Mathematics Syllabus 2011 Onwardstcst.org.uk/wp-content/uploads/2012/04/maths-curriculum201112.pdf · Mathematics Syllabus 2011 Onwards Introduction Mathematics is a subject that

Mathematics Syllabus 2011 Onwards

Introduction Mathematics is a subject that represents order and beauty through processes, rules and

symbols. It is a form of thinking that enables pupils to express their understanding of God’s

creation logically and methodically and theorise about the order God has created.

God has created a universe that is knowable and beautiful. He has put his image in Man so that

we are able to reason about the universe and perceive its beauty.

Mathematics enables us to represent the rationality and symmetry of what God has created

knowing, in doing so, we have discovered truth because of the beauty and order that is intrinsic

to creation.

We can explore truths about creation in Science even beyond what we can observe because of

the power of Mathematics.

God has commanded man to subdue the creation. Mathematics is the language that informs the

ingenuity of Man and furthers the development of technology to enable us to derive benefit

from what God has made for our good.

Justice is important to God. Mathematics enables the fulfilment of justice in commerce through

the ability to test and verify the fairness of transactions.


Aims

We aim to help all pupils to

acquire a sound concept of number and be confident in their use of figures

develop their thinking skills through tackling a variety of tasks

acquire good mathematical techniques for calculation and solution of

problems

be well equipped to use their maths in the real world

develop mental methods and mental visualising

understand how or why the mathematical concepts they use work and when

they are appropriate to use

be able to tackle problems in a logical and systematic way, applying skills

they have learnt

learn to make hypotheses and test them, refining their ideas as they go

identify different routes through problems so that they fully explore the

maths they can use to solve a task.

make connections and deductions from the results they obtain

develop more of an idea of mathematical proof and argument

use ICT to support and enhance their mathematics

present all their working in a mathematical way and be able to

communicate their maths in a variety of forms.

We aim to enable each pupil to achieve the highest grade of which they are capable

at GCSE through supporting progress throughout the school. Progress is made

when knowledge and skills are robust and transferable.

We want to send them all out in the world with a good understanding, particularly

of arithmetic, so that they will take this into their future studies and jobs, whether

or not they continue to study mathematics. We want what is learned in school to be

a source of inspiration for mathematical thinking outside the classroom.

We want to make sure that throughout the GCSE years they continue to find

mathematics a stimulating and enjoyable subject, getting satisfaction from success

in their work, and well prepared for further studies if they choose.

We want to use the exploratory possibilities as well as the rigours of mathematical reasoning as a

means to help pupils develop their learning and thinking skills.


learners should be able to:

recall and use their knowledge of the GCSE prescribed content (AO1)

select and apply mathematical methods in a range of contexts (AO2)

interpret and analyse problems and generate strategies to solve them (AO3)

Objectives

The Key Concepts specified in the National Curriculum are:

1.1 Competence

a. applying suitable mathematics accurately within the classroom and beyond

b. communicating mathematics effectively

c. selecting appropriate mathematical tools and methods, including ICT.

1.2 Creativity

a. combining understanding, experiences, imagination and reasoning to construct new

knowledge

b. using existing mathematical knowledge to create solutions to unfamiliar problems

c. posing questions and developing convincing arguments.

1.3 Applications and implications of mathematics

a. knowing that mathematics is a rigorous, coherent discipline

b. understanding that mathematics is used as a tool in a wide range of contexts

c. recognising the rich historical and cultural roots of mathematics

d. engaging in mathematics as an interesting and worthwhile activity.

1.4 Critical understanding

a. knowing that mathematics is essentially abstract and can be used to model, interpret or

represent situations

b. recognising the limitations and scope of a model or representation.

There are three assessment objectives for the GCSE.

The objectives are assessed across the three units.


In order to ensure a good breadth of study the curriculum will include:

practical activities

working in groups

a wide variety of both closed and open and extended tasks

discussion around topics such as probability, using statistics, statistics in real life

data handling tasks with hypotheses and interpretation of results. Comparison with

existing research.

investigative tasks which lead to rules and generalisations

use of ICT

using calculators appropriately and efficiently

teaching deductive reasoning and progressing towards formal proof including

consideration of constraints and assumptions.

using good mental and written methods in all areas of number

opportunities to solve a wide variety of problems and to talk about the work

tasks which can be solved in more than one way

opportuntites to make connections between different areas of maths

tasks whose solutions can be presented in more than one way

the use of maths in other curriculum areas such as geography, science and finance.

