programme of study - year 10 and 11 - intermediate ... · web viewidentify the parts of a circle...

Year 10

AUTUMN TERM A TOPIC 1

Topic: Integers and Powers Target Grade: E/D/C

Edexcel Content:NA2a: Understanding place value in whole numbersNA3a: Long multiplication and long division without using a calculatorNA3a: 4-rules using negative numbersNA2a: Rounding off to a given power of tenNA2b: Use the terms square, positive square root, negative square root, cube and cube rootNA3b: Use brackets and the hierarchy of operationsNA3a: Find the prime factor decomposition of positive integers Prior Knowledge:Knowledge of times tables and strategies for multiplying and dividing whole numbers by 10.

Learning Objectives:Write integers in words and digits Do long multiplication and long division without using a calculatorWork confidently without the aid of a calculator, including the four rules with negative

numbersEstimating answers by rounding to 1 significant figureUse the terms square, positive square root, negative square root, cube and cube rootUse BIDMAS to work out answersUse prime factor decomposition to find the HCF of integers. Find the LCM using

multiples.

Differentiation & Extension:Non-calculator maths: 3 (or more) digit numbers multiplied/divided by 3 (or more) digit numbers.Use prime factors to find LCM.

Notes:All of this topic should be revision, but these are things that need to be revised regularly.All working should be presented clearly.Non-calculator methods should show remainders and carries as evidence.London Reference:Book 1 Chapter 1 p.1 - 12

Other references:

Discussion opportunities:Which is the best method for long multiplication/division? Show various methods and let the students decide.Pair / Group Work:Students could write non-calculator questions (or a mental test) for a partner to answer.Factors/multiple board game in pairs.ICT Links:www.bbc.co.uk - for Mental arithmetic practice (see ICT folder).Investigation:Investigate why the grid method works for long multiplication.When you multiply a number does it always increase?Spiritual, Moral, Citizenship and Literacy links:Numbers can be positive or negative – so can humans.Writing numbers in words helps literacy.Time: 6 - 7 lessons


Topic: Fractions and Decimals Target Grade: E/D/C/B

Edexcel Content:NA2c: Using diagrams to find equivalent fractionsNA2c: Cancelling fractionsNA3d: Interchanging improper fractions and mixed numbersNA2d & NA3c: Interchanging fractions and decimals and using recurring decimalsNA2c: Ordering fractions using common denominatorsNA3c: Adding and subtracting fractions using common denominatorsNA3d: Multiplying and dividing fractionsNA3d: Using fractions in problems involving multiplication and divisionNA3c: Calculating a fraction of a quantityNA3c: Writing a given number as a fraction of another NA3a: Place value, multiplication and division of decimal numbers by powers of ten

Prior Knowledge:A basic understanding of fractions as being ‘parts of a whole unit’.Use of a calculator with fractions.Learning Objectives:

Equate one fraction with another, and simplify fractions to their lowest terms Understand and change between improper fractions and mixed numbers Perform the four basic operations with fractions

Place value, multiplication and division of decimal numbers by powers of ten Put decimals in order of size Multiply and divide decimals Convert fractions into decimals and vice-versa, including recurring decimals Order decimals and fractions

Differentiation & Extension:Mental maths problems with negative powers of 10, e.g. 2.5 x 0.01, 0.001.Relating the basic fractions to readily remembered percentages and vice-versa.For very able students cancelling down of algebraic expressions could be considered.Notes:Constant revision of this topic is needed. All work needs to be presented clearly with the relevant stages of working shown.London Reference:Book 1 Chapter 2 p.13 - 24

Other references:

Discussion opportunities:Why does the division rule work?Pair / Group Work:Students could write questions for a partner to solve. Revision can be done as some kind of group quiz.Domino/Bingo/Snap games – match equivalent fractionsICT Links:Calculator Tennis (see ICT folder, Graphical Calculator section) to understand multiplying and dividing by numbers between 0 and 1.Calculators can be used to check answers. Number Foundations (Outware Education on laptop).Investigation:Some four rules work (e.g. division) could be approached investigatively.Patterns with Fractions.Spiritual, Moral, Citizenship and Literacy links:What fraction of the House of Commons does each political party occupy? Fractions can be equivalent, simplified, improper and mixed – can humans?Time: 8 - 9 lessons


Topic: Percentages Target Grade: E/D/C

Edexcel Content:NA2e: Understanding percentagesNA3e: Interchanging between percentages, fractions and decimalsNA3j: Finding percentages, and percentage changesNA3j: Calculating percentage profit or loss

Prior Knowledge:Topic 2.

Learning Objectives: Change between percentages, fractions and decimals

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

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

Differentiation & Extension:Include percentages with recurring decimals (e.g. 33 %), and percentages over 100%Combine multipliers to simplify a series of percentage changes.

Notes:Amounts of money should be rounded to the nearest penny (but only at the end of the question).Working out should always be shown.

London Reference:Book 1 Chapter 3 p.27 - 33

Other references:

Discussion opportunities:Plenty of opportunity, especially when dealing with real-life situations.

Pair / Group Work:Domino/Bingo/Snap games – match equivalent fractions, decimals and percentages.

ICT Links:Use of Excel for budgeting.

Investigation:VAT, credit, interest, mortgages – the students can research all these applications of percentages.

Spiritual, Moral, Citizenship and Literacy links:How much should we be taxed? Facts relating to the third world often involve percentages.What percentage of 18 year olds voted in the last general election? Discuss.

Time: 4 - 5 lessons


Topic: Coordinates and the Elements of Algebra

Target Grade: E/D/C/B

Edexcel Content:NA6b: Plot points in all four quadrantsNA5a: Using letters to represent numbersNA5b: Collecting like termsNA5b: Removing a single pair of brackets NA5b: Multiplying with letters and numbersNA5b: Factorising with a single pair of bracketsNA5g: Using word formulaeNA5g: Using algebraic formulaeNA5d: Substituting into expressions involving squares or cubes

Prior Knowledge:Negative numbers and indices. Experience of using a letter to represent a number.

Learning Objectives:

Plot coordinates in all four quadrants

Differentiation & Extension:Further work on simplifying, e.g. three variablesFactorising with three or more termsSubstitution into more difficult formulae (Algebra crossword)

Notes:Emphasise the need to show working out and correct use of symbolic notation (e.g. 3x rather than 3 x x). Encourage students to check their factorising by expanding the brackets.

London Reference:Book 1 Chapter 4 p.34 – 40

Other references:

Discussion opportunities:What is the point of coordinates and algebra? Discuss real life examples.

