level3/4 s2/3 course outline - madras college level...level3/4 s2/3 course outline ... pupils are...

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

CfE LEVEL 3 MATHEMATICS (from August 2012)

The Curriculum for Excellence Level 3 course in maths covers the Learning Outcomes at Level 3

allowing for progression, depth and differentiation. Through S1 and the start of S2, 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 3 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 E

Teejay EFT

Teejay Level F

Maths in Action S1-3

Maths in Action S1-2

Maths in Action S1-1/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)

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.

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.

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 April of S1, 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 S1 reports (May) and be used

to channel pupils into suitable classes in 2/3.

S1 Parent’s evening – 11/2/13

WHOLE NUMBERS

(MNU 3 – 01a, 3-03a, b)

MNU 3-03a

MNU 3-03b

Basic numeracy skills are weak in many pupils and this unit should help to identify gaps as well as

to improve skills. The work should include both mental and non-calculator tasks. Class discussion

of appropriate strategies should be encouraged.

Pupils should be able to:

Round to the nearest 10, 100, 1000 etc

Read and write numbers up to a million

Mentally:

a) add and subtract: eg 120 + 130

82 – 38

b) multiply and divide:

within all tables up to 10

whole numbers by single digits (simple cases)

e.g. 280 8, 13 4

by 10, by 100 or a multiple of 10 or 100

e.g. 18 x 30

With written working:

a) add and subtract: eg 1251 – 375

b) multiply and divide: whole numbers by single digits

e.g. 474

Recognise patterns in the multiplication tables, e.g. 9 times table

Know the meaning of multiple

Apply the above in problems involving money and measurement

Resources

Textbook resources Practical/Activity/IT

TJ Level E Ch 1 P9 – 24

TJ EFT Ch 1 P5 - 10

S11 ch1

S12 ch1 p1-24 S13 ch 1 p1 – 5 S21 ch 1

Mymaths:

number/add subtract written/adding in columns number /add subtract written/subtraction columns number / multiply divide mental/ multiplying by 10 100 number / multiply divide mental/ dividing by 10 100 number /estimating and accuracy/rounding to 10 100

I can round a number using an appropriate degree of accuracy, having taken into account the context of the problem.

MNU 3-01a

I can use a variety of methods to solve number problems in familiar contexts, clearly communicating my processes and solutions.

I can continue to recall number facts quickly and use them accurately when making calculations.

Essential Skills in Mathematics Bk2 p10-12, 14-19

GRAPHS AND TABLES

(MNU 3-20a, b, MTH 3-21a) I can work collaboratively, making appropriate use of technology, to source information presented in a range of ways, interpret what it conveys and discuss whether I believe the information to be robust, vague or misleading.

MNU 3-20a

When analysing information or collecting data of my own, I can use my understanding of how bias may arise and how sample size can affect precision, to ensure that the data allows for fair conclusions to be drawn.

MTH 3-20b

MTH 3-21a

This topic gives an opportunity for pupils to get to know each other by involving them in paired

or group activities. It is important that pupils think about the results obtained, so charts should

normally be accompanied by comments on what they tell us. The use of ICT should be heavily

encouraged and any teaching and learning ideas shared amongst the department.


Conduct a class survey, including a questionnaire designed by the class

Organise results using tables with row and column headings - designed by the teacher or pupil

Display results using bar graphs / line graphs

Understand the need for proper scales, labelling of scales, and title

Interpret by retrieving information from tables, bar-graphs, line-graphs and pie-charts

Display and interpret bar- and line-graphs with more difficult scales, e.g. units of 100

Review newspapers/magazines for information displayed graphically, discuss special features of

the displays, and bias in vague/misleading displays

Calculate the mean average of a data set

Resources


TJ Level E P104 -117

TJ EFT P 38 - 41

S11 ch5 & ch18

S12 ch5 & ch18 p402-411

S13 ch5 p73 – 77, ch18 p284, 287-291

ESM Bk2 p111-119, p123-125 (pie charts)

ESM Bk3 p133-139 (construction of pie

charts)

Mymaths:

data /presenting data/frequency tables and

bar charts

data /pictograms and bar charts

data /line graphs and two way tables

I can display data in a clear way using a suitable scale, by choosing appropriately from an extended range of tables, charts, diagrams and graphs, making effective use of technology.

