Scheme of Work - Level 2 Award and Level 3 Award in ... · Web viewTitle Scheme of Work - Level 2 Award and Level 3 Award in Algebra - Word version Author cummingg Last modified by

Edexcel Level 2 Award in Algebra (AAL20)

Scheme of work

Contents

IntroductionLevel 2 scheme of workLevel 2 course overviewLevel 2 modulesLevel 2 concepts and skills (AAL20)Resources TableLevel 2

IntroductionThis scheme of work has been designed for teachers delivering the Edexcel Award in Algebra. This scheme of work is based upon a course model which can be taught over a single year, or more years if desired, for both Level 2 and Level 3 tier students.

The scheme of work is structured so each topic contains:

Module number Recommended teaching time, though of course this is adaptable according to individual

student needs Level Contents, referenced back to the specification GCSE specification references Prior knowledge and links with the alternative level Objectives for students at the end of the module Links to the GCSE scheme of work modules At level 3 links to (C1) GCE Mathematics Ideas for differentiation and extension activities Notes for general mathematical teaching points and common misconceptions

Updated versions of this scheme of work will be available via a link from the Edexcel Mathematics Awards website (www.edexcel.com /mathsawards ).

This course can be taught as a stand-alone course.Alternatively it can be taught as an introduction to GCSE Mathematics, with differentiation extending the content from an Awards course into GCSE topics where possible. The links to the GCSE schemes of work are given for this reason. The level 2 course can also stand alongside GCSE Mathematics. The level 3 course can be used as an introduction to A(S) Mathematics, or even as a bridge between GCSE Mathematics and A(S) Mathematics.

This course can be supported by a range of resources. At the end of the document we have provided a table which can be populated with the resources and links of choice to support delivery.

Edexcel Awards in Algebra Scheme of work © Pearson Education Ltd 2012 1

http://www.edexcel.com/


The Edexcel Awardin Algebra

Level 2 (AAL20)

Scheme of work


Level 2 course overview

The table below shows an overview of modules in the Level 2 scheme of work.Teachers should be aware that the estimated teaching hours are approximate and should be used as a guideline only.

Module number Title Estimated teaching hours

1 Roles of symbols 32 Algebraic manipulation 63 Formulae 54 Linear equations 45 Graph sketching 56 Linear inequalities 47 Number sequences 48 Gradients of straight line graphs 69 Straight line graphs 410 Graphs for real-life situations 711 Simple quadratic functions 612 Distance-time and speed-time graphs 6

Total 60


Module 1 Time: 4 – 5 hours

Awards Tier: Level 2

Contents: Roles of symbols

1.1 Distinguish between the roles played by letter symbols in algebra using the correct notation

1.2 Distinguish in meaning between the words equation, formula and expression1.3 Write an expression to represent a situation in ‘real life’

GCSE SPECIFICATION REFERENCESA a Distinguish the different roles played by letter symbols in algebra, using the

correct notationA b Distinguish in meaning between the words ‘equation’, ‘formula’, and

‘expression’A c Manipulate algebraic expressions by collecting like terms, by multiplying a

single term over a bracket, and by taking out common factors, multiplying two linear expressions, factorise quadratic expressions including the difference of two squares and simplify rational expressions

PRIOR KNOWLEDGEExperience of using a letter to represent a numberAbility to use negative numbers with the four operationsRecall and use BIDMASWriting simple rules algebraically

OBJECTIVESBy the end of the module the student should be able to:Edexcel Awards in Algebra Scheme of work © Pearson Education Ltd 2012 5

Use notation and symbols correctly Write an expression Select an expression/equation/formula from a list

LINKS TO LEVEL 3 (extension work)Module 1 Roles of symbols

LINKS TO GCSE SCHEME OF WORK (2-year)A/Module 4 B/Module 2-8


DIFFERENTIATION & EXTENSIONThis topic can be used as a reminder of the KS3 curriculum and could be introduced via investigative material, eg frogs, handshakes, patterns in real life, formulae Use examples where generalisation skills are requiredExtend the above ideas to the equation of the straight line, y = mx + c

Look at word formulae written in symbolic form, eg F = 2C + 30 to convert temperature (roughly) and compare with F = C + 32

NOTESEmphasise good use of notation, eg 3n means 3 × nPresent all working clearly




