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KEMNAY ACADEMY

MATHEMATICS DEPARTMENT

NATIONAL 5

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KEMNAY ACADEMY

NATIONAL 5

LEARNER GUIDE

Page 3 INTRODUCTION Page 4 MATHEMATICS PRESENTATION POLICY FOR NATIONAL QUALIFICATION

COURSES Page 5 PERSONAL TARGET SETTING Pages 6-8 COURSE CONTENT Page 9 ASSESSMENT Page 10 ACHIEVING A UNIT Pages 11-12 INTERNAL ASSESSMENT RECORD OF ACHIEVEMENT Page 13 TOP TIPS – UNIT AND EXTERNAL ASSESSMENT

Page 14 NATIONAL 5 MATHEMATICS ASSESSMENT CALENDAR Please take this booklet home and ensure that it has been read and signed by

both you and your parent/carer before the end of AUGUST.

Learner Name ______________________

Class

__________

Teacher Name ______________________

I have read and acknowledged the course information.

Parent/Carer Signature .

Date ____________________

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NATIONAL 5 MATHEMATICS - INTRODUCTION

• The main purpose of each Course at National 3/4/5 and Higher Mathematics is

to provide you with the opportunity to further develop the skills of reasoning

algebraically, linking mathematical concepts, selecting and communicating

processes and solutions and justifying choice of strategies you use in order to interpret and use mathematics effectively.

• The National 5 Course will also promote the development of your numeracy

skills and mental agility.

• Respect, responsibility, determination, aspiration, success, excellence are at the heart of all learning and teaching in mathematics

Course Aims

The National 5 Mathematics Course offers you the opportunity to develop and extend a wide range of skills. In particular, the Course aims to enable you to: ¨ select and apply mathematical techniques in a variety of mathematical and real-

life situations ¨ manipulate abstract terms in order to solve problems and to generalise ¨ interpret, communicate and manage information in mathematical form ¨ develop skills in using mathematical language to explore mathematical ideas

¨ develop skills relevant to learning, life and work COURSE CONTENT

The successful learner in National 5 Mathematics will have achieved the outcomes in each of the units shown on pages 6, 7 and 8. ASSESSMENT

The award of National 5 Mathematics will be based on a combination of internal

and external assessment. To gain the award, you must achieve a pass in all the units of the course as well as a pass in the external assessment. External assessment will provide the basis for grading your attainment through an External Examination made up of two papers: non-calculator and calculator.

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MATHEMATICS PRESENTATION POLICY

FOR NATIONAL QUALIFICATION COURSES

COURSE ENTRY LEVELS You should note that the successful completion of a Mathematics course in S4-6 depends upon each of the following criteria: 1. Your progression from Courses you have successfully completed in this subject

in S3, S4 and, if applicable, S5. 2. Realistic awareness of your own strengths, development needs, ability and

aptitude in this subject. 3. The recommendation made to you at the end of S3/4 and the advice given to you

by your current class teacher based upon your attainment during the course. It is essential that you begin the course at the appropriate level for you. Your

teacher will take into account your performance in the Mathematics and

Numeracy experiences and outcomes by the end of S3 and/or your

performance in National 4 in S4, as appropriate. This will prevent serious

difficulties at a later stage.

NATIONAL 5 MATHEMATICS COURSE ENTRY LEVELS

¨ Learners who have achieved a minimum standard of attainment as demonstrated

in Number, money & measure (NMM), Shape, position & movement (SPM),

Information handling (IH) at Fourth Level in S3 are recommended for National 5 Mathematics in S4.

¨ Learners who have attained National 4 Mathematics. Progression routes from National 5 Mathematics

• Higher Mathematics in S5/6 • Exit to employment • Further Education • No further study of mathematics

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PERSONAL TARGET SETTING

It is expected that learners will demonstrate high levels of commitment and

motivation to coursework and homework. Furthermore, learners must engage

in ongoing revision of the topics studied.

Use this section of your profile to help you set your targets at an appropriate level.

My Curriculum for Excellence Level for

Mathematics/Numeracy at the end of S3

(tick one of each NMM,SPM, IH)

o NMM 3rd level

o SPM 3rd level

o IH 3rd level

o NMM 4th level

o SPM 4th level

o IH 4th level

My National 4 attainment in S4

o Pass

My Presentation Level at the beginning of S4/S5

(tick one)

o National 4

o National 5

My Target Grade at National 5 is

o A

o B

o C

o D

Start of session: Learner Signature Date

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NATIONAL 5 MATHEMATICS - COURSE CONTENT

EXPRESSIONS AND FORMULAE

SUB-SKILLS WITHIN EACH ASSESSMENT STANDARD

1.1 1.2 1.3 1.4 2.1 2.2

Outcomes (assessment standards): Apply numerical skills to simplify surds/expressions using the laws of indices Applying algebraic skills to manipulate expressions Applying algebraic skills to algebraic fractions Applying geometric skills linked to the use of formulae Interpret a situation where mathematics can be used and identify a valid strategy Explain a solution and/or relate it to a context