TIME AND TEMPERATURE

(MNU 3-04a),

(MNU 3-10a)

MNU 3-04a

Using simple time periods, I can work out how long a journey will take, the speed travelled at or distance covered, using my knowledge of the link between time, speed and distance.

MNU 3-10a

This unit should be as practical as possible, using watches, timed activities, timetables and newspaper reports of athletic events. Pupils are to be introduced to negative numbers through a number line in contexts such as temperature and sea level. Pupils should be able to:

Use a calendar Understand and convert between am/pm and 24 hour notation Convert between minutes and hours/minutes e.g. 100 mins = 1h 40min Convert between minutes and fractions or decimals of an hour e.g. 15 mins = ¼ h = 0.25 h Be able to use a timetable, mentally if possible Record elapsed time, if possible using a stopwatch

- in seconds - in hundredths of a second

Calculate speeds simple examples only Use positive and negative numbers descriptively and make simple calculations with the aid of a number line Resources


TJ Level E P43 – 48 P 59 - 63

TJ EFT P 18 – 19 P 25 - 26

S11 ch6

S12 ch6

S13 ch6, S13 ch1 p11-17

S21 ch6

S12 Ch6 p150 Ch7 p171-173

S13 Ch1 p11-13 Ch7 p117-119

Mymaths:

number/counting and place value/ negative

numbers 1 & 2

shape/measures/time and timetables

shape/measures/time calculations

shape/measures/speed

I can use my understanding of numbers less than zero to solve simple problems in context.

INTRODUCTION TO PERCENTAGES

(MNU 3-07a)

I can solve problems by carrying out calculations with a wide range of fractions, decimal fractions and percentages, using my answers to make comparisons and informed choices for real-life situations. MNU 3-07a

In this unit it is hoped that a whole school approach to working out percentages could

be established early in a students career at Madras. Pupils should understand the

meaning of a percentage. Teacher should allude to school produced poster and video.


1) Find any percentage of a quantity using a calculator by finding 1% first. 2) Mentally use simple equivalent fractions eg 75% = ¾ to find percentages of

other numbers Resources


TJ Level E P72 - 76

TJ EFT P29 -30

School produced worksheet

Essential Skills in Mathematics Bk2

p28-38

Tarsia puzzle

Mymaths:

number/percentages/percentages of amounts

1 & 2

www.topmarks.co.uk percentage chains

DECIMALS

(MNU 3 -03a, 3-07a)

MNU 3-03a


This is another topic in which many pupils will need careful practice, both in mental and written

work. Class discussion of helpful strategies should be encouraged. If time permits, rounding

could be covered here.


1. Work with decimals to 2 decimal places

2. Mentally

a) add and subtract: e.g. 7.3 + 8.2

b) multiply and divide:

- e.g.14.68 x 100 - e.g. 7.28 ÷ 1000

3. With written working a) add and subtract: e.g. 12.3 + 4.9 e.g. 6.7 – 2.83

b) multiply and divide: e.g. 14.25 3 e.g. 16.71 7 e.g. 4.6 8

4. Apply the above in problems involving money and measurement

5. Round any number to nearest whole, 1 decimal place, etc

6. Check calculations by rounding and mental work

Resources


TJ Level E P25 – 42 TJ EFT 12 - 17 S11 ch2 S12 ch2 S13 ch2 S21 ch2 ESM Bk3 p2 Heylings Fractions and Decimals p64-66, 69 (part 1), 82-85, 96

Mymaths:

number/decimals/any lessons

I can use a variety of methods to solve number problems in familiar contexts, clearly communicating my processes and solutions.

ANGLE

(MTH 3-17a)

I can name angles and find their sizes using my knowledge of the properties of a range of 2D shapes and the angle properties associated with intersecting and parallel lines.

MTH 3-17a

This unit covers the basic idea of angle as a rotation, and as a measurable quantity.

Practical skills of accurate drawing and measuring should be developed.

Note that pupils are required to have their own protractors.