Pair / Group Work:Battleship – to practice coordinatesDomino/Bingo/Snap games – match expressions with their factorised equivalentAlgebra crosswordICT Links:Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.Autograph or graphics calculators could be used to show the equivalence of expressions.Excel work on substitution (see ICT folder)Investigation:Beyond Pythagoras involves a lot of rearranging equations, as does Opposite Corners.Factorisation could be approached investigatively.Spiritual, Moral, Citizenship and Literacy links:Literacy: It is important to arrange variables in alphabetical order e.g. ‘abc’ rather than ‘cab’Time: 5 - 6 lessons

AUTUMN TERM B TOPIC 5

Topic: Algebraic Equations Target Grade: E/D/C/B

Edexcel Content:NA5f: Inverse operationsNA5e: Simple linear equationsNA5e: Equations combining operationsNA5f: Solving equations with the unknown on both sidesNA5f: Solving equations with brackets and negative solutionsNA5e: Set up simple equationsNA5e: Using algebraic equations to solve problemsNA5f: Linear equations with fractional coefficientsNA5e: Solve equations with the unknown as the denominator

Prior Knowledge:Topic 4. An understanding of balancing methods. Squares and square roots.

Learning Objectives: Solve equations using inverse operations.

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

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

Differentiation & Extension:The work can be extended to include more complex algebraic manipulation and equations.

Notes:Students need to realise that not all linear equations can easily be solved by observation or trial and improvement, so use of a formal method is vital. Answers can be left as fractions where appropriate.London Reference:Book 1 Chapter 5 p.41 - 51

Other references:

Discussion opportunities:Discuss the ‘best’ way to solve an equation.Why do quadratic equations have two solutions (usually)?Pair / Group Work:Equation loop cards could be played as a class. Equation dominoes could be played in groups.

ICT Links:Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.

Investigation:Investigate the history of algebra.

Spiritual, Moral, Citizenship and Literacy links:How can equations be used to solve real life problems?

Time: 6 - 7 lessons


Topic: Sequences Target Grade: E/D/C/B

Edexcel Content:NA6a: Extending diagrammatic sequencesNA6a: Extending number sequencesNA6a: Generating common number sequencesNA6a: Finding the nth term (linear expressions)

Prior Knowledge:The ability to follow a series of instructions and appreciate that symbols can represent numbers.

Learning Objectives: Continue linear and non-linear sequences of numbers and find term to term rules

Find and use the nth term for linear sequences

Continue sequences of shapes and find associated rules

Differentiation & Extension:Try to emphasise the difference between a term-to-term rule and a position-to-term rule.Recurrance sequences e.g. Fibonacci (especially if you are planning to do the Flagging coursework). Pascal’s triangle.

Notes:Try to emphasise the difference between a term-to-term rule and a position-to-term rule.


Other references:

Discussion opportunities:Describe in words what is happening in each sequence. What is the best way to represent this in algebra?Pair / Group Work:Some pattern spotting could be done in pairs. Students could make up sequences for a partner to find the rule.ICT Links:Use of Excel to generate sequences (see ICT folder). Powerpoint – students put each number in their own sequence on a different slide (see ICT folder).Graphics calculatorsInvestigation:You could bring in some short investigations which lead to simple number sequences – see Rayner p.48-51Flagging and The Pay Phone Problem involve recurrence sequences.

Spiritual, Moral, Citizenship and Literacy links:Fibonacci’s “Golden Ratio”.The numbers in sequences all follow the same rule – this is an excellent example of teamwork.

Time: 4 - 5 lessons


Topic: Properties of Shapes Target Grade: E/D/C

Edexcel Content:SSM2d: Angles of regular polygonsSSM2b: Angle properties of trianglesSSM2c: Classify quadrilaterals by their geometric propertiesSSM2h: Definition of a circle and the meaning of related terms

Prior Knowledge:Experience of measuring and drawing angles with a protractor.

Learning Objectives: Name polygons with up to ten sides

Understand the names and properties of triangles Understand the names and properties of quadrilaterals Identify the parts of a circle and its properties

Differentiation & Extension:Inscribe regular polygons in circles

Notes:Emphasise the need for accurate drawings using a pencil and ruler (and protractor).

London Reference: Other references:

Book 1 Chapter 7 p.64 - 70

Discussion opportunities:“What is the largest angle you can have in a triangle?” – this should set off a lively debate.Encourage the use of proper vocabulary here, particularly with circles.

Pair / Group Work:Match up pictures of polygons with the description of their properties.

ICT Links:Cabri Geometry (see ICT folder)LOGO (see ICT folder).

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

Spiritual, Moral, Citizenship and Literacy links:Literacy: Use a dictionary to look up the terms used to describe polygons.

Time: 3 - 4 lessons

Note: If students are unsure how to complete an investigation, use Edexcel Int.(new) chapter 9A to introduce the coursework.

COURSEWORK 1: Choose a task from the Edexcel coursework folder (in the maths staff room)All groups will do this piece at the same time.Time: 2 weeks + half term.

SPRING TERM A TOPIC 8

Topic: Line and Rotational Symmetry

Target Grade: E/D/C

Edexcel Content:SSM3a: Specifying transformationsSSM3b: Line symmetrySSM3b: Rotational symmetrySSM3b: Planes of symmetrySSM3b: Transforming 2D shapes by reflection, rotation and translation

Prior Knowledge:Co-ordinates, sketching 3D shapes, angles.


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

Sketch planes of symmetry on 3D shapesReflect a 2D shape in a vertical, horizontal or diagonal line and state the equation of the

line.Rotate a 2D shape about the origin or a point other than the origin, stating the angle,

direction and centre of rotation.Translate a 2D shape using a vector

Differentiation & Extension:Attempt to draw up to 3 shapes each which have exactly 1, 2, 3, …8 lines of symmetry.Mirrors could be used to make the topic easier.

Notes:Emphasise the need for accurate drawings using a pencil and ruler (and protractor).Students can lose marks in their GSCE for neglecting to mention one part of a transformation, e.g. the centre of rotation.London Reference:Book 1 Chapter 8 p.71 - 83

Other references:

Discussion opportunities:What real life objects in the classroom are symmetrical?Discuss how to find the centre of a rotation.

Pair / Group Work:Display work could be done in groups or pairs.The ICT work below could be done in pairs.

ICT Links:Geometry Transformations (Outware Education) on department laptop. Powerpoint presentation on laptop. Cabri Geometry (see ICT folder).Transformation Golf on the internet – www.mymaths.co.uk/lessonplans/transformations/golf.aspInvestigation:Investigation into different ways of transforming an object onto a particular image.

Spiritual, Moral, Citizenship and Literacy links:Many wonderful works of art are symmetrical.

Time: 5 - 6 lessons


Topic: Angles, Constructions and Bearings

Target Grade: E/D/C

Edexcel Content:SSM4b: Draw approximate constructions of triangles and other 2D shapesSSM4b: Construct specified 3D shapesSSM2a: Use parallel lines, alternate and corresponding anglesSSM2d: Calculate and use the angles of regular polygonsSSM4a: Use bearings to specify direction

Prior Knowledge:Estimating angles, use of a protractor.

