LEVEL3/4 S2/3 COURSE OUTLINE - Madras · PDF fileLEVEL 3 S1/2 COURSE OUTLINE ... Results of these tests along with the mini assessments will inform S2 reports ... BLOCK 4 Maths in

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LEVEL 3 S1/2 COURSE OUTLINE LEVEL 3 LEVEL 3 LEVEL 3 LEVEL 3

Block 1 Block 2 Block 3 Block 4

Whole Numbers Graphs and Tables Time and Temperature Introduction to Percentages

Decimals Angles Introduction to Algebra Equations Coordinates and Bearings History of Maths Project

Length and Perimeter Fractions Decimals and Percentages Patterns and Relationships & Formulae and Sequences (combine) Triangles

Factors and Prime Numbers Area Symmetry Finance Project

LEVEL3/4 S2/3 COURSE OUTLINE

LEVEL 3 LEVEL 4 LEVEL 4 LEVEL 4 Block 5 Block 1 Block 2 Block 3 Volume Ratio and Scales Probability 2D shapes

Whole number operations Positive & Negative numbers Equations Rotational symmetry

Decimals Area & Volume Formulae & Sequences Money

Probability Brackets Powers & roots Circles Equations 2 Fractions & percentages

LEVEL 4 LEVEL 4 LEVEL 4

Block 4 Block 5 Block 6

Proportion Common Factors Statistics Similarity & Enlargement Maths in the Real World

Percentages Finance Straight Lines Standard Form Pythagoras Theorem Time, distance & speed

Area & Volume 2 Fractions +, -, x Right angled trigonometry Transformations Circle Properties

TOP SETS (P,Q, R) aim to complete all LEVEL 4 L.O.s by mid S3 then move on to NAT 5 work. Pupils from R may choose to continue with NAT 5 or do NAT 4 in S4 depending on success with the start of NAT 5.

LOWER SETS aim to complete all LEVEL 4 L.O.s by end of S3 and move on to NAT 4 Maths/ Lifestyle Maths in S4

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CfE LEVEL 4 MATHEMATICS (from August 2012)

The Curriculum for Excellence Level 4 course in maths continues on from the Level 3 course covered in S1 and start of S2, covering the Learning Outcomes at Level 4 and allowing for progression, depth and differentiation. Through S2 and the start of S3, pupils should follow the same topics to appropriate depths, depending on their ability. Wherever possible, topics should be introduced through an active learning / investigative teaching approach. AIMS

The aims of the Level 4 course are to develop the four capacities of CfE – successful learners, effective contributors, responsible citizens and confident individuals through:

• developing powers of logical thinking. • helping pupils cope with the mathematical demands of other school subjects and of

everyday life. • reinforcing and developing fundamental concepts and skills relating to numeracy,

measurement, shape and relationships. • developing a body of mathematical knowledge, including standard vocabulary and notation. • developing practical skills, including an appreciation of the need for accuracy and clarity

of expression. • developing resourcefulness in applying knowledge and skills in problem solving and

experiences. • providing a firm grounding, appropriate to each pupil's ability, for the work of future

courses. MAIN RESOURCES

Teejay Level F Teejay EFT Teejay Level E Maths in Action S2-3 Maths in Action S2-2 Maths in Action S2-1 Other suitable resources which may be used from time to time include: M in A - Further Questions (containing exercises for the more able) M in A - Extra Questions (containing sets of easier questions) Maths in Action PLUS Book 2 M in A - Teacher's Resource Book. Heylings books Essential Skills in Maths Books 3 and 4 Challenging Maths Mathland – Novice and Expert IT RESOURCES – mymaths, conquer maths, nrich, school website, Cimt.plymouth.ac.uk etc.

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SKILLS DEVELOPMENT

Basic Numeracy Skills -

These are an important part of the course. The requirements are listed in the sections on Whole Numbers , Decimals and Fraction & Percentages. They should be taught and practised on a regular basis throughout the year. A useful resource for this is 10 Quick Questions. Enquiry Skills and Problem Solving

Developing resourcefulness in problem solving and investigating is an important aim of this course. Active learning and investigative teaching approaches allow pupils to share ideas and develop their problem solving abilities and skills at an appropriate pace. Literacy

Literacy and communication is a skill which lends itself to some unique applications in maths, where a concise mathematical language and notation is fundamental for progress. Pupils should be made aware of both the general and the specific development of literacy skills. Listening and Talking (LIT301-8, LIT 401-8) This is developed through encouraging pupils to make relevant contributions to class discussions and group work. Teachers take time to ensure that pupils are listened to and their contributions valued. Asking pupils to rephrase questions in their own words is an excellent way to develop and assess a pupil’s understanding of a task. In listening to or watching others, pupils are encouraged to identify key statements and facts, make notes, develop thinking skills and recall information. They can then, in turn, explain processes and show their understanding in summing up ideas using relevant mathematical language. Reading (LIT 311-18, LIT 411-18) Pupils are encouraged to source relevant materials for independent learning e.g. textbook, website, support sessions, to identify key statements and facts and to organise them into their own words. Pupils are taught to extract and analyse information from tables and graphs. Writing (LIT320-29, LIT 420 -29) Communication of answers in maths is developed through setting out clear logical thinking, step by step working and by proper mathematical notation. Specialist vocabulary is encouraged in written explanations, as is well set out and labelled graphs / diagrams.

Health and Wellbeing

Ensuring the Health and Wellbeing of pupils is paramount and, as with other skills, pupils should be made aware of how and when these skills are developed in and through Maths. Examples of how these are addressed in maths are: Relationships (HWB3-44,5 HWB4-44,5) – through group work, “think,pair,share”, peer assessment, collaborative learning, positive learning atmosphere Planning for choices and change (HWB 3-19, HWB4-19) – through target setting, self assessment, progress sheets, work done on careers involving maths, money management, extra support sessions Social Wellbeing (HWB309-14 HWB 409-14) – high expectations of respect & behaviour, clear consequences of unacceptable behaviour, praise and rewards used to encourage pupils, pupils encouraged to actively participate in class, wider school life, maths competitions etc. Pupils’ work displayed on website Physical Wellbeing (HWB315-18, HWB 415-18) Maths in context of health, diet, fitness, awareness of general safety issues e.g fire procedures, classroom / corridor behaviour Mental and Emotional Wellbeing (HWB 301-8, HWB 401 -8) Availability/ approachableness of staff, use of guidance referrals, positive classroom atmosphere, active learning, challenging activities, group work Posters are displayed on classroom walls to inform pupils of how they are developing their

Literacy skills and H&W skills in maths.

