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This is intended as a starting point for lesson planning

The main textbook resource will be “London GCSE Maths – Foundation course” and this is referenced throughout

the scheme

It is expected that you will supplement this through the use of other resources such as

- KS4 Boardworks software package - Vickers level 3 to 6

- SMP 11-16 Green course books 1 to 8 - Heinemann foundation A and B books

- Greer textbook basic course - Use of other ICT packages as appropriate

Each module has sections “ICT” and “Other Resources”. If you use a different resource in your lessons and it

proves successful please update the electronic version of this scheme (in maths shared area) so that other staff will have the option of also trying the resource. In this way the scheme will evolve and we will also share good

practice with each other.

MODULE 1 TIME: 10 hours

GCSE TIER: Foundation TARGET GRADE: E/F/G

CONTENT: Number

Understanding place value in whole numbers NA2a Reading, writing and ordering whole numbers NA2a Mental addition, subtraction, multiplication and division of whole numbers NA3a Written addition, subtraction, multiplication and division of whole numbers NA3a Problems involving the four rules with whole numbers NA3a Order of operations (excluding powers) NA3b Writing numbers to the nearest ten, hundred and thousand and use for estimating NA2a Negative numbers in context NA3a Understanding place value in decimal numbers NA2d Ordering decimals NA2d Writing decimal numbers to the nearest whole number and to 1 or 2 decimal placesNA2h

PRIOR KNOWLEDGE

The ability to order numbers. Appreciation of place value. Experience of the 4rules on whole numbers and decimals. Knowledge of integer complements to 100. Knowledge of multiplication facts to 10 × 10.

OBJECTIVES

By the end of the module the students should be able to: Work confidently on the 4rules of number with and without the use of a calculator, including long multiplication and long division, and understand the order in which operations should be applied. Understand the concept of rounding, including questions where remainders are included. Understand and work confidently with negative numbers in context. Understand place value in decimals including the use of decimal notation in money

DIFFERENTIATION & EXTENSION

More work on long multiplication and division without using a calculator. Estimating answers to calculations. Rounding to any number of decimal places.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 1, pages 116, 1921 Chapter 2, pages 28, 29 Chapter 6, pages 8386

OTHER RESOURCES

ICT

NOTES

Present all working clearly, emphasising that all working is to be shown. For noncalculator methods make sure that remainders and “carry’s” are shown.


GCSE TIER: Foundation TARGET GRADE: D/E/F/G

CONTENT: Algebra

Using letters to represent numbers NA5a Adding with letters NA5b Simplifying expressions with one letter NA5b Collecting like terms NA5b Multiplying with letters and numbers NA5b Multiplying simple algebraic expressions NA5b Removing a single pair of brackets NA5b

PRIOR KNOWLEDGE

Some idea that letters can be used instead of numbers.

OBJECTIVES

By the end of the module the students should be able to: Understand the contents of the module. Manipulate expressions by collecting like terms and removing brackets.


Further work on collecting like terms, involving negative terms. Collecting terms where each term may consist of more than one letter, e.g. 3ab + 4ab.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 2, pages 2227, 3033

OTHER RESOURCES

ICT

NOTES

Present all work neatly, writing out the questions with the answers to aid revision at a later stage.



CONTENT: Statistics

Different ways of collecting data HD1a Designing questions to collect data HD1a Collecting data by sampling HD1a Collecting data by observation HD3a Collecting data by experiment HD3a Obtaining data from a database, tables and lists HD3b Sorting and presenting data HD3a Grouping data in tally tables and grouped frequency tables HD3a Drawing simple bar charts HD4a Comparing data using dual bar charts HD5b Drawing pictograms HD4a Interpreting simple bar charts and pictograms HD5b

PRIOR KNOWLEDGE

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

OBJECTIVES

By the end of the module the students should be able to: Understand the contents of the module. Design a simple questionnaire, and appreciate deficiencies in a question. Understand the concept of sampling a population, and what makes a fair sample. Collect data from a variety of sources. Sort and collect data in a tally table and grouped frequency table. Draw and interpret dual bar charts and pictograms. Extract data from lists and tables.


