The tasks set can be Similar triangles* SSM2g Y11 202-, Use scale factors to solve problems extended to include Similarity of standard shapes SSM2g 3 involving similar shapes. combinations of Y11 92-3 transformations, Translations SSM3a Y11 85-, Recognise translations as sliding including those from Understanding and using vector notation* SSM3f 86 movements, and translate simple 2D other modules. shapes within a plane using words or , Investigation into vector notation. different ways of transforming an object Describing transformations in full (enlargements Y11 95-, Work on tasks involving these into a particular image. and translations) SSM3a 96 transformations.
Using and interpreting maps and scale drawings Y10 120-, Use scale to interpret maps and scale , Scale drawing of the
SSM3d 124 drawings. classroom/bedroom.
, H/W SumBooks 8
NOTES
Emphasis 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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1387/1388 (STAGE TWO) MODULE 19 Substitution and formulae
TIME: 4 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 3, 5, 8. Rearranging simple formulae NA5g Y11 171-H/W SumBooks 32 , Change the subject of formulae. ,
Rearranging formulae where the subject occurs 5 , Further practice in , Rearrange simple and complex , Ability to follow a series of twice or is raised to a power* NA5g formulae, including cases where the rearranging formulae instructions. subject occurs more than once. involving powers, and
several operations. Substituting into expressions involving squares or Y11 176-, Undertake simple substitution and , Experience of powers, cubes NA5d 77 substitution involving squaring. , Formulae involving equations, and formulae. reciprocals of the Generating a formula NA5g Y11 178 , Generate algebraic formulae from subject. information. , More use of directed Using trial and improvement to find approximate Y11 183-, Use trial and improvement methods to numbers with powers. solutions of equations NA5m 184 solve non-trivial equations such as
, H/W SumBooks 29 cubics, usually to 1 d.p.
NOTES
When 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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1387/1388 (STAGE TWO) MODULE 20 Pythagoras’ Theorem
TIME: 4 hours
TARGET GRADE: C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 2, 3, 5, 8, 19. Using Pythagoras? Theorem to find the Y11 126-, Identify the hypotenuse of a right-angled , The orientation of the
Hypotenuse SSM2f 134 triangle. triangle should be , Knowledge of different Using Pythagoras? Theorem to find the shorter varied. , Recall Pythagoras? theorem.
sides SSM2f types of triangle. , Further work can be , Pick out right-angled triangles from Using Pythagoras? Theorem to solve problems developed on applying diagrams, (e.g. circles, isosceles , Ability to use a calculator SSM2f Pythagoras, theorem in triangles). Calculating lengths of lines on a grid * SSM3e sensibly, particularly to three-dimensional , Use Pythagoras? theorem to find the problems. length of any side of a right angled find squares and square , Find Pythagorean triangle.
roots. triples. , Use Pythagoras? theorem to solve
H/W SumBooks 39 , problems such as bearings, areas of , Knowledge of simple triangles, diagonals of rectangles etc. bearings.
RESOURCES
Channel 4 – Shape, Space & Handling data programme 1
Coursework task Beyond Pythagoras.
NOTES
Consult 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE TWO) MODULE 21 Trigonometry
TIME: 6 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 2, 20. Tangent, sine and cosine ratios SSM2g Y11 135-, Identify appropriately the various sides , Further work can be
Uses of the three ratios SSM2g 153 of a right-angled triangle as the developed on applying , Knowledge of Pythagoras? Angles of elevation and depression SSM2g Hypotenuse, Opposite and Adjacent. the ratios in three-
Bearings and trigonometry SSM2g theorem. dimensional problems. , Recall the ratios for sine, cosine and
tangent. , Work on the sine and , Ability to use a calculator cosine rules could be , Identify which of sine, cosine and
to change fractions to developed (Higher tangent are required to solve a problem.
syllabus). , Use information given to write down the decimals. , Given two properties sine, cosine and tangent of an angle.
, Knowledge of basic of a right-angled , Use information given to find angles triangle find the others. using the appropriate ratio. concepts of ratio. H/W SumBooks 40, , , Use the appropriate ratio to find the , Mental testing of ability to 41, 42, 43 lengths of sides in a right-angled
triangle. recall ratios of sine, cosine , Find angles of elevation and depression and tangent. using the appropriate ratio.