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HOMEWORK and ASSESSMENT

Regular homework, at least once a fortnight, should be issued to pupils and monitored. Homework may be in the form of revision questions of topics already covered, ideas to investigate as an introduction to a new topic, tasks on mymaths, problem solving etc. Constructive feedback on the HW tasks should be given to pupils, either from teacher marking, self or peer marking. Self assessment booklets should be used to encourage pupils to take responsibility for their learning and to be aware of their next steps to success. Homework tasks and the Self Assessment exercises should be signed by a parent so they are aware of the work expected and the standard of work pupils are completing.

Assessment of L.O.s covered should be done at appropriate times in each block using the mini assessments. Results for these should be recorded in the database and evidence of success of the L.O.s filed in the pupils’ folders. In March of S2, pupils will sit a more formal assessment of the work covered to date comprising of two papers Paper 1: Approx 45 mins, non calculator, with questions accessible to most pupils (aiming for Nat 4) Paper 2: Approx 45 mins, with calculator. Pupils will sit either an extension paper (aiming for Nat 5) or a simpler paper (Nat 3) Results of these tests along with the mini assessments will inform S2 reports (April) and be used to channel pupils into suitable courses in S3/4

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LEVEL 4 TOPIC

Whole number operations Inc factors, multiples & powers , and rounding

Positive & Negative numbers Including coordinates

Equations Up to ax +b = cx+d

BLOCK 1

Rotational symmetry

Decimals

Area & Volume Rectangle/triangle/cuboid & prism

Formulae & Sequences

BLOCK 2

Money Budgeting, HP, Foreign Ex

Probability

Brackets Bodmas & distributive law

Powers & roots

Circles

Equations 2 Inc brackets/ negatives & constructing

BLOCK 3

Fractions & percentages Mainly non calc – using fractions

Proportion

Common Factors

Statistics

Similarity & Enlargement

BLOCK 4

Maths in the real world

Percentages Calc & non calc - % inc/dec, interest etc

Finance

Straight Lines

Standard Form

Pythagoras Theorem

BLOCK 5

Time, distance & speed

Area & Volume 2 Area of quadrilaterals –kite etc Surface area, volume of cylinder

Fractions +, -, x Top sets include algebraic fractions and division

Right angled trigonometry

Transformations

BLOCK 6

Circle Properties

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WHOLE NUMBERS MNU 4 -03

Number and number processes addition, subtraction, multiplication, division Having recognised similarities between new problems and problems I have solved before, I can carry out the necessary calculations to solve problems set in unfamiliar contexts.

MNU 4-03a Pupils should be able to:

• Read and write whole numbers up to one million • Add and subtract mentally:

- 1 digit to or from 3 or more digits for multiples of 10 eg 130 + 20 - 2 or more digits for multiples of 10 and 100

• Add and subtract with written working • 2 and 3 digit numbers • 4 digit numbers • Multiply and divide with written working: • whole numbers by a single digit • 2 digits by 2 digits (multiplication only) • Round to the nearest whole number, ten or hundred • Know the meaning of multiple, factor, product, remainder, quotient, power • Find the least common multiple of two numbers • List the factors of a number • Know the meaning of Prime Number • Learn the prime numbers up to 19 • Write a number as a product of prime factors e.g. 12 = 2 x 2 x 3

Resources

Textbook resources Practical/Activity/IT

S2-3 Ch 1 P 1- 4, 7 - 10 S2-2 Ch 1 P 1 -17 TJ Level E P9-22, P162 – 166 TJ Level EFT P5-10, P62-64 TJ Level F P28-36 ESM Bk 2 P 1- 9, Bk 3 P 1 - 3 Departmental “Mental Skills” booklet

Various number games - Sheets N10, 14, 20 – 34, 119, 120, 332, 333, 451 Calculate & colour sheets Mymaths

number/add subtract mental (any exercises) number/add subtract written (any exercises) number/counting and place value/multiples number/counting and place value/factors and primes

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POSITIVE AND NEGATIVE NUMBERS MNU 4-03a/MTH 4-18a

Number and number processes including addition, subtraction, multiplication, division and negative numbers Having recognised similarities between new problems and problems I have solved before, I can carry out the necessary calculations to solve problems set in unfamiliar contexts.

MNU 4-03a Angle, symmetry and transformation I can plot and describe the position of a point on a 4-quadrant coordinate grid.

MTH 4-18a This unit consolidates the concept of negative numbers and extends it to include addition, subtraction, multiplication and division. The equivalence of 5+ (-2) and 5 – 2 should also be explained, prior to dealing with problems like 5 – (-2). Encourage pupils to visualise or draw a blank number line, including 0, to help with calculations – especially the difference between negatives. 3 17 eg 17 – 20: _________________________________________ ? 0 17 Pupils should be able to:

REVIEW

• Locate positive and negative numbers on a number line – horizontal and vertical • Understand and use the idea of order among integers, using > and <

MAIN CONTENT

• Add and subtract positive and negative numbers • Multiply and divide positive and negative numbers • Plot and work with coordinates in all quadrants (give plenty of practice with this) • Do calculations with negative numbers in a variety of contexts.

EXTENSION

• Evaluate expressions involving negative numbers eg 3ab when a = 4, b = –2 or 4a – 5b • Simplify expressions eg 3a + 5b – 4a

Resources


S2-3 Ch 1 P 11 – 16 S2-2 Ch 1 P 19 – 26 TJ Level E Ch 5 P 59 – 65 TJ Level EFT P25 – 26 TJ Level F P9 – 18 Heylings Negative Numbers and Graphs P 8 – 23, P30 – 34 (coordinates) ESM Bk 2 P 20 – 27, Bk 3 P9-11, Bk 4 P48 – 49 (coordinates)

Sheets 371, 92, 122 (Coordinate pictures) Cimt.plymouth.ac.uk – year 7 interactive unit 15

Mymaths: number/counting and place value/negative numbers 1 & 2 algebra/inequalities/inequations

algebra/coordinates 1 & 2 algebra/expressions&formulae/substitution1 algebra/algebraic manipulation/simplifying 1

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Resources

Textbook resources Practical/Activity / IT

S2-3 Ch 8 P 117 - 124 S2-2 Ch 8 P177 – 191 TJ Level E P96 – 101 TJ Level EFT P35 TJ Level F P171 - 173 ESM Bk 3 P54, Bk 4 P54 - 57 Maths in Action Bk2 p126-130 Maths in Action S2 Extra ch 11 p63-64 (no brackets)

Tarsia puzzles Mymaths: algebra/equations – linear/ solving equations algebra/equations – linear/equations with fractions

EQUATIONS 1 MTH 4-15a Expressions and equations Having discussed the benefits of using mathematics to model real-life situations, I can construct and solve inequalities and an extended range of equations.