Carry out a statistical investigation of their own including; designing an appropriate means of gathering the data, and an appropriate means of displaying the results. Use a spreadsheet to collect data in tables and draw different types of graphs

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 8, pages 106115 Chapter 10, pages 133141

OTHER RESOURCES

ICT

NOTES

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


GCSE TIER: Foundation TARGET GRADE: F/G

CONTENT: Measure

Estimating lengths, capacities and weights SSM4a Choosing appropriate metric and imperial units of measure SSM4a Reading scales and dials SSM4a Measure/draw a line accurately SSM4d

PRIOR KNOWLEDGE

A basic idea of: How long is a metre? How heavy is a packet of tea? How much space does a litre take up ?

OBJECTIVES

By the end of the module the students should be able to: Understand the contents of the module. Make estimates of lengths, volumes and weights in a real life context. Read scales in a wide variety of contexts, including graduated scales and scales using decimals. Measure lengths to the nearest millimetre, including marking midpoints of lines. Choose appropriate units with which to measure.


This could be made a practical activity by collecting assorted everyday items and weighing, measuring to check the estimates of their lengths, weights and volumes. Use ICT and reference books to find the weights, volumes and heights of large structures such as buildings, aeroplanes and ships.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 7, pages 93105

OTHER RESOURCES

ICT

NOTES

Measurement is essentially a practical activity. Use a range of everyday objects to make the lesson more real.



CONTENT: Number – Decimals and introducing percentages

Addition of decimals without a calculator NA3j Subtraction of decimals without a calculator NA3j Multiplication of decimals without a calculator* NA3i Division of decimals without a calculator* NA3i Converting between simple fractions and decimals NA3c Understanding percentages * NA2e Converting percentages to fractions and decimals ** NA3e

PRIOR KNOWLEDGE

Module 1. 4 rules of number. The basic ideas of the concepts of a fraction and a decimal. Number bonds and times tables.

OBJECTIVES

By the end of the module the students should be able to: Understand the content of the module. Work confidently on the 4 rules of decimals without the use of a calculator. Answer questions involving decimal notation in money e.g. bills. Understand and change between percentages, fractions and decimals. DIFFERENTIATION & EXTENSION

Further and harder work on the 4 rules of decimals, including multiplying and dividing decimals with 3 and 4 digits all without using a calculator. Changing fractions and decimals to percentages.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 6, pages 8792 Chapter 14, pages 182184 Chapter 24, page 311

OTHER RESOURCES

ICT

NOTES

Present all working clearly with decimal points in line; emphasising that all working is to be shown. For noncalculator methods make sure that remainders and carry’s are shown. *For 1388 this is only as far as one decimal place in Stage 1, and should be developed further in Stage 3. **For 1388 this is not tested until Stage 2.


GCSE TIER: Foundation TARGET GRADE: F/G

CONTENT: Probability

Using the language of likelihood HD5g Using the probability scale from 0 to 1 HD4c Writing probabilities as numbers* HD4c Certain and impossible events HD5g Listing systematically outcomes for single events or two successive events HD4e

PRIOR KNOWLEDGE

Some idea of chance and the likelihood of an event happening, and a recognition that some events are more likely than others.

OBJECTIVES

By the end of the module the students should be able to: Mark the position of a probability on the probability scale. Describe in words the likelihood of an event, and recognise events which are least or most likely. Write down the probability of a single event occurring. Understand certainty and impossibility. List outcomes for one or two events.


Write down their own probabilities of events that may or may not happen. Play simple probability games, predicting outcomes e.g. horse race for sum of 2 dice.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Where possible introduce practical work to support the theoretical work. *For 1388 this is not tested until Stage 2.



CONTENT: Shape – 2D

Recognising triangles and quadrilaterals SSM2f Drawing 2D shapes on squared paper SSM4d Congruent shapes* SSM2d Recognise regular and irregular polygons SSM1f Using vocabulary of circles SSM2i & SSM1f Tessellations SSM2g Turning quarter and half turns clockwise and anticlockwise SSM3b Naming acute, obtuse, right and reflex angles SSM2b Measuring and drawing angles with a protractor SSM4d Using bearings to specify direction SSM4b Drawing 2D shapes with ruler, protractor and compasses SSM4d Drawing and measuring scaled lines SSM4d STAGE TWO Simple scale drawings SSM3d STAGE TWO

PRIOR KNOWLEDGE

Some knowledge of the names of the different types of triangles and quadrilaterals. An understanding of angle as a measure of turning. Experience of drawing and measuring using a ruler. Module 4.

