UG010896 – Edexcel GCSE Mathematics – Teachers’ Guide ...



Module |Stage |TIME |Target Grades |Previous Module |Homework SumBooks Sheet | |

|1 Number |1 |7 hours |E/D/C | |1 Multiplication and Division |

| | | | | |2 Negative Numbers |

| | | | | |3 Use of the Calculator |

|2 Geometry |1 |8 hours |E/D/C | |33 Bearings |

| | | | | |34 Parallel Lines |

| | | | | |36 Triangles |

| | | | | |37 Regular Polygons |

| | | | | |38 Irregular Polygons |

|3 Numbers and Powers |1 |5 hours |E/D | |10 Prime Factors |

| | | | | |29 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 Substitution |

| | | | | |22 Simplifying Expressions |

| | | | | |24 Multiplying Brackets Ex 1 and 2 |

| | | | | |25 Factorising |

|6 Transformations |1 |5 hours |E/D/C/B |2 |44 Reflections, Rotations and Translations 1 |

| | | | | |45 Reflections, Rotations and Translations 2 |

| | | | | |46 Reflections, Rotations and Translations 3 |

| | | | | |47 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 5 |

| | | | | |90 Recurring Decimals |

|8 Equations and inequalities |1 |5 hours |E/D/C/B |5 |26 Equations |

| | | | | |27 More Equations Ex 1 |

| | | | | |30 Inequalities |

|9 Percentages |1 |5 hours |E/D/C/B |1, 7 |5 Fractions, Decimals and Percentages 1 |

| | | | | |6 Fractions, Decimals and Percentages 2 |

| | | | | |7 Interest |

|10 Sequences |1 |3 hours |E/D/C/B |5 |11 Number Patterns and Sequences 1 |

| | | | | |12 Number Patterns and Sequences 2 |

|Module |Stage |TIME |Target Grades |Previous Module |Homework SumBooks Sheet |

|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 1 |

| | | | | |76 Probability 2 |

| | | | | |77 Probability 3 |

|13 Shape, volume and surface area |1/2 |7 hours |E/D/C |11 |55 Area and Perimeter |

| | | | | |56 Volume Ex 2 |

| | | | | |81 Constructions |

|14 Ratio and proportion |2 |5 hours |E/D/C |1, 3, 7 |8 Scale Drawings and Ratio |

| | | | | |57 Compound Measure - Speed and Density |

| | | | | |58 Compound Measure - Best Buy and a Mixed Exercise |

|15 Displaying data |2 |6 hours |E/D/C |2, 4 |62 Pie Charts |

| | | | | |63 Frequency Polygons 1 |

| | | | | |64 Frequency Polygons 2 |

| | | | | |91 Stem and Leaf Diagrams |

| | | | | |92 Box Plots |

|16 Approximation |2 |4 hours |E/D/C |1 |3 Use of the Calculator |

| | | | | |4 Estimation |

| | | | | |53 Degree of Accuracy |

|17 Average and spread |2 |5 hours |E/D/C | |65 Mean, Median, Mode and Range |

| | | | | |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 |

|Module |Stage |TIME |Target Grades |Previous Module |Homework SumBooks Sheet |

|18 Transformations |2 |5 hours |C/B |6 |8 Scale Drawings and Ratio |

| | | | | |48 Enlargements 1 |

| | | | | |49 Enlargements 2 |

| | | | | |50 Similar Shapes |

|19 Substitution and formulae |2 |4 hours |C/B |3, 5, 8 |29 Trial and Improvement |

| | | | | |32 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 1 |

| | | | | |41 Trigonometry 2 |

| | | | | |42 Trigonometry 3 |

| | | | | |43 Trigonometry 4 |

|22 Scatter diagrams |2 |3 hours |D |4, 15 |73 Scatter Diagrams 1 |

| | | | | |74 Scatter Diagrams 2 |

|23 Cumulative Frequency |2 |4 hours |C/B |4, 15, 17 |71 Cumulative Frequency 1 |

| | | | | |72 Cumulative Frequency 2 |

| | | | | |84 Using Quadratic Equation |

|24 Probability |2 |4 hours |D/C/B |12 |78 Tree diagrams |

| | | | | |79 Relative Frequency 1 |

| | | | | |80 Relative Frequency 2 |

|25 Quadratics |2 |4 hours |C/B |5, 8 |24 Multiplying Brackets Ex 3 |

| | | | | |27 More Equations Ex 2 |

|26 Algebraic graphs |2 |7 hours |E/D/C/B |5, 8, 19, 25 |13 Distance Time Diagrams 1 |

| | | | | |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 |

| | | | | |28 Straight Line Graphs and Sim Eqns Ex 1 |

|Module |Stage |TIME |Target Grades |Previous Module |Homework SumBooks Sheet |

|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 1 |

| | | | | |52 Locus Problems 2 |

|29 Indices and surds |3 |7 hours |C/B |3 |23 Indices |

| | | | | |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 hours |D/C |11, 13 |35 Nets and Isometric Drawing |

| | | | | |87 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 1 |

| | | | | |HIGHER 38 Geometry of a Circle 2 |

|33 Algebra |3 |8 hours |C/B |8, 25, 26 |28 Straight Line Graphs and Simultaneous Equations Ex 2 |

| | | | | |31 Inequalities - Graphs |

| | | | | |82 Simultaneous Equations |

|34 Co-ordinates and transformations |3 |4 hours |C/B |6, 18 |HIGHER 89 3 Dimensional Co-ordinates 1 |

| | | | | |HIGHER 90 3 Dimensional Co-ordinates 2 |

|35 Data Handling |3 |3 hours |C/B |4, 12, 15, 17, 22 | |

1387/1388 (STAGE ONE)

MODULE 1 Number

TIME: 7 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Ruff Guide|DIFFERENTIATION / EXTENSION / HOMEWORK |

|The ability to order large numbers and |Understanding place value in whole numbers NA2a | |22 | |

|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. | | | | |

| |Place value, multiplication and division of decimal numbers by | |168, 172 |Draw tables to illustrate ×100, ÷10 of |

| |powers of ten NA3a | | |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, |Write out a series of calculations |

| | | |168,176 |(possibly as a flowchart) for placing a|

| | | | |series of numbers in order of size |

| |Long multiplication and long division without using a calculator| |11-13, 17 |Non-calculator maths: 3-digit numbers |

| |NA3a | | |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 |

| | |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 | |Investigate the largest/smallest |

| | |the answers. | |numbers on a calculator. |

| | | | |H/W SumBooks 3 |

NOTES

All working should be presented clearly.