1. Understand the idea of size of an angle, related to fitting round a point

2. Understand the degree unit of angle

3. Interpret angle as a measure of rotation

4. Know that a right angle is 90°, a straight angle is 180º, and a complete turn is

360º

5. Use a protractor accurately to draw and measure angles

6. Name angles using letters, e.g. angle ABC

7. Know the meaning of acute, obtuse and reflex for angles

8. Know that vertically opposite angles are equal

9. Calculate missing angles using angles in a straight line or round a point

Resources


TJ Level E P 146 -150

TJ EFT P 55 -57

S11 ch3

S12 ch3

S13 ch3

ESM Bk2 p78-82 (measurement), 90

(outcome 7)

ESM Bk3 p75 – 78 (measurement), p79-

81 (calculation)

Heylings Geometry and Trigonometry

p12-17

Mymaths:

Shape/Angles/position and turning

Shape/Angles/measuring angles

Shape/Angles/angle sums

Shape/Angles/angle reasoning

Shape/Angles/angles in parallel lines

INTRODUCTION TO ALGEBRA

(MTH 3-14a)

I can collect like algebraic terms, simplify expressions and evaluate using substitution.

MTH 3-14a

This unit introduces the use of letters for numbers in a variety of contexts. It includes evaluation of expressions and simplification by combining “like terms”. It is important to give plenty of practice with the numerical aspect of evaluation of expressions. This can be used to check equivalences and non-equivalences – eg 4x + 2 is not 6x.

Pupils should be able to: 1. Find missing numbers, e.g. 8 + � = 15 2. Use a simple “function machine” e.g. 7 → x 2 → ? 3. Use a “function machine” in reverse e.g. ? → x 3 → 21 4. Understand the use of letters for unknown numbers in a variety of contexts 5. Evaluate simple expressions e.g. 3x, xy, 4x + 2 6. Understand equivalence of expressions, and collect like terms, in simple cases e.g. 2x + 3y + 5x 7. Know the effect of multiplying by zero e.g. 5a = 0 when a = 0 8. Use two stage “function machines” 9. Understand and use power notation (squares only) e.g. x², 3y² Resources


TJ Level E P 92 – 95 TJ EFT P34 - 35 S11 ch4 S12 ch4 S13 ch4 p59-68 Essential Skills in Mathematics Bk2 p45, 49-53, 64-65 Heylings Algebra p18 q1-36 *Maths in Action Plus 1 ch 3 *Maths in Action 1 Extra ch 3

Mymaths:

algebra/algebraic manipulation/simplifying 1

algebra/expressions and formulae/substitution 1

EQUATIONS

(MTH 3-14a)

(MTH 3-15a)

I can collect like algebraic terms, simplify expressions and evaluate using substitution.

MTH 3-14a

Having discussed ways to express problems or statements using mathematical language, I can construct and use appropriate methods to solve, a range of simple equations.

MTH 3-15a

This unit introduces the “cover-up” method of solving equations. The importance of

clear recording of steps should be emphasised, as training for later work. The link

between equations and “function machines in reverse” should be made clear.


1. Find missing number mentally by counting forwards or backwards e.g. 8 + � = 12

2. Solve one-step equations using the “cover-up “ methoD e.g. x + 5 = 12, 14 – x = 9

3. Communicate clearly using correct notation e.g. x + 5 = 12

so x = 7

4. Solve two-step equations using the “cover up” method e.g. 2N + 3 = 8

5. Form equations from problems in words, solve them and interpret the solution

e.g. “I think of a number….” (THOANs)

6. Understand the balance method of solving equations

7. Use the balance method to solve equations in which the unknowns appear on both

sides. e.g. 4x – 2 + 2x = 15

8. Check solutions by substitution

Resources


TJ Level E P 96 - 103

TJ EFT P 35 - 37

S11 ch8

S12 ch8 p184-196

S13 ch8 p127-131

Essential Skills in Mathematics Bk3

p51-53, 59-60

Heylings Algebra p13-14, p15 (part 8 only),

p16 part 11, 12, p24 part 3 q1-7,21-32,

*p34-35

Mymaths:

algebra/equations-linear/simple equations

algebra/equations-linear/solving equations

COORDINATES AND BEARINGS

(MTH 3-17b, 3-18a)

Having investigated navigation in the world, I can apply my understanding of bearings and scale to interpret maps and plans and create accurate plans, and scale drawings of routes and journeys.

MTH 3-17b

MTH 3-18a

This unit revises and consolidates previous work on co-ordinates. Initial work will deal

with the first quadrant only, but this should be extended to include all quadrants. This

will also help to consolidate the idea of negative numbers.