MTH 4-15a This unit revises the ‘balance method’ of solving equations, and introduces a more concise layout. Modelling of a problem by creating an equation is an important part of this unit. Interpreting the solution and checking it in the original context is crucial for a full understanding. Pupils should be able to: REVIEW

• Understand the “balance” model of an equation • Use the balance method to solve equations e.g. 5x + 8 = 23 • Use the balance method with harder equations e.g. 8x + 3 = 6x + 23 • Construct and solve equations from problems described in words or diagrams • Gain more practice in using the balance method,

MAIN CONTENT • Aiming at clear and concise layout of working:

e.g. 8x + 3 = 6x + 23 (– 3) 8x = 6x + 20 (– 6x) 2x = 20 (÷2) x = 10

• Solve inequalities by selecting appropriate values from a set of options. •

EXTENSION

• Solve simple inequalities algebraically

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ROTATIONAL SYMMETRY MTH 4-19a Angle, symmetry and transformation Having investigated patterns in the environment, I can use appropriate mathematical vocabulary to discuss the rotational properties of shapes, pictures and patterns and can apply my understanding when completing or creating designs.

MTH 4-19a

This introductory unit provides an opportunity to assess pupils’ geometrical insight and visualisation skills. It is intended primarily as a practical unit, using tracing paper and/or mirrors, but the goal should be for pupils to be able to visualise and complete symmetrical shapes unaided. This an appropriate stage to undertake the Pentominoes investigation. Pupils should be able to: .

• Recognise shapes possessing rotational symmetry • Know the meaning of the term centre of symmetry, order of symmetry. • Determine the order of rotational symmetry of a given shape. • Complete partial figures given the centre and order of symmetry.

Resources

Textbook resources Practical/Activity / IT

S2-3 Ch S2-2 Ch 10 p230 -240 TJ Level E P79 – 86 TJ Level EFT P32 Essential Skills in Mathematics Bk2 p86-90 Sheet 338 Booklet: Tiling and Symmetry

Rotation patterns mymaths shape/symmetry/rotationalsymmetry

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DECIMALS MNU 4-03 Number and number processes including addition, subtraction, multiplication, division Having recognised similarities between new problems and problems I have solved before, I can carry out the necessary calculations to solve problems set in unfamiliar contexts.

MNU 4-03a Pupils should be able to:

• Add and subtract mentally - 2 digit decimals, eg 7.3 + 8.2

• Multiply and divide mentally: - 4 digit decimals by 10 or 100 - any number by 10, 100 or 1000

• Add and subtract with written working: • 4 digit with at most 2 decimals places • Multiply and divide with written working: • 4 digit numbers with 2 decimal places by a single digit • harder problems eg 18.697 × 40 000

o 0.6 × 0.3 o 0.08 ÷ 0.2

• Round numbers to given numbers of decimal places • Round numbers to 1, 2 or 3 significant figures

Resources

Textbook resources Practical/Activity IT

S2-3 Ch 2 P 19 – 29 S2-2 Ch 2 P 31 – 53 TJ Level E Ch 2 P 25 - 40 TJ Level EFT P12 - 16 TJ Level F P56 - 70 Departmental “Mental Skills” Booklet ESM bk 4 P 6 – 9 ( rounding)

“Numbers Up” cards Sheets 524, 525 N15 place value grid N20 level F loop games

Mymaths: number/Decimals/ Adding Decimals Mental number/Decimals/Add Subtract Decimals number/Estimating and Accuracies/ Rounding Decimals number/Estimating and Accuracies/ Decimal places

number/Estimating and Accuracies/ Significant Figures Cimt.plymouth.ac.uk – year 7 unit 4, 6, 8

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AREA & VOLUME MNU 4-11a, b, c Measurement I can apply my knowledge and understanding of measure to everyday problems and tasks and appreciate the practical importance of accuracy when making calculations.

MNU 4-11a Through investigating real-life problems involving the surface area of simple 3D shapes, I can explore ways to make the most efficient use of materials and carry out the necessary calculations to solve related problems.

MTH 4-11b I have explored with others the practicalities of the use of 3D objects in everyday life and can solve problems involving the volume of a prism, using a formula to make related calculations when required.

MTH 4-11c This unit should have a practical bias, with measurements being obtained from real objects as well as diagrams. Insist on correct units in answers. Problems such as “How could you design a carton which would hold exactly 1 litre?” could be included. Pupils should be able to: REVIEW

• Know standard units of area (mm², cm², m², hectare) • and volume (mm³, cm³, litre, m³) • Know the relationships involved e.g. 1 ha = 10 000 m² 1 l = 1000 cm³ • Know that the area of a rectangle is A = lb • Know that the volume of a cuboid is V = lbh

MAIN CONTENT

• Calculate the area of a compound rectangular shape • Know that the area of any triangle is A = ½bh • Find the surface area of a cuboid • Calculate the volume of a prism with compound rectangular ends • Know the standard units of weight (g, kg, tonne) • and the relationships involved

EXTENSION

• Calculate the area of a rectangle whose sides are expressed algebraically e.g. 2x, 3x • Calculate the volume of a cuboid whose sides are expressed algebraically

Resources


S2-3 Ch 11 P 165 – 169 Ch 17 P261-2 S2-2 Ch 11 P 253 – P266, Ch 17 P408- 414 TJ Level E P118 – 130, P 234-9, P183 – 191 TJ Level EFT P44 – 47, P74 - 77 TJ Level F P101 - 105 Maths in Action Bk2 p103 – 104, 117 – 125 Essential Skills in Maths Bk3 p112-118 Essential Skills in Maths Bk4 116-124 Heylings Area and Volume p29 - 38, 57 – 60

1m x 1m giant cube Mymaths

shape/volume & surface area/nets, surface areas shape/volume & surface areas/volume of cuboids &

volume of prisms

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FORMULAE & SEQUENCES MTH4-13a

Patterns and relationships Having explored how real-life situations can be modelled by number patterns, I can establish a number sequence to represent a physical or pictorial pattern, determine a general formula to describe the sequence, then use it to make evaluations and solve related problems.