Non-calculator methods should show remainders & carries as evidence.

1387/1388 (STAGE ONE)

MODULE 2 Geometry

TIME: 8 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Ruff Guide|DIFFERENTIATION / EXTENSION / HOMEWORK|

|Knowledge of the names and properties of |Calculating angles on a straight line and at a point* SSM2a |Calculate angles at a point and on a straight line. |206 | |

|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. | | | | |

| |Recognising opposite angles at a vertex* SSM2a | |206 | |

| |Calculating angles in triangles SSM2b |Use the angle sum for triangles and quadrilaterals to find |207 |H/W SumBooks 36 |

| | |other angles in the shapes. | | |

| |Using angle properties of isosceles, equilateral and right-angled| |207 | |

| |triangles SSM2b | | | |

| |Using parallel lines, alternate angles and corresponding angles |Calculate angles on parallel lines, at a point and on a |208-9 |H/W SumBooks 34 |

| |SSM2a |straight line. | | |

| |Understanding the proof that the angle sum of a triangle is 180 |Understand the two proofs relating to angles in a triangle.|211 | |

| |degrees SSM2a | | | |

| |Understanding the proof regarding exterior angles of triangles | |211 | |

| |SSM2a | | | |

| |Recalling names and recognising properties of special | |212-3 | |

| |quadrilaterals SSM2c | | | |

| |Explaining why the angle sum of a quadrilateral is 360 degrees | |211 | |

| |SSM2b | | | |

| |Calculating angles in quadrilaterals SSM2b |Use the angle sum for triangles and quadrilaterals to find |214 | |

| | |other angles in the shapes. | | |

| |Interior and Exterior angles of quadrilaterals, pentagons, |Know how to work out the angle sum for any given polygon, |220-1 |H/W SumBooks 37 |

| |hexagons and regular polygons SSM2d |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. |

| |Using the angle properties of parallelograms SSM2a | | | |

| |Drawing and measuring bearings SSM4a |Draw and measure three figure bearings accurately. |139 |H/W SumBooks 33 |

| |Converting between measurements** SSM4a | |117-119 | |

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.

1387/1388 (STAGE ONE)

MODULE 3 Numbers and Powers

TIME: 5 hours

TARGET GRADE: E/D

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Ruff Guide|DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Basic number bonds and |Square and cube numbers NA2b |Calculate square and cube numbers. |32-33 | |

|multiplication/division facts. | |Recognise the different types of numbers. | | |

|Awareness of position of numbers on number| | | | |

|lines. | | | | |

|Ability to recognise basic number | | | | |

|patterns. | | | | |

|Mental test to check knowledge of squares | | | | |

|and cubes. | | | | |

| |Squares and square roots NA2b |Find square and cube roots of numbers including decimals |34-36 | |

| |Cubes and cube roots NA2b |by trial and improvement and by calculator methods. | | |

| |Trial and improvement methods NA2b (to find square and cube | | |H/W SumBooks 29 |

| |roots of numbers including decimals) | | | |

| |Factors and multiples NA2a |Use lists of multiples to find the lowest common multiple.|44-45 |Use prime factors to find LCM. |

| |Finding Highest Common Factor and Lowest Common Multiple NA2a |Write numbers in terms of their factors/prime factors and | |H/W SumBooks 10 |

| | |use prime factors to find the HCF. | | |

| |Powers of numbers* NA2b |Calculate powers of whole numbers including negative |308-309 |Further work on indices to include |

| | |numbers. | |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.

1387/1388 (STAGE ONE)

MODULE 4 Collecting and sorting data

TIME: 3 hours

TARGET GRADE: E

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|An understanding of why data needs to be |Different ways of collecting data HD1a | | |Carry out a statistical investigation|

|collected and some idea about different | | | |of their own including; designing an |

|types of graphs. | | | |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 HD3b | | | |

| |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.

1387/1388 (STAGE ONE)

MODULE 5 Simplifying and substituting

TIME: 4 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 1, 3. |Using letters to represent numbers NA5a |Substitute positive and negative numbers into word |82-87 |H/W SumBooks 21 |

|Experience of using a letter to represent |Using negative numbers NA5d STAGE TWO |formulae and algebraic formulae. | | |

|a number. |Using word formulae NA5g | | | |

|Ability to use negative numbers with the | | | | |

|four rules. | | | | |

| |Using algebraic formulae NA5g | |91 | |

| |Collecting like terms NA5b |Simplify algebra by collecting like terms – answers may |99 |H/W SumBooks 22 |

| | |involve negative coefficients. | | |

| |Multiplying with letters and numbers NA5b | | | |

| |Removing a single pair of brackets NA5b |Remove and factorise a single pair of brackets – including|100 |H/W SumBooks 24 Ex 1 & 2 |

| | |cases where a 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).