1. Understand the use of co-ordinates to locate a point on a standard grid. 2. Plot points and specify co-ordinates in the first quadrant. 3. Use the terms co-ordinates, axis, origin correctly. 4. Complete specified quadrilaterals given the co-ordinates of 3 vertices. 5. Plot and specify co-ordinates in all four quadrant. 6. Draw pictures by connecting vertices dot to dot 7. Understand simple scales 8. know bearings of main directions N, S, E, W, NE, SE, SW, NW 9. Draw and identify 3 figure bearings 10. Follow and draw simple scale drawings involving bearings Extension 11. Identify and draw straight lines with equations x=a, y=b, y=-x 12. Identify and draw straight lines with equations y =mx, y=x+c ( integers only)

Resources


TJ Level E P63 – 65 P194 -207

TJ EFT P 26 – 27 P78 - 84 S12 p166-173 P S13 p117-124 P ESM Bk 2 p68 - 71 (first quadrant) ESM Bk 3 p67 – 69 (all quadrants) Heylings Negatives Numbers and Graphs p2830(1st Quadrant), p30-34 (all quadrants) Booklet: Co-ordinates

Spiderman journey poster

Mymaths:

Algebra/ Coordinates 1 and 2

Shape / Scale and Similarity/ Scale Drawing

and Map Scales

Shape/ Angles/Bearings

I can use my knowledge of the coordinate system to plot and describe the location of a point on a grid.

FAMOUS MATHEMATICIAN / MATHEMATICAL TOPIC

(MTH 3 -12a)

I have worked with others to research a famous mathematician and the work they are known for, or investigated a mathematical topic, and have prepared and delivered a short presentation.

MTH 3-12a

LENGTH AND PERIMETER

(MNU 3-11a)

I can solve practical problems by applying my knowledge of measure, choosing the appropriate units and degree of accuracy for the task and using a formula to calculate area or volume when required.

MNU 3-11a

1. Measure and draw in standard units and know the relationships between mm, cm,

m, km 2. Estimate lengths and heights in m and cm, in m and mm 3. Convert between units, eg 345 cm = 3 m 45 cm or 3.45 m 4. Be aware of common Imperial units (inches, feet, yards, mile) 5. Understand the meaning of perimeter 6. Calculate the perimeter of a polygon by adding lengths 7. Apply in contexts, e.g. cost of fencing a park, perimeter of floor of classroom 8. Calculate the perimeter of a compound rectangular shape with some missing

lengths, by first calculating the lengths 9. Find a formula for the perimeter of a rectangle

Resources


TJ Level E P118 – 122

TJ EFT P 42 - 43

S11 ch9 S12 ch9 S13 ch9 p142-148 ( not part 4 ) Heylings Fractions and Decimals p126-131

Mymaths:

Shape / Area & Perimeter / Perimeter

FRACTIONS, DECIMALS & PERCENTAGES

(MNU 3-07a: MTH 3-07b, c)


By applying my knowledge of equivalent fractions and common multiples, I can add and subtract commonly used fractions. MTH 3-07b

Having used practical, pictorial and written methods to develop my understanding, I can convert between whole or mixed numbers and fractions. MTH 3-07c

The idea of a fraction as an acceptable answer to a problem needs to be constantly emphasised. More time than before seems to be needed to develop and reinforce the concept of fractions. Understanding of equivalences between fractions, decimals and percentages will need a lot of careful work and frequent practise. The teaching aid ‘Fractiondial 12’ will be useful here. There is a demonstration dial and a set of 16 dials for pupils to work in pairs. They give a concrete representation of fractions laid out on a circular scale, with equivalent fractions. Simple fractions only at this stage.