• Working with surds

• Simplifying expressions using laws of indices

• Calculations using scientific notation

• Working with algebraic expressions involving expansion of brackets

• Factorising algebraic expressions

• Completing the square in quadratic expressions with unitary x2 coefficient

• Reducing an algebraic fraction to its simplest form

• Applying four operations to algebraic fractions

• Determining the gradient of a straight line, given two points

• Calculating the length of arc or area of sector of a circle

• Calculating the volume of a standard solid - sphere, cone, pyramid

• Rounding to a given number of significant figures Reasoning skills applied to all of above Reasoning skills applied to all of above

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NATIONAL 5 MATHEMATICS - COURSE CONTENT

RELATIONSHIPS

SUB-SKILLS WITHIN EACH ASSESSMENT STANDARD

1.1 1.2 1.3 1.4 1.5 2.1 2.2

Outcomes (assessment standards): Apply algebraic skills to linear equations Apply algebraic skills to graphs of quadratic relationships Apply algebraic skills to quadratic equations Apply geometric skills to lengths, angles and similarity Apply trigonometric skills to graphs and identities Interpret a situation where mathematics can be used and identify a valid strategy Explain a solution and/or relate it to a context

• Determining the equation of a straight line, given gradient

• Working with linear equations and inequations

• Working with simultaneous equations

• Changing subject of a formula

• Recognising and determining the equation of a quadratic function from its graph

• Sketching a quadratic function

• Identifying the features of a quadratic function

• Solving a quadratic equation which has been factorised

• Solving a quadratic equation using the quadratic formula

• Using the discriminant to determine the number of roots

• Applying the Pythagoras’ theorem (complex situations, converse and 3D)

• Applying the properties of shapes to determine an angle

• Using similarity – length, area, volume

• Working with graphs of trigonometric functions

• Working with trigonometric relationships in degrees Reasoning skills applied to all of above Reasoning skills applied to all of above

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NATIONAL 5 MATHEMATICS - COURSE CONTENT

APPLICATIONS SUB-SKILLS WITHIN EACH ASSESSMENT STANDARD

1.1 1.2 1.3 1.4 2.1 2.2

Outcomes (assessment standards): Apply trigonometric skills to triangles which do not have a right angle Applying geometric skills to vectors Applying numerical skills to fractions and percentages Applying statistical skills to analysing data Interpret a situation where mathematics can be used and identify a valid strategy Explain a solution and/or relate it to a context

• Calculating the area of a triangle using trigonometry

• Using the sine and cosine rules to find a side or angle

• Using bearings with trigonometry

• Working with 2D vectors

• Working with 3D coordinates

• Using vector components

• Calculating the magnitude of a vector

• Working with reverse percentages

• Working with appreciation/depreciation (including compound interest)

• Working with fractions, including mixed numbers (four operations)

• Comparing data sets using statistics (standard deviation, semi-interquartile range)

• Forming a linear model from a given set of data (scattergraphs and equation of the line of best fit) Reasoning skills applied to all of above Reasoning skills applied to all of above

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NATIONAL 5 MATHEMATICS - ASSESSMENT

INTERNAL ASSESSMENT EXTERNAL ASSESSMENT (EXAMINATION)

Each unit assesses all outcomes, including reasoning content. To pass a unit, you must achieve either :

• at least 60% of the total available marks across all outcomes

• or at least 50% of the available marks per outcome (1.1 – 1.5) AND one mark for each of outcomes 2.1 and 2.2

In the event of failure to achieve one of these thresholds:

• you will be given one further attempt to resit each of the failed outcomes

• in discussion with your teacher, you should identify areas for further study and agree a date for reassessment, within about a fortnight

• information on suggested resources will be made available, to use in conjunction with the textbook issued to you at the start of the session

• in discussion with your parents/carers, you should plan and work through a period of study to ensure success at the reassessment stage

In the event of failure of the reassessments, you will be advised of possible next steps, for example:

• continue working at the same level and work towards achieving (some) units only

• drop to the next level down

All units must be passed, to be able to sit the external assessment (exam)

You will sit an estimate examination in January, which will include all content studied by then. Your estimate examination result will contribute to the final estimate grade passed to SQA in the weeks before the external examination. The format of the estimate and external examinations are the same: Paper 1: non-calculator 40 marks 1 hour Paper 2: calculator 50 marks 1 hour 30 minutes The purpose of the external (course) examination is to assess the added value of the course as well as confirming attainment of the course and awarding a grade. The added value focusses on:

• breadth – drawing on knowledge and skills from across the course

• challenge – requiring greater depth or extension of knowledge and/or skills

• application – requiring application of knowledge and/or skills in practical or theoretical contexts as appropriate

All units and the examination must be passed to gain an overall award

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ACHIEVING A UNIT This is what it looks like to achieve a unit