Learning Objectives:Construct triangles and other 2D shapesUse nets to construct 3D shapes

Calculate angles on parallel lines, and a point and on a straight lineCalculate the angle sum of a polygon and the interior and exterior angles of a regular

polygonDraw and measure three figure bearings accurately

Differentiation & Extension:Find all possible nets of a cube.Draw shapes made from multi-link on isometric paper.Build shapes from cubes, which are represented in 2D.

Notes:Students are often confused about the position from where a bearing is measured. Emphasise the fact that bearings are given in three figures.


Other references:

Discussion opportunities:Which nets will work? Discuss why or why not.Where are bearings used in real life? Why use three digits e.g. 045º ?Pair / Group Work:Could use multi-link cubes in pairs or groups.

ICT Links:Cabri Geometry (see ICT folder). LOGO (see ICT folder).Powerpoint presentation on angles in polygons (on laptop).

Investigation:Angles in polygons could be approached investigatively, as could the work on nets

Spiritual, Moral, Citizenship and Literacy links:People can be described as 2-dimensional or 3-dimensional. Is there such a thing as the 4th dimension?Time: 6 – 7 lessons


Topic: Handling Data Target Grade: E/D

Edexcel Content:HD3a: Collect data using various methodsHD3b: Gather data from secondary sourcesHD3c: Design and use two-way tables for discrete and grouped dataHD3d: Deal with practical problems such as non-response or missing data

Prior Knowledge:An understanding of why data needs to be collected. Simple inequalities (for grouped tables)

Learning Objectives:Understand the difference between primary and secondary dataDesign a simple questionnaire and appreciate deficiencies in a question.Undertake steps to eliminate bias.Sort and collect data in a tally table and grouped frequency table.Design and use two-way tables.

Differentiation & Extension:Stratified random sampling could be introduced here as it is important in the Data Handling coursework.You could use data from newspapers, censusatschool, class experiments (reaction times) etc.

Notes:This chapter is quite straightforward and should be revision. Try to make it as practical as possible.London Reference:Book 1 Chapter 10 p.95 - 98

Other references:

Discussion opportunities:What makes a good questionnaire? Discuss bias in questionnaires.

Pair / Group Work:Questionnaires can be done in pairs and then presented to a group or the whole class for constructive criticism.

ICT Links:Excel – collect data in tables and draw different types of graphs.www.censusatschool.co.uk - provides interesting raw data to take samples from and analyse

Investigation:Students could carry out a statistical investigation of their own, including designing an appropriate means of gathering the data.

Spiritual, Moral, Citizenship and Literacy links:When conducting a survey everyone must be included, regardless of race, religion, wealth etcThink about the rights and responsibilities of consumers, employers and employees.Literacy: Questionnaires must be easy to follow and well written.

Time: 3 - 4 lessons


Topic: Probability Target Grade: E/D/C

Edexcel Content:HD4c: Listing systematically outcomes for single events or two successive eventsHD4c,d: Writing probability as numbersHD4d: Equally likely and mutually exclusive eventsHD4d: The probability of an event not happeningHD4d: Using the sum of probabilities equalling 1HD4b: Predicting outcomes using simple probabilitiesHD4b: Estimating probability by experimenting

Prior Knowledge:Experience of using the language of likelihood.Knowledge of a probability scale from 0 to 1, including impossible and certain events.Decimals and Fractions.Learning Objectives:

Write down the theoretical probabilities of a single event happening Establish the estimated probability of an event happening Find the probability of an event not happening given the probability of an event happening

Predict how many times an event may happen given the probability Understand the concepts of exclusivity and independence

List outcomes of one or two events

Differentiation & Extension:The work can be extended to include that of the higher syllabus.Use of notation such as P(not n) = 1 – P(n).Notes:Most of this should be revision. It is a good opportunity for practical work.


Other references:

Discussion opportunities:Which games are fair/unfair? Why?Pair / Group Work:Any practical work can be done in pairs.ICT Links:See the Probability section in the ICT folder.Powerpoint presentations on probability (laptop)Investigation:You can test theoretical probabilities experimentally, encouraging students to develop their own experiments.Spiritual, Moral, Citizenship and Literacy links:Gambling – right or wrong?Time: 4 - 5 lessons

SPRING TERM B:

REVISION FOR GCSE MODULAR EXAMINATION (PAPER 9)Revise individual topics and Examination papers (there is a practice paper at the back of the textbook)Note: Try to begin book 2 before Easter if you have time

SUMMER TERM A TOPIC 12

Topic: Working with Number Target Grade: E/D/C/B

Edexcel Content:NA3h: Approximation to decimal places and significant figuresNA4b: Use of rounding to one significant figure for checking answersNA4b: Recognising limitations on the accuracy of measurements NA2f: Basic ideas of ratioNA2f: Simplifying ratiosNA2f: Relating ratio form to fractionsNA3f: Dividing in a given ratio

Prior Knowledge:Understanding place value in whole numbers and decimals. Fractions.

Learning Objectives: Round to a number of decimal places Round to a number of significant figures

Select an appropriate degree of accuracy for answers Understand and simplify ratios Write ratios as fractions

Divide quantities in a given ratio

Differentiation & Extension:Upper and lower bounds for decimals.Discuss appropriateness of types of rounding in particular contexts.

Notes:Some of this will be revision of Year 9 work. Only round off at the end of a calculation. Rounding will lead to a number of the same magnitude as the original answer.London Reference:Book 2 Chapter 1 p.1 - 9

Other references:

Discussion opportunities:Discussion of what degree of accuracy is appropriate in different situations.Why do we need to round numbers? Why use significant figures?Where are ratios used in life? (maps, recipes?)Pair / Group Work:Any map work could be done in pairs.

ICT Links:Number Foundations (Outware Education on laptop).Demonstration of Excel facilities for rounding off.Powerpoint presentations on laptopInvestigation:Investigate scales on maps.

Spiritual, Moral, Citizenship and Literacy links:Human beings can never be rounded off – every part of us is unique.

Time: 5 - 6 lessons


Topic: Indices and Calculators Target Grade: E/D/C/B

Edexcel Content:NA5d: Using indices in expressionsNA3o: Reading a calculator display to appropriate accuracyNA3o: Use a calculator efficiently for complex calculations NA5m: Solving equations by trial and improvementNA2b: Use standard index form, expressed in conventional notation on a calculator display

Prior Knowledge:BIDMAS, algebraic substitution, squares, cubes and roots.