MTH 4-13a Pupils should be able to: REVIEW:

• Find a formula for the perimeter of a given shape with sides given algebraically • Find a formula for the area of a given shape with sides given algebraically • Find a formula for the volume of a given shape with sides given algebraically

MAIN CONTENT

• Understand the difference between “rule for finding the next term” and “formula for the nth term”.

• Generate a sequence given a formula for the nth term • Find a formula for the nth term of a sequence with constant differences.

EXTENSION

• Use difference tables to extend harder sequences. Resources

Textbook resources Practical/Activity /IT

S2-3 Ch 12 P183 – 191 S2-2 Ch 12 P 277 – 299 TJ Level E Ch 11 P133 – 145 TJ Level EFT P 49 Maths in Action Bk 2 p35-37 (perimeter, area, volume) ch16 (sequences) Sheets 13, 14 *Maths in Action S2 Plus ch 16 *Maths in Action S2 Extra ch 16, ch 3 p16-19

Mymaths Algebra/ Sequences / nth term

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MONEY MNU 4-09a

Number and number processes I can discuss and illustrate the facts I need to consider when determining what I can afford, in order to manage credit and debit and lead a responsible lifestyle. MTH 4-09a Pupils should be able to: REVIEW

• Work with both whole numbers and decimal numbers involving money in context. • Calculate the change to be given after making a purchase.

MAIN CONTENT

• Calculate weekly/monthly/yearly pay. • Calculate pay involving commission or overtime. • Interpret common household bills. • Calculate hire purchase cost. • Calculate and use exchange rates.

Resources


S2-3 Ch 2 P33 - 35 TJ Level E Ch 4 P49 - 58 TJ Level EFT P20 – 23 TJ Level F P67 - 70 Maths in Action Bk 2 P 2/3 Complete maths p24 TJ 3G Ch 6 p64-84 Ch 18 p182-194

Mymaths: number/money&finance/ money problems

number/money&finance/incomes 1 number/money&finance/budgeting RBS material

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PROBABILITY MNU 4-22a

Ideas of chance and uncertainty By applying my understanding of probability, I can determine how many times I expect an event to occur, and use this information to make predictions, risk assessment, informed choices and decisions.

MNU 4-22a

This will be a fairly short unit. Although the central concept should be fairly accessible to most pupils. Probabilities may be expressed as fractions or decimals. Some classes will be able to carry out experiments to compare theoretical probability with experimental probability, eg tossing two coins. Pupils should be able to: REVIEW

• Locate given fractions on a number line between 0 and 1.

MAIN CONTENT

• Use appropriate words (likely, highly unlikely, …) to describe the probability of an outcome • List possible outcomes of simple random events • Know that probability is a measure of chance between 0 and 1;

probability of an impossible event is 0, of a certain event is 1. • Determine probability in simple cases using the standard definition, where the outcomes are

equally likely.

EXTENSION

• Carry out statistical experiments to obtain relative frequencies, and understand the concept of experimental probability (eg tossing a drawing pin).

Resources:


S2-3 Ch 18 P 283 – 285 S2-2 Ch 18 P 438 – 441 TJ Level F P 87 - 88 Maths in Action Bk2 ch 17 ESM Bk 2 p133 – 138 Bk 3 p148 – 151 Bk 4 p160 – 163 *Maths in Action Plus 2 ch 17 *Maths in Action S2 Extra ch 17

Dice horse racing game Sheets 559 – 560 “Risk is all about us” 650 Probability Mymaths – dice simulation

Data/probability/probability intro Data/probability/simple probability Data/probability/listing outcomes

Data/probability/probability revision ATM Software – probability Cimt.plymouth.ac.uk year 7 unit 21

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BRACKETS MNU4-03a/MTH 4-14a

Number and number processes including addition, subtraction, multiplication, division and negative numbers Having recognised similarities between new problems and problems I have solved before, I can carry out the necessary calculations to solve problems set in unfamiliar contexts.

MNU 4-03a Expressions and equations Having explored the distributive law in practical contexts, I can simplify, multiply and evaluate simple algebraic terms involving a bracket.

MTH 4-14a

Pupils should be able to: MAIN CONTENT

• Understand order of operation rules (BODMAS) • Evaluate expressions involving brackets eg 4(x + 2y) + 8x, given x and y • Understand power notation eg 3x2

• Simplify expressions eg 3y × 2y • Collect like terms eg x2 + 3x2 + x • Multiply out brackets eg 3(2x + 5 • 6x(3x – 4)

Resources


S2-3 P54 – 62 S2-2 P83 - 96 TJ Level E P92 – 95 TJ Level F P48 - 50 Complete maths P76 Maths in Action Bk 2 p38-42 Essential Skills in Maths Bk3, p49 – 50 Heylings Algebra p70, 71

Dice substitution game – can be adapted for easy/difficult expressions Jigsaw (resources in computer) S1 –S4 Algebra Mymaths: algebra/algebraic manipulation/brackets algebra/expressions and formulae/order of operations algebra/expressions and formulae/substitution

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POWERS AND ROOTS MTH 4-06a/MNU 4-01a Powers and roots I have developed my understanding of the relationship between powers and roots and can carry out calculations mentally or using technology to evaluate whole number powers and roots, of any appropriate number.

MTH 4-06a

Estimation and rounding Having investigated the practical impact of inaccuracy and error, I can use my knowledge of tolerance when choosing the required degree of accuracy to make real-life calculations.

MNU 4-01a

Pupils should be able to:

MAIN CONTENT (with calculator)

• Use calculators appropriately • (Note the two types of calculators - check type by entering 5 + 2 ÷ 3 = ?) • Calculate squares and cubes and use appropriate keys on calculator • Know the meaning of square root, and calculate using √ key • Round after a calculation or division, e.g. 3 ÷ 7 • rounding to 1 or 2 decimal places

Know the meaning of recurring decimal

Resources:


S2-3 Ch 1 P3 - 6 S2-2 Ch 1 P17 - 19 TJ Level F P202 - 203 TJ 3G P 151 - 153

Happy Numbers – find 3-digit perfect squares that between them contain the digits 1 – 9 Nrich ATM software Mymaths: number/powers and roots/squares and cubes

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CIRCLES MTH 4-16b Properties of 2D shapes and 3D objects Having investigated the relationships between the radius, diameter, circumference and area of a circle, I can apply my knowledge to solve related problems. MTH 4-16b This topic lends itself to a practical approach, which may include measurement of circumferences of everyday objects, and estimation of areas on grids. Pooling of measurements within the class can produce a good approximation to π. It is important throughout to emphasise the distinction between circumference (perimeter) and area. Pupils should be able to: REVIEW