1387/1388 (STAGE ONE)

MODULE 6 Transformations

TIME: 5 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Text |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 2. |Co-ordinates in first quadrant SSM3e/NA6b |Plot and read co-ordinates in four quadrants. |189-190 | |

|Some experience of plotting points. |Co-ordinates in four quadrants SSM3e/NA6b | | | |

|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. | | | | |

| |Congruent shapes* SSM2d |Recognise congruency | |Given a shape on squared paper, |

| | | | |produce as many other different |

| | | | |congruent shapes as possible. |

| |Line symmetry* SSM3b |Sketch planes of symmetry on simple shapes. |191-3 |An attempt to draw up to 3 shapes |

| |Planes of symmetry SSM3b |State the properties of each 2-D shape and classify a | |each which have exactly 1, 2, 3, … 8 |

| | |shape according to its symmetrical properties. | |lines of symmetry, and investigate |

| | |Identify lines of symmetry or the order of rotational | |whether a rule exists between the |

| | |symmetry in 2-D shapes. | |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 | |194-6 | |

| |Transforming 2D shapes by reflection SSM3b |Reflect a 2D shape in a vertical, horizontal or diagonal |197-203 |H/W SumBooks 44, 45 |

| |Specify a mirror line parallel to axes SSM3a |line and state the equation of the line. | | |

| |Rotating shapes SSM3b |Rotate a 2D shape about the origin or a point other than |197, 204-5 |H/W SumBooks 46, 47 |

| |Transforming 2D shapes by rotation SSM3b |the origin, stating the angle, direction and centre of | | |

| |Describing transformations in full (rotations, reflections and |rotation. | | |

| |translations) SSM3a | | | |

| |Translations SSM3b |Translate a 2D shape and describe the translation in |197 | |

| | |words. | | |

* Not specifically mentioned in Intermediate specification.

1387/1388 (STAGE ONE)

MODULE 7 Fractions

TIME: 5 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 1, 3. |Interchanging improper fractions and mixed numbers. NA3d |Understand and change between improper fractions and |151-2 | |

|A basic understanding of fractions as | |mixed numbers. | | |

|being ‘parts of a whole unit’. | | | | |

|Use of a calculator with fractions. | | | | |

| |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 |154 | |

| | |to their lowest terms | | |

| | |Write one number as a fraction of another. | | |

| |Cancelling fractions. NA2c | |155-156 |For very able students cancelling |

| |Writing a given number as a fraction of another. NA3c | | |down of algebraic expressions could |

| | | | |be considered. |

| |Interchanging fractions and decimals and using recurring |Understand the concept of a recurring decimal. |169, |Relating the basic fractions to |

| |decimals. NA2d & NA3c |Convert fractions into decimals and vice versa, including|175-178??179-180|readily remembered percentages and |

| | |recurring decimals. |, |vice-versa. |

| | | | |H/W SumBooks 5 Ex1 |

| | | | |H/W SumBooks 90 |

| |Ordering fractions using common denominators. NA2c |Order fractions using common denominators or decimal |161 | |

| | |conversions. | | |

| |Adding and subtracting fractions using common denominators. |Perform the four basic operations with fractions. |157-160 | |

| |NA3c | | | |

| |Multiplying and dividing fractions. NA3d | |162-165 | |

| |Using fractions in problems involving multiplication and |Solve problems involving fractions. |166-167 | |

| |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.

1387/1388 (STAGE ONE)

MODULE 8 Equations and inequalities

TIME: 5 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Text |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 5. |Inverse operations NA5f |Solve problems requiring inverse operations. | |Use of inverse operations and |

|Experience of finding missing numbers. | | | |rounding to 1 sig. fig. could be |

|The idea that some operations are | | | |applied to more complex calculations.|

|‘opposite’ to each other. | | | | |

|An understanding of balancing methods. | | | | |

| |Reverse rate problems NA4a STAGE THREE | | | |

| |Simple linear equations NA5e |Solve linear equations including those with an unknown on |94 |Derive equations from practical |

| | |both sides, those that require prior simplification (e.g. | |situations (such as angle |

| | |brackets), fractional equations, and those where the | |calculations). |

| | |answers are either negative or a fraction. | |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 | |96-97 | |

| |Solving 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 | |106 | |

| |Using algebraic equations to solve problems NA5e |Derive algebraic expressions from information given and |107 | |

| | |extend this to derive equations. | | |

| |Solving simple inequalities* NA5j |Solve linear inequalities through both algebraic methods |Y11 pg 168-170| |

| | |and listing possible 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.

1387/1388 (STAGE ONE)

MODULE 9 Percentages

TIME: 5 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 ??? |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 1, 7. |Understanding percentages NA2e | | |The inclusion of percentages which |

|A basic understanding of the concept of a | | | |lead to recurring decimals (e.g. 33 |

|percentage. | | | |1/3%), and situations which lead to |

|An understanding of the ideas behind VAT, | | | |percentages of more than 100%. |

|and interest. | | | |Problems which lead to the necessity |

|Mental methods of calculating common | | | |of rounding to the nearest penny |

|percentages (e.g. 17½% using 10%, 5%, | | | |(e.g. real-life contexts). |

|2½%). | | | |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|313-317 | |

| | |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. | | |

| |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 calculations, |

| | | | |leading to the use of fractions or |

| | | | |formulae in compound interest |

| | | | |methods. |

| | | | |H/W SumBooks 7 |

| |Using compound interest* NA3k | |316 | |

RESOURCES

Channel 4 – Number and Algebra programme 1

*In 1388 this is not tested until Stage 3.

NOTES

Amounts 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.

1387/1388 (STAGE ONE)

MODULE 10 Sequences

TIME: 3 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 5. |Extending diagrammatic sequences NA6a |Continue sequences of diagrams. |49-51 |Match stick problems |

|The ability to follow a series of | | | |Fibonacci sequence, Pascal’s |

|instructions and appreciate that symbols | | | |triangle. |

|can represent numbers. | | | |Uses of algebra to describe real |

|Use of mental maths in the substitution of| | | |situation e.g. n quadrilaterals have |

|simple numbers into expressions. | | | |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 NA6a |Generate sequences from given information. |57-58 | |

| |Generating number sequences using term-to-term and | | | |

| |position-to-term definitions NA6a | | | |

| |Finding the nth term (linear expressions) NA6a |Investigate number patterns, describing them in words and |52-56, 59-62 | |

| | |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.