Useful websites to support learning: https://www.mymaths.co.uk/ http://www.bbc.co.uk/education/subjects/ztrjmp3 http://maths.qahs.org.uk/home-study-2/sqa-past-papers/ http://courses.scholar.hw.ac.uk/vle/scholar/ http://www.millburnacademy.co.uk/?page_id=8071

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NATIONAL 5 MATHEMATICS – INTERNAL ASSESSMENT RECORD OF ACHIEVEMENT

EXPRESSIONS AND

FORMULAE NEXT STEPS AND DATE OF RE-ASSESSMENT

PARENT SIGNATURE FOR

EACH RE-ASSESSMENT

1.1 Pass/Fail

1.2 Pass/Fail

1.3 Pass/Fail

1.4 Pass/Fail

RELATIONSHIPS NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR

EACH RE-ASSESSMENT

1.1 Pass/Fail

1.2 Pass/Fail

1.3 Pass/Fail

1.4 Pass/Fail

1.5 Pass/Fail

APPLICATIONS NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR

EACH RE-ASSESSMENT

1.1 Pass/Fail

1.2 Pass/Fail

1.3 Pass/Fail

1.4 Pass/Fail

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If you have changed from National 5 to National 4 level, please complete the following Record of Achievement.

NATIONAL 4 MATHEMATICS – INTERNAL ASSESSMENT RECORD OF ACHIEVEMENT

NATIONAL 4 – EXPRESSIONS AND

FORMULAE

NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR EACH RE-ASSESSMENT

1.1 Pass/Fail

1.2 Pass/Fail

1.3 Pass/Fail

NATIONAL 4 – RELATIONSHIPS

NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR EACH RE-ASSESSMENT

1.1 Pass/Fail

1.2 Pass/Fail

1.3 Pass/Fail

1.4 Pass/Fail

NATIONAL 4 – NUMERACY

NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR EACH RE-ASSESSMENT

Outcome 1 Pass/Fail

Outcome 2 Pass/Fail

NATIONAL 4 – ADDED VALUE

NEXT STEPS AND DATE OF RE-ASSESSMENT PARENT SIGNATURE FOR EACH RE-ASSESSMENT

Pass/Fail

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Top Tips – Unit and External Assessment

• Regular practice of numerical skills without a calculator. You should have quick recall and be fluent with multiplication tables (up to at least 10), including squares and square roots (up to at least 152 = 225)

• Read question carefully, pick out key words to identify what is being asked – which topic, what strategy to use, what level of rounding is asked for?

• Questions which are broken into parts (a) and (b) are linked – use your answer from part (a) to help you with part (b). The word “hence” is a hint to do this

• Show all steps of working including units, where appropriate. See the number of marks available – you should expect to link the number of marks with the number of steps of working. Correct answers without working are likely to mean a (significant) loss of marks

• When asked to justify your solution, write a sentence and link your conclusion to the context of the question. If a comparison of values is required, state this to gain the final mark, eg “the angle of the ramp is within safety guidelines because 7·2° is less than 9°”

• Look through all questions and do those you are most confident with, first, to maximise your marks (make sure you clearly number the questions for the marker!). Remember – the external assessment is time limited

• It is possible to pass unit assessments without being able to evidence knowledge and understanding of all topics. You must ensure that you continue to work on/revisit weaker topics, as they will be tested in the external assessment

• Complete specimen question papers and past paper questions. Ensure you look at marking instructions as these often contain course content and they will help you to improve your exam techniques

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National 5 Mathematics Assessment Calendar

Please note and record the following key course dates in your Planner, complete the tear-off acknowledgement label attached and return it to your Mathematics Teacher by the end of August.

Date Unit Assessments Estimate examination

June

Expressions and Formulae 1.1

August – October holidays (assessment at end of each

block of learning, at approximately two week

intervals)

Expressions and Formulae 1.2 Expressions and Formulae 1.3 Expressions and Formulae 1.4

October holidays

October- Christmas holidays

(assessment at end of each block of learning, at

approximately two week intervals)

Relationships 1.1 Relationships 1.2 Relationships 1.3 Relationships 1.4

Christmas holidays

January – February mid-term (assessment at end of each

block of learning, at approximately two week

intervals)

Relationships 1.5 Applications 1.1

Estimate examination covering all of Expressions and Formulae unit and Relationships unit outcomes 1.1 – 1.4

February mid-term

Feb mid-term – Easter holidays

(assessment at end of each block of learning, at

approximately two week intervals)

Applications 1.2 Applications 1.3 Applications 1.4

Easter holidays

April – study leave

Exam preparation

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National Qualifications: Mathematics Assessment Calendar

Learner Name ______________________

Class

__________

Teacher Name ______________________

I have read and acknowledged the major course deadlines for assessment.

My son/daughter has transferred these dates into his/her student planner.

I agree to my son/daughter being presented at an appropriate level in line with the guidance outlined herein.

.

Parent/Carer Signature

Date

____________________

____________________ Please complete the tear-off acknowledgement label attached and return it to your Mathematics Teacher by the end of AUGUST