Wednesday, March 29, 2017
AA

Maths

“Mathematics equips pupils with a uniquely powerful set of tools to understand and change the world. These tools include logical reasoning, problem-solving skills, and the ability to think in abstract ways. Mathematics is important in everyday life, many forms of employment, science and technology, medicine, the economy, the environment and development, and in public decision-making. Different cultures have contributed to the development and application of mathematics. Today, the subject transcends cultural boundaries and its importance is universally recognised. Mathematics is a creative discipline. It can stimulate moments of pleasure and wonder when a pupil solves a problem for the first time, discovers a more elegant solution to that problem, or suddenly sees hidden connections. ” Taken from The National Curriculum Online

 

with added responsibility

Annette Alsopp Subject Leader  
Tom Baker Assistant Subject Leader  
Carol Onley-Gregson Teacher of Mathematics  
Chris Blaxland Teacher of Mathematics  
Aysha Abdulraza Teacher of Mathematics  
Sarah Dienes Teacher of Mathematics  
Claire Foster Teacher of Mathematics  
Sophie Reiness Teacher of Mathematics  
Dr Michelle Bannon Teacher of Mathematics  
Jane Snow Specialist Mathematics
Teaching Assistant
 
Jane Jenks Specialist Mathematics
Teaching Assistant
 

 

Years 7, 8 and 9 follow programmes of study reflecting the National Numeracy Strategy which:

recognises a student’s achievement in their previous school. enables a student to follow the appropriate programme of study. is based upon a variety of teaching and learning styles. sets topics in context as appropriate. enables students to practice routine skills. recognises the numeracy demands of other curriculum areas in planning the order of topics and the style of delivery.

Students in Years 10 and 11 follow programmes of study reflecting the Key Stage 4 programmes of study.  Students will be assessed by the Edexcel Linear GCSE or entry level.  Students have the option to choose statistics at GCSE and this will also be assessed by Edexcel.

Marking ethos (adapted from the department handbook).

 

Work in Mathematics generates a great deal of marking, and it is not usually possible, nor, in general, desirable for a teacher to mark every piece of work which is done.”  Cockcroft 417.

Responding to students’ work is an essential part of the teaching and learning process.  It is important to give students regular feedback about how they progress.  This feedback may be verbal or written.  In general it must be diagnostic and supportive.

It has been accepted that there should be a whole school approach to marking students’ work.  This is as follows:

-            Monitoring of students’ work should be undertaken on a regular basis and in a manner that gives prompt acknowledgement of students’ efforts.

-            Teachers are encouraged to comment (verbally or in written form) on students’ work as a matter of course.

Within the context of the Mathematics Team this is to be interpreted in the following way.

 

Marking policy

Teachers will often mark work as they circulate the class in order to identify misconceptions.  Students can mark their own work and strategies can be developed for establishing what needs to be gone over as a class.  Students may also from time to time peer assess each other’s work. 

Homework on the whole should be marked by staff.  Staff should initial and date the exercise book.  The purpose of marking is: 

to help students know what they can do, where they are wrong and why, and see ways forward in understanding. to give students a clear idea of what they have achieved. to encourage students and give them confidence to tackle new and more difficult work. to make clear expectations and acknowledge well-presented work.

 

Summative Assessment

Students’ work is assessed formally: Teachers will be required to submit a level at the end of each term and the report will indicate the levels of progress and effort the student has made.  These levels are determined from a combination of classwork, homework and half termly assessments. If a student’s performance is significantly higher or lower than those of other students in their group, set moves may be considered. At the end of year 7, 8 and 9 students will sit Optional tests which provide a nationally recognised benchmark.  In year’s 10 and 11 students will sit modular assessments to track their progress every 6 weeks. These results are useful for providing a forecast  at GCSE.

KS3:  List of the key objectives for each year group

Year 7

Simplify fractions by cancelling all common factors; identify equivalent fractions.

- Recognise the equivalence of percentages, fractions and decimals.

- Extend mental methods of calculation to include decimals, fractions and percentages.

- Multiply and divide three-digit by two-digit whole numbers; extend to multiplying and dividing decimals with one or two places by single-digit whole numbers.

- Break a complex calculation into simpler steps, choosing and using appropriate and efficient operations and methods.

- Check a result by considering whether it is of the right order of magnitude.

- Use letter symbols to represent unknown numbers or variables.

- Know and use the order of operations and understand that algebraic operations follow the same conventions and order as arithmetic operations.

- Plot the graphs of simple linear functions.

- Identify parallel and perpendicular lines; know the sum of angles at a point, on a straight line and in a triangle.