• Know meaning of radius, diameter, circumference • Know that d = 2r • Find by careful measurement that C is a little more than 3 times d

MAIN CONTENT

• Know that C = πd and that π = 3.14 approximately • Know how to use π button on calculator • Use the circumference formula appropriately in problems • Know that A = πr² • Use the area formula appropriately in problems, • including calculating areas of discs • Express answers to given number of significant figures

EXTENSION

• Calculate diameter given circumference • Calculate radius given area • Calculate perimeter and area of compound shapes with semicircular sections

Resources:


S2-3 Ch 11 P 173 – 178 S2-2 Ch 11 P 270 – 274 TJ Level E Ch 19 P228 – 231 (C only) TJ Level EFT P94 - 96 TJ Level F P118 - 126 S2 Plus Ch 8 Ex 1 – 7, M in A 2 Ch 8 Essential Skills in Maths Bk3 p118-120 Essential Skills in Maths Bk4 p113-115 Heylings Fractions and Decimals p132-137 Heylings Area and Volume p61-66

Measuring diameters/ circumferences to find relationship Circle patterns Sheet 204: company motif (investigation) Mymaths shape/area & perimeter/circumference of a circle shape/area & perimeter/area of circles

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EQUATIONS 2 MTH 4-15a

Expressions and equations Having discussed the benefits of using mathematics to model real-life situations, I can construct and solve inequalities and an extended range of equations.

MTH 4-15a Pupils should be able to: MAIN CONTENT

• Solve equations using the balance method eg 6x – 23 = 8x - 3 • Solve equations with brackets eg 2(4x – 3) + 7 = 9 • Construct and solve equations from problems described in words or diagrams.

Resources


S2-3 Ch 8 P 124 - 132 S2-2 Ch 8 P191 – 198 TJ Level E P96 – 101 TJ Level EFT P35 TJ Level F P173 - 176 ESM Bk 3 P54, Bk 4 P54-55 Maths in Action ch 11 p126-133 Complete Mathematics p81, ex 6, p83, 84, 242-244 Heylings Algebra p16, p15 parts 7, 9, p16 part 13, p31 part 3, p32 parts 6,7, p33. *Maths in Action S2 Extra p64 *Essential Skills in Maths Bk 3 p54 TJ Level F ch 43

Tarsia puzzles Mymaths: Algebra/equations-linear/ simple equations Algebra/equations-linear/solving equations Algebra/equations-linear /equations with fractions algebra/inequalities/inequations algebra/inequalities/negative inequations

18

FRACTIONS DECIMALS AND PERCENTAGES MNU 4 – 07

Fractions, decimal fractions and percentages I can choose the most appropriate form of fractions, decimal fractions and percentages to use when making calculations mentally, in written form or using technology, then use my solutions to make comparisons, decisions and choices.

MNU 4-07a In this unit, the focus is the relationship between fractions, decimals and percentages e.g finding 75% using ¾, finding 30% using 3 x 10% etc. Pupils should be able to:

• Find fractions of a quantity mentally: - 1/3, 1/5, 1/10 of 1 and 2 digit numbers - simple fractions, eg ¾, 20/100 of 4 digits (easy cases only) - widely used fractions of whole number quantities

• Find percentages of quantity mentally: - by finding equivalent fractions eg 75% = 3/4 - by using multiples of 10% and 1% - find VAT using 20% = 2 x 10%

Resources


S2-3 Ch 15 P 223 -4 P 229 - 232 S2-2 Ch 15 P 344 – 349 P 352 P357 TJ Level E Ch 6 P 67 – 71 Q2, P 74 - 76 TJ Level EFT P29 – 30 TJ Level F P92 - 93 Maths in Action Teachers Resource Bk1 p64-66 Bk2 p24-26 Essential Skills in Mathematics Bk2 p28-38

“Show Me” boards Sheets N1 Level C loop games N2 Fractions and Percentages N4-9 Fractions/percent sort cards N11 Fraction of a quantity grids N12 Percent of a quantity grids N16-19 Dominoes N20 Level F loop games N25 Mini sort cards Mymaths: number/Fractions/Equivalent Fractions

number/Fractions/Fractions to Decimals number/Fractions/Adding Subtracting Fractions number/Percentages/Frac Dec Perc 1 number/Percentages/Percentages of Amounts 1

19

PROPORTION – DIRECT AND INVERSE MNU 4-08a Fractions, decimal fractions and percentages including ratio and proportion Using proportion, I can calculate the change in one quantity caused by a change in a related quantity and solve real-life problems.

MNU 4-08a Pupils should be able to: MAIN CONTENT

• Understand the principle of direct proportion. • Complete tables of values for variables in direct proportion. • Solve problems involving variable sin direct proportion. • Sketch graphs showing the relationship of variables in direct proportion. • Understand the principle of inverse proportion. • Complete tables of values for variables in inverse proportion. • Solve problems involving variables in inverse proportion. • Sketch graphs showing the relationship of variables in inverse proportion.

Resources


S2-3 Ch 14 P 206 - 216 S2-2 Ch 14 P 324 – 342 TJ Level E Ch15 P 175 – 181 (ratio only) TJ Level EFT P69 – 72 (ratio only) TJ Level F P157 - 169 S2 -1 Ch 14 (simple proportion) Maths in Action Bk2 p145-151 *Maths in Action Plus 2 ch 12 *Maths in Action S2 Extra ch 12

Mymaths: Number/Ratio and Proportion/Proportion Unitary MethodNumber/Ratio and Proportion/Direct and Inverse Proportion

20

COMMON FACTORS MTH 4-14b

Expressions and equations I can find the factors of algebraic terms, use my understanding to identify common factors and apply this to factorise expressions.

MTH 4-14b Pupils should be able to: REVIEW

• Multiply out brackets eg 2(x + 7) • Factorise numbers eg 15 = 3 ×5

MAIN CONTENT • Find numerical common factor eg 12x + 16 = 4(3x + 4)

EXTENSION

• Find algebraic common factors eg 12x2 + 16x = 4x(3x + 4) • Check result of a factorisation by multiplying out

Resources


S2-3 Ch 4 P 63 – 64 S2-2 Ch 4 P97 -98 TJ Level E Ch13 P 162- 164 TJ Level F P30 – 31, P 54 Heyling Algebra P 72 Essential Skills in Maths Bk 5 p40

Tarsia Mymaths: algebra/algebraic manipulation/factorising linear algebra/algebraic manipulation/single brackets (revision)

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STATISTICS MTH 4-20a, b/ MTH 4-21a

Data and analysis I can evaluate and interpret raw and graphical data using a variety of methods, comment on relationships I observe within the data and communicate my findings to others.