, Apply trigonometric ratios and Pythagoras? Theorem to solve assorted
problems, including those involving
bearings.
RESOURCES
Channel 4 – Shape, Space & Handling data programme 2
NOTES
For 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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1387/1388 (STAGE TWO) MODULE 22 Scatter diagrams
TIME: 3 hours
TARGET GRADE: D
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 4, 15. Plotting and interpreting scatter diagrams HD4a & Y10 262-, Plot and use a scatter graph to describe , Vary the axes required on
HD5f 4 correlation. a scatter graph to suit the , Plotting co-ordinates Describing correlation from a scatter graph HD5f ability of the class. , Describe a relationship between two Drawing and using a line of best fit HD4i & HD5f (Module 8). H/W SumBooks 73, variables as illustrated by a scatter ,
diagram. 74 , An understanding of the , Describe correlation in terms of the two concept of a variable. variables, and as positive, weak,
negative, or strong. , Recognition that a change , Draw a line of best fit where possible
in one variable can affect “by eye”, and use this to make
predictions. another.
NOTES
Pupils 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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1387/1388 (STAGE TWO) MODULE 23 Cumulative Frequency
TIME: 4 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 4, 15, 17. Completing cumulative frequency tables HD4a Y10 274-, Design and complete a cumulative , Compare two
Plotting cumulative frequency diagrams HD4a 6 frequency table, identifying class cumulative frequency , Experience of plotting Using cumulative frequency to find the median boundaries where necessary. diagrams, to comment
HD4e points. on the differences , Plot a cumulative frequency curve using Using cumulative frequency to find quartiles and between distributions. upper class boundaries. , Experience of reading from interquartile range HD4e , Collect a set of , Solve problems using a cumulative
graphs. continuous data e.g. frequency curve (e.g. How many____
weights of 2p coins, were more than…). , Some concept of a „running draw grouped , Use a cumulative frequency curve to
frequency table, total?. estimate the median, lower quartile, cumulative frequency upper quartile, and interquartile range. graph and calculate
mean, median, mode,
range, quartiles.
H/W SumBooks 71, ,
72
NOTES
Pupils 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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1387/1388 (STAGE TWO) MODULE 24 Probability
TIME: 4 hours
TARGET GRADE: D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Year 11 DIFFERENTIATION / STARTER OBJECTIVES Text EXTENSION / HOMEWORK , Module 12. Using relative frequency HD4b 69-72 , Estimate probabilities and use relative , Use the fraction button
Estimating probability from theoretical models frequencies to make predictions or test for of a calculator to work , Writing probabilities as HD4b bias. with harder fractions.
Using probability estimates to compare results fractions, decimals or , Appreciate that a larger sample size will , Use venn diagrams to HD5h give a more accurate estimate. solve probability percentages. Understanding the effect of sample size on questions.
probability estimates HD5i , Probability of an event , Make predictions of Using the vocabulary of probability to interpret , outcomes for happening or not results HD5g probability games and
Recognising independent events HD4h STAGE 73-75 happening. , Know when to use the P(A) + P(B) „OR? then test the THREE rule, and the P(A) × (B) „AND’ rule. predictions. H/W SumBooks 79, ,
Calculating with mutually exclusive events HD4h 76-77 , 80 Relative STAGE THREE Frequency Use tree diagrams to represent outcomes of 78-82 , Complete tree diagrams as a means of , H/W SumBooks 77 compound events HD4h STAGE THREE showing outcomes for two successive , H/W SumBooks 78 events and related probabilities. Tree Diagrams
NOTES
Pupils 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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GCSE Intermediate Scheme of Work
1387/1388 (STAGE TWO) MODULE 25 Quadratics
TIME: 4 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK
Expanding brackets – the product of two linear Y11 157-, Modules 5, 8. , Expand and simplify two pairs of linear , Difference of two
expressions NA5b 160, Y11 brackets, e.g. (x + 2)(x – 4), (3x + 2y)(4x squares. , Removing and factorising Factorising of quadratic expressions. NA5b 179-181 + y), (x + p)(a + g) etc. with one pair of brackets. , More difficult 2Solving quadratic equations by factorising NA5k , Factorise a trinomial, e.g. x – 5x + 6 = quadratics to factorise. , An appreciation that if the (x – 6)(x + 1). product of two numbers is , Using the quadratic
, Expand the square of a linear expression. equation formula zero then one of the