Convert one metric unit to another (e.g. grams to kilograms); read and interpret scales on a range of measuring instruments.

- Compare two simple distributions using the range and one of the mode, median or mean.

- Understand and use the probability scale from 0 to 1; find and justify probabilities based on equally likely outcomes in simple contexts.

- Solve word problems and investigate in a range of contexts, explaining and justifying methods and conclusions.        

 

Year 8

Add, subtract, multiply and divide integers.

- Use the equivalence of fractions, decimals and percentages to compare proportions; calculate percentages and find the outcome of a given percentage increase or decrease.

- Divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion.

- Use standard column procedures for multiplication and division of integers and decimals, including by decimals such as 0.6 or 0.06; understand where to position the decimal point by considering equivalent calculations.

- Simplify or transform linear expressions by collecting like terms; multiply a single term over a bracket.

- Substitute integers into simple formulae.

- Plot the graphs of linear functions, where y is given explicitly in terms of x ; recognise that equations of the form y = mx + c correspond to straight-line graphs.

- Identify alternate and corresponding angles; understand a proof that the sum of the angles of a triangle is 180° and of a quadrilateral is 360°.

- Enlarge 2-D shapes, given a centre of enlargement and a positive whole-number scale factor.

- Use straight edge and compasses to do standard constructions.

- Deduce and use formulae for the area of a triangle and parallelogram, and the volume of a cuboid; calculate volumes and surface areas of cuboids.

- Construct, on paper and using ICT, a range of graphs and charts; identify which are most useful in the context of a problem.

- Find and record all possible mutually exclusive outcomes for single events and two successive events in a systematic way.

- Identify the necessary information to solve a problem; represent problems and interpret solutions in algebraic, geometric or graphical form.

- Use logical argument to establish the truth of a statement.

 

Year 9

- Add, subtract, multiply and divide fractions.

- Use proportional reasoning to solve a problem, choosing the correct numbers to take as 100%, or as a whole.

- Make and justify estimates and approximations of calculations.

-Construct and solve linear equations with integer coefficients, using an appropriate method.

- Generate terms of a sequence using term-to-term and position-to-term definitions of the sequence, on paper and using ICT; write an expression to describe the nth term of an arithmetic sequence.

- Given values for m and c, find the gradient of lines given by equations of the form y = mx + c.

- Construct functions arising from real-life problems and plot their corresponding graphs; interpret graphs arising from real situations.

- Solve geometrical problems using properties of angles, of parallel and intersecting lines, and of triangles and other polygons.

- Know that translations, rotations and reflections preserve length and angle and map objects on to congruent images.

- Know and use the formulae for the circumference and area of a circle.

- Design a survey or experiment to capture the necessary data from one or more sources; determine the sample size and degree of accuracy needed; design, trial and if necessary refine data collection sheets.

- Communicate interpretations and results of a statistical enquiry using selected tables, graphs and diagrams in support.

- Know that the sum of probabilities of all mutually exclusive outcomes is 1 and use this when solving problems.

- Solve substantial problems by breaking them into simpler tasks, using a range of efficient techniques, methods and resources, including ICT; give solutions to an appropriate degree of accuracy.

- Present a concise, reasoned argument, using symbols, diagrams, graphs and related explanatory text.

 

The table below is an overview of the module Structure for the KS4 programme of study.

Foundation Overview

Unit A

Unit B

Unit C

Unit D

Unit E

Summer Year 9

Autumn 1 Year 10

Autumn 2 Year 10

Autumn / Spring 1 Year 10

Spring Year 10

1. Integers

2. Decimals

3. Coordinates

 

4. Angles, lines and triangles

5. Reading scales and converting units

6. Collecting data

 

7. Charts and graphs

8. Symmetry, similarity and congruence

9. Types of number

 

10. Introduction to algebra

11. Constructions

 

12. Patterns and sequences

13. Properties of quadrilaterals and parallel lines

Unit F

Unit G

Unit H

Unit I

Unit J

Spring/ Summer Year 10

Summer Year 10

Summer Year 10

Autumn Year 11

Autumn Year 11

 

14. Fractions

15.Pie Charts

16. Fractions, decimals and percentages

 

17. Applications of percentages

18. Algebra using powers and brackets

19. Ration and proportion

 

20. Linear equations and inequalities

21. Perimeter and area

22. 3-D shapes

 

 

23. Real-life graphs

24. Straight line graphs

25. Compound measures

 

 

26. Timetables and distance-time graphs

27. Volume

28. Probability

 

Unit K

Unit L

Unit M

Revision

 