1387/1388 (STAGE ONE /TWO)

MODULE 13 Shape, volume and surface area

TIME: 7 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10/11 Text |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 11 – area and circumference of |Constructing triangles SSM4b | |132-134 | |

|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 2-D shapes SSM4b |Construct 2D shapes using ruler, pencil, protractor and |135-137 |H/W SumBooks 81 |

| | |compasses. | | |

| |Finding areas of plane shapes using formulae** SSM4d |Find the perimeter and area of simple shapes, such as |Y11 text pg |Simple fencing problems. |

| | |rectangles squares, triangles, parallelograms, trapezia, |97-108 |H/W SumBooks 55 |

| | |kites, and composites of rectangles and triangles. | | |

| | |Know the formulae for area and volume of the shapes | | |

| | |mentioned. | | |

| |Using the language of 3D shapes* SSM2i |Construct 3D shapes using ruler, pencil, protractor and |144-8 |Find all possible nets of a cube. |

| |Constructing 3-D shapes SSM4b |compasses. | |Investigate the different nets that |

| |Nets of simple solids SSM2i STAGE THREE | | |can be used to make certain 3-D |

| | | | |shapes |

| |Developing, knowing and using the formula for the volume of a |Work confidently with 3-D shapes and be able to calculate |Y11 text pg |Additional work using symbolic |

| |cuboid** SSM4d |the volume of cuboids, prisms, solids made from cuboids |117-118 |expressions. |

| |Finding volume of solids made from cuboids** SSM4d |Find how many boxes of a given size fit into a larger box.| |H/W SumBooks 56 Ex 1 |

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

| |SSM4d | | | |

| |Finding volume of prisms** SSM4d | |Y11 text pg | |

| | | |120-121 | |

| |Finding surface area of solids with triangular and rectangular |Be able to calculate the surface area of solids with |Y11 text | |

| |faces** SSM4d |triangular and rectangular faces. |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.

1387/1388 (STAGE ONE /TWO)

MODULE 12 Probability

TIME: 4 hours

TARGET GRADE: E/D

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 Text |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Experience of using the language of |Writing probability as numbers HD4c, d |Write down theoretical probabilities of a single event | |The work can be extended to include |

|likelihood. | |happening. | |that of the Higher syllabus. |

|Knowledge of a probability scale from 0 to| | | | |

|1, including impossible and certain | | | | |

|events. | | | | |

|Ability to read from a two-way table. | | | | |

| |Equally likely events HD4d | |331-334, |H/W SumBooks 75 |

| |The probability of an event not happening HD4d |Find the probability of an event not happening given the |335 | |

| |Using the sum of probabilities equalling 1 HD4d |probability of an event happening. | | |

| |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 |List outcomes of one or two events. |337-342 |H/W SumBooks 76 |

| |successive events HD4c | | | |

| |Sample spaces and theoretical probabilities* HD4b | | | |

| |Design and use two-way tables HD3c | | | |

| |Mutually exclusive events |Understand the concepts of exclusivity and independence. |350-1 |H/W SumBooks 77 |

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

1387/1388 (STAGE ONE /TWO)

MODULE 11 Circles

TIME: 5 hours

TARGET GRADE: D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 & 11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 2. |Recalling terms relating to a circle SSM2h |Use the vocabulary of a circle (circumference, radius, |Y10 187-8 | |

|Knowledge of basic circle vocabulary, and | |diameter, sector, segment, chord, tangent) | | |

|ability to construct a circle. | | | | |

| |Understanding and using right angles between tangent and |Calculate angles within circles using rules relating to |Y11 208 | |

| |radius** SSM2h |tangents and radii. | | |

| |Understanding and using tangents of equal length** SSM2h | | | |

| |Inscribing regular polygons in circles* SSM2h | |Y10 217?? | |

| |Calculating circumferences* SSM4d |Recall and apply the formulae for the area and |Y11 109-112 |Find area or perimeter of parts of a |

| |Using pi in exact calculations*** NA3n |circumference of a circle given either the radius or | |circle (halves, quarters or simple |

| | |diameter, using various approximations to pi or leaving pi| |sectors). |

| | |as part of an irrational answer. | |H/W SumBooks 54 Circumference of |

| | |Recognise that units of volume or area cannot be converted| |Circles |

| | |using linear conversion factors. | | |

| |Calculating areas of circles* SSM4d | |Y11 113-5 | |

| |Recalling formulae for areas of circles* SSM4d | | | |

| |Using pi in exact calculations*** NA3n | | | |

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.

1387/1388 (STAGE TWO)

MODULE 14 Ratio and proportion

TIME: 5 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 1, 3, 7. |Basic ideas of ratio NA2f |Recognise a ratio as a way of showing the relationship |Y10 pg280-1 Y11 | |

|Basic number skills and ability to | |between two numbers. |6-7 | |

|recognise common factors. | | | | |

|Calculator skills. | | | | |

| |Simplifying ratios NA2f |Simplify a ratio by dividing both its numbers by a common |Y10 pg282 Y11 8 |Similar triangles. |

| | |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. | | |

| |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 |Y10 pg 283-4 Y11 |H/W SumBooks 8 |

| | |parts). |9-10 | |

| |Unitary method NA4a |Use the unitary method as a way of solving ratio and | |H/W SumBooks 58 |

| | |proportion problems (e.g. recipes). | | |

| |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 |Y11 250-1 |Currency calculations using |

| | |conversion factors are given. | |current exchange rates. |

| |Knowing and using metric equivalents of common imperial units* |Convert between a variety of units using knowledge of |Y10 pg 126-7 | |

| |SSM4a |metric equivalents of common imperial units. | | |

| |Calculate speed and other compound measures SSM4a |Calculate speed and other compound measures. |Y10 pg 322-4 Y11 |H/W SumBooks 57 |

| | | |48-50 | |

| | | |Y11 218-222 | |

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

1387/1388 (STAGE TWO)

MODULE 15 Displaying data

TIME: 6 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 2, 4. |Grouping data in tally tables and grouped frequency tables HD3a |Sort and collect data in a tally table and grouped |Y10 252-3 |Carry out a statistical investigation|

|Measuring and drawing angles. | |frequency table. | |of their own including; designing an |

|Fractions of simple quantities. | | | |appropriate means of gathering the |

|Plotting co-ordinates. | | | |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 |Construct and interpret line graphs for all types of data.|Y10 270-1 | |

| |series* HD4a | | | |

| |Constructing and interpreting stem and leaf diagrams HD4a |Construct and interpret ordered and unordered stem and |Y10 244-5 | |

| | |leaf diagrams. | | |

| |Box plots HD4a |Construct box plots. |Y10 277 | |

| |Calculating the angles to draw a pie chart HD4a |Use a pie chart to display data as appropriate. |Y10 230-3 | |

| |Drawing Pie Charts HD4a |Interpret given pie charts. | | |

| |Calculating using pie charts HD5b | | | |

NOTES

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

Angles should be within 2 degrees.