According to the National Curriculum, these are the essential skills and processes in

mathematics that pupils need to learn to make progress.

2.1 Representing

Pupils should be able to:

a. identify the mathematical aspects of a situation or problem

b. choose between representations

c. simplify the situation or problem in order to represent it mathematically, using appropriate

variables, symbols, diagrams and models

d. select mathematical information, methods and tools to use.

2.2 Analysing

Use mathematical reasoning


a. make connections within mathematics

b. use knowledge of related problems

c. visualise and work with dynamic images

d. identify and classify patterns

e. make and begin to justify conjectures and generalisations, considering special cases and

counter-examples

f. explore the effects of varying values and look for invariance and covariance

g. take account of feedback and learn from mistakes

h. work logically towards results and solutions, recognising the impact of constraints and

assumptions

i. appreciate that there are a number of different techniques that can be used to analyse a

situation

j. reason inductively and deduce.


Use appropriate mathematical procedures


k. make accurate mathematical diagrams, graphs and constructions on paper and on screen

l. calculate accurately, selecting mental methods or calculating devices as appropriate

m. manipulate numbers, algebraic expressions and equations and apply routine algorithms

n. use accurate notation, including correct syntax when using ICT

o. record methods, solutions and conclusions

p. estimate, approximate and check working.

2.3 Interpreting and evaluating


a. form convincing arguments based on findings and make general statements

b. consider the assumptions made and the appropriateness and accuracy of results and

conclusions

c. be aware of the strength of empirical evidence and appreciate the difference between

evidence and proof

d. look at data to find patterns and exceptions

e. relate findings to the original context, identifying whether they support or refute conjectures

f. engage with someone else’s mathematical reasoning in the context of a problem or particular

situation

g. consider the effectiveness of alternative strategies.

2.4 Communicating and reflecting


a. communicate findings effectively

b. engage in mathematical discussion of results

c. consider the elegance and efficiency of alternative solutions

d. look for equivalence in relation to both the different approaches to the problem and different

problems with similar structures

e. make connections between the current situation and outcomes, and situations and outcomes

they have already encountered.


Method

KS3 Mathematics: Year 7 and Year 8 Course

Course Book: Exploring Maths Published by Pearson Longman

This course has been adopted to help meet the renewed KS3 Framework.

It has been adopted because of its flexible structure allowing pupils to complete two levels of

progress. Its tier-based approach enables the teacher to select materials that meet pupils’

specific needs with everyone catered for, including those needing support and those with

exceptional gifts.

The course also enables us to more carefully enable pupils who are able, to take GCSE Maths

when they are ready.

Mathematics Syllabus 2011 Onwards The structure of the course enables pupils at different Tiers to be taught in the same group and a lesson structured to differentiate for all the needs

of the pupils.

In Year 7 most pupils will be using Tier 3, consolidating level 4.