OBJECTIVES

By the end of the module the students should be able to: Name the different types of triangles, quadrilaterals and polygons. Understand and recognise regularity of shapes. Recognise and draw acute, obtuse and reflex angles. Measure and draw bearings of all sizes. Draw 2D shapes on plain and squared paper using ruler, protractor and compasses (including a circle or arc). Recognise shapes that are congruent and in different orientations, and create congruent shapes by rotating them through half and quarter turns. Recognise shapes that will tessellate and be able to continue the tessellating pattern. Describe a circle using the words radius, diameter and circumference. Use simple scales to construct shapes. Construct an equilateral triangle using a ruler and compasses.


More complicated shapes can be drawn. Congruent shapes in more difficult orientations. Measuring angles in polygons.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Make sure that all pencils are sharp and drawings are neat and accurate. Angles should be within 2 degrees.


GCSE TIER: Foundation TARGET GRADE: G

CONTENT: Coordinates, reflection and rotation

Coordinates in first quadrant SSM3e/NA6b Coordinates in four quadrants SSM3e/NA6b Line symmetry SSM3b Rotational symmetry SSM3b Planes of symmetry* SSM3b Transforming 2D shapes by reflection and rotation SSM3b Specify a mirror line parallel to axes SSM3a Rotating shapes about the origin SSM3a Describing transformations in full (rotations and reflections) SSM3a & SSM3b

PRIOR KNOWLEDGE

Module 7. Experience of plotting points. Directed numbers.

OBJECTIVES

By the end of the module the students should be able to: Specify the coordinates of any point in 4 quadrants. Recognise shapes that have line and rotational symmetry. Draw lines and planes of symmetry on simple shapes. Reflect in specified mirror lines. Identify equations of mirror lines parallel to axes.


Symmetries of more complex shapes Use LOGO to design a symmetrical pattern with given order of rotation, lines of symmetry

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 9, pages 116117 Chapter 18, pages 220230 Chapter 22, pages 280284

OTHER RESOURCES

ICT

NOTES

Make sure that all pencils are sharp and drawings are neat and accurate. *For 1388 this is not tested until Stage 3.



CONTENT: Measure Changing metric units for length, capacity and weight SSM4a Changing metric to imperial units and vice versa* SSM4a Telling the time from analogue and digital clocks SSM4a Changing 12 hour to 24 hour clocks and vice versa SSM4a Calculating with time SSM4a Working with dates NA1e Timetables – bus and train NA1e

PRIOR KNOWLEDGE

Modules 4, 5. How to multiply and divide by powers of 10. Knowledge of the conversion facts for metric lengths, weight and capacity. Knowledge of the conversion facts between seconds, minutes and hours. Knowledge of the number of days in months.

OBJECTIVES

By the end of the module the students should be able to: Change between units for length, volume and weight. Know the basic conversion facts from metric to imperial units of length, volume and weight and be able to change between them. Change between hours, minutes and seconds and deal with problems with adding and subtracting times. Work with adding and subtracting days from a calendar. Work with bus and train timetables.


Work with more difficult examples. Work with “real” timetables and “real” holiday brochures for working out holiday dates.

RESOURCES


OTHER RESOURCES

ICT

NOTES All working should be shown with multiplication or division by powers of 10. *For 1388 this is not tested until Stage 3.


GCSE TIER: Foundation TARGET GRADE: E/F

CONTENT: Pie Charts

Drawing Pie Charts HD4a Calculating the angles to draw a pie chart NA3a & SSM4d Calculating using pie charts HD5b

PRIOR KNOWLEDGE

Module 3. Measuring and drawing angles (Module 7). Fractions of simple quantities.

OBJECTIVES

By the end of the module the students should be able to: Use a pie chart to display data as appropriate. Interpret given pie charts.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Accurate drawing skills need to be reinforced. Angles should be within 2 degrees.