Contents: Algebraic manipulation

2.1 Collect like terms2.2 Multiply a single term over a bracket2.3 Factorise algebraic expressions by taking out all common factors2.4 Use index laws for multiplication, division and raising a power to a power

GCSE SPECIFICATION REFERENCESA c Manipulate algebraic expressions by collecting like terms, by multiplying a

single term over a bracket, and by taking out common factors, multiplying two linear expressions, factorise quadratic expressions including the difference of two squares and simplify rational expressions

A c Simplify expressions using rules of indices

PRIOR KNOWLEDGEAbility to use negative numbers with the four operationsRecall and use BIDMAS

OBJECTIVESBy the end of the module the student should be able to:

Recall and manipulate algebraic expressions by collecting like terms Multiply a single term over a bracket Simplify expressions using index laws Use index laws for integer powers and powers of a power Factorise algebraic expressions by taking out common factors


LINKS TO LEVEL 3 (extension work)Module 2 Algebraic manipulation

LINKS TO GCSE SCHEME OF WORK (2-year)A/module 4 B/module 2-9, 3-5

DIFFERENTIATION & EXTENSIONPractise factorisation where the factor may involve more than one variable

NOTESAvoid oversimplificationEnsure cancelling is only done when possible (particularly in algebraic fractions work)




Contents: Formulae

3.1 Substitute numbers into a formula3.2 Change the subject of a formula where the subject only appears once

GCSE SPECIFICATION REFERENCESA f Derive a formula, substitute numbers into a formula and change the subject of

a formula

PRIOR KNOWLEDGEExperience of using a letter to represent a numberAbility to use negative numbers with the four operationsRecall and use BIDMAS


Derive a formula Use formulae from mathematics and other subjects Substitute numbers into a formula Substitute positive and negative numbers into expressions such as 3x2 + 4 and 2x3

Change the subject of a formula where the subject only appears once

LINKS TO LEVEL 3 (extension work)Module 3 Formulae



DIFFERENTIATION & EXTENSIONConsider more complex expressionsChanging the subject of a formula including cases where the subject is on both sides of the original formula or where a power of the subject appears

NOTESBreak down any manipulation into simple steps all clearly shown




Contents: Linear equations

4.1 Solve linear equations with integer coefficients where the variable appears oneither side or on both sides of the equation

4.2 Solve linear equations which include brackets, those that have negative signs occurring anywhere in the equation, those with negative and fractional solutions and those with fractional coefficients

GCSE SPECIFICATION REFERENCESA d Set up and solve simple equations

PRIOR KNOWLEDGEExperience of finding missing numbers in calculationsThe idea that some operations are the reverse of each otherAn understanding of balancingExperience of using letters to represent quantitiesUnderstand and recall BIDMAS


Set up linear equations from word problems Solve simple linear equations Solve linear equations, with integer coefficients, in which the unknown variable appears on either side or on both sides of the equation Solve linear equations that include brackets, those that have negative signs occurring anywhere in the equation and those with a

negative and fractional solution


Solve linear equations in one unknown with fractional coefficients

LINKS TO LEVEL 3 (extension work)No direct link

LINKS TO GCSE SCHEME OF WORK (2-year)A/module 14 B/module 3-6

DIFFERENTIATION & EXTENSIONUse negative numbers in formulae involving indicesUse investigations to lead to generalisationsApply changing the subject to y = mx + cDerive equations from practical situations (such as finding unknown angles in polygons or perimeter problems)NOTESEmphasise good use of notation, eg 3ab means 3 × a × bStudents need to be clear on the meanings of the words expression, equation, formula and identityRemind students 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 importantStudents can leave their answers in fractional form where appropriate




Contents: Graph sketching

5.1 Sketch graphs of quadratic functions, considering orientation and labelling the point of intersection with the y-axis, considering what happens to y for large positive and negative values of x

GCSE SPECIFICATION REFERENCESA t Generate points and plot graphs of simple quadratic functions, and use these to

find approximate solutions

PRIOR KNOWLEDGERecognising quadratic graphs as parabolasThe link between linear equations as graphs and intersection with the y-axisSubstitution into quadratic expressionsFour rules of negative numbers


Understand the form of a quadratic function Understand the relationship between a quadratic function and its graph Sketch graphs for simple quadratic functions Understand what happens to function values when values of x get large