Tier 1 Tier 2 Tier 3 Tier 4 Tier 5 Tier 6 Tier 7

N1.1 Properties of

numbers

N2.1 Properties of

numbers

N3.1 Properties of

numbers

N4.1 Properties of

numbers

N5.1 Powers and roots N6.1 Powers and roots N7.1 Powers and roots

N1.2 Adding and

subtracting

N1.3 Multiplying and

dividing

N1.4 Mental calculations

N2.2 Whole numbers N3.2 Whole numbers and

decimals

N4.2 Whole numbers,

decimals and

fractions

N1.5 Fractions

N1.6 Money and decimals

N1.7 Number and

measures

N2.3 Fractions, decimals

and percentages

N2.4 Decimals

N2.5 Decimals and

measures

N3.3 Fractions and

percentages

N3.4 Decimals and

measures

N4.3 Fractions, decimals

and percentages

N5.3 Calculations and

calculators

N6.3 Decimals and

accuracy

N7.2 Decimals and

accuracy

N1.8 Multiplying and

dividing 2

N2.6 Fractions,

percentages and

direct proportion

N3.5 Percentages, ratio

and proportion

N4.4 Proportional

reasoning

N5.2 Proportional

reasoning

N6.2 Proportional

reasoning

N7.3 Proportional

reasoning

N1.9 Solving number

problems

N2.7 Solving number

problems

N3.6 Solving number

problems

N4.5 Solving problems N5.4 Solving problems N6.4 Using and applying

maths

N7.4 Using and applying

maths

A1.1 Patterns and

sequences

A2.1 Patterns and

sequences

A2.2 Sequences,

functions and

graphs

A3.1 Sequences and

patterns

A3.3 Functions and

graphs

A3.4 Using algebra

A4.1 Linear sequences

A4.3 Functions and

graphs

A4.5 Using algebra

A5.1 Sequences and

graphs

A5.3 Functions and

graphs

A5.4 Using algebra

A6.2 Linear functions and

graphs

A6.3 Quadratic functions

and graphs

A6.4 Using algebra

A7.2 Linear graphs and

inequalities

A7.4 Functions and

graphs

A2.3 Expressions and

equations

A3.2 Equations and

formulae


formulae

A4.4 Equations and

formulae

A5.2 Equations and

formulae

A5.5 Equations, formulae

and graphs


formulae


formulae

A7.3 Equations

G1.1 Properties of shapes

G1.5 More properties of

shapes

G2.5 Properties of

shapes

G3.4 Properties of shapes

Mathematics Syllabus 2011 Onwards G1.2 Angles and

symmetry

G2.2 Angles G3.2 Angles G4.1 Angles and shapes G5.2 2D and 3D shapes

G3.5 Constructions G4.4 Constructions G5.4 Angles and

constructions

G6.1 Geometrical

reasoning

G7.1 Geometrical

reasoning

G1.2 Angles and

symmetry

G2.3 Symmetry and

reflection

G3.3 Transformations G4.3 Transformations G5.3 Transformations G6.3 Transformations and

loci

G7.4 Transformations and

vectors

G1.3 Measures 1

G1.4 Measures 2

G1.6 Measures 3

G2.1 Length, perimeter

and area

G2.4 Measures

N2.5 Decimals and

measures

G3.1 Area and perimeter

N3.4 Decimals and

measures

G4.2 Measures and

mensuration

G5.1 Measures and

mensuration

G6.4 Measures and

mensuration

G7.3 Measures and

mensuration

G6.2 Trigonometry 1

G6.5 Trigonometry 2

G7.2 Trigonometry 1

G7.5 Trigonometry 2

S1.1 Graphs and charts 1 S2.1 Graphs, charts and

tables

S3.1 Grouped data and

simple statistics

S1.2 Graphs and charts 2 S2.3 Enquiry 1 S3.3 Enquiry 1 S4.2 Enquiry 1 S5.1 Enquiry 1 S6.1 Enquiry 1 S7.1 Enquiry 1

S1.3 Graphs and charts 3 S2.5 Enquiry 2 S3.4 Enquiry 2 S4.3 Enquiry 2 S5.3 Enquiry 2 S6.3 Enquiry 2 S7.3 Enquiry 2

S2.2 Probability 1 S3.2 Probability 1 S4.1 Probability S5.2 Probability 1 S6.2 Probability 1 S7.2 Probability 1

S2.4 Probability 2 S3.5 Probability 2 S5.4 Probability 2 S6.4 Probability 2 S7.4 Probability 2

R2.1 Revision unit 1 R2.1 Revision unit 1 R3.1 Revision unit 1 R4.1 Revision unit 1 R5.1 Revision unit 1 R6.1 Revision unit 1 R7.1 Revision unit 1

R2.2 Revision unit 2 R2.2 Revision unit 2 R3.2 Revision unit 2 R4.2 Revision unit 2 R5.2 Revision unit 2 R6.2 Revision unit 2 R7.2 Revision unit 2


Y9 Mathematics Course

The course followed is either

SMP Interact Foundation Tier Transition book

Or

SMP Interact Higher Tier Transition book.

(http://www.smpmaths.org.uk/twotiergcse.htm)

These have practice books for homework and provide level specific content to support the

transition to GCSE.

GCSE Mathematics Course

Class Groups

We start the GCSE in the Summer Term of Y9. This allows us to cover the course

without a sense of time pressure. As a result we can explore topics and extend the

curriculum beyond the syllabus requirements. It also means that able pupils can

be “fast-tracked” to take their GCSE early and to progress to Further Maths, As

level or FSMQ.