1387/1388 (STAGE TWO)

MODULE 16 Approximation

TIME: 4 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 or 11 TEXT|DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 1. |Rounding to the nearest 10, 100, 1000 NA3h |Round numbers of any size to the nearest 10, 100, and 1000|Y10 285-6 Y11 |Discuss appropriateness of types of |

|BODMAS. |Carrying out appropriate rounding given the context NA4b |or to any specified number of significant figures or |11-12 |rounding in particular contexts. |

|Quick fire mental test for rounding values| |decimal places. | |H/W SumBooks 4 Estimations |

|to different degrees of accuracy. | |Use rounding methods to make estimates for simple and | | |

| | |complex calculations. | | |

| |Approximation to decimal places and significant figures NA3h | |Y10 304-5 Y11 | |

| |Use of rounding to one significant figure for checking answers | |30-31 | |

| |NA4b | | | |

| |Maximum and minimum values for rounded measurements* NA4b |Recognise the upper and lower bounds of rounded numbers. |Y10 325-6 Y11 |Upper and lower bounds for decimals. |

| |Recognising limitations on the accuracy of measurements NA4b |Recognise the limitations of a measurement. |51-2 |H/W SumBooks 53 |

| |Reading a calculator display to appropriate accuracy NA3o |Use a calculator correctly and efficiently for complex |Y10 293-303 |H/W SumBooks 3 |

| |Use a calculator efficiently for complex calculations NA3o |calculations (possibly involving powers and roots) and |Y11 19-29 | |

| | |round 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.

1387/1388 (STAGE TWO)

MODULE 17 Average and spread

TIME: 5 hours

TARGET GRADE: E/D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|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. |Y10 268 |Discuss occasions when one average is|

| | |Compare distributions using averages and range. | |more appropriate, and the limitations|

| | | | |of each average. |

| |Finding the mode from a discrete frequency table HD5d |Calculate mean and modal class from a discrete or grouped |Y10 246-7 |Look at the median class and |

| |Calculating the total frequency from a discrete frequency table |frequency table. | |approximate the median. |

| |HD1f | | |H/W SumBooks 67, 68, 69, 70 |

| |Calculate the mean from a discrete frequency table HD4e | | | |

| |Mean and median for continuous data HD4e | |Y10 248-256 | |

| |Modal class for continuous data HD5d | | | |

| |Calculating a moving average* HD4f |Calculate and interpret the meaning of a moving average. |Y10 272 |H/W SumBooks 89 |

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.

1387/1388 (STAGE TWO)

MODULE 18 Transformations

TIME: 5 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 6. |Enlarging assorted shapes using various centres of enlargement |Enlarge shapes using a variety of positive scale factors. |Y11 89-91 |H/W SumBooks 48 and 49 Enlargements |

|Plotting co-ordinates. |and integer scale factors SSM3c |Understand which are the invariant properties of | |H/W SumBooks 50 Similarity |

|An understanding of the concept of |Enlarging assorted shapes using non-integer scale factors SSM3c |enlargements. | |The tasks set can be extended to |

|enlargement. |Enlargement calculations SSM3d | | |include combinations of |

| | | | |transformations, including those from|

| | | | |other modules. |

| | | | |Investigation into different ways of |

| | | | |transforming an object into a |

| | | | |particular image. |

| |Similar triangles* SSM2g |Use scale factors to solve problems involving similar |Y11 202-3 | |

| |Similarity of standard shapes SSM2g |shapes. |Y11 92-3 | |

| |Translations SSM3a |Recognise translations as sliding movements, and translate|Y11 85-86 | |

| |Understanding and using vector notation* SSM3f |simple 2D shapes within a plane using words or vector | | |

| | |notation. | | |

| |Describing transformations in full (enlargements and |Work on tasks involving these transformations. |Y11 95-96 | |

| |translations) SSM3a | | | |

| |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 |

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.

1387/1388 (STAGE TWO)

MODULE 19 Substitution and formulae

TIME: 4 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 3, 5, 8. |Rearranging simple formulae NA5g |Change the subject of formulae. |Y11 171-5 |H/W SumBooks 32 |

|Ability to follow a series of |Rearranging formulae where the subject occurs twice or is raised|Rearrange simple and complex formulae, including cases | |Further practice in rearranging |

|instructions. |to a power* NA5g |where the subject occurs more than once. | |formulae involving powers, and |

|Experience of powers, equations, and | | | |several operations. |

|formulae. | | | |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 |Y11 176-77 | |

| | |squaring. | | |

| |Generating a formula NA5g |Generate algebraic formulae from information. |Y11 178 | |

| |Using trial and improvement to find approximate solutions of |Use trial and improvement methods to solve non-trivial |Y11 183-184 | |

| |equations NA5m |equations such as 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.