LINKS TO LEVEL 3 (extension work)Module 10 Graphs of functions



DIFFERENTIATION & EXTENSIONSketch graphs for reciprocal or exponential functions

NOTESBuild up the algebraic techniques slowlyLink the graphical solutions with quadratic graphs and changing the subject and use practical examples, eg projectilesUse of graph-plotting software would enhance investigation of graphs




Contents: Linear inequalities

6.1 Show inequalities on a number line, using solid circles to show inclusive inequalities and open circles to show exclusive inequalities

6.2 Write down an inequality shown on a number line6.3 Solve simple linear inequalities in one variable

GCSE SPECIFICATION REFERENCESA g Solve linear inequalities in one variable, and represent the solution set on a

number line

PRIOR KNOWLEDGEExperience of finding missing numbers in calculationsThe idea that some operations are the reverse of each otherAn understanding of balancingExperience of using letters to represent quantitiesUnderstand and recall BIDMASOrdering numbersKnowledge of inequality signs <, >, ≤, ≥



Solve simple linear inequalities in one variable and represent the solution set on anumber line

Use the correct notation to show inclusive and exclusive inequalities

LINKS TO LEVEL 3 (extension work)Module 7 Inequalities


DIFFERENTIATION & EXTENSIONDerive inequalities from practical situations (such as finding unknown angles in polygons or perimeter problems)

NOTESStudents can leave their answers in fractional form where appropriate




Contents: Number sequences

7.1 Generate terms of a sequence using term-to-term definition or using position-to-term definition

7.2 Find and use the nth term of a linear arithmetic sequence

GCSE SPECIFICATION REFERENCESA i Generate terms of a sequence using term-to-term and position-to-term

definitions of the sequenceA j Use linear expressions to describe the nth term of an arithmetic sequence

PRIOR KNOWLEDGEExperience of using a letter to represent a numberRecall and use BIDMASRecognise simple number patterns, eg 1, 3, 5Writing simple rules algebraically


Generate simple sequences of numbers, squared integers and sequences derived from diagrams

Describe the term-to-term definition of a sequence in words Identify which terms cannot be in a sequence Generate specific terms in a sequence using the position-to-term and

term-to-term rules


Find and use the nth term of a linear arithmetic sequence

LINKS TO LEVEL 3 (extension work)Module 8 Arithmetic series


DIFFERENTIATION & EXTENSIONSequences and nth term formula for triangle numbers, Fibonacci numbers etcProve a sequence cannot have odd numbers for all values of nExtend to quadratic sequences whose nth term is an2 + bn + c


NOTESEmphasise good use of notation, eg 3n means 3 × nWhen 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




Contents: Gradients of straight lines

8.1 Find the gradient of a straight line graph8.2 Interpret the gradient of real-life graphs

GCSE SPECIFICATION REFERENCESA l Recognise and plot equations that correspond to straight-line graphs in the

coordinate plane, including finding gradientsA m Understand that the form y = mx + c represents a straight line and that m is

the gradient of the line and c is the value of the y-interceptA n Understand the gradients of parallel linesA s Interpret graphs of linear functions

PRIOR KNOWLEDGESubstitute positive and negative numbers into algebraic expressionsRearrange to change the subject of a formula


Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane Find the gradient of a straight line from a graph Analyse problems and use gradients to interpret how one variable changes in relation to another Interpret and analyse a straight-line graph Understand that the form y = mx + c represents a straight line


Find the gradient of a straight line from its equation Use the fact that when y = mx + c is the equation of a straight line then the gradient of a line parallel to it will have a gradient of m

LINKS TO LEVEL 3 (extension work)Module 9 Coordinate geometry



DIFFERENTIATION & EXTENSIONUse a spreadsheet to generate straight-line graphs, posing questions about the gradient of linesUse a graphical calculator or graphical ICT package to draw straight-line graphsStudents should explore lines that are not only parallel, but also perpendicular to given lines

NOTESCareful annotation should be encouraged; Students should label the coordinate axes and origin and write the equation of the lineStudents need to recognise linear graphs and hence when data may be incorrectLink to graphs and relationships in other subject areas, eg science, geographyLink conversion graphs to converting metric and imperial units




Contents: Straight line graphs

9.1 Recognise, plot and draw graphs of the form y = mx + c9.2 Given a straight line graph, find its equation


coordinate plane, including finding gradientsA m Understand that the form y = mx + c represents a straight line and that m is

the gradient of the line and c is the value of the y-interceptA s Interpret graphs of linear functions