(Higher level). numbers must be zero. , Use a factorised trinomial in one , Confidence with the four variable to solve a quadratic equation. , H/W SumBooks 24
rules for directed numbers. , Make efficient use of techniques Ex3 Multiplying out
covering signs, products and sums. , Mental testing of pairs of brackets
numbers with a specific , H/W SumBooks 27 sum and product. Ex2 Solving equations
,
NOTES
There 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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1387/1388 (STAGE TWO) MODULE 26 Algebraic graphs
TIME: 7 hours
TARGET GRADE: E/D/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 5, 8, 19, 25. Plotting graphs of functions where y is expressed Y11 213-H/W SumBooks 13-, Plot a straight-line graph from a given ,
in terms of x, leading to a straight line NA6b 217 set of values. 20 , The ability to plot points , H/W SumBooks 28 that follow a simple rule (in Find gradients of straight lines, and exploring Y11 223-, Realise that an equation of the type y = Ex1 gradients of parallel lines* NA6c 230 mx + c represents a straight line graph, , More able students four quadrants). Recognising the y-intercept of a straight line* and plot this graph. could extend to , The ability to substitute NA6c , Understand the relevance of m and c in identifying regions Exploring graphs of the form y = mx + c* NA6b the above equation. relating to straight-line positive and negative , From a given graph, find the gradient graphs. values into a non-linear and y-intercept and hence the equation of , Students performing the graph. below grade C will formula. , Draw a straight-line graph without struggle with much of plotting points. this module and
Plotting the graph of a quadratic function NA6e Y11 231-examples should be set , Plot curves from given quadratic and
Plotting graphs of simple cubic and reciprocal 3 cubic functions. , accordingly. functions* NA6f , Having drawn the Recognising characteristics of graphs* NA6f 3graph of type y = ax + 2 Plotting linear graphs from real-life problems Y11 244-, Interpret and plot real-life graphs such as bx + cx, investigate NA6d 9 conversion graphs and distance/time how it can be used to Interpret graphs representing real-life situations graphs. solve equations of the NA6d 32, Recognise graphs e.g. filling different , type ax + bx + cx + k shaped containers. = 0, where a, b, c and k
are constants.
, Use of a graphic
calculator.
RESOURCES NOTES
Channel 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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1387/1388 (STAGE THREE) MODULE 27 Percentages
TIME: 4 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 1, 7, 9. Understanding the multiplicative nature of HIGHER H/W , Recognise that an increase of e.g. 15% ,
percentages as operators NA3e leads to 115% and a decrease of e.g. SumBooks 6 , The concept of percentage, 15% leads to 85%. Understanding the concept and use of a reciprocal and an understanding of the , Find the original amount e.g. price NA3a
before a sale, price before VAT. Finding 100% when another amount is known Y10 318 , Combine multipliers to effects of increasing and , Write down a decimal multiplier which NA3e simplify a series of decreasing by a percentage. is equivalent to an increase or decrease Solving reverse percentage problems NA3e percentage changes. in percentage. Solving percentage problems NA3e , Use multipliers to solve reverse Solving problems involving compound interest R3 88-89 , Calculate original price percentage and compound interest NA3k before compound problems. interest.
NOTES
Pupils typically answer compound interest questions incorrectly, either by using simple interest or by
calculating over the wrong number of years.
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE THREE) MODULE 28 Constructions
TIME: 5 hours
TARGET GRADE: E/C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Module 2. Constructing triangles SSM4c , Construct shapes from given information
using only compasses and a ruler. , An ability to use a pair of Constructing a perpendicular bisector and finding Y11 191- , Construct perpendicular bisectors, and compasses. the mid-point of a line segment SSM4c 2 angle bisectors using only compasses
Constructing perpendiculars to a line SSM4c and a ruler. , Understanding of the Bisecting an angle SSM4c
term?s perpendicular, Finding Loci SSM4e Y11 193-, Construct LOCI in terms of distance , Solve LOCI problems that
Constructing graphs of simple loci NA6h (perhaps 7 from a point, equidistance from two require a combination of bisecting, parallel. should be diagrams of simple loci??) points, distance from a line, LOCI
H/W SumBooks 51, , equidistance from two lines and line of ,
sight. 52
, Shade regions using LOCI to solve
problems e.g. vicinity to lighthouse/
port.