Learning Objectives: Substitute numbers into algebraic expressions involving squares and cubes

Differentiation & Extension:Round large or small numbers to 1 sig. figure to make estimates in standard form e.g. distance between planets, speed of light.Use of graphics calculators to check answers to trial and improvement.

Notes:Students must remember to write ‘x 10’ before the power of 10 or they will get no marks on standard form.All stages of working must be shown for trial and improvement.


Other references:

Discussion opportunities:Students will already understand how to use many functions on their calculator. You could begin the topic by discussing what they already know.Why use standard form? Why can’t solutions to trial and improvement questions be found exactly?Pair / Group Work:Calculator Golf could be done in pairs to reinforce trial and improvement methods.

ICT Links:How do scientific/graphics calculators represent standard form?Distance of planets from sun can be looked up on the Internet.Use of graphics calculators or Autograph to check answers to trial and improvement.Excel for trial and improvement (see ICT folder).Investigation:Trial and improvement could be approached investigatively as could calculator methods.

Spiritual, Moral, Citizenship and Literacy links:Are GCSEs easier now, because of the use of calculators, compared to 50 years ago?

Time: 5 - 6 lessons


Topic: Graphs Target Grade: E/D/C/B

Edexcel Content:NA6b: Plotting graphs of functions where y is expressed in terms of x, leading to a straight lineNA6d: Plotting linear graphs from real-life problemsNA6d: Interpret graphs representing real-life situationsNA6e: Plotting the graph of a quadratic function

Prior Knowledge:The ability to plot points that follow a simple rule (in four quadrants).The ability to substitute values into algebraic formulae.


Plot a straight line graph from a linear equation Use a straight line graph to solve real-life problems

Interpret and sketch graphs of real-life situations

Differentiation & Extension:Currency graphs, e.g. Pounds to Euros, may help weaker students understand the importance of line graphs. Although not tested in this module, able students could be asked about the gradient and y-intercept of linear graphs and solutions of quadratic equations.Notes:Try to use ICT in this topic, especially graphics calculators and Autograph.London Reference:Book 2 Chapter 3 p.19 – 34

Other references:

Discussion opportunities:Real-life situations give opportunity for this.How can you tell which graph will match which equation?Pair / Group Work:ICT work could be done in pairs.Travel graphs can be introduced as a group activity.Currency exchange graphs could be worked out in pairs.Dominoes/Pairs – match graphs to their equations.ICT Links:Autograph – see ICT folder for good worksheets on introducing y = mx + c (also see Omnigraph section).Graphics calculators (see ICT folder).Investigation:Links with the Science department could yield many experiments that would give rise to straight line relationships.The shape of a quadratic graph could be approached investigatively.Drawing graphs may help to analyse the Open Box problem.Spiritual, Moral, Citizenship and Literacy links:Currency conversion could lead to a discussion on whether we should join the Euro.Quadratics can be “happy” or “sad”.Literacy: Look up the words linear and quadratic in the dictionary.Time: 6 - 7 lessons


Topic: Working with Algebra Target Grade: D/C/B

Edexcel Content:NA5b: Expanding brackets – the product of two linear expansions NA5b: Factorising of quadratic expressionsNA5g: Rearranging simple formulaeNA5j: Solving linear inequalities in two variables and represent the solution set on a number line

Prior Knowledge:Negative numbers and indices. Experience of using a letter to represent a number.


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

Factorise a quadratic, e.g. x2 – 5x + 6 = (x – 6)(x + 1).

Change the subject of formula

Display inequalities on a number line

Solve linear inequalities through both algebraic methods and listing possible integer values.

Differentiation & Extension:Further practice in rearranging formulae, including cases where the subject occurs more than once and formulae involving reciprocals of the subject. Vary the difficulty of quadratics to factorise. Difference of two squares.

Notes:Encourage students to check their factorising by expanding the brackets.


Other references:

Discussion opportunities:Which is the best method for expanding double brackets (FOIL, smiley face etc)? Show various methods and let the students decide.

Pair / Group Work:Domino/Bingo/Snap games – match expressions with their factorised equivalent

ICT Links:Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.Autograph or graphics calculators could be used to show that, for example, x2 – 5x + 6 is equivalent to (x – 6)(x + 1) or www.waldomaths.com.Investigation:Beyond Pythagoras involves a lot of rearranging equations, as does Opposite Corners.Try to find a method for factorising quadratics before being told.The difference of two squares could be approached investigatively.

Spiritual, Moral, Citizenship and Literacy links:Quadratics are used in mechanics (e.g. projectiles)

Time: 6 - 7 lessons

SUMMER TERM B TOPIC 16

Topic: Handling Data Target Grade: D/C/B

Edexcel Content:HD4a: Drawing pie chartsHD4a: Line graphs for discrete and continuous data, including time seriesHD4a: Frequency diagramsHD4a: Constructing and interpreting stem and leaf diagramsHD4b: Finding the mode, median, mean and range from simple dataHD4b: Selecting the most appropriate averageHD5d: Finding the mode from a discrete frequency table

HD4e: Calculate the mean from a discrete frequency tableHD4e: Mean and median for continuous dataHD5d: Modal class for continuous dataHD4f: Calculating a moving averageHD4a: Completing cumulative frequency tablesHD4a: Plotting cumulative frequency diagramsHD4e: Using cumulative frequency to find the median, quartiles and interquartile rangeHD4a: Box plotsHD5d: Comparing distributions using measures of range and spread

Prior Knowledge:Averages from a list of numbers, measuring and drawing angles, fractions of quantities, co-ordinates.Learning Objectives:

Differentiation & Extension:Collect data from class – children per family etc. Collect data from newspapers.Compare two cumulative frequency diagrams, comment on the differences between distributions.More able students could draw histograms with bars of various widths.Notes:Cumulative frequency – emphasise the use of the upper boundary, and of drawing a curve.Clearly label all axes on graphs and use a ruler to draw straight lines.London Reference:Book 2 Chapter 10 p.96 - 118

Other references:

Discussion opportunities:Why are there 3 types of average? Discuss occasions when one average is more appropriate, and the limitations of each average.What are the advantages and disadvantages of stem and leaf diagrams, box plots etc?Pair / Group Work:Any practical work or computer work can be done in pairs or groups.ICT Links:Autograph – especially useful for calculating averages, box plots, histograms & cumulative frequency graphs (many good worksheets). www.censusatschool.co.uk - many good worksheets on averages and has relevant raw data. StatsAid (Outware Education) on department laptop. Excel (see ICT folder).Investigation:Hypothesis testing e.g. Girls get higher effort grades than boysSpiritual, Moral, Citizenship and Literacy links:Is there an average person in Year 10? No-one is average – everyone is unique!Consider the uses of statistics in society.Is there any correlation between wealth and happiness?Time: 7 – 8 lessons

COURSEWORK 2 (Data Handling): NewspapersAll groups will do this piece at the same time.Time: 2 weeks + Year 10 study leave.