1. Understand a fraction both as a number and as a division process 2. Understand the idea of equivalent fractions 3. Express simple fractions as decimals 4. Be familiar with the decimal values of fractions out of 4, 5, 10, 20, 50, 100

5. Mentally find simple fractions of quantities e.g. 30£5

3of

6. Understand the meaning of percentage 7. Mentally convert simple percentages to fractions 8. Convert between whole or mixed numbers and fractions 9. Mentally find simple percentages of quantities e.g. 20% of 80m 10. Add/subtract commonly used fractions

Resources


TJ Level E P67 - 78

TJ EFT P28 - 30

S11 ch15 S12 ch15 p329-350 S13 ch15 p232-236 ‘Fractiondial 12’ equipment and sheets (in main store) ESM Bk 2 p28-40 ESM Bk 3 p17 Heylings Fractions & Decimals p32-33, 112-116 (be selective)

Tarsia puzzles

Mymaths:

number/fractions/fractions to decimals number/decimals/recurring decimals 1 & 2

/ number/percentages/frac dec perc 1 & 2

PATTERNS AND RELATIONSHIPS FORMULAE AND SEQUENCES

(MTH 3-13a) (MTH 3-15B)

Having explored number sequences, I can establish the set of numbers generated by a given rule and determine a rule for a given sequence, expressing it using appropriate notation.

MTH 3-13a

I can create and evaluate a simple formula representing information contained in a diagram, problem or statement.

MTH 3-15b

The crucial idea in this unit is the use of algebra to express a relationship between two

quantities.

The aim is to enable pupils to confidently translate a linear relationship given from a context or

a table of values into a formula. It is such an important skill that it should not be rushed.

Pupils could be asked to construct actual patterns using matches or cocktail sticks.

(Headless matches are available in the main store).


1. Recognise and describe simple relationships using a table or words

2. Create a formula to describe a relationship between two sets of numbers

3. Find and use a formula to describe a linear relationship, defined from either a

table of values or a description

4. Use algebra notation correctly, eg 5x2

5. Use a formula to describe a simple relationship

6. Create a formula to describe a simple relationship defined from a table of values

or a description.

7. Substitute correctly into a given formula.

8. Continue and describe sequences, including: Constant differences, Fibonacci,

and Squares

9. Understand the concept of n-th term.

10. Use difference tables to find formulae for the n-th term Resources:


TJ Level E P132 – 145

TJ EFT P 49 - 54

S11 ch12

S12 ch12 p260-283

S13 ch12

Essential Skills in Mathematics Bk3 p40 – 48

Heylings Algebra p19 – 23, 108 – 112 (select)

Mymaths:

Algebra/ Sequences/ Sequences Algebra/ Sequences/ nth term Algebra/ Expressions & Formulae/Rules

& Formulae

TRIANGLES

(MTH 3-16a)

Having investigated a range of methods, I can accurately draw 2D shapes using appropriate mathematical instruments and methods.

MTH 3-16a

This unit should be as concrete as possible, using accurate diagrams and measurements. Pupils should be able to:

1. Know how to name angles in diagrams, eg angle PQR 2. Know the meaning of acute, obtuse, reflex for angles 3. Know that a straight line angle is 180° 4. Know that the angle sum of a triangle is 180° 5. Calculate missing angles using the angle-sum, or angles making a straight line, or

angles round a point 6. Identify angles on parallel lines – alternate / corresponding 7. Know the meaning of isosceles, equilateral, and be able to name triangles

appropriately. 8. Construction of triangles

Resources


TJ Level E P151 - P161 P168 - 174

TJ EFT P 57 – 61 P 65 - 68 S11 ch13

S12 ch13

S13 ch13


p45 – 53 (triangles)

p40 – 41 (missing angles)

p65 (angles in triangles)

Essential Skills in Maths Bk 3

p79 (missing angles)

p80 – 81 (angles in triangles)

Mymaths:

Shape/Angles/angle sums

Shape/Angles/angle reasoning

Shape/Angles/angles in parallel lines

Shape/2D and 3D shapes/properties of

triangles

shape/construction/constructingtriangles

FACTORS AND PRIME NUMBERS

(MTH 3-05a, b: 3-06a)

MTH 3-05a

I can apply my understanding of factors to investigate and identify when a number is prime. MTH 3-05b

Having explored the notation and vocabulary associated with whole number powers and the advantages of writing numbers in this form, I can evaluate powers of whole numbers mentally or using technology.

MTH 3-06a

Fluency with multiplication tables is essential for this unit, which should be introduced

with some practice of mental division skills. The aim is to develop an understanding of

the importance of prime numbers as the “building blocks” of the number system.