Autumn Year 11

Spring Year 11

Spring Year 11

Summer Year 11

 

 

29. Formulae

30. Angle properties of polygons

31. Transformations

 

 

32. Scatter graphs and correlation

33. Averages and Range

34. Quadratics graphs

 

 

34. Quadratics graphs

35. Trial and improvement

36. Circles

37.Pythagoras Theorem

 

 

 

Higher Tier Overview 

Unit A

Unit B

Unit C

Unit D

Module E

Summer Year 9

Autumn 1 Year 10

Autumn 2 Year 10

Autumn / Spring 1 Year 10

Spring Year 10

1. Integers and decimals

2. Coordinates

3. Fractions

 

4. Algebra

5. Shape and angle

6. Collecting data

7. Displaying data

8. Construction and loci

9. Types of number

10. Patterns and sequence

11. 2-D and 3-D shapes

12. Perimeter and Area

13. Fractions, Decimals and Percentages

 

Unit F

Unit G

Unit H

Unit I

Module J

Spring/ Summer Year 10

Summer Year 10

Summer Year 10

Autumn Year 11

Autumn Year 11

14. Formulae and Linear Equations

15. Linear Graphs 

16. Simultaneous Equations

 

17. Probability

18. Ratio and scale

 

19. Averages and range

20. Pythagoras and Trigonometry

21. Trial and improvement

 

22. Surface area and volume

23.Compound measures

24. Transformations

 

25. Similarity and congruence

26. Quadratic functions, graphs and equations

 

Unit K

Unit L

Unit M

Revision

 

Autumn Year 11

Spring Year 11

Spring Year 11

Summer Year 11

 

27. Index notation and surds

28. Circle theorems

 

29. Sine and cosine rules

30. Vectors

31. Further graphs and functions

32. Transformations of graphs

 

 

 

Meeting the needs of all students is an important factor in teaching and learning.  Students who are identified as gifted and talented will be provided with extension and enrichment oppurtunities.  We currently take part in the national maths challenges for years 7 – 11.  Students in year 8 and 9 are selected to take part in a national team challenge and similar opputunities are available in year 10 and 11.  One of our most popular events is the G&T enrichment workshop day at Queen Elizabeth College Crediton. 

Students with SEN will receive suitably differentiated teaching, extra support and intervention to ensure they make good progress.   

KS3:  Year 9 SOL differentiated

Module A:  Autumn Term:  Half term 1

 

Extension

NMF 3

Core

NMF 2

Support

NMF 1

Resources

6 hours - Algebra 1 & 2

Find the next term and the nth term of quadratic sequences and functions and explore their properties

 

Deduce properties of the sequences of triangular and square numbers from spatial patterns.

 

Recognise that equations of the form y=mx+c

 

Plot the graph of the inverse of a linear function;

 

Know simple properties of quadratic functions

 

1-5

 

 

4-5

 

 

8

 

8

 

9-12

Generate and describe simple integer sequences using term-to-term and position-to-term definitions of the sequence

 

Generate terms of a simple sequence, given a rule

 

Generate sequences from practical contexts

 

Write an expression to describe the nth term of an arithmetic sequence

 

Generate terms of a quadratic sequence

 

Find the inverse of a linear function

 

Construct functions arising from real-life problems and plot their corresponding graphs

2-3

 

 

 

2-5

 

2-5

 

2-3

 

 

4-5

 

7-8

 

9-11

Generate and describe integer sequences.

 

Express simple functions in symbols;

 

 Represent mappings expressed algebraically

 

Plot the graphs of linear functions, where y is given explicitly in terms of x, on paper and using ICT.

 

 

 

2-8

 

10-12

 

13-14

 

13-14

 

9 hours- Number 1

Add and subtract fractions

 

Multiply and divide fractions

 

Solve problems involving percentage changes

 

Understand and use proportionality and calculate the result of any proportional change using only multiplicative methods

 

Interpret and use ratio in a range of contexts

 

Estimate calculations by rounding numbers to one significant figure and multiplying or dividing mentally

 

Find the Reciprocal of a number

18

 

18-19

 

21-24

 

26-27

 

 

 

29-31

 

32-36

 

 

34-35

Add and subtract fractions

 

Multiple and divide fractions

 

Recognise when fractions or percentages are needed to compare proportions

 

Solve problems involving percentage changes

 

Interpret and use ratio in a range of contexts

 

Use proportional reasoning to solve a problem

 

Understand the order of precedence and effect of powers (BODMAS)

 

Make  estimates and approximations of calculations

17-18

 

20

 

22-23

 

 

22-26

 

27-28

 

27-28

 