MNU 4-20a In order to compare numerical information in real-life contexts, I can find the mean, median, mode and range of sets of numbers, decide which type of average is most appropriate to use and discuss how using an alternative type of average could be misleading.

MTH 4-20b I can select appropriately from a wide range of tables, charts, diagrams and graphs when displaying discrete, continuous or grouped data, clearly communicating the significant features of the data.

MTH 4-21a This unit covers basic handling of data, stem-and-leaf charts and scattergraphs. Pupils should generate their own data to use throughout this unit. The emphasis should be on the use of statistics to help interpret data sets. Pupils should be able to: REVIEW

• Calculate mean, range, mode and median for a set of data • Compare sets of data by comparing the above measures

MAIN CONTENT

• Construct a frequency table (ungrouped) from a set of data. • Display data using stem-and-leaf charts. • Conduct a class-survey to gather two pieces of data from each pupil. • eg height and hand-span, or day and month of birth • Organise resulting in tabular form • Display results using a scattergraph. • Describe correlation in general terms from a scattergraph • Eg “strong positive correlation”

Resources:


S2-3 Ch5 P66 – 76, Ch 18 P272 - 278 S2 -2 Ch5 P101 – 119, Ch 18 p421 – 437 TJ level E Ch 9 P104 – 115 TJ Level EFT P38 – 39 (averages only) TJ Level F P73 – 77, 83 - 88 Maths in Action Plus 2 ch 4 p32-36 Maths in Action S2 Extra ch 4

Super Villain Statistics challenge Survey, organising, displaying information ATM software and Make the Average Olympic Games – data & graphs (nrich) Mymaths: data/presenting data/ scattergraphs & line of best fit data/ processing data/ mean& mode, median and range, all averages, stem and leaf

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SIMILARITY AND ENLARGEMENT MTH 4-16a/MTH 4-17b

Properties of 2D shapes and 3D objects I have explored the relationships that exist between the sides, or sides and angles, in right-angled triangles and can select and use an appropriate strategy to solve related problems, interpreting my answer for the context.

MTH 4-16a Angle, symmetry and transformation I can apply my understanding of the properties of similar figures to solve problems involving length and area.

MTH 4-17b

Pupils should be able to: REVIEW

• Draw scale drawings using a given scale factor

MAIN CONTENT

• Understand the mathematical concept of similar shapes. • Identify similar shapes using ratios of sides. • Use the concept of a scale factor k with similar shapes. • Calculate missing lengths using the scale factor k. • Understand that k > 1 for enlargements and k < 1 for reductions.

EXTENSION • Solve problems like:

4 3 3 x

Resources:


S2-3 Ch 10 P 152 – 158 S2 -2 Ch 10 P 246 – 250 TJ level E Ch 17 P194 (scale drawing?) TJ Level F P141 – 143 (scale factor) *Essential Skills in Maths 3 p102 – 105 Essential Skills in Maths Bk 4 p86 - 90 Essential Skills in Maths Bk 5 p98 – 103 Complete Mathematics p141 – 142 M in A 3B Ch 2 M in A 3A Ch 4 P 44- 59 TJ 3G P50 – 51 TJ 4G P 103 – 110 *Action Maths 3 p6 – 9 *Action Maths 2 p52, 53 (similar rectangles), p54 (similar designs)

*Sheets 472-474, 480, 481, 487, 488 (scale drawings) mymaths: Shape/Scale and Similarity/Similar Triangles

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MATHS IN THE REAL WORLD MTH 4-12a Mathematics – its impact on the world, past, present and future I have discussed the importance of mathematics in the real world, investigated the mathematical skills required for different career paths and delivered, with others, a presentation on how mathematics can be applied in the workplace.

MTH 4-12a Pupils should be able to: MAIN CONTENT

Resources:


Booklets from careers service

www.mathscareers.org.uk - videos, careers info

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PERCENTAGES MNU 4 -07a Fractions, decimal fractions and percentages I can choose the most appropriate form of fractions, decimal fractions and percentages to use when making calculations mentally, in written form or using technology, then use my solutions to make comparisons, decisions and choices.

MNU 4-07a One of the aspects that needs to be made explicit is that there are several methods for doing percentage calculations, and it is important to be clear about when each method is appropriate. Having done percentages earlier using fractions, this unit concentrates more on percentages of amounts, percentage increase and decrease and other applications. Calculators should be used where appropriate but % key on the calculator should not be used. Pupils should be able to: REVIEW

• Understand the meaning of a percentage • Mentally convert simple percentages to fractions • Mentally find simple percentages of quantities • e.g. 20% of £80

MAIN CONTENT

• With a calculator find any percentage of a quantity • Estimate a percentage of a quantity mentally, • eg 12% of £80 is a bit more than £8 • Calculate the new value of a quantity after a given percentage increase or decrease • Apply to problems involving inflation, depreciation, interest on loans

EXTENSION

• Express one quantity as a percentage of another • Use this to calculate percentage profit and loss

Resources:


S2-3 Ch 15 P226 – 229, P 224 – 226 S2 -2 Ch 15 P349 – 350 P354 – 355, P 353 TJ level E Ch 6 P 72 – 3 Ex 4, P 71 Q 3 – 5 TJ Level EFT P29 - 30 TJ Level F P90 - 99 Essential Skills in Maths Bk3 p27-30 Essential Skills in Maths Bk4 p27-35 Heylings Fractions and Decimals p112-116, 120 Complete Mathematics p7 – 11 *Maths in Action Plus 2 ch 5 *Maths in Action S2 Extra ch 5 *Progress in Maths ch12 *More Practice books

Mymaths: Number/Percentages/Percentages of Amounts 2 Number/Percentages/Percentage Change 1 Number/Percentages/Change as a percentage

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MONEY & FINANCE MNU 4-09c

Number and number processes I can research, compare and contrast a range of personal finance products and, after making calculations, explain my preferred choices.