Pupils are grouped in order to meet individual needs and abilities as far as

practicable.

Tier of entry

Pupils and their teacher decide together which level of entry to take in each

module.

Differentiation

Over the years we have successfully taught classes in which pupils are working

towards different tiers. The small numbers means that it is easy to organise

lessons in such a way that the each child is given work appropriate to their needs.

Starters which involve every pupil whatever their level of ability help give a sense

of cohesion to the lesson.

Particularly able pupils work with the year above and complete the GCSE in Y10.

This gives them the option of taking AS modules in Y11.

http://www.smpmaths.org.uk/twotiergcse.htm

Mathematics Syllabus 2011 Onwards GCSE Chapter Teaching hours Grades AQA Modular specification reference

Y9

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UNIT 2: Number and Algebra

9. Estimation and currency conversion

2 D, C Working with numbers and the number system: N1.1, N1.2, N1.4, N1.4h

10. Factors, powers and roots

2 D, C Working with numbers and the number system: N1.6, N1.7, N1.8

11. Fractions 4 D, C, B Working with numbers and the number system: N1.2, N1.3, N1.5 Fractions, Decimals and Percentages: N2.1, N2.2

12. Basic rules of algebra 4 D, C, B The Language of Algebra: N4.1, N4.2h Expressions and Equations: N5.1, N5.1h, N5.4

13. Decimals 4 D, C, B, A Working with numbers and the number system: N1.2 Fractions, Decimals and Percentages: N2.3, N2.4

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14. Equations and inequalities

5 D, C, B Expressions and Equations: N5.4, N5.4h, N5.7

15. Formulae 3 D, C, B The Language of Algebra: N4.2 Expressions and Equations: N5.6

16. Indices and standard form

6 C, B, A, A* Working with numbers and the number system: N1.9, N1.9h, N1.10h, N1.11h, N1.12h

17. Sequences and proof 6 D, C, B, A, A* Expressions and Equations: N5.9, N5.9h Sequences, Functions and Graphs: N6.1, N6.2

18. Percentages 3 D, C, B Fractions, Decimals and Percentages: N2.6, N2.7, N2.7h

19. Linear graphs 6 D, C, B, A Expressions and Equations: N5.4h, N5.7h Sequences, Functions and Graphs: N6.3, N6.4, N6.5h, N6.6h, N6.11, N6.12

7. Ratio and proportion 6 D, C, B, A Ratio and Proportion: N3.1, N3.2, N3.3, N3.3h

20. Quadratic equations 7 B, A, A* Expressions and Equations: N5.2h, N5.5h

21. Further algebra 6 B, A, A* Expressions and Equations: N5.3h, N5.4h, N5.6

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UNIT 1: Statistics and Number

1. Data collection 4 D, C, A, A* The Data Handling Cycle: S1 Data Collection: S2.1, S2.2, S2.3, S2.4, S2.5 Data presentation and analysis: S3.1

2. Fractions, decimals and percentages

3 D, C Working with numbers and the number system: N1.14 Fractions, Decimals and Percentages: N2.5, N2.6, N2.7

3. Interpreting and representing data

6 D, C, A, A* Data presentation and analysis: S3.2, S3.2h Data Interpretation: S4.2, S4.3, S4.4

4. Range and averages 4 D, C, A Data presentation and analysis: S3.3 Data Interpretation: S4.1

5. Probability 7 D, C, B, A, A* Probability: S5.1, S5.2, S5.3, S5.4, S5.5h, S5.6h, S5.7, S5.8, S5.9

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6. Cumulative frequency 5 B Data presentation and analysis: S3.2h, S3.3h Data Interpretation: S4.4

8. Complex calculations and accuracy

7 C, B, A, A* Working with numbers and the number system: N1.10h, N1.13h Fractions, Decimals and Percentages: N2.7h

Mathematics Syllabus 2011 Onwards Y

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UNIT 3: Geometry and Algebra

22. Number skills 1 Working with numbers and the number system: N1.3, N1.4h, N1.14 Fractions, decimals and Percentages: N2.1, N2.5, N2.7 Ratio and Proportion: N3.1

23. Angles 2 D, C Properties of angles and shapes: G1.1, G1.2 Measures and Construction: G3.6

24. Triangles, polygons and constructions

3 D, C Expressions and Equations: N5.4 Properties of angles and shapes: G1.1, G1.2, G1.3, G1.4 Measures and Construction: G3.8, G3.9, G3.10