1387/1388 (STAGE TWO)

MODULE 20 Pythagoras’ Theorem

TIME: 4 hours

TARGET GRADE: C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 2, 3, 5, 8, 19. |Using Pythagoras’ Theorem to find the Hypotenuse SSM2f |Identify the hypotenuse of a right-angled triangle. |Y11 126-134 |The orientation of the triangle |

|Knowledge of different types of triangle. |Using Pythagoras’ Theorem to find the shorter sides SSM2f |Recall Pythagoras’ theorem. | |should be varied. |

|Ability to use a calculator sensibly, |Using Pythagoras’ Theorem to solve problems SSM2f |Pick out right-angled triangles from diagrams, (e.g. | |Further work can be developed on |

|particularly to find squares and square |Calculating lengths of lines on a grid * SSM3e |circles, isosceles triangles). | |applying Pythagoras, theorem in |

|roots. | |Use Pythagoras’ theorem to find the length of any side of | |three-dimensional problems. |

|Knowledge of simple bearings. | |a right angled triangle. | |Find Pythagorean triples. |

| | |Use Pythagoras’ theorem to solve problems such as | |H/W SumBooks 39 |

| | |bearings, areas of triangles, diagonals of rectangles etc.| | |

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.

1387/1388 (STAGE TWO)

MODULE 21 Trigonometry

TIME: 6 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 2, 20. |Tangent, sine and cosine ratios SSM2g |Identify appropriately the various sides of a right-angled|Y11 135-153 |Further work can be developed on |

|Knowledge of Pythagoras’ theorem. |Uses of the three ratios SSM2g |triangle as the Hypotenuse, Opposite and Adjacent. | |applying the ratios in |

|Ability to use a calculator to change |Angles of elevation and depression SSM2g |Recall the ratios for sine, cosine and tangent. | |three-dimensional problems. |

|fractions to decimals. |Bearings and trigonometry SSM2g |Identify which of sine, cosine and tangent are required to| |Work on the sine and cosine rules |

|Knowledge of basic concepts of ratio. | |solve a problem. | |could be developed (Higher syllabus).|

|Mental testing of ability to recall ratios| |Use information given to write down the sine, cosine and | |Given two properties of a |

|of sine, cosine and tangent. | |tangent of an angle. | |right-angled triangle find the |

| | |Use information given to find angles using the appropriate| |others. |

| | |ratio. | |H/W SumBooks 40, 41, 42, 43 |

| | |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. | | |

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.

1387/1388 (STAGE TWO)

MODULE 22 Scatter diagrams

TIME: 3 hours

TARGET GRADE: D

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 4, 15. |Plotting and interpreting scatter diagrams HD4a & HD5f |Plot and use a scatter graph to describe correlation. |Y10 262-4 |Vary the axes required on a scatter |

|Plotting co-ordinates (Module 8). |Describing correlation from a scatter graph HD5f |Describe a relationship between two variables as | |graph to suit the ability of the |

|An understanding of the concept of a |Drawing and using a line of best fit HD4i & HD5f |illustrated by a scatter diagram. | |class. |

|variable. | |Describe correlation in terms of the two variables, and as| |H/W SumBooks 73, 74 |

|Recognition that a change in one variable | |positive, weak, negative, or strong. | | |

|can affect another. | |Draw a line of best fit where possible “by eye”, and use | | |

| | |this to make predictions. | | |

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.

1387/1388 (STAGE TWO)

MODULE 23 Cumulative Frequency

TIME: 4 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 4, 15, 17. |Completing cumulative frequency tables HD4a |Design and complete a cumulative frequency table, |Y10 274-6 |Compare two cumulative frequency |

|Experience of plotting points. |Plotting cumulative frequency diagrams HD4a |identifying class boundaries where necessary. | |diagrams, to comment on the |

|Experience of reading from graphs. |Using cumulative frequency to find the median HD4e |Plot a cumulative frequency curve using upper class | |differences between distributions. |

|Some concept of a ‘running total’. |Using cumulative frequency to find quartiles and interquartile |boundaries. | |Collect a set of continuous data e.g.|

| |range HD4e |Solve problems using a cumulative frequency curve (e.g. | |weights of 2p coins, draw grouped |

| | |How many____ were more than…). | |frequency table, cumulative frequency|

| | |Use a cumulative frequency curve to estimate the median, | |graph and calculate mean, median, |

| | |lower quartile, upper quartile, and interquartile range. | |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.

1387/1388 (STAGE TWO)

MODULE 24 Probability

TIME: 4 hours

TARGET GRADE: D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Year 11 Text |DIFFERENTIATION / EXTENSION / HOMEWORK|

|Module 12. |Using relative frequency HD4b |Estimate probabilities and use relative frequencies to make|69-72 |Use the fraction button of a |

|Writing probabilities as fractions, |Estimating probability from theoretical models HD4b |predictions or test for bias. | |calculator to work with harder |

|decimals or percentages. |Using probability estimates to compare results HD5h |Appreciate that a larger sample size will give a more | |fractions. |

|Probability of an event happening or not |Understanding the effect of sample size on probability estimates |accurate estimate. | |Use venn diagrams to solve probability|

|happening. |HD5i | | |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) × |73-75 | |

| | |(B) ‘AND’ rule. | | |

| |Calculating with mutually exclusive events HD4h STAGE THREE | |76-77 | |

| |Use tree diagrams to represent outcomes of compound events HD4h |Complete tree diagrams as a means of showing outcomes for |78-82 | |

| |STAGE THREE |two successive events and related probabilities. | | |

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’.

1387/1388 (STAGE TWO)

MODULE 25 Quadratics

TIME: 4 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 5, 8. |Expanding brackets – the product of two linear expressions NA5b |Expand and simplify two pairs of linear brackets, e.g. (x |Y11 157-160, |Difference of two squares. |

|Removing and factorising with one pair of |Factorising of quadratic expressions. NA5b |+ 2)(x – 4), (3x + 2y)(4x + y), (x + p)(a + g) etc. |Y11 179-181 |More difficult quadratics to |

|brackets. |Solving quadratic equations by factorising NA5k |Factorise a trinomial, e.g. x 2 – 5x + 6 = (x – 6)(x + 1).| |factorise. |

|An appreciation that if the product of two| |Expand the square of a linear expression. | |Using the quadratic equation formula |

|numbers is zero then one of the numbers | |Use a factorised trinomial in one variable to solve a | |(Higher level). |

|must be zero. | |quadratic equation. | |H/W SumBooks 24 Ex3 Multiplying out |

|Confidence with the four rules for | |Make efficient use of techniques covering signs, products | |brackets |

|directed numbers. | |and sums. | |H/W SumBooks 27 Ex2 Solving equations|

|Mental testing of pairs of numbers with a | | | | |

|specific sum and product. | | | | |

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.