31-32

 

 

33

Order 4 digit numbers

 

Add and subtract fractions by writing them with a common denominator;

 

calculate fractions of quantities (fraction answers);

 

multiply and divide an integer by a fraction

 

Interpret percentage as the operator ‘so many hundredths of’; express one given number as a percentage of another

 

Reduce a ratio to its simplest form, including a ratio expressed in different units;

 

 divide a quantity into two or more parts in a given ratio; use the unitary method to solve simple word problems involving ratio and direct proportion

 

Use inverse proportion

19-20

 

21-22

 

 

23

 

23

 

 

 

 

25-27

 

 

25-27

 

 

 

28-29

 

6 hours – Algebra 3

Construct and solve linear equations

 

Use trial and improvement methods

 

Solve a pair of simultaneous linear equations by eliminating one variable

 

Solve linear equations involving fractions

 

 Link a graphical representation of an equation or a pair of equations to the algebraic solution; consider cases that have no solution or an infinite number of solutions.

43-44

 

 

 

45-48

 

 

49-50

 

51-56

Distinguish the different roles played by letter symbols

 

Simplify or transform algebraic expressions

 

Construct and solve linear equations

 

Use trial and improvement methods to find approximate solutions to equations

 

Use graphs to solve direct proportion problems

 

 

 

 

41-42

 

43-45

 

47-49

 

 

51-52

Know the meanings of the words formula and function.

 

Substitute positive integers into expressions

 

Construct and solve linear equations with integer coefficients (unknown on either or both sides) using appropriate methods (e.g. inverse operations, transforming both sides in the same way).

 

Begin to use graphs and set up equations to solve simple problems involving direct proportion.

 

 

35-36

 

35

 

 

35-44

 

 

 

 

45-46

 

 

 

KS4:  Year 11 SOL differentiated

Module A:  Autumn Term:  Half term 1

GCSE Tier:             Higher

Contents:              Algebra

A a

Distinguish the different roles played by letter symbols in algebra, using the correct notation

A b

Distinguish in meaning between the words ‘equation’, ‘formula’, ‘identity’and ‘expression’

A c

Manipulate algebraic expressions by collecting like terms, by multiplying a single term over a bracket, and by taking out common factors, multiplying two linear expressions, factorise quadratic expressions including the difference of two squares and simplifying rational expressions

PRIOR KNOWLEDGE:

Experience of using a letter to represent a number

Ability to use negative numbers with the four operations

Recall and use BIDMAS

 

OBJECTIVES

Higher Plus

Higher

Other

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

 

 

 

Use notation and symbols correctly                                                                                                                                               (2.1)

 

Pg185ExA2.1

 

Write an expression                                                                                                                                                           (2.1)

Pg121ExA1.2

Pg189ExA2.3

 

Select an expression/identity/equation/formula from a list                                                                                          (13.6)

 

Pg195ExA2.6

 

Manipulate algebraic expressions by collecting like terms                                                                             (2.1)

 

Pg185ExNa1.2

 

Multiply a single term over a bracket                                                                                                                         (9.1)

Pg121ExA1.2

Pg187ExA2.2

 

Factorise algebraic expressions by taking out common factors                                                                            (9.2)

 

Pg191ExA2.4

 

Expand the product of two linear expressions                                                                                                     (9.3)

Pg121ExA1.2

Pg189ExA2.3

 

Factorise quadratic expressions including the difference of two squares                                                                 (9.4)

Pg123ExA1.3

 

Pg123ExA1.3

 

 

Simplify rational expressions  by cancelling, adding, subtracting, and multiplying                             (32.1–32.3)

Pg199ExA3.3

Pg201ExA3.4

 

 

 

DIFFERENTIATION & EXTENSION

This topic can be used as a reminder of the KS3 curriculum and could be introduced via investigative material eg frogs, handshakes, patterns in real life, formulae

Use examples where generalisation skills are required

Extend the above ideas to the ‘equation’ of the straight line, y = mx + c

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

Practise factorisation where the factor may involve more than one variable

                 

NOTES

                  There are plenty of old exam papers with matching tables testing knowledge of the ‘Vocabulary of Algebra’

                  (See Emporium website)

Students who perform well in the maths challenges will receive nationally recognised certificates. We also reward their efforts and provide a Heads lunch to recognise their efforts.  

Tiverton High School has forged close links with Petroc College and staff  are involved in a joint teaching and learning co-operative between the sites.  This year has seen a rise in the number of students who chose to study A level maths at Petroc . The aim is to provide continuity from KS4 to KS5 as part of the TLP (Tiverton Learning Partnership). 

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