CONTENT: Factors, multiples and fractions

Factors, multiples and common factors NA2a Fractions from pictures and from words NA2c Equivalent fractions NA2c Simplifying fractions using common factors NA2c Finding a fraction of a quantity NA3c Using common denominators to order fractions NA2c Simple multiplication of a fraction NA3d Converting simple fractions to decimals NA3c Converting a simple fraction to a ratio* NA2f Simplifying a ratio * NA2f PRIOR KNOWLEDGE

Module 5. Some concept of a fraction. Using multiplication tables to find factors. Recognise multiples and factors.

OBJECTIVES

By the end of the module the students should be able to: Recognise shaded diagrams representing simple fractions, decimals and percentages. Recognise fractions presented in different formats. Find fractions of quantities. Use factors, multiples and common factors to calculate equivalent fractions, and order fractions. Multiply a fraction by an integer and by a unit fraction. Convert fractions to decimals and ratio. Simplify fractions and ratios.


Using a calculator to find fractions of given quantities. Using the four rules of fractions. Using a calculator to change fractions into decimals and looking for patterns. Working with improper fractions and mixed numbers. Use a number square to find primes (Sieve of Erastosthenes). Calculator exercise to check factors of larger numbers.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Understanding of equivalent fractions is the key issue in order to be able to tackle the other content. Oral discussion should be used to ensure understanding of the meaning of the words factor and multiple and to avoid confusion between them. Calculators should only be used when appropriate.


GCSE TIER: Foundation TARGET GRADE: F CONTENT: Averages

Finding the mode, median, mean and range from simple data HD4b Selecting the most appropriate average HD1c Finding the mode from a discrete frequency table HD4b Calculating the total frequency from a discrete frequency table HD1f Calculate the mean from a discrete frequency table HD4b Mean and median for continuous data* HD4b STAGE TWO Modal class for continuous data* HD4b STAGE TWO

PRIOR KNOWLEDGE

Module 3. Some idea of the concept of average.

OBJECTIVES

By the end of the module the students should be able to: Calculate mode, mean, median and range for simple data. Calculate mean and modal class from a discrete or grouped frequency table. Compare distributions using averages and range.


Collect data from class – children per family etc. Collect data from newspapers. Discuss occasions when one average is more appropriate, and the limitations of each average.

RESOURCES


OTHER RESOURCES

ICT

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.



CONTENT: Powers

Odd and even numbers NA2a STAGE ONE Squares, cubes and square roots of whole numbers NA2b Using power notation for integer powers NA5c Order of operations including powers (BODMAS) NA3b STAGE ONE Using a calculator effectively, including squares, powers and reciprocals NA3o

PRIOR KNOWLEDGE

Module 1. Experience of classifying integers. Multiplication tables.

OBJECTIVES

By the end of the module the students should be able to: Understand the meaning of an index, and evaluate powers with and without a calculator. Use and understand the terms odd, even, square, cube, root, and reciprocal. Recall the squares and cubes of 2, 3, 4, 5 and 10.


Calculator exercise to find squares, cubes and square roots of larger numbers (linked to trial and improvement).

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 1 Pages 1619 Chapter 2 Pages 2728

OTHER RESOURCES

ICT

NOTES

Oral discussion should be used to ensure: Recognition of odd and even numbers. Calculators are only used when appropriate.


GCSE TIER: Foundation TARGET GRADE: E

CONTENT: Geometry

Calculating angles on a straight line and at a point SSM2a Recognising opposite angles at a vertex SSM2a Calculating angles in triangles SSM2d Using angle properties of isosceles, equilateral and rightangled triangles SSM2d Explaining why the angle sum of a quadrilateral is 360 degrees SM2d Calculating angles in quadrilaterals SSM2d Interior and Exterior angles of quadrilaterals, pentagons, hexagons and regular polygons SSM2g Polygons inscribed in circles SSM2i

PRIOR KNOWLEDGE

Module 7. The concept of an angle measured in degrees. Adding and subtracting whole numbers.

OBJECTIVES

By the end of the module the students should be able to: Solve angle problems on a straight line, at a point and through opposite angles. Know and use angle properties of all types of triangles, quadrilaterals. Solve problems involving interior and exterior of all regular polygons, and irregular polygons with 4, 5 or 6 sides. Construct polygons within circles.


Measuring and totalling angles in polygons. Solving problems involving more than one step, or more than one of the above properties.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Pupils should be able to estimate angles from 0 to 360 degrees and use angle names confidently.