1. Understand the meaning of factor.

2. Express a number as a product of factors

eg 12 = 2 × 6 or 3 × 4 or 1 × 12

3. Express a number as a product of factors

eg 12 = 2 × 6 or 3 × 4 or 1 × 12

4. Understand the meaning of prime

5. List the primes up to 19 from memory.

6. Express a number as a product of prime factors eg 12 = 2 × 2 × 3.

Resources


TJ Level E 162 - 167

TJ EFT P 62 - 64 S12 ch1 p25/26 S13 ch1 p9/10, 16 Essential Skills in Maths 4 p5 Heylings General Arithmetic p69

Mymaths:

number/counting and place value/multiples

number/counting and place value/factors and

primes

I have identified strategies for identifying common multiples and common factors, explaining my ideas to others, and can apply my understanding to solve related problems.

AREA

(MTH 3-11a, b)


MNU 3-11a

Having investigated different routes to a solution, I can find the area of compound 2D shapes and the volume of compound 3D objects, applying my knowledge to solve practical problems.

MTH 3-11b

Many pupils find the concept of area surprisingly difficult, and frequently confuse it

with perimeter. This is one reason why the ability to estimate areas in terms of grid

squares or blackboard squares is so important and should not be rushed.

Later pupils should be asked to calculate (and estimate) both area and perimeter and

distinguish them carefully.


1. Find areas of shapes made from rectangles drawn on cm grids

2. Estimate areas of irregular shapes drawn on cm grids

3. Know standard units of area, using notation sq cm, sq m, cm2 and m2

4. Estimate small areas using sq mm (mm2)

5. Calculate areas of rectangles and squares using the formula A=lb

6. know meaning of hectare, and relationships with sq m and sq km

7. Calculate areas of compound rectangular shapes

8. Calculate areas of right-angled triangles

9. Calculate the area of any triangle using the formula bhA2

1=

Resources


TJ Level E P123 -131

TJ EFT P44 - 48

S11 ch11

S12 ch11

S13 p173-180, ch17 p274-276

ESM Bk 2 p105-106

Heylings Area and Volume p20-23,

29-33, 57-60

Mymaths:

shape / area & perimeter / area of rectangles

shape / area & perimeter / area of a triangle

SYMMETRY

(MTH 3-19a)

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:

1) Recognise shapes possessing line symmetry 2) Identify and draw lines of symmetry, up to 4 3) Complete partial figures given 1 or 2 lines of symmetry Extension (level 4)

4) Recognise shapes possessing rotational symmetry 5) Know the meaning of the term centre of symmetry, order of symmetry. 6) Determine the order of rotational symmetry of a given shape. 7) Complete partial figures given the centre and order of symmetry.

Resources


TJ Level E P 79 – 81 (ext P82- 86)

TJ EFT P 31 (ext P32)

S11 ch10 p117-123 S12 ch10 p224, 227-231, 236-238 S13 ch10 p157, 159-163 Essential Skills in Mathematics Bk2 p86-90

Mymaths:

shape/symmetry/linesymmetry

I can illustrate the lines of symmetry for a range of 2D shapes and apply my understanding to create and complete symmetrical pictures and patterns.

MTH 3-19a

FINANCE PROJECT

(3 – 09a, b)

MNU 3-09a

I can budget effectively, making use of technology and other methods, to manage money and plan for future expenses.

MNU 3-09b

Suggestions:

1. design and furnish a house: money scale drawings argos catalogues 2. mobile phone tariffs and contracts: use internet, budget for phone

calls, monthly costs 3. RBS visits or similar


TJ Level E P49 -58

TJ EFT 20 - 24

When considering how to spend my money, I can source, compare and contrast different contracts and services, discuss their advantages and disadvantages, and explain which offer best value to me.

VOLUME

(MTH 3-11b)


MNU 3-11a

Having investigated different routes to a solution, I can find the area of compound 2D shapes and the volume of compound 3D objects, applying my knowledge to solve practical problems.

MTH 3-11b

The concept of volume as the filling of space needs careful development, and may require a substantial practial element. Use of the small cubes, rods, flats and blocks available in the main store is recommended as well as the large frame work metre cube. Pupils should be able to:

1. Understand volume in terms of the filling up of space 2. Know the standard units of weight (g, kg) and volume (ml, l, cm3, m3) and

the relationships between them. 3. Know that volume = l x b x h for a cuboid

(Work with integer lengths only to begin with) 4. Be aware of common Imperial units (pint, gallon, ounce, pound) 5. Calculate the volume of any cuboid. 6. Estimate volumes of solids or spaces, e.g. amount of air in the classroom.