MNU 4-09c Pupils should be able to: REVIEW

• Work with percentages on Money • Calculate the total hire purchase cost of a given item

MAIN CONTENT

• Given a budget of around £1000 decide upon 3 items from a catalogue they wish to buy • Calculate the total hire purchase cost of buying the items from the catalogue over a 1 year

period • Investigate different methods of borrowing £1000 and try to come up with the cheapest

method of borrowing over the 1 year period

EXTENSION

• Investigate what different factors affect a person’s Credit Score


Catalogues: Argos etc This unit could be done on its own or in conjunction with a project such as design a bedroom Price comparison websites Bank, Building Society websites

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STRAIGHT LINES MTH 4-13 b, c, d

Patterns and relationships I have discussed ways to describe the slope of a line, can interpret the definition of gradient and can use it to make relevant calculations, interpreting my answer for the context of the problem.

MTH 4-13b Having investigated the pattern of the coordinate points lying on a horizontal or vertical line, I can describe the pattern using a simple equation.

MTH 4-13c

I can use a given formula to generate points lying on a straight line, plot them to create a graphical representation then use this to answer related questions.

MTH 4-13d This unit represents an informal approach to the idea of graphs of straight lines, as a development of the “finding the formula” work in unit A3. Concept of gradient should be introduced. Pupils should be able to: REVIEW

• Plot points from a table of values for points where x = a, y = b, y = x, y = –x • Recognise equations of lines of the above forms.

MAIN CONTENT

• Find the gradient of a given straight line using (change in y) ÷(change in x) • Plot points from a table and observe the connection between the gradient of a straight line

and the equation of the line, for lines of the form y = mx. • Repeat for tables of values of formulae like y = 3x + 2. Use a variety of contexts and work

with positive gradients only. Some contexts will only work with positive co-ordinates, others will extend into other quadrants.

• TAKE TIME TO DEVELOP THIS CAREFULLY!

• Find the equation of a line from a graph or table of values – link this with finding a formula from a pattern.

EXTENSION

• Investigate graphs of the form y = mx + c, including negative values of m. • (The idea is to establish that c gives the y-intercept and m gives the gradient.)

Resources

Textbook resources

Practical/Activity/IT

S2-3 Ch 7 P 107 – 114 S2 -2 Ch 7 P 171 - 173 TJ level F P195 – 196 (introduction only) M in A 3B P123 – 4 TJ 4G P63 – 77 M in A 4A Ch 1 Complete maths P 125 / 258 Heylings Negative Numbers and Graphs p70 (part 2), p78-79 Essential Skills in Maths Bk3 p70-72, Bk4 p48-53

Standard Units A10 - Classify straight lines A7 – matching graphs Mymaths: Algebra/ Graphs/ Gradients , y=mx+c

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STANDARD FORM MTH 4-06b Powers and roots Within real-life contexts, I can use scientific notation to express large or small numbers in a more efficient way and can understand and work with numbers written in this form.

MTH 4-06b This unit focuses on standard form (also called scientific notation) and aims to create awareness of why and when it is used. Lower sets should be introduced to the idea of powers of 10 and very simple single digit standard form numbers e.g. 5000 = 5 x 104 Pupils should be able to:

• Convert large and small numbers to standard form, and vice versa. • Carry out calculations with numbers in standard form using a calculator. • Solve problems involving numbers written in standard form.

Resources


S2-3Ch 1 P29-32 S2- 2 Ch 1 P54-55 TJ Level F P37 - 44 Essential Skills 3 P11/12 ? Heylings General Arithmetic p74-76? Certificate Arithmetic Unit 3 (available as a booklet) Complete Mathematics p193 – 194? Worksheets

Jigsaw / Tarsia puzzles Standard Units N4 estimating lengths using standard form Mymaths: number/standard form/standard form large number/standard form/standard form small

number/standard form/standard form calcs

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PYTHAGORAS’ THEOREM MTH 4-16a Properties of 2D shapes and 3D objects I have explored the relationships that exist between the sides, or sides and angles, in right-angled triangles and can select and use an appropriate strategy to solve related problems, interpreting my answer for the context.

MTH 4-16a This important topic should be introduced carefully. One possibility is to measure sides of right angled triangles and look for patterns. Some guidance will be required to find the correct formula! There are a lot of good links in the home-learning pages of our web-site. Pupils should be able to:

• Calculate squares and square roots using a calculator • Calculate the length of the hypotenuse using Pythagoras’ theorem • Calculate a shorter length using Pythagoras’ Theorem • Solve problems using Pythagoras’ Theorem • (Give plenty of practice with problems in a variety of contexts.)

Resources:


S2-3 Ch 9 P 133 – 148 S2- 2 Ch 9 P 214 – 224 TJ Level F P204 - 216 Essential Skills in Maths 4 p104 – 109 Essential Skills in Maths 5 p89 - 97 Central Maths ch6 Heylings Geometry and Trigonometry p125-129 (Pythagoras), p140-141 (with bearings) TJ 3G Ch ? Hypotenuse only

*Sheets 636 – 641 mymaths: Shape/Pythagoras/Pythagoras Theorem

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TIME, DISTANCE AND SPEED MNU 4-10a, b Time I can research, compare and contrast aspects of time and time management as they impact on me. MNU 4-10a

I can use the link between time, speed and distance to carry out related calculations.

MNU 4-10b Pupils should be able to:

• Read and convert between am/pm and 24-hour notation • Add and subtract times using am/pm and 24 hour notation. • Calculate time difference in years, months and days using knowledge of the calendar • Extract information from timetables and calculate journey times. • Know the Time-Distance-Speed relationships • Convert hours and minutes to decimal form, and vice versa • Solve problems involving time, distance, speed • Interpret distance-time graphs and use them to calculate speeds.

Resources


S2-3 Ch 6 P85 – 97 S2- 2 Ch 6 P 125 – 146 TJLevel E Ch 3 P 43 – 47 (time only) TJ Level EFT P 18 (time only) TJ Level F P 179 - 191 TJ 3G P 107 – 123 Heylings General Arithmetic p179-184 Complete Mathematics p116 - 124

Measuring distance using trundle wheels Walk/run – measuring time & distance to calculate speed. Cimt.plymouth.ac.uk Year 7 interactive unit 14 (time) Year 8 interactive unit 18 (speed) Mymaths: Algebra/graphs/distance time graphs Shape/measures/speed

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AREA AND VOLUME 2 MNU 4-11a, MTH 4 -11b Measurement I can apply my knowledge and understanding of measure to everyday problems and tasks and appreciate the practical importance of accuracy when making calculations.

MNU 4-11a Through investigating real-life problems involving the surface area of simple 3D shapes, I can explore ways to make the most efficient use of materials and carry out the necessary calculations to solve related problems.