SUMMER TERM B TOPIC 17

Topic: Pythagoras and Trigonometry Target Grade: C/B

Edexcel Content:SSM2f: Using Pythagoras’ Theorem to find the HypotenuseSSM2f: Using Pythagoras’ Theorem to find the shorter sidesSSM2f: Using Pythagoras’ Theorem to solve problems

SSM2g: Tangent, sine and cosine ratiosSSM2g: Uses of the three ratios SSM2g: Angles of elevation and depressionSSM2g: Bearings and trigonometry

Prior Knowledge:Knowledge of different types of triangle. Using a calculator to find squares and square roots. Knowledge of simple bearings. Rounding to decimal places and significant figures. Basic concepts of ratio. Learning Objectives:

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

Identify appropriately the various sides of a right-angled triangle as the Hypotenuse, Opposite and Adjacent. Recall the ratios for sine, cosine and tangent.

Use the information given to find angles using the appropriate ratio.

Use the appropriate ratio to find the length 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.

Differentiation & Extension:Find Pythagorean triples.Proof of why Pythagoras’ theorem works (e.g. Perigal’s dissection is straightforward and practical)Does the theorem still work if you have equilateral triangles or regular pentagons on the sides (rather than squares)?3D Pythagoras and trigonometry. Sine and cosine rules (Higher syllabus).Given two properties of a right-angled triangle find the others.Notes:Encourage students to label the two sides involved in a trigonometry problem. Clearly show all stages of working.London Reference:Book 2 Chapter 5 p.46 - 62

Other references:

Discussion opportunities:Plenty of opportunity here, especially when solving problems and initial investigations. You can also get some interesting mnemonics for SOHCAHTOA.Where is trigonometry used in real life?Pair / Group Work:Some problems or initial investigations could be done in pairs. Later practical work (e.g. using a clinometer) could be done in groups. You could get the students to make their own Powerpoint presentations in groups.ICT Links:There are many Powerpoint presentations on Pythagoras and trigonometry (laptop). You could get students to make their own.Pythagorean Shoe Laces (see ICT folder, Excel section)The history of Pythagoras – research on the InternetInvestigation:Initial discoveries regarding ratios can be done investigatively.Beyond Pythagoras coursework task (investigating Pythagorean triples).The Fencing Problem requires trigonometry to reach higher levels (though it may be better to leave this until after the circles topic).Spiritual, Moral, Citizenship and Literacy links:Pythagoras’ theorem can be proved from simple axioms – so much in life requires faith rather than proof (religion, love etc). What was life like for Pythagoras?Time: 7 – 8 lessons

Year 11


Topic: Properties of Circles Target Grade: D/C/B

Edexcel Content:SSM2h: The tangent at any point on a circle is perpendicular to the radius at that pointSSM2h: Tangents from an external point are equal in lengthSSM4d: Circumferences of circles and areas enclosed by circles

Prior Knowledge:An understanding of perpendicular lines. The ability to label parts of a circle. Angle facts for polygons. Rounding answers to a degree of accuracy.

Learning Objectives:Understand what is meant by a tangent to a circle Use the properties of tangents to solve problems involving circlesRecall and apply the formulae for the area and circumference of a circle given either the

radius or diameter, using various approximations to or leaving as part of an irrational answer.

Find the area or perimeter of parts of a circle (halves or quarters).

Differentiation & Extension:Find the area or perimeter of sectors.

Notes:Circles could be on non-calculator paper – leave answers in terms of .You could get the students to discover the circle theorems themselves by LOCI or by the ICT links below.London Reference:Book 2 Chapter 6 p.63 - 68

Other references:

Discussion opportunities:What is ? How is it found?What constitutes a proof? Why do we need proofs in mathematics?

Pair / Group Work:On p.310 (Edexcel Int. (new)) there is a practical “proof” for the area of a circle, which could be done in pairs.Investigative work could be done in pairs.ICT Links:Research the history of on the Internet. Powerpoint presentations on laptop.Cabri Geometry.

Investigation:The Fencing Problem.LOCI questions may be used to discover circle theorems (see p.137 of Edexcel GCSE Higher (old edition).Spiritual, Moral, Citizenship and Literacy links: is a very special number and was even mentioned in the bible.Both pi and phi are discussed in ‘The DaVinci Code’, a best-seller by Dan BrownTime: 3 - 5 lessons


Topic: Translations, Enlargements and Scale Drawings


Edexcel Content:SSM3a: Translations specified by a vectorSSM3a: Enlargements specified by a centre and positive scale factorSSM3c: Recognise, visualise and construct enlargements of objectsSSM3d: Recognise that enlargements preserve angle but not lengthSSM3d: Identify the scale factor of an enlargementSSM3d: Use and interpret maps and scale drawings

Prior Knowledge:Co-ordinates, fractions, ratio, drawing angles with a protractor.

Learning Objectives:Recognise translations as sliding movements, and translate simple 2D shapes within a

plane using vector notation.Understand which are the invariant properties of enlargements.Enlarge shapes using a variety of positive scale factors (including fractions)Use scale to interpret maps and complete scale drawings.

Differentiation & Extension:

Enlargement using negative scale factors. Scale drawing of the classroom.

Notes:All working should be presented clearly and accurately.Students can lose marks in their GSCE for neglecting to mention one part of a transformation, e.g. the centre of enlargement.London Reference:Book 2 Chapter 7 p.69 - 77

Other references:

Discussion opportunities:Discuss how to find the centre of an enlargement.

Pair / Group Work:Map work could be done in pairs.

ICT Links:Geometry Transformations (Outware Education) on department laptop. Powerpoint presentation on laptop. Cabri Geometry (see ICT folder).Transformation Golf on the internet – www.mymaths.co.uk/lessonplans/transformations/golf.aspInvestigation:Investigation into different ways of transforming an object onto a particular image.

Spiritual, Moral, Citizenship and Literacy links:When shapes are transformed, do they still have same properties? We can also transform our personalities – are we still the same?

Time: 3 - 5 lessons


Topic: Mensuration Target Grade: E/D/C/B

Edexcel Content:SSM4a: Measurements to the nearest whole unit may be inaccurate by up to one half in either directionSSM4d: Finding surface area of solids with triangular and rectangular facesSSM4d: Developing, knowing and using the formula for the volume of a cuboidSSM4d: Finding the volume of prismsSSM4b: Recalling formulae for areas of circlesSSM4a: Calculate speed and other compound measures

Prior Knowledge:Area and perimeter of circles. Rounding answers to a degree of accuracy. Using and rearranging formulae.

Learning Objectives:Understand that measurements to the nearest whole unit may be inaccurate by up to one

half in either direction.Calculate the surface area of simple 3D shapes.Calculate the volume of cuboids.Calculate the volume of prisms and composite shapes.Calculate the surface area and volume of cylinders.Calculate speed and density.