NOTES
All working should be presented clearly, and accurately. Sturdy pair of compasses are essential. 37 of 44
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1387/1388 (STAGE THREE) MODULE 29 Indices and surds
TIME: 7 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Module 3. Using indices in expressions NA5d Y11 165-, Know the rules of indices (adding, , Use index
Using index laws for multiplication and division 7 subtracting and multiplying indices), and manipulation in , An understanding of (integer powers) NA2b simplify expressions. problems involving
Simplifying expressions using the rules of indices powers and roots. standard form. , Evaluate fractional and negative indices.
NA5d H/W SumBooks 23 , Experience of using Using index notation NA2b Y11 167 , Recall the cubes of 2, 3, 4, 5 and 10 squared and cubed units for Recalling integer cubes, squares and corresponding , Recall integer squares and corresponding
square roots NA3g square roots to 15 × 15. area and volume. Y11 53 Using surds and pi in exact calculations without a , Calculate exact answers by manipulating , H/W SumBooks 85 , Experience of using calculator NA3n simple surds without a calculator.
Converting between units of area or volume , Use powers of scale factors to convert , Combine formulae to find perimeter, SSM4d between units of area and volume. enlargement/similar area and volume. triangle problems with
area and volume , Mental test to check conversions. knowledge of cubes and , H/W SumBooks 29
squares/roots. Ex 1
Understanding the dimensions of formulae for Y11 185-, Recognise the purpose of a formula by , H/W SumBooks 59, perimeter, area and volume SSM3d 7 considering its dimensions. 60
NOTES
Pupils should work with powers of both numbers and algebraic variables. 38 of 44
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE THREE) MODULE 30 3D, volumes and surface areas
TIME: 5 hours
TARGET GRADE: D/C
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK
2D representations of 3D objects SSM2i Y11 198-, Modules 11, 13. , Draw 2D representations of 3D objects, , Draw shapes made from
9 including the use of isometric paper. multi-link on isometric , Finding areas of plane
paper. shapes, and volumes of
H/W SumBooks 35 cuboids and prisms. ,
Plans and elevations SSM2i Y11 200-, Finding area and , Use plans and elevations to answer , Make solids using
circumference of a circle. 1 questions. 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 Y11 117-, Draw nets of simple solids and use these , Build shapes from
rectangular faces* SSM4d STAGE TWO 124 to calculate surface areas of prisms, cubes which are
Solving problems involving surface area SSM2i cylinders and shapes with represented in 2D.
Investigating the geometry of cubes, cuboids and , rectangular and triangular faces. , H/W SumBooks 35 shapes made from cuboids SSM2f , Solve problems involving volumes of Solving problems involving volumes of prisms prisms, cylinders and solids made from SSM2i cuboids.
NOTES
Accurate drawing skills need to be reinforced.
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1387/1388 (STAGE THREE) MODULE 31 Standard index form
TIME: 3 hours
TARGET GRADE: B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK
Using standard index form* NA2b STAGE TWO Y11 13-, Modules 3, 16, 29. , Recognise that some numbers are too , Round large or small
Converting between ordinary and standard index 18 large or too small to be represented numbers to 1 , An understanding of the form representations NA3h Y11 36-8 normally on a calculator. significant figure to effect of multiplying and
Using standard index form to make estimates make estimates in dividing by powers of 10. , Represent standard form as a number NA3h standard form. between 1 and 10 multiplied by a , An ability to round to Calculating with standard index form NA3m positive or negative power of ten. , BODMAS and significant figures. Using a calculator for standard index form NA3r standard form. , Convert between standard form and
„normal? numbers. , Distance of planets
from the sun. , Solve problems involving standard form,
using the correct calculator method , Research constants that
where possible. are expressed in
standard form e.g. the , Interpret a calculator display showing a
number in standard form. speed of light.
, H/W SumBooks 9
RESOURCES
Channel 4 – Number and Algebra programme 2
NOTES
When transferring an answer from the calculator, pupils forget to write „× 10? before the power of 10, and
this could exclude them from all the marks in a GCSE question.
*For 1388 this is assessed in Stage 2.