25. More equations and formulae

2 D, C, B, A Expressions and Equations: N5.4, N5.6, N5.8

26. Compound shapes and 3-D objects

4 D, C, A Properties of angles and shapes: G1.6 Geometrical reasoning and calculation: G2.4 Mensuration: G4.1, G4.4

27. Circles, cylinders, cones and spheres

7 D, C, A, A* Properties of angles and shapes: G1.5 Geometrical reasoning and calculation: G2.4 Mensuration: G4.1h, G4.3, G4.3h, G4.4, G4.5h

28. Measures and dimensions

3 D, C, B Measures and Construction: G3.4, G3.7

29. Constructions and loci 3 C, B Measures and Construction: G3.10, G3.11

30. Reflection, translation and rotation

3 D, C Properties of angles and shapes: G1.7 Vectors: G5.1

31. Enlargement 2 D, C, A Properties of angles and shapes: G1.7, G1.7h Measures and Construction: G3.2

32. Congruency and similarity

5 C, B, A, A* Properties of angles and shapes: G1.8 Geometrical reasoning and calculation: G2.3, G2.3h Measures and Construction: G3.2h

33. Pythagoras’ theorem and trigonometry

7 C, B, A, A* Working with numbers and the number system: N1.14h Sequences, Functions and Graphs: N6.3h Geometrical reasoning and calculation: G2.1, G2.1h, G2.2h

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34. Circle theorems 4 B, A, A* Properties of angles and shapes: G1.5h

35. Non-linear graphs 9 D, C, B, A, A* Expressions and Equations: N5.2h, N5.5h Sequences, Functions and Graphs: N6.7h, N6.8h, N6.10h, N6.11h, N6.13

36. Further trigonometry 7 A, A* Sequences, Functions and Graphs: N6.8h Geometrical reasoning and calculation: G2.2h Mensuration: G4.2h

37. Transformations of graphs

4 B, A* Sequences, Functions and Graphs: N6.9h

38. Vectors 4 A, A* Vectors: G5.1h

REVISION FOR JUNE EXAM (19 HOURS) Y11 SUMMER

TERM


Learning strategies (Sue Humphries)

My main strategy is to make sure that every pupil understands each step of

each topic and feels confident. This seems to be one of the main keys to enjoying

mathematics – success. Thinking carefully how to introduce a topic is therefore

very important. As is having a variety of approaches / resources.

(4.a,b)

We usually learn new topics together as a group through a starter problem or

activity, discussion, board work, and practise questions. Group and paired

activities encourage active participation in the exploration of new ideas; practical

activities reinforce learning through their “hands-on” nature; and more visual

demonstration using real life aids helps provide a context. Use of the small white

boards means that everyone is actively involved and the teacher can check that

everyone is following and understanding.

Plenty of opportunity to practise. Maths should be much more about doing

than listening and we choose to have longer rather than shorter lessons so that

there is plenty of time for pupils to use the mathematics and to find out if they

have really understood. The textbooks quickly introduce questions that require

thought through application of a method rather than just straightforward testing

of a skill. Some require multi-stage solutions and these develop the pupils’ ability

to work their way through a problem logically as well as requiring them to present

clear reasoned working. I do set homework 2 or 3 times a week but much prefer

that the bulk of practise be done when I am there to help and to check working.

This enables us to teach good habits of presentation prevent confusion and use

more challenging material than could be given to pupils to work on alone. It also

helps prevent anyone getting into a mindset of” not being able to do maths” as

there is someone to sort out any problems straightaway.

My second main strategy is regular reviewing. Most children seem to find it

hard to retain mathematical concepts – even some of the most basic ones. I like to

include “quick check” questions at the start of some lessons to keep topics familiar.

Use of the individual white boards means that I can see every pupil’s work and

this is an excellent chance to find out who knows what.

I have recently reintroduced the “Mental Arithmetic” books from Schofield and

Sims (book 6) for some pupils. These reinforce a wide range of basic number skills

with decimals, fractions, percentages, compound measure, metric – imperial

conversion, familiar angle and area. The questions are often carefully chosen to

highlight good mental arithmetic techniques, giving opportunities for useful

discussion. However, some of the questions will keep pupils using standard

written techniques too – despite the title of the books. Even some able students

need to have opportunities to practise written arithmetic. It would be better to

have some lessons with calculator bans to keep this skills current than to have

exercises out of any context.