1387/1388 (STAGE TWO)

MODULE 26 Algebraic graphs

TIME: 7 hours

TARGET GRADE: E/D/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 5, 8, 19, 25. |Plotting graphs of functions where y is expressed in terms of x,|Plot a straight-line graph from a given set of values. |Y11 213-217 |H/W SumBooks 13-20 |

|The ability to plot points that follow a |leading to a straight line NA6b | | |H/W SumBooks 28 Ex1 |

|simple rule (in four quadrants). | | | |More able students could extend to |

|The ability to substitute positive and | | | |identifying regions relating to |

|negative values into a non-linear formula.| | | |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. |

| | | | |Use of a graphic calculator. |

| |Find gradients of straight lines, and exploring gradients of |Realise that an equation of the type y = mx + c represents|Y11 223-230 | |

| |parallel lines* NA6c |a straight line graph, and plot this graph. | | |

| |Recognising the y-intercept of a straight line* NA6c |Understand the relevance of m and c in the above equation.| | |

| |Exploring graphs of the form y = mx + c* NA6b |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. | | |

| |Plotting the graph of a quadratic function NA6e |Plot curves from given quadratic and cubic functions. |Y11 231-3 | |

| |Plotting graphs of simple cubic and reciprocal functions* NA6f | | | |

| |Recognising characteristics of graphs* NA6f | | | |

| |Plotting linear graphs from real-life problems NA6d |Interpret and plot real-life graphs such as conversion |Y11 244-9 | |

| |Interpret graphs representing real-life situations NA6d |graphs and distance/time graphs. | | |

| | |Recognise graphs e.g. filling different shaped containers.| | |

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.

1387/1388 (STAGE THREE)

MODULE 27 Percentages

TIME: 4 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 1, 7, 9. |Understanding the multiplicative nature of percentages as |Recognise that an increase of e.g. 15% leads to 115% and a| |HIGHER H/W SumBooks 6 |

|The concept of percentage, and an |operators NA3e |decrease of e.g. 15% leads to 85%. | | |

|understanding of the effects of increasing| |Find the original amount e.g. price before a sale, price | | |

|and decreasing by a percentage. | |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. | | |

| |Understanding the concept and use of a reciprocal NA3a | | | |

| |Finding 100% when another amount is known NA3e | |Y10 318 |Combine multipliers to simplify a |

| |Solving reverse percentage problems NA3e | | |series of percentage changes. |

| |Solving percentage problems NA3e | | | |

| |Solving problems involving compound interest NA3k | |R3 88-89 |Calculate original price before |

| | | | |compound interest. |

NOTES

Pupils typically answer compound interest questions incorrectly, either by using simple interest or by

calculating over the wrong number of years.

1387/1388 (STAGE THREE)

MODULE 28 Constructions

TIME: 5 hours

TARGET GRADE: E/C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 2. |Constructing triangles SSM4c |Construct shapes from given information using only | | |

|An ability to use a pair of compasses. | |compasses and a ruler. | | |

|Understanding of the term’s perpendicular,| | | | |

|bisecting, parallel. | | | | |

| |Constructing a perpendicular bisector and finding the mid-point |Construct perpendicular bisectors, and angle bisectors |Y11 191-2 | |

| |of a line segment SSM4c |using only compasses and a ruler. | | |

| |Constructing perpendiculars to a line SSM4c | | | |

| |Bisecting an angle SSM4c | | | |

| |Finding Loci SSM4e |Construct LOCI in terms of distance from a point, |Y11 193-7 |Solve LOCI problems that require a |

| |Constructing graphs of simple loci NA6h (perhaps should be |equidistance from two points, distance from a line, | |combination of LOCI |

| |diagrams of simple loci??) |equidistance from two lines and line of sight. | |H/W SumBooks 51, 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.

1387/1388 (STAGE THREE)

MODULE 29 Indices and surds

TIME: 7 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Module 3. |Using indices in expressions NA5d |Know the rules of indices (adding, subtracting and |Y11 165-7 |Use index manipulation in problems |

|An understanding of powers and roots. |Using index laws for multiplication and division (integer |multiplying indices), and simplify expressions. | |involving standard form. |

|Experience of using squared and cubed |powers) NA2b |Evaluate fractional and negative indices. | |H/W SumBooks 23 |

|units for area and volume. |Simplifying expressions using the rules of indices NA5d | | | |

|Experience of using formulae to find | | | | |

|perimeter, area and volume. | | | | |

|Mental test to check knowledge of cubes | | | | |

|and squares/roots. | | | | |

| |Using index notation NA2b |Recall the cubes of 2, 3, 4, 5 and 10 |Y11 167 | |

| |Recalling integer cubes, squares and corresponding square roots |Recall integer squares and corresponding square roots to | | |

| |NA3g |15 × 15. | | |

| |Using surds and pi in exact calculations without a calculator |Calculate exact answers by manipulating simple surds |Y11 53 |H/W SumBooks 85 |

| |NA3n |without a calculator. | | |

| |Converting between units of area or volume SSM4d |Use powers of scale factors to convert between units of | |Combine enlargement/similar triangle |

| | |area and volume. | |problems with area and volume |

| | | | |conversions. |

| | | | |H/W SumBooks 29 Ex 1 |

| |Understanding the dimensions of formulae for perimeter, area and|Recognise the purpose of a formula by considering its |Y11 185-7 |H/W SumBooks 59, 60 |

| |volume SSM3d |dimensions. | | |

NOTES

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

1387/1388 (STAGE THREE)