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1387/1388 (STAGE THREE) MODULE 32 Angles in circles
TIME: 4 hours
TARGET GRADE: B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 TEXT DIFFERENTIATION / STARTER OBJECTIVES EXTENSION /
HOMEWORK
Understanding and using circle theorems SSM2h , Modules 2, 13. , Understand and apply the geometry rules , Questions for
included in the module content. which a , The geometry of an
The angle subtended by an arc at the centre of a Thereom 1 pg combination of isosceles triangle.
circle is twice the angle subtended at any point on 205, 206 the above rules the circumference SSM2h are needed.
Angles in the same segment are equal SSM2h Thereom 2 pg , H/W
205, 206 SumBooks
The angle subtended at the circumference by a Thereom 4 pg HIGHER 37, semi-circle is a right angle. SSM2h 207 38 Opposite angles of a cyclic quadrilateral add up to Thereom 3 pg 180 degrees SSM2h 207
Explain why the perpendicular from the centre of a Have I lost it, or
chord bisects the chord SSM2h is this not
obvious?? Any
Possibly: The line which bisects a chord at right line thro the
angles is always a diameter centre of the
But this isn?t in the Edexcel text?? chord will bisect
the chord (NO?)
NOTES
Pupils should be able to describe how they find each angle.
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1387/1388 (STAGE THREE) MODULE 33 Algebra
TIME: 8 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 8, 25, 26 Using the difference of two squares NA5b 180 , Factorise using the difference of two
squares and use this to solve problems. , Factorising quadratics.
, Drawing linear and Simplify expressions by cancelling common 182 , Use factorising methods to simplify
factors NA5b algebraic fractions. quadratic graphs. Solving simultaneous equations using elimination 161-164 , Solve simultaneous equations by , Simultaneous , Mental test of simple NA5i eliminating a variable, using them to equations that need
solve problems. rearranging before one simultaneous equations. of the methods can be
used.
H/W SumBooks 82 ,
Finding approximate solutions to quadratics using 231-33 , Solve quadratics by constructing an , Use graphical
graphs NA6e appropriate graph. calculators to enable
pupils to get through , Use terms like „minimum point?
examples more rapidly. „maximum point? „quadratic function?„.
, Use graphical methods to find the maximum or minimum of a quadratic function.
, Solve cubics where the graph is given
Solving simultaneous equations using a graphical 234-238 , Solve simultaneous equations by , Use gradient and
method NA5i graphical methods, using them to solve intercept to draw lines.
problems. , H/W SumBooks 28
Ex 2
Solving linear inequalities in two variables NA5j 239-243 , Use regions on a graph to solve , H/W SumBooks 31
inequality problems in two variables.
NOTES
Inaccurate graphs could lead to incorrect solutions.
Could lead to investigations such as Car hire, Mobile Phones.
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GCSE Intermediate Scheme of Work
1387/1388 (STAGE THREE) MODULE 34 Co-ordinates and transformations
TIME: 4 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y11 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 6, 18. Co-ordinates in 1, 2 and 3 dimensions SSM3e 210-1 , Use co-ordinates in 3 dimensions and , Pythagoras on a 3-D
use these to solve problems such as mid-grid. , An understanding of the Finding midpoints of lines SSM3e points of lines. 212 , H/W SumBooks
four types of HIGHER 89,90
Understanding similarity of plane figures SSM2g 92-94 , Solve problems involving similar transformation. polygons. Transforming 2-D shapes by translation, rotation, 95-96 , Use and describe fully the four types of
enlargement and reflection SSM3b transformations in a variety of
Combinations of transformations SSM3b combinations.
NOTES
Pupils 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. 43 of 44
W Robertson
GCSE Intermediate Scheme of Work
1387/1388 (STAGE THREE) MODULE 35 Data Handling
TIME: 3 hours
TARGET GRADE: C/B
PRIOR KNOWLEDGE/ CONTENT MAIN OBJECTIVES Y10 DIFFERENTIATION / STARTER OBJECTIVES TEXT EXTENSION / HOMEWORK , Modules 4, 12, 15, 17, 22. Identifying trends in time series HD5b Y10 270-, Understand the module content. , Additional work on
3 making predictions based , Experience of collecting, Comparing shapes of distributions HD5d Y10 278 on current trends, using
interpreting, displaying and time series and/or moving Comparing distributions using measures of range Y10 268
and spread HD5d averages calculating with data. Using a calculator for statistical calculations HD4j
NOTES
All working should be presented clearly, with descriptions of trends expressed as clearly as possible.
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