PRIOR KNOWLEDGESubstitute positive and negative numbers into algebraic expressionsRearrange to change the subject of a formula


Draw, label and scale axes Recognise that equations of the form y = mx + c correspond to straight-line graphs in the coordinate plane Plot and draw graphs of straight lines with equations of the form y = mx + c Understand that the form y = mx + c represents a straight line Find the equation of a straight line from its graph

LINKS TO LEVEL 3 (extension work)Edexcel Awards in Algebra Scheme of work © Pearson Education Ltd 2012 24

Module 9 Coordinate geometry


DIFFERENTIATION & EXTENSIONStudents should find the equation of the line through two given pointsStudents should find the equation of the perpendicular bisector of the line segment joining two given pointsUse a graphical calculator or graphical ICT package to draw straight-line graphs


NOTESCareful annotation should be encouraged; students should label the coordinate axes and origin and write the equation of the lineStudents need to recognise linear graphs and hence when data may be incorrectLink to graphs and relationships in other subject areas, eg science, geography




Contents: Graphs for real-life situations

10.1 Understand that straight and curved graphs can represent real-life situations10.2 Draw, and interpret information from graphs of real-life situations


coordinate plane, including finding gradientsA r Construct linear functions from real-life problems and plot their corresponding

graphsA s Interpret graphs of linear functions

PRIOR KNOWLEDGEScaling and labelling graphsDrawing graphs from tabular informationWork out points for plotting from conversion or foreign currency rates


Draw and interpret straight-line graphs for real-life situations such as:– Ready reckoner graphs– Conversion graphs– Fuel bills, eg gas and electric– Fixed charge (standing charge) and cost per unit


Analyse problems and use gradients to interpret how one variable changes in relation to another

Interpret and analyse a straight-line graph

LINKS TO LEVEL 3 (extension work)None



DIFFERENTIATION & EXTENSIONUse Functional Elements in terms of mobile phone billsUse a spreadsheet to generate straight-line graphs, posing questions about the gradient of linesUse a graphical calculator or graphical ICT package to draw straight-line graphsLink to scatter graphs and correlation

NOTESCareful annotation should be encouraged; students should label the coordinate axes and origin and write the equation of the lineStudents need to recognise linear graphs and hence when data may be incorrectLink to graphs and relationships in other subject areas, eg science, geographyLink conversion graphs to converting metric and imperial units




Contents: Simple quadratic functions

11.1 Plot graphs of simple quadratic functions11.2 Find approximate solutions of a quadratic equation from the graph of the

corresponding quadratic function

GCSE SPECIFICATION REFERENCESA e Solve quadratic equationsA r Construct linear, quadratic and other functions from real-life problems and

plot their corresponding graphsA t Generate points and plot graphs of simple quadratic functions, and use

these to find approximate solutions

PRIOR KNOWLEDGEAn introduction to algebra Substitution into expressions/formulaeLinear functions and graphsSolving equations


Generate points and plot graphs of simple quadratic functions, then more general quadratic functions Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function


LINKS TO LEVEL 3 (extension work)Module 10 Graphs of functions


DIFFERENTIATION & EXTENSIONUse graphical calculators or ICT graph package where appropriateDraw graphs of reciprocal or exponential functions


NOTESBuild up the algebraic techniques slowlyLink the graphical solutions with linear graphs and changing the subject and use practical examples, eg projectilesEmphasise that inaccurate graphs could lead to inaccurate solutions; encourage substitution of answers to check they are correctIn problem-solving, one of the solutions to a quadratic equation may not be appropriate




Contents: Distance-time and speed-time graphs

12.1 Draw distance-time graphs and speed-time graphs12.2 Interpret distance-time graphs and speed-time graphs12.3 Understand that the gradient of a distance-time graph represents speed12.4 Find speed and distance from information on a travel graph

GCSE SPECIFICATION REFERENCESA r Construct linear functions from real-life problems and plot their corresponding

graphsA s Interpret graphs of linear functions

PRIOR KNOWLEDGEA basic understanding of speedInterpret the slope of a graph as its gradientInterpret the gradient within a real life context


Draw distance-time and speed-time graphs Interpret distance-time and speed-time graphs Understand that the gradient of a distance-time graph represents speed Calculate speed using distance-time graphs