MTH 4-11b I have explored with others the practicalities of the use of 3D objects in everyday life and can solve problems involving the volume of a prism, using a formula to make related calculations when required. MTH 4-11c The work of this unit can be presented in quite a practical way. Initially shapes should be presented as full-sized accurate drawings, gradually moving to sketches. Pupils should be able to:

• Calculate the areas of a square, rectangle, triangle • Calculate the circumference and area of a circle. • Calculate the area of a kite, rhombus, parallelogram, composite shape. • Calculate the volume of a cuboid, cylinder, triangular prism. • Calculate the surface area of a cuboid, cylinder, triangular prism.

Resources


S2-3 Ch 11 P170 – 172 Ch 17 P 254-260 S2- 2 Ch 11 P 267 – 269, Ch 17 P412 – 414 TJLevel EFT P75 (volume) TJ Level F P 118-123 (circles), P103-115 (area) Heylings Area and Volume p29 -42, 50-53 (area) p62-64 (circles) p90-91, 99-107 (volume) p150-153 (surface area) Essential Skills in Maths Bk4 p110-125 Essential Skills in Maths Bk5 p124 – 125 (area), 132 – 136 (volume) Complete Mathematics Unit 4 p50 - 65 *Action Maths 4 p38 - 39 *Essential Skills in Maths 3 p112-120

Mymaths: shape/area & perimeter/area of circle shape/area & perimeter/area of parallelogram shape/volume & surface area/volume of cuboids shape/volume & surface area/volume of prisms shape/volume & surface area/nets, surface area

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FRACTIONS MTH 4-07b Fractions, decimal fractions and percentages I can solve problems involving fractions and mixed numbers in context, using addition, subtraction or multiplication.

MTH 4-07b Pupils should be able to:

• Calculate a fraction of a quantity • Understand and use equivalence of fractions

• Understand that a fraction represents a division operation eg 3

5 means 3 ÷ 5

• Add, subtract and multiply fractions including mixed fractions. • (Divide by a fraction, preferably in a context.) • Apply to problems in a variety of contexts, including pie-charts.

Resources


S2-3 Ch 15 P229 – 239 S2- 2 Ch 15 P 358 - 364 TJLevel E P 69 – 70 TJ Level EFT P29 (fraction of a quantity) TJ Level F P 128 - 139 Heylings Fractions and Decimals p20-21 (multiplication) p22-24 (division) p25-31 (addition and subtraction) p32-33 (fraction of a quantity) Essential Skills in Maths Bk3 p17 – 34 (be selective) Essential Skills in Maths Bk4 p20 – 25, 31 Complete Mathematics p186 - 187 *Action Maths 5 p1 - 3 (fractions and pie-charts)

Coolmath4kids.com – lessons on fractions Math-play.com – adding & subtracting fractions (hard) Mymaths: number/fractions/any lesson in this section

32

TRIGONOMETRY IN RIGHT-ANGLED TRIANGLES MTH 4-16a Properties of 2D shapes and 3D objects I have explored the relationships that exist between the sides, or sides and angles, in right-angled triangles and can select and use an appropriate strategy to solve related problems, interpreting my answer for the context.

MTH 4-16a Pupils should be able to:

• Name the sides of a right-angled triangle- opposite, adjacent and hypotenuse • Use scale drawings to obtain ratios of sides, eg

oppadj for selected angles, to 1 decimal place.

• Use ratios found to calculate missing sides and angles in appropriate triangles.

Resources


S2-3 Ch 13 P199 – 203 S2- 2 Ch TJLevel E TJ 3G Ch 15 ? Tan only

Draw lots of 30/60/90 triangles – measure sides in ratio – establish similarity. Sun & shadows – measure height of objects & their shadows to find ratio & hence heights of larger objects – need a sunny day!! Mymaths: Shape/trigonometry/trig missing angles Shape/trigonometry/trig missing sides

33

TRANSFORMATIONS MTH 4-16a Angle, symmetry and transformation I can apply my understanding of the 4 quadrant coordinate system to move, and describe the transformation of, a point or shape on a grid.

MTH 4-18b

Transformations of a shape on a 4 quadrant coordinate grid. Transformations - symmetry, glide reflections, rotational symmetry Pupils should be able to:

• Move and describe a translation on a 4 quadrant coordinate grid • Recognise translation & rotational symmetry in designs

Design and create tiling patterns which have translation, rotational & reflective symmetry

Resources


S2-3 Ch 10 p150 S2- 2 Ch 10 p227 TJLevel E P87 – 89 TJ EFT P33 The Tessellations File : Teachers’ Notes and sheets

Rangoli patterns Puzzle sheets Escher drawings Mymaths shape/transformations/any lesson in this section translating shapes on coordinate grid Mathsonline.co.uk – post the shapes adn transformational golf

34

CIRCLE PROPERTIES MTH 4-17a Properties of 2D shapes and 3D objects Having investigated the relationship between a radius and a tangent and explored the size of the angle in a semi-circle, I can use the facts I have established to solve related problems.

MTH 4-17a

This topic lends itself to a practical approach, which may include drawing and measuring the angle made by tangents to the radius at the point of contact and the angle produced by connecting the end points of a diameter to any point on the circumference. Pupils should be able to: REVIEW

• Know meaning of radius, diameter, circumference • Be able to use a protractor accurately • Is familiar with triangle properties ( sum of angles in triangle = 180o)

MAIN CONTENT:

• Know that the radius forms a right angle at the point of contact with the tangent • Know that the angle formed in a semi - circle is a right angle • Use the above facts appropriately to solve related problems • Using : Circle properties Pythagoras SOHCAHTOA

EXTENSION:

• Can give a proof of the angle in a semi-circle theorem • Can investigate relationship between angles formed at the centre/ circumference of circles

etc … from • ‘6 Angle in circle theorems’ Heylings P 81 – P92

Resources:


MiA 4a CH 9 P 112 – P 121 MiA 4B Ch 3 P 32 – P 35 TJ INT 2 BK 1 P106,108-109 New M i A ch 10 p 180 – P 185 Heylings Geometry and Trigonometry P 86 and P 88

Pupils can connect both ends of a diameter to ANY point on the circumference of the circle and measure the resulting angle. Pupils can draw any tangent to a circle and produce a radius at the point of contact to check that the resulting angle is 90o

Mymaths.co.uk Shape/circle theorems/circle theorems – page 5 http://www.mathopenref.com/semiinscribed.html http://www.mathopenref.com/tangentline.html Includes an applet demonstrating these properties

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