Differentiation & Extension:Find the volume of a can of soup given only it’s label.Calculate the speeds of athletes using world record times.

Notes:Many students find it difficult to accept that the upper bound is e.g. 53.5 rather than 53.499999….You could use formula triangles for speed and density.


Other references:

Discussion opportunities:Discuss upper and lower bounds. Rounding off in speed and density questions – only round off at the end.Pair / Group Work:Practical experiments involving speed/density could be done in groups.Nets of 3D shapes could be made to help understand surface area.

ICT Links:Solving problems involving volumes of cylinders (see ICT folder, Excel section).

Investigation:Investigate the speed of world records, does the speed decrease as distance increases? Speed inversely proportional to distance?

Spiritual, Moral, Citizenship and Literacy links:When talking about speed you could discuss drug taking in athletics and fair play.

Time: 5 - 6 lessons


Topic: Probability and Scatter Graphs


Edexcel Content:HD4b: Predicting outcomes using simple probabilitiesHD4b: Estimating probability by experimentingHD4a&HD5f: Plotting and interpreting scatter diagramsHD5f: Describing correlation from a scatter graphHD4i&HD5f: Drawing and using a lime of best fit

Prior Knowledge:Topic 11. Coordinates.

Learning Objectives:Use experimental results to estimate probabilities and make predictions.Plot and use a scatter graph to describe correlation.Describe a relationship between two variables as illustrated by a scatter diagram.Draw a line of best fit where possible “by eye”, and use this to make predictions.

Differentiation & Extension:Vary the axes required on a scatter graph to suit the ability of the class.Find the equation of the line of best fit.Notes:

The first section on probability is very similar to topic 11 and is very straight forward.Clearly label all axes on graphs and use a ruler to draw straight lines.London Reference:Book 2 Chapter 9 p.86 – 95

Other references:

Discussion opportunities:Scatter graphs – Discuss correlation. How do we know where to put the line of best fit?Pair / Group Work:Practical work e.g. do tall people also have large hand spans?ICT Links:See the Probability section in the ICT folder.Autograph – especially useful for scatter graphs (many good worksheets).www.censusatschool.co.uk - provides interesting raw data to take samples from and draw graphs.StatsAid (Outware Education) on department laptop. Excel (see ICT folder).Investigation:Investigate if there is correlation between two variables.You can test theoretical probabilities experimentally, encouraging students to develop their own experiments.Spiritual, Moral, Citizenship and Literacy links:Is there any correlation between wealth and happiness?Time: 3 - 4 lessons

COURSEWORK 3: Choose a task from the Edexcel coursework folder (in the maths staff room)Time: 2 weeks + half term

Note: A third piece of coursework is not essential, but may be helpful for many students.


Topic: Index Notation and Standard Form


Edexcel Content:NA2b: Using index notationNA3g: Recalling integer cubes, squares and square rootsNA5d: Using indices in expressionsNA2b: Using index laws for multiplication and divisionNA5d: Simplifying expressions using the rules of indicesNA3a: Understand the term reciprocal as multiplicative inverseNA3h: Use standard index form to make estimatesNA3m: Calculating with standard index form

Prior Knowledge:Topic 13. Basic number bonds, multiplying and dividing by powers of 10.

Learning Objectives:Memorise all the square numbers from 22 to 152 and the corresponding square roots.Memorise the cubes of 2, 3, 4, 5 and 10.Use index notation and solve equations such as from 2x = 32.Use index laws (multiplication and division) to simplify expressions.Understand that any non-zero number multiplied by its reciprocal is 1.Solve problems involving standard form, using a calculator method where appropriate.

Differentiation & Extension:Fractional indices will be very challenging even for the more able students.

Notes: This topic is not assessed until June.All the earlier work in this topic is easily reinforced by starter and end activities. Students must remember to write ‘x 10’ before the power of 10 or they will get no marks on standard form.Explain the difference between ‘simplify’ and ‘evaluate’ when dealing with indices.


Other references:

Discussion opportunities:Why do the rules for indices work? Why use standard form?Is there a clever way to memorise square and cube numbers?

Pair / Group Work:‘Quick Draw’ – Indices pairs game

ICT Links:‘Quick Draw’ on laptop.How do scientific/graphics calculators represent standard form?Distance of planets from sun can be looked up on the Internet.Investigation:Rules for indices can be approached investigatively.

Spiritual, Moral, Citizenship and Literacy links:Literacy: Look up the word reciprocal in the dictionary.

Time: 4 - 5 lessons


Topic: Percentage Target Grade: C/B

Edexcel Content:NA3e: Understand the multiplicative nature of percentages as operatorsNA3e: Calculate an original amount after a percentage changeNA3e: Solving reverse percentage problemsNA3s: Use calculators for reverse percentage problems

Prior Knowledge:Topic 3. Fractions and decimals.

Learning Objectives:Use multipliers to calculate percentage increase and decrease. Find the original amount before a percentage change.

Differentiation & Extension:Include percentages with recurring decimals (e.g. 33 %), and percentages over 100%Combine multipliers to simplify a series of percentage changes.Notes: This topic is not assessed until June.Even the most able students will find it difficult to calculate the original amount – emphasise that

this is 100%.Amounts of money should be rounded to the nearest penny (but only at the end of the question).London Reference:Book 3 Chapter 2 p.10 – 15

Other references:

Discussion opportunities:Plenty of opportunity, especially when dealing with financial questions.What is the best way to calculate the original amount e.g. the formula method on p.12?

Pair / Group Work:The more able students could explain to the class or to a group how to calculate the original amount after a percentage change.

ICT Links:Use of Excel for budgeting.

Investigation:VAT, credit, interest, mortgages – the students can research all these applications of percentages.

Spiritual, Moral, Citizenship and Literacy links:Explain how the economy functions, including the role of business and financial services.

Time: 2 - 3 lessons


Topic: Proportion Target Grade: C/B

Edexcel Content:NA3l: Calculate an unknown quantity from quantities that vary in direct proportionNA3k: Represent repeated proportional change using a multiplier raised to a power (compound interest)

Prior Knowledge:Percentage increase and decrease - use of multipliers. Ratio, fractions, calculator skills, rounding off.

Learning Objectives:Recognise that two numbers are in proportion if their ratios stay the same as the quantities

get larger or smaller.Use the unitary method as a way of solving ratio and proportion problems (e.g. recipes).Represent repeated proportional change using a multiplier raised to a power.Solve compound interest problems.

Differentiation & Extension:Currency calculations using current exchange rates.Inverse proportion.

Notes: This topic is not assessed until JuneTeach both methods for direct proportion as one might be easier than the other without a calculator.