MODULE 30 3D, volumes and surface areas

TIME: 5 hours

TARGET GRADE: D/C

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 11, 13. |2D representations of 3D objects SSM2i |Draw 2D representations of 3D objects, including the use |Y11 198-9 |Draw shapes made from multi-link on |

|Finding areas of plane shapes, and volumes| |of isometric paper. | |isometric paper. |

|of cuboids and prisms. | | | |H/W SumBooks 35 |

|Finding area and circumference of a | | | | |

|circle. | | | | |

| |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 |Draw nets of simple solids and use these to calculate |Y11 117-124 |Build shapes from cubes which are |

| |faces* SSM4d STAGE TWO |surface areas of prisms, cylinders and shapes with | |represented in 2D. |

| |Solving problems involving surface area SSM2i |rectangular and triangular faces. | |H/W SumBooks 35 |

| |Investigating the geometry of cubes, cuboids and shapes made |Solve problems involving volumes of prisms, cylinders and | | |

| |from cuboids SSM2f |solids made from cuboids. | | |

| |Solving problems involving volumes of prisms SSM2i | | | |

NOTES

Accurate drawing skills need to be reinforced.

1387/1388 (STAGE THREE)

MODULE 31 Standard index form

TIME: 3 hours

TARGET GRADE: B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 3, 16, 29. |Using standard index form* NA2b STAGE TWO |Recognise that some numbers are too large or too small to |Y11 13-18 |Round large or small numbers to 1 |

|An understanding of the effect of |Converting between ordinary and standard index form |be represented normally on a calculator. |Y11 36-8 |significant figure to make estimates |

|multiplying and dividing by powers of 10. |representations NA3h |Represent standard form as a number between 1 and 10 | |in standard form. |

|An ability to round to significant |Using standard index form to make estimates NA3h |multiplied by a positive or negative power of ten. | |BODMAS and standard form. |

|figures. |Calculating with standard index form NA3m |Convert between standard form and ‘normal’ numbers. | |Distance of planets from the sun. |

| |Using a calculator for standard index form NA3r |Solve problems involving standard form, using the correct | |Research constants that are expressed|

| | |calculator method where possible. | |in standard form e.g. the speed of |

| | |Interpret a calculator display showing a number in | |light. |

| | |standard form. | |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.

1387/1388 (STAGE THREE)

MODULE 32 Angles in circles

TIME: 4 hours

TARGET GRADE: B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION |

| | | | |/ HOMEWORK |

|Modules 2, 13. |Understanding and using circle theorems SSM2h |Understand and apply the geometry rules included in the | |Questions for which a |

|The geometry of an isosceles triangle. | |module content. | |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 | |Thereom 1 pg 205, 206 | |

| |twice the angle subtended at any point on the circumference | | | |

| |SSM2h | | | |

| |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 | |Thereom 4 pg 207 | |

| |right angle. SSM2h | | | |

| |Opposite angles of a cyclic quadrilateral add up to 180 degrees| |Thereom 3 pg 207 | |

| |SSM2h | | | |

| |Explain why the perpendicular from the centre of a chord | |Have I lost it, or is | |

| |bisects the chord SSM2h | |this not obvious?? Any | |

| | | |line thro the centre of | |

| |Possibly: The line which bisects a chord at right angles is | |the chord will bisect | |

| |always a diameter | |the chord (NO?) | |

| |But this isn’t in the Edexcel text?? | | | |

NOTES

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

1387/1388 (STAGE THREE)

MODULE 33 Algebra

TIME: 8 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 8, 25, 26 |Using the difference of two squares NA5b |Factorise using the difference of two squares and use this|180 | |

|Factorising quadratics. | |to solve problems. | | |

|Drawing linear and quadratic graphs. | | | | |

|Mental test of simple simultaneous | | | | |

|equations. | | | | |

| |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, |161-164 |Simultaneous equations that need |

| | |using them to solve problems. | |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. |231-33 |Use graphical calculators to enable |

| | |Use terms like ‘minimum point’ ‘maximum point’ ‘quadratic | |pupils to get through examples more |

| | |function’‘. | |rapidly. |

| | |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 method NA5i |Solve simultaneous equations by graphical methods, using |234-238 |Use gradient and intercept to draw |

| | |them to solve problems. | |lines. |

| | | | |H/W SumBooks 28 Ex 2 |

| |Solving linear inequalities in two variables NA5j |Use regions on a graph to solve inequality problems in two|239-243 |H/W SumBooks 31 |

| | |variables. | | |

NOTES

Inaccurate graphs could lead to incorrect solutions.

Could lead to investigations such as Car hire, Mobile Phones.

1387/1388 (STAGE THREE)

MODULE 34 Co-ordinates and transformations

TIME: 4 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y11 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 6, 18. |Co-ordinates in 1, 2 and 3 dimensions SSM3e |Use co-ordinates in 3 dimensions and use these to solve |210-1 |Pythagoras on a 3-D grid. |

|An understanding of the four types of | |problems such as mid-points of lines. | |H/W SumBooks HIGHER 89,90 |

|transformation. | | | | |

| |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 |Use and describe fully the four types of transformations |95-96 | |

| |and reflection SSM3b |in a variety of combinations. | | |

| |Combinations of transformations SSM3b | | | |

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.

1387/1388 (STAGE THREE)

MODULE 35 Data Handling

TIME: 3 hours

TARGET GRADE: C/B

|PRIOR KNOWLEDGE/ STARTER OBJECTIVES |CONTENT |MAIN OBJECTIVES |Y10 TEXT |DIFFERENTIATION / EXTENSION / |

| | | | |HOMEWORK |

|Modules 4, 12, 15, 17, 22. |Identifying trends in time series HD5b |Understand the module content. |Y10 270-3 |Additional work on making predictions|

|Experience of collecting, interpreting, | | | |based on current trends, using time |

|displaying and calculating with data. | | | |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 | | | |

NOTES

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

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