Developing mathematical thinking.

The Maths Challenge questions provide a rich source of questions across the

syllabus to encourage good mathematical thinking. Often they make the solver

look at a question in a different way in order to find a solution in the most efficient

manner. They draw on an understanding of number relationships and logic and

encourage algebraic approaches. They are all non-calculator questions, so not only

reduce calculator dependence but also reinforce the strengths of working with

fractions, pi and roots rather than decimals. The more open “Olympiad” questions

require rigour and many underline the need for algebra in seeking and/or

justifying solutions.

Every topic is a chance to use mathematical thinking – from thinking about

accuracy and using mental arithmetic approximation to get a “ball park” figure to

asking “what if…” to talking about true mathematical proof and methods of

presentation.

The ATM book “Thinkers” provides examples of how to encourage pupils to look

for:

general results,

peculiar cases and exceptions

characteristics

unexpected results

open and closed questions

how to sort and order

(2.2f)

Together with an extract from ATM’s “Questions and Prompts for mathematical

thinking” this gives plenty of ideas for good questioning techniques in the

classroom.

We have a textbook “Are you sure?” which starts with a familiar proof of

“1 = 2” to get pupils thinking; and interested. It has a variety of formal proofs of

various topics – some a little too advanced for us.

In fact there is a wealth of opportunities for proof in many areas and I have put

together some of these possibilities for use as appropriate.

Approaching all topics in a good mathematical way and with attention to detail

will hopefully ensure that the non topic-specific skills as listed below are well

covered:

(choice of) accuracy, units of measure, checking answers are sensible,

understanding what the answer is telling you,

mental methods,

communicating mathematically, using efficient methods of working,

using different ways of solving the same problem,

making inferences,

thinking about constraints and assumptions made,

justifying,

breaking down tasks and problem solving, deductive reasoning, proof.


looking for exceptions.

differentiating between standard methods and methods suited to non-calculator

situations – particularly for number topics in module three.

Note taking.

Notes made on each new topic go into a notes folder. The hope is that this folder is

referred to throughout the year. I would like to think that pupils to go to this for

help before coming to me since this requires an active effort on their part rather

than a more passive receiving – and hopefully improves the learning level as a

result.

Making notes is a good way of summarising and consolidating at the end of a

topic. Getting pupils to make their own notes is a way of testing their level of

understanding.

Two-tier maths.

The two-tier system means that grade B students are being entered for an

examination which in some areas will be above their ability. As one of my key

philosophies is that understanding maths leads to enjoying it, this is not an ideal

situation. I need to find ways of working which will enable pupils to tackle higher

tier work without losing confidence. Introducing topics at a straightforward level

and differentiating subsequent work is one approach, together with careful

preparation for the exams and teaching them how to concentrate on their

strengths. Starting in Y9 should help make sure there is time to cover even some

of the harder topics in a step by step way which makes them accessible to these

candidates.


Assessment

Ongoing day-to-day.

We are currently developing the practise of using formative rather than summative assessment

in school. With the small numbers in the class the teacher is always monitoring the level of

understanding – from oral questioning, helping with work in class and marking homework.

This then informs the teacher as to what to teach next. Marked work is corrected and the

corrections are marked.

Assessment will be primarily based on class responses and used to judge level of

understanding, interest, concentration, effort.

Further feedback will be given by the written answers to exercises in class and

from homework.

Marks and comments in class books provide a written record. This can be

sufficient since we know our small number of pupils so well.

Pupils in Y7 and 8 have an ongoing record of what they have learned and how

they are doing through the homework book and the “Points to Remember” which

they copy out before doing the exercise. The teacher may provide additional

examples where the pupil has not understood

Pupils in Y9 keep records for revision of the results of Chapter Self Tests and

Review exercises.

Pupils doing the GCSE map their progress through analysis of Review Exercises.

Set objectives

for the lesson Oral

questioning in

class, marking

work

assess level of

understanding

corrections /

reinforcement /

extra help


Periodic.