GCSE TIER: Foundation TARGET GRADE: G/E/D

CONTENT: Displaying and comparing data

Line graphs for discrete and continuous data, including time series* HD4a Constructing and interpreting stem and leaf diagrams HD4a Plotting and interpreting scatter diagrams HD4a Describing correlation from a scatter graph HD5f Drawing and using a line of best fit HD4h & HD5f

PRIOR KNOWLEDGE

Modules 3, 12. Plotting coordinates (Module 8) An understanding of the concept of a variable. Recognition that a change in one variable can affect another.

OBJECTIVES

By the end of the module the students should be able to: Construct and interpret line graphs for all types of data. Construct and interpret ordered and unordered stem and leaf diagrams (e.g. finding median or mode) Plot and use a scatter graph to describe correlation. Describe a relationship between two variables as illustrated by a scatter diagram. Describe correlation in terms of the two variables, and as positive, weak, negative, or strong. Draw a line of best fit where possible “by eye”, and use this to make predictions.


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

RESOURCES


OTHER RESOURCES

ICT

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.


GCSE TIER: Foundation TARGET GRADE: G/F/E/D

CONTENT: Algebra and sequences

Powers and indices for letters NA5c Extending diagrammatic sequences NA6a Number sequences and letters NA6a Number pattern rules NA6a

PRIOR KNOWLEDGE

Modules 2, 13. Some experience of sequences of numbers which follow a rule.

OBJECTIVES

By the end of the module the students should be able to: Continue sequences of diagrams. Continue linear and nonlinear sequences of numbers. Recognise algebraic terms and interpret them. Use powers, brackets and simplify terms. Investigate number patterns, describing them in words and using the nth term for linear expressions.


Match stick problems.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 2, pages 3439 Chapter 12, pages 160168 Chapter 24, pages 314318

OTHER RESOURCES

ICT

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.


GCSE TIER: Foundation TARGET GRADE: G/E/D

CONTENT: Area and perimeter

Perimeters of triangles, rectangles and straight line shapes SSM4f Calculate area by counting squares SSM4f Developing, knowing and using the formula for the area of a rectangle SSM4f Deducing formulae for the area of a parallelogram and a triangle SSM2e Knowing and using formulae for the area of a parallelogram and a triangle SSM4f Calculating areas of compound shapes made from rectangles and trianglesSSM4f Find the area of a trapezium using the formula SSM4f

PRIOR KNOWLEDGE

Modules 1, 7. Knowledge of the shape and properties of rectangles, parallelograms and triangles. Units of measurement. Four rules of number.

OBJECTIVES

By the end of the module the students should be able to: Count area and perimeter of simple shapes. Recognise and use the relationships between the areas of rectangle, parallelograms and triangles. Calculate areas of rectangles, parallelograms, triangles and trapezia. Calculate areas of compound shapes made from triangles and rectangles e.g. regular hexagon, kite.

DIFFERENTIATION & EXTENSION Calculating areas and volumes using formulae. Using compound shape methods to investigate areas of other standard shapes such as a trapezium or a kite. Measure 3 London Foundation book pages 238 to 245. Practical activities. e.g. using estimation and accurate measuring to calculate perimeters and areas of classroom/corridor floors.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Discuss the correct use of language and units. Ensure that pupils can distinguish between perimeter and area.


GCSE TIER: Foundation TARGET GRADE: F/E

CONTENT: Probability

Writing probability as numbers HD4d The probability of an event not happening HD4f Using the sum of probabilities equalling 1 HD4f Predicting outcomes using simple probabilities HD5h Estimating probability by experimenting HD4d Sample spaces and theoretical probabilities HD4d Using twoway tables to find probabilities HD3c STAGE THREE

PRIOR KNOWLEDGE

Module 6. Reading data from twoway tables.

OBJECTIVES

By the end of the module the students should be able to: Write down 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. Solve probability problems using sample spaces and twoway tables.


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

RESOURCES


OTHER RESOURCES

ICT

NOTES

Many Foundation students appear unsure of the relationship P(not n) = 1 – P(n) as seen in their examination performance. Only fractions, decimals or percentages should be used for probability.