Other references:

Discussion opportunities:Deciding whether two quantities are in proportion. What would the graph look like?

Pair / Group Work:‘Battle of the Banks’ for compound interest.

ICT Links:Use of Autograph or Graphics calculators to test proportionality.

Investigation:Investigate which variables are proportional to each other.Compound interest could be approached investigatively.

Spiritual, Moral, Citizenship and Literacy links:Is a human’s health inversely proportional to his/her age? Is intelligence directly proportional to age?Proportional representation in government.Time: 3 - 4 lessons


Topic: Manipulation and Formulae Target Grade: C/B

Edexcel Content:NA5b: The difference of two squaresNA5b: Cancelling common factors in rational expressionsNA5d: Index notation for simple integer powers and index lawsNA5g: Change the subject of a formula

Prior Knowledge:Topic 15 and 22. Negative numbers and indices.

Learning Objectives:Use the difference of two squares to factorise quadratics.Simplify expressions by cancelling algebraic fractions.Use all the index laws to simplify expressions.Use negative indices.Change the subject of a formula, including cases where the subject occurs twice, or where

a power of the subject appears.

Differentiation & Extension:Further practice in rearranging formulae involving powers, and several operations.Formulae involving reciprocals of the subject.

Notes: This topic is not assessed until June.Encourage students to check their factorising by expanding the brackets.There may be a need to remove the HCF of a quadratic to make factorising easier.London Reference:Book 3 Chapter 4 p.22 - 32

Other references:

Discussion opportunities:Why does any number to the power of 0 equal 1? What do negative indices mean? Pair / Group Work:Domino/Bingo/Snap games – match expressions with their factorised or simplified equivalent.

ICT Links:Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.Autograph or graphics calculators could be used to show the equivalence of algebraic expressions.Investigation:Index laws could be approached investigatively, as could the difference of two squares.

Spiritual, Moral, Citizenship and Literacy links:Literacy: What does it mean to ‘change the subject’ of a conversation? Time: 6-7 lessons

SPRING TERM A:

REVISION FOR GCSE MODULAR EXAMINATION (PAPER 12)Revise individual topics and Examination papers (there is a practice paper at the back of the textbook)


Topic: Equations and Inequalities Target Grade: C/B

Edexcel Content:NA5i: Solving simultaneous equations using elimination NA5j: Solving linear inequalities in two variablesNA5i: Solving simultaneous equations using a graphical methodNA5j: Solving several linear inequalities in two variables and find the solution setNA5k: Solving quadratic equations by factorising

Prior Knowledge:An understanding of balancing methods. Factorising quadratics. Drawing linear graphs.

Learning Objectives:Solve simultaneous equations by graphical methods.Solve simultaneous equations by eliminating a variable Use regions on a graph to solve inequality problems in two variables. Solve a quadratic equation by factorising.

Differentiation & Extension:Using the quadratic equation formula (Higher Level).

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

Notes:Try to use ICT in this topic, especially graphics calculators and Autograph.Many pupils find locating regions difficult – it is often useful to choose a particular point on one side of the line to check if it fits the inequality.


Other references:

Discussion opportunities:Discuss which is the best way to solve a simultaneous equation.

Pair / Group Work:The ICT work below could be done in pairs.‘Buried Treasure’ using inequality graphs.

ICT Links:Using graphical calculators or Autograph to solve simultaneous equations (see ICT folder).Algebra Foundations/ Algebra Tutor (Outware Education) on department laptop.www.mathslessons.co.uk - for simultaneous equations (see ICT folder).

Investigation:Car hire, Mobile Phones (coursework tasks).

Spiritual, Moral, Citizenship and Literacy links:How can simultaneous equations be used to solve business problems? (see Edexcel Int. (new) p.468)Time: 6 – 8 lessons


Topic: Graphs, Gradients and Loci Target Grade: D/C/B

Edexcel Content:NA6b: Plotting graphs of functions where y is expressed in terms of x, leading to a straight lineNA6c: Find gradients of straight linesNA6c: Recognising the y-intercept of a straight lineNA6b: Exploring graphs of the form y = mx + cNA6h: Construct the graphs of simple loci

NA6e: Plotting the graph of a quadratic functionNA6f: Plotting graphs of simple cubic and reciprocal functionsNA6f: Recognising characteristics of graphsNA6e: Finding approximate solutions to quadratics using graphs

Prior Knowledge:The ability to plot points that follow a simple rule (in four quadrants).The ability to substitute values into algebraic formulae.The ability to substitute positive and negative values into a non-linear formula.Learning Objectives:

Rearrange a linear equation into the form y = mx + c.Realise that an equation of the type y = mx + c represents a straight line graph.Understand the relevance of m and c in the above equation.From a given graph, find the gradient and y-intercept and hence the equation of the graph.Draw a straight line graph without plotting points.Construct the graphs of simple loci.Plot curves from a given quadratic equation.Solve quadratics by constructing an appropriate graph.

Plot curves from a given cubic or reciprocal equationSolve cubic and reciprocal equations using graphical methods.

Differentiation & Extension:Students performing below grade C will struggle with this topic and examples should be set accordingly.Investigate how the graph of a cubic equation can be used to solve it.Notes:This is an excellent opportunity to use ICT (see below).The students will probably have a deeper understanding if they discover the relevance of m and c themselves.London Reference:Book 3 Chapter 6 p.45 - 54

Other references:

Discussion opportunities:The interpretation of y = mx + c is a good discussion point.How can you tell which graph will match which equation?Pair / Group Work:ICT work could be done in pairs (one person investigates a change in m, the other investigates a change in c).Dominoes/Pairs – match graphs to their equations.ICT Links:Autograph – see ICT folder for good worksheets on introducing y = mx + c (also see Omnigraph section).Graphics calculators (see ICT folder). www.waldomaths.comThe Open Box Problem (see Edexcel Teacher’s guide – ICT)Investigation:Drawing graphs may help to analyse the Open Box problem.y = mx + c can be approached investigatively – see ICT work.Spiritual, Moral, Citizenship and Literacy links:Literacy: What do the words quadratic, cubic and quartic mean? What comes next?Time: 6 - 7 lessons


Topic: Shapes and Transformations Target Grade: E/D/C/B

Edexcel Content:SSM2f: The geometry of cuboids and shape made from cuboidsSSM2g: Similarity of triangles and other plane figuresSSM2i: Use 2D representations of 3D shapes, including plan and elevationSSM3b: Combinations of transformationsSSM2f: Distance between two coordinates and the midpoint of the line

Prior Knowledge:Ratio, Pythagoras’ Theorem, coordinates and negative numbers.

Learning Objectives: Find planes of symmetry in 3D shapes. Draw 2D representations of 3D objects, including the use of isometric paper.