LINKS TO LEVEL 3 (extension work)Module 12 Distance-time and speed-time graphs


DIFFERENTIATION & EXTENSIONDraw distance-time graphs of journeys of several stagesConsider the link between distance-time and speed-time graphs


NOTESConsider the importance of understanding zero gradient in both types of graphUse of different scales in accurate reading and drawing of graphsAccuracy of plotting is importantCalculating the gradient from given information regarding speed and/or acceleration is worth practising


Level 2 concepts and skillsWhat students need to learn:

Topic Concepts and skills1. Roles of symbols 1. Distinguish between the roles played by letter

symbols in algebra using the correct notation2. Distinguish in meaning between the words

equation, formula and expression3. Write an expression to represent a situation in ‘real

life’2. Algebraic manipulation 1. Collect like terms

2. Multiply a single term over a bracket3. Factorise algebraic expressions by taking out all

common factors4. Use index laws for multiplication, division and

raising a power to a power3. Formulae 1. Substitute numbers into a formula

2. Change the subject of a formula where the subject only appears once

4. Linear equations 1. Solve linear equations with integer coefficients where the variable appears on either side or on both sides of the equation

2. Solve linear equations which include brackets, those that have negative signs occurring anywhere in the equation, those with negative and fractional solutions and those with fractional coefficients

5. Graph sketching 1. Sketch graphs of quadratic functions, considering orientation and labelling the point of intersection with the y-axis, considering what happens to y for large positive and negative values of x


6. Linear inequalities 1. Show inequalities on a number line, using solid circles to show inclusive inequalities and open circles to show exclusive inequalities

2. Write down an inequality shown on a number line3. Solve simple linear inequalities in one variable

7. Number sequences 1. Generate terms of a sequence using term-to-term definition or using position-to-term definition

2. Find and use the nth term of a linear arithmetic sequence

8. Gradients of straight linegraphs

1. Find the gradient of a straight line graph2. Interpret the gradient of real-life graphs

9. Straight line graphs 1. Recognise, plot and draw graphs of the form y = mx + c

2. Given a straight line graph, find its equation 10. Graphs for real-life

situations1. Understand that straight and curved graphs can

represent real-life situations2. Draw, and interpret information from graphs of

real-life situations11. Simple quadratic functions 1. Plot graphs of simple quadratic functions

2. Find approximate solutions of a quadratic equation from the graph of the corresponding quadratic function

12. Distance-time and speed-time graphs

1. Draw distance-time graphs and speed-time graphs2. Interpret distance-time graphs and speed-time

graphs3. Understand that the gradient of a distance-time

graph represents speed4. Find speed and distance from information on a

travel graph


Resources TableLevel 2

Module number Title Resources Web resources

1 Roles of symbols

2 Algebraic manipulation

3 Formulae

4 Linear equations

5 Graph sketching

6 Linear inequalities

7 Number sequences

8 Gradients of straight line graphs

9 Straight line graphs

10 Graphs for real-life situations

11 Simple quadratic functions

12 Distance-time and speed-time graphs


Edexcel, a Pearson company, is the UK’s largest awarding body, offering academic and vocational qualifications and testing to more than 25,000 schools, colleges, employers and other places of learning in the UK and in over 100 countries worldwide. Qualifications include GCSE, AS and A Level, NVQ and our BTEC suite of vocational qualifications from entry level to BTEC Level 2 National Diplomas, recognised by employers and Level 2 education institutions worldwide.We deliver 9.4 million exam scripts each year, with more than 90% of exam papers marked onscreen annually. As part of Pearson, Edexcel continues to invest in cutting-edge technology that has revolutionised the examinations and assessment system. This includes the ability to provide detailed performance data to teachers and students which help to raise attainment.

AcknowledgementsThis document has been produced by Edexcel on the basis of consultation with teachers, examiners, consultants and other interested parties. Edexcel would like to thank all those who contributed their time and expertise to its development.

References to third-party material made in this document are made in good faith. Edexcel does not endorse, approve or accept responsibility for the content of materials, which may be subject to change, or any opinions expressed therein. (Material may include textbooks, journals, magazines and other publications and websites.)

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Scheme of Work - Level 2 Award and Level 3 Award in ... · Web viewTitle Scheme of Work - Level 2 Award and Level 3 Award in Algebra - Word version Author cummingg Last modified by