CONTENT: Equations and formulae

Inverse operations NA5f Simple linear equations NA5e Equations combining operations NA5e Using word formulae NA5f Using algebraic formulae NA5f Using negative numbers NA5c Using algebraic equations to solve problems NA5e

PRIOR KNOWLEDGE

Modules 1, 2. An idea of which pairs of simple operations are opposite. Understanding of how letters are used to represent numbers. Expressions, terms, collecting like terms and simple algebraic manipulation.

OBJECTIVES

By the end of the module the students should be able to: Work comfortably with letters representing numbers. Balance equations, remove brackets in an equation and solve simple equations including examples where the unknown appears on both sides. Use word formulae and algebraic formulae to represent a relationship between quantities. Substitute into rules and formulae using positive and negative numbers. Use simple equations to solve problems.


The work can be extended to include more complex algebraic manipulation and equations.

RESOURCES


OTHER RESOURCES

ICT

NOTES Using multilink cubes or Cuisenaire rods to represent algebraic expressions often helps to demythologise algebraic work.


GCSE TIER: Foundation TARGET GRADE: G/F/E

CONTENT: 3D and Volume

Finding volumes by counting cubes SSM4g Developing, knowing and using the formula for the volume of a cuboid SSM4g Finding volume of solids made from cuboids SSM4g Using the formula for the volume of a cuboid to solve problems SSM4g Using the language of 3D shapes SSM2j STAGE THREE Nets of simple solids SSM2k STAGE THREE Finding surface area of solids with triangular and rectangular faces* SSM4f

PRIOR KNOWLEDGE

Module 17. Experience of constructing cubes or cuboids.

OBJECTIVES

By the end of the module the students should be able to: Describe solid shapes in terms of edges, vertices and faces. Draw nets of simple solids and use them to evaluate surface area. Find volume of simple solids by counting cubes. Know and use the formula of a cuboid to solve problems. Find how many small boxes will fit into a larger box.


Extend volume work to look at shapes covered in the Intermediate syllabus.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 11, pages 150159 Chapter 19, pages 237, 243245

OTHER RESOURCES

ICT

NOTES

Many students have little real understanding of perimeter, area and volume. Practical experience is essential to clarify these concepts. *In 1387 this may be best left until module 28


GCSE TIER: Foundation TARGET GRADE: E/D

CONTENT: Transformations

Enlarging assorted shapes using various centres of enlargement and integer scale factors SSM3c Enlarging assorted shapes using noninteger scale factors greater than 1 SSM3c Enlargement calculations SSM3d Similar triangles SSM3d Similarity of standard shapes* SSM3c Translations SSM3b Describing transformations in full (enlargements and translations) SSM3a

PRIOR KNOWLEDGE

Modules 7, 8. Recognition of basic shapes. Simple properties of shapes. Coordinates in four quadrants. Basic concepts of enlargement from scale drawing.

OBJECTIVES

By the end of the module the students should be able to: Recognise translations as sliding movements, and translate simple 2D shapes within a plane. Understand which are the invariant properties of enlargements. Enlarge shapes using a variety of positive scale factors. Work on tasks involving these transformations. Solve problems involving similar shapes.


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

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 22, pages 277280,284290

OTHER RESOURCES

ICT

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



CONTENT: Fractions

Expressing a given number as a fraction of another NA3c Converting between simple fractions of a whole and percentages of a whole NA3e Mixed numbers and top heavy fractions NA3e Adding and subtracting fractions* NA3c Multiplying and dividing fractions* NA3l Dividing a fraction by an integer* NA3l

PRIOR KNOWLEDGE

Module 11. Basic number skills and ability to recognise common factors. Calculator skills.

OBJECTIVES

By the end of the module the students should be able to: Understand the contents of the module. Recognise equivalence between simple fractions and percentages. Add and subtract fractions including simple cases involving mixed numbers. Multiply and divide simple fractions where the answers may involve mixed numbers.


Solve word problems involving fractions.

RESOURCES


OTHER RESOURCES

ICT

NOTES

The main thrust of this module is that pupils should be able to operate with fractions without the aid of a calculator. Students may have difficulty with the concept of dividing by a fraction, a useful book to help understand student difficulties is Kerslake, D, Fractions: Children's strategies and errors (NFER Nelson, 1986). *In 1388 these are not assessed until Stage 3



CONTENT: Graphs

Reading from reallife graphs NA6c Linear conversion graphs NA6e Speed calculations SSM4c Distance/time graphs and calculation of speed NA6c Using coordinates to solve problems SSM3e Straight line graphs NA6b Recognising curves in graphs NA6e

PRIOR KNOWLEDGE

Modules 7, 19. Experience at plotting points in all quadrants (Module 8).