Use cross-sections, plans and elevations to answer questions.Replace two transformations by a single transformation which has the same result.Use scale factors to solve problems involving similar shapes.Find the distance between two coordinates and the midpoint of the line


http://www.waldomaths.com/

Draw shapes made from multi-link on isometric paper.Draw sketches of the classroom from different aspects.

Notes:Emphasise the need for accurate drawings using a pencil and ruler (and protractor).For similar triangles, it sometimes helps if the students draw the smaller triangle inside the larger one.London Reference:Book 3 Chapter 7 p.55 - 65

Other references:

Discussion opportunities:Mental imaging could be used with 2D representations of 3D shapes – discuss what the students imagined.Pair / Group Work:Could use multi-link cubes in pairs or groups.Practical work on scale drawing could be done in pairs or groups.

ICT Links:LOGOCabri Geometry 2 PlusInvestigation:See if students can find their own method for similarity or for finding the distance between two coordinates and the midpoint of the line.

Spiritual, Moral, Citizenship and Literacy links:We need to look at 3D shapes from different angles – similar to confrontation and conflict.

Time: 6 - 7 lessons

SPRING TERM B TOPIC 29

Topic: Shape and Space Target Grade: D/C/B

Edexcel Content:SSM2h: Understanding and using circle theoremsSSM2h: The angle subtended by an arc at the centre of a circle is twice the angle subtended at any point on the circumferenceSSM2h: The subtended at the circumference by a semi-circle is a right angleSSM2h: Angles in the same segment are equal SSM2h: Opposite angles of a cyclic quadrilateral add up to 180 degreesSSM2h: Explain why the perpendicular from the centre of a chord bisects the chord SSM2h: Understanding and using right angles between tangent and radiusSSM2h: Understanding and using tangents of equal lengthSSM4c: Constructing trianglesSSM4c: Constructing a perpendicular bisector and finding the mid-points of a line segmentSSM4c: Constructing perpendiculars to a lineSSM4c: Bisecting an angleSSM4e: Finding Loci

Prior Knowledge:The ability to measure angles with a protractor. An understanding of parallel lines.The ability to label parts of a circle.Learning Objectives:

Understand and use circle theorems (listed above in the Edexcel Content)

Construct shapes from given information using only compasses and a ruler.Construct perpendicular bisectors, and angle bisectors using only compasses and a ruler.Construct loci in terms of distance from a point, equidistance from two points, distance

from a line, equidistance from two lines and line of sight.Shade regions using loci to solve problems e.g. vicinity to lighthouse/port.

Differentiation & Extension:Questions which involve more than one of the circle theorems.Solve loci problems that require a combination of loci.Notes:It is important to give reasons for answers on circle theorems.All working should be clearly shown in constructions. For loci, try to use past exam papers to cover objectives.London Reference:Book 3 Chapter 8 p.66 – 78

Other references:

Discussion opportunities:Mental imaging could be used with loci – discuss what the students imagined.Pair / Group Work:Circle theorems – laminated wall questions.Practical work on constructions and loci could be done in pairs or groups.ICT Links:Geo Constructions (Outware education) on department laptop.Cabri Geometry (see ICT folder). LOGO (see ICT folder).www.waldomaths.com Investigation:Circle theorems could be approached investigatively. Loci work can be investigative e.g. find where on a map buried treasure is located given some clues.Spiritual, Moral, Citizenship and Literacy links:Loci and buried treasure could lead to a discussion on the Holy Grail.Time: 6 - 7 lessons


Topic: Mensuration Target Grade: D/C/B

Edexcel Content:SSM4d: Finding volume of prismsSSM4d: Finding surface area of solids with triangular and rectangular facesSSM3d: Understand the difference between formulae for perimeter, area and volume by considering dimensions

Prior Knowledge:Area and perimeter of circles. Rounding answers to a degree of accuracy. Using and rearranging formulae.

Learning Objectives: Work out the volume and surface area of prisms. Work out the volume and surface area of a cylinder.

Convert m2 into cm2, m3 into cm3 and vice versa.Recognise whether a formula represents a length, area or voume.


http://www.waldomaths.com/

Find the volume of a can of soup given only it’s label.

Notes:Answers for cylinders could be left in terms of .Many students have trouble when considering dimensions – explain this carefully.Converting m2 into cm2 and m3 into cm3 is also quite tricky for many students.


Other references:

Discussion opportunities:Dimensional analysis – debate whether a formula represents a length, area, volume or none of these.

Pair / Group Work:Domino/Bingo/Snap games – match formulae for length, area, volume or none of these.

ICT Links:Solving problems involving volumes of cylinders (see ICT folder, Excel section).

Investigation:‘Tennis Ball Packaging’ – investigate the best package to sell 4 tennis balls

Spiritual, Moral, Citizenship and Literacy links:It is quite amazing that 1m2 equals 1000000cm2. Why is this?

Time: 3 - 5 lessons


Topic: Handling Data Target Grade: C/B

Edexcel Content:HD4f: Calculating a moving averageHD5b: Identifying trends in time seriesHD5d: Comparing shapes of distributionsHD5d: Comparing distributions using measures of range and spreadHD5f: Describing correlation from a scatter graphHD4j: Using a calculator for statistical calculations HD4h: Use tree diagrams to represent outcomes of compound events

Prior Knowledge:Experience of plotting points and reading from graphs. Averages and fractions.Writing probabilities as fractions, decimals or percentages. Probability of an event happening or not happeningLearning Objectives:

Calculate and interpret the meaning of a moving average.Compare shapes of distributions from diagramsCompare distributions using measures of range and spreadDescribe correlation in terms of the two variables, and as positive, weak, negative& strongUse a calculator to work out the mean and give a random number.

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

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

Differentiation & Extension:Some students will find it hard to draw tree diagrams – initial questions could have the diagrams already drawn. Calculate the probability of winning the National Lottery.Notes:Pupils can often forget to multiply along the branches of a tree diagram.Students can often lose marks at probability due to inability to manipulate fractions.London Reference:Book 3 Chapter 10 p.86 - 101

Other references:

Discussion opportunities:Deciding if events are mutually exclusive or independent.Pair / Group Work:Collect data from class and make statistical comparisons – children per family etc. Collect data from newspapers.ICT Links:See the Probability section in the ICT folder.Powerpoint presentation on laptop.Investigation:The Dice Game coursework task.Spiritual, Moral, Citizenship and Literacy links:National Lottery – is it moral to gamble if the money raised goes to charity?Time: 6 - 7 lessons

REVISION FOR GCSE TERMINAL EXAMINATIONS (PAPERS 16 AND 17)Revise individual topics and Examination papers (there are practice papers at the back of the textbook).

programme of study - year 10 and 11 - intermediate ... · web viewidentify the parts of a circle...

Documents