Small tests on specific areas of the curriculum. corrections / revision / retest

Pupil and peer assessment after a section of work or an extended task target or goal

setting as appropriate review after given timescale

End of session tests predicted grade / results given in school report

In Y7 and Y8 the check-up section of the CD ROM for each Tier based on each unit

will show whether pupils have retained skills and whether they can apply their

knowledge independently.

Pupils are allowed to use their homework notes for these tests. It encourages them

to search out facts they have forgotten and helps them realise that they can

sometimes solve their own problems since in a test situation there is no one else to

ask.

Reports to parents go out in the new year shortly before the parents’ evening.

Formal Reporting.

Half termly effort grades and comments.

Reporting to parents in February and June as set out in the school policy.

In Year 7 and 8 the end of year exam covers the whole course and pupils gain a

percentage mark for their work. This gives them some idea of how much they are

retaining and what areas they need to concentrate on.

Marks from the end of year exam are recorded, together with a simple analysis of

how the pupil did. Marks are also recorded on the exam report which goes home at

the end of the school year.

With the pupil, the teacher checks through the Key Objectives so the pupil can see what they

have achieved.


Resources Folders of spider diagrams together with supporting worksheets and ideas for

activities forms the basis of support for the course.

For exercises of questions to use in class to extend the text book, we draw mainly

from Longman AQA GCSE Mathematics and the SMP Interact course, which

provides good coverage and plenty of examples. This is supplemented by a variety

of other material.

To encourage estimation and stimulate mental maths in everyday contexts: Round

About sheets. Really good for giving them strategies for everyday life.

Mental maths sheets: great ideas for visualising. Good fun too.

TEXTS

KS3 Course Book: Exploring Maths Published by Pearson Longman

SMP Interact Two Tier Transition books

Longman AQA GCSE Maths for Higher Sets

Longman AQA GCSE Maths for Middle Sets

Longman AQA GCSE Maths for Lower Sets

Mental Arithmetic 6.

AQA Functional maths (Longman)

Active Maths books are aimed at higher ability. They include many “real life”

based questions which provide some interesting/unusual facts and hence add extra

interest to some of the numerical areas of maths. Also useful:

AM3: graphs

AM4: Growth and decay, Similar Solids

AM5: Circle geometry, Sequences (to extend topic), Standard deviation

Oxford GCSE Higher Tier: Sketch graphs, percentage error, upper and lower

bounds, SIF, Calculator skills and fun with calculator words, Loci, Trial and

Improvement in contexts.

In Your Head – not mental arithmetic but encouraging visualisation eg of £D

situations.

ICT: two graph plotting programs.Curvus.pro and Autograph. One has

transformations and data handling spreadsheets

Manga High

LOGO

Revision CD Rom

RAF Maths Mission CD-Rom


Tesselmania

Defence Dynamics (graphs, loci, proof and trig)

Whiteboard facilities and web resources including 3D geom. via Nrich.

TV: We have the BBCs GCSE bitesize revision programmes on video.

See spider diagrams for relevant programmes.

PRACTICAL ACTIVITIES: Symmetry shape puzzles

3D solids to make

Curve stitching

Potz game – 3D visulaisation / views

TEACHER RESOURCES: Thinkers

Are you sure

Geometry

In Our Classrooms


PROOFS in “Are You Sure?

Number

Divisibility p38

Consecutive odd numbers make a sure number by diagram p33

by summation p33

Consecutive numbers and products (see also SMP Interact) p34

Prime numbers proof by contradiction p35

algebraic approach p36

More on primes

Geometry / trig

Dividing by 0 in “proofs” p31

Angles in a triangle p9

Angles in a polygon p11

+ angles in a circle – in Interact

Platonic solids by exhaustion p12

by Euler p13

Three polygons meeting at a point p15

Area of a trapezium p16

Pythagoras various approaches p17

Proof with vectors p29

2r² < area of a circle < 4r² (by diagram) p58

+ Proof by congruence is an excellent way of seeing mathematical rigour.

+ sine and cosine rules are proofs they can start to find themselves

Algebra

½(a + b) ab (also by diagram) p47 and p50

proof by induction p51

Note the relationship between regions and nodes is an excellent example of why proof is

needed over observation. (p66)

Documents

Mathematics Syllabus 2011 Onwardstcst.org.uk/wp-content/uploads/2012/04/maths-curriculum201112.pdf · Mathematics Syllabus 2011 Onwards Introduction Mathematics is a subject that