Resources


TJ Level E P 183 – 193

TJ EFT P74 - 77

S11 ch14 S12 ch14 S13 p277-279 ESM Bk 2 p107-108 ESM Bk 3 p117-118 Heylings Area and Volume p85, 88-93

Mymaths:

shape / volume and surface area / volume of

cuboids

RATIOS AND SCALES

(MNU 3-08a)

(MTH 3 -17c) I can show how quantities that are related can be increased or decreased proportionally and apply this to solve problems in everyday contexts. MNU 3-08a

I can apply my understanding of scale when enlarging or reducing pictures and shapes, using different methods, including technology.

MTH 3-17c

This unit introduces the concept of ratio as well as the basic notation. The link with fractions should be made clear, and the concept illustrated with a variety of contexts. Pupils should be able to:

1) Interpret simple ratios a : b. 2) Understand the idea of equivalent ratios. 3) Express a ratio in simplest form. 4) Find ratios between quantities 5) Use simple ratios in calculations eg “ boys : girls = 1 : 2. 6 boys, how many girls?” 6) Interpret plans or maps using scales given in the form 1 cm to 5 m or as a ratio eg 1 : 200. 7) Calculate actual distances or map distances using given scales. 8) Use proportional division, eg “divide £60 in the ratio 2:1” 9) Enlarge / reduce shapes given a simple scale factor 10) Apply scale factor to determine length of missing side

Resources


TJ Level E P 175 – 182

EFT P 69 - 73

S12 ch7 p174-179, ch9 p219-220 ch13 p301-303, ch15 p350-354 S13 ch7 p114-116, ch13 p212-214, ch14 p219-225 ESM Bk2 101-104 (scales) ESM Bk3 p35-37 (ratio) Heylings General Arithmetic p42-49

Mymaths: number/ratio &proportion/ratio introduction number/ration& proportion/ratio 1 & 2 shape/scale & similarity/scale drawing shape/scale & similarity/map scales

PROBABILITY

(MNU 3-22a)

I can find the probability of a simple event happening and explain why the consequences of the event, as well as its probability, should be considered when making choices.

MNU 3-22a

This topic gives the opportunity for pupils to express the probability og an event happening. It will be a fairly short unit and where possible should involve practical exercises. The central concept of probability should be accessible to all pupils. Pupils should be able to:

1. use appropriate words ( likely, impossible etc. ) to describe the probability of an outcome

2. list the possibility of an outcome 3. know probability is a measure of chance between 0 and 1 and can be expressed

as a fraction or as a decimal 4. be able to calculate the probability of a simple event happening 5. estimate probabilities, then compare to actual probabilities of a practical

situation e.g. sweets in a bag Resources


S13ch 18 p297-299 ESM BK 2 p133 – 138

3 p148 – 151 4 p160 – 163

Mymaths: data/probability/ probability intro

data /simple probability

data /listing outcomes

data /relative frequency

data /probability revision

2D SHAPES

(MTH 3-16a) Having investigated a range of methods, I can accurately draw 2D shapes using appropriate mathematical instruments and methods.

MTH 3-16a

This unit introduces the concept of ratio as well as the basic notation. The link with fractions should be made clear, and the concept illustrated with a variety of contexts. Pupils should be able to:

1. Recognise and identify the 6 quadrilaterals Square, rectangle, rhombus, parallelogram, kite, trapezium

2. Know their symmetry properties 3. Know that vertically opposite angles are equal 4. Find missing angles and length using geometrical reasoning 5. Find missing angles in diagrams by using equality of vertically opposite,

alternate and corresponding angles 6. Create tilings from other quadrilaterals and variants (use imagination!) – note

the possibility of using these to prove that the angle sum of any quadrilateral is 360°

Resources


TJ Level E Ch 18 P208 –

TJ EFT Ch18 P87 – 92

ESM Bk4 p74-81

Heylings Area and Volume p8 – 12

(tilings)


p42-44 (related angles)

Tangrams

level3/4 s2/3 course outline - madras college level...level3/4 s2/3 course outline ... pupils are...

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