OBJECTIVES

By the end of the module the students should be able to: Read from reallife graphs, distance/time graphs and conversion graphs to answer questions. Calculate speed from numerical data and from a graph. Calculate speed from a graph and use gradients to compare speed. Use coordinates to locate midpoints of lines. Plot graphs of the form y = ax + b using a table to generate points.


Plot graphs of the form y = ax + b where pupil has to generate their own table and set out their own axes. Use a spreadsheet to generate straightline graphs, posing questions about the gradient of lines.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Clear presentation with axes labelled correctly is vital. Recognise linear graphs and hence when data may be incorrect.


GCSE TIER: Foundation TARGET GRADE: F/E/D

CONTENT: Geometry

Recognising parallel and perpendicular lines SSM2a, c Using parallel lines, alternate angles and corresponding angles SSM2c Using the angle properties of parallelograms SSM2c Understanding the proof that the angle sum of a triangle is 180 degrees SSM2c Understanding the proof regarding exterior angles of triangles SSM2c

PRIOR KNOWLEDGE

Modules 7, 14. Ability to recognise parallel lines and right angles. A concept of the word proof.

OBJECTIVES

By the end of the module the students should be able to: Recognise and draw parallel and perpendicular lines. Recognise and solve problems involving corresponding and alternate angles. Use parallel line properties of a parallelogram or rhombus to solve problems. Prove the two results involving angles in triangles.


The work can be extended to include other angle properties studied in module 14. Look at question involving more than one intersecting line.

RESOURCES

London GCSE Mathematics Foundation Course (Old Edition) Chapter 3, page 50

OTHER RESOURCES

ICT

NOTES

A firm knowledge of obtuse and acute angles helps pupils to recognise which of the angles generated by parallel and intersecting lines are the same.


GCSE TIER: Foundation TARGET GRADE: F/E/D

CONTENT: Percentages

Calculating percentages of amounts NA3m Solving percentage problems NA2e Increasing and decreasing by a percentage NA3m Writing one number as a percentage of another NA3e STAGE TWO

PRIOR KNOWLEDGE Modules 1, 11, 22. Understand the concepts of VAT, interest, profit, loss, and tax.

OBJECTIVES

By the end of the module the students should be able to: Use percentages to solve simple problems without a calculator. Use percentages to describe increases and decreases. Use percentages to solve problems involving VAT, taxation, bills, profit and loss. Use percentages to compare amounts.


Fractional percentages of amounts.

RESOURCES


OTHER RESOURCES

ICT

NOTES

In preparation for this unit students should be reminded of basic percentages and recognise their fraction and decimal equivalents.



CONTENT: Ratio and conversions

Basic ideas of ratio NA2f STAGE ONE Simplifying ratios NA2f STAGE ONE Dividing in a given ratio NA3f Unitary method NA3n Simple proportion NA3n Scales in maps and diagrams SSM3d Converting between units given conversion factors NA4a STAGE ONE Knowing and using metric equivalents of common imperial units SSM4a

PRIOR KNOWLEDGE

Module 11. Basic number skills and ability to recognise common factors. Calculator skills.

OBJECTIVES

By the end of the module the students should be able to: Recognise a ratio as a way of showing the relationship between two numbers. Simplify a ratio by dividing both its numbers by a common factor. Recognise when a ratio is in its lowest terms. Recognise that two numbers are in proportion if their ratios stay the same as the quantities get larger or smaller. Use the unitary method as a way of solving ratio and proportion problems. Interpret and use a scale to show the relationship between a distance on a map and the distance on the ground. Convert between a variety of units and currencies where conversion factors are give. Convert between a variety of units using knowledge of metric equivalents of common imperial units.


Currency calculations using current exchange rates. Similar triangles.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Students often cope well with ratios of two quantities. They have greater difficulty with ratios of three quantities and particular attention needs to be given to this.


GCSE TIER: Foundation TARGET GRADE:G/F/E/D

CONTENT: Estimation

Rounding to decimal places and significant figures NA3h Using a calculator effectively, and interpreting the calculator display NA3q Estimate answers to complex calculations NA3h Using estimation and inverse operations to check the validity of solutions NA4c Reverse rate problems NA4a Trial and improvement NA4b

PRIOR KNOWLEDGE

Modules 1, 13. Using a calculator for simple problems. Rounding off to the nearest integer.

OBJECTIVES

By the end of the module the students should be able to: Understand the content of the module. Round numbers of any size to significant figures or decimal places. Use one significant figure to estimate answers without a calculator. Use approximation and inverse operations to check validity of solutions. Use trial and improvement in general problem solving.


Simple examples of upper and lower bounds. Estimating answers to more complicated calculations.

RESOURCES

OTHER RESOURCES

ICT

NOTES

Rounding is often tested in context, and this should be regularly tested through examples from other modules. Candidates should be encouraged to write the full answer to a solution before writing the rounded answer in case an error in rounding leads to a seemingly incorrect answer.



CONTENT: 3D shapes

2D representations of 3D objects SSM2k Plans and elevations SSM2k Using the language of 3D shapes SSM2j Planes of symmetry* SSM3b Nets of simple solids SSM2k Finding surface area of solids with triangular and rectangular faces** SSM4f

PRIOR KNOWLEDGE

Module 20.

OBJECTIVES

By the end of the module the students should be able to: Draw 2D representations of 3D objects, including the use of isometric paper. Use plans and elevations to answer questions. Find and sketch the planes of symmetry of simple solids. Draw nets of simple solids and use these to calculate surface areas.


Make solids using equipment such as clixi or multilink. Draw shapes made from multilink on isometric paper. Build shapes from cubes that are represented in 2D.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Accurate drawing skills need to be reinforced. *In 1387 this may have been best covered in module 8. ** In 1388 this was assessed in stage 2.



CONTENT: Algebra

Factorising NA5b Solving equations using brackets and negative solutions NA5e Define new expressions NA5a Derive formulae NA5f Derive formulae NA5f Substituting into expressions involving powers NA5c

PRIOR KNOWLEDGE

Modules 2, 13, 19. Understanding of the mathematical meaning of the words expression, simplifying, formulae and equation. Substituting into expressions and formulae. Powers and indices for letters. Using brackets in numerical calculations and removing brackets in simple algebraic expressions.

OBJECTIVES

By the end of the module the students should be able to: Generate expressions involving two or more terms. Generate formulae in words or symbols from given information Factorise with a constant term outside a single pair of brackets. Derive and solve any linear equations. Substitute positive into expressions including powers.


Use negative numbers in formulae involving indices. Develop algebraic skills through the Intermediate syllabus. Various investigations leading to generalisations.

RESOURCES


OTHER RESOURCES

ICT

NOTES

Emphasis on good use of notation 3ab means 3 × a × b. Students need to be clear on the meanings of the words expression, equation, word formulae and algebraic formulae as they can find this confusing.


GCSE TIER: Foundation TARGET GRADE: D

CONTENT: Circles

Knowing the language of a circle SSM2i Knowing and using the formula for circumference SSM4h Knowing and using the formula for area of a circle SSM4h Converting between area measures and volume measures SSM4i

PRIOR KNOWLEDGE

Module 17. Experience of constructing circles.

OBJECTIVES

By the end of the module the students should be able to: Use the vocabulary of a circle (circumference, radius, and diameter) Recall and apply the formulae for the area and circumference of a circle. Recognise that units of volume or area cannot be converted using linear conversion factors. Convert between units of area or volume.


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

RESOURCES


OTHER RESOURCES

ICT

NOTES

π can be 3 or 3.14 depending on accuracy required.


GCSE TIER: Foundation TARGET GRADE: F/E

CONTENT: Data Handling

Design and use twoway tables for discrete and continuous data HD3c Draw and produce line graphs for time series HD4a Interpret social statistics HD5k

PRIOR KNOWLEDGE

Modules 3, 6, 10, 12, 15, 18, 23.

OBJECTIVES

By the end of the module the students should be able to: Understand the contents of the module.


Make predictions by considering trends of line graphs for time series.

RESOURCES

OTHER RESOURCES

ICT

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