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MX1000CA course and assessment guide ncea level 1

2015


mathematics and statistics level 1 (mx1000) teacher contact details When you first make contact with your teacher, please fill out their details below, for future reference. Name: Telephone: 0800 65 99 88

Ext:

Alternative telephone number: Email address: Private Bag 39992, Wellington Mail Centre, Lower Hutt 5045 Please keep your Mathematics and Statistics Level 1 (MX1000) Course and assessment guide in a safe place so that you can use it to plan your study and to record your assessment results. For further information about courses at this level, please refer to Student Guide to Years 11–13 and the Student Guide to National Certificates.

Cover image: © iStockphoto.com, 6080650. Copyright © 2011 Board of Trustees of Te Aho o Te Kura Pounamu, Private Bag 39992, Wellington Mail Centre, Lower Hutt 5045, New Zealand. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means without the written permission of Te Aho o Te Kura Pounamu. © te ah o o te k u ra p ou n am u


contents 1

Welcome to MX1000

2

Getting started information

3

MX1000 course and assessment summary

4

Assessment information

5

Suggested programme plan

6

My Mathematics and Statistics Level 1 assessment record (MX1000)

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welcome to mx1000 Welcome to the Level 1 Mathematics and Statistics (MX1000) course offered by Te Aho o Te Kura Pounamu. This Course and assessment guide gives you information about the MX1000 course. Keep it so that you can refer to it when you need to.

aims of mx1000 Mathematics is more than just numbers! It is the exploration and use of patterns and relationships in quantities, space and time. Statistics focuses on patterns and relationships in data. Both will equip you with powerful communication and problem solving tools for investigating, interpreting and making sense of the world. Using symbols, graphs and diagrams, you will investigate and model real-life and hypothetical situations in a range of contexts – social, cultural, scientific, technological, health, environmental and economic. Mathematics develops your ability to think creatively, critically, strategically and logically as you learn to organise, process and communicate information. What this course involves This NCEA Level 1 course covers all major areas of mathematics and statistics at curriculum level 6. You will learn skills, use and apply mathematical and/or statistical concepts that are needed in solving problems involving number, algebra, geometry, measurement, probability and statistics. This course can be endorsed with Merit or Excellence if, in a single year, you gain 14 or more Level 1 Mathematics and Statistics credits at Merit and/or Excellence. At least three of these credits must be externally assessed and at least three internally.

assessment (internal and external) Internal Internal assessments are assessed by your teacher. You can be assessed any time you and your supervisor are ready, though each assessment task has conditions that you must follow. Both you and your supervisor must make sure that you keep to these conditions and you are both required to sign a statement to say that you have done so. External External assessment means that your grade is decided by an examination. The NCEA examinations take place at the end of each year and have a strict timetable. If you enter for an examination, you must attend these at the specified location and time. After you have sat the examination at an examination centre, it is sent off to be assessed by NZQA. Te Aho o Te Kura Pounamu provides practice examinations late in term three to help you prepare for the NZQA external assessments. Common Assessment Task set externally but assessed internally (CAT) Achievement standard 91027, ‘Apply algebraic procedures in solving problems,’ is an assessment run by NZQA each year. No calculator or technology of any kind is allowed in this paper-based exam. 2

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welcome to mx1000

achievement standards and national certificates Throughout your programme you will have many opportunities to be assessed and to gain credits towards National Certificates and/or build up your NZQA Record of Learning. Without sitting examinations you can gain credits towards NCEA level 1 with the grades of Achieved, Merit or Excellence for up to nine internally assessed achievement standards.

external achievement standards by examination Your programme could be designed to prepare you for up to four achievement standards that can be gained only through the NZQA examinations held each year. If you are aiming to do this, you should be confident in a range of mathematics and statistics skills at curriculum level 6. nzqa examination-assessed achievement standards

interested ✓ or X

Apply algebraic procedures in solving problems AS91027 (CAT)

Investigate relationships between tables, equations and graphs AS91028

Apply geometric reasoning in solving problems AS91031

Demonstrate understanding of chance and data AS91037

You will not need to make a final decision about this until July. You will be contacted by the Qualifications team here at Te Kura. If you decide to attempt the external achievement standards you will be sent trial examination activities in term 3 to assist your preparation. For further information, refer to section 4 (Assessment information) in this guide.

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welcome to mx1000

your programme There are many reasons why you have enrolled in this MX1000 course. If your circumstances or goals change, you can negotiate alterations to your programme with your teacher. Please let your teacher know about your wishes when you send in your work. Your teacher may also make further recommendations based on your progress. You will be provided with revision notes you may need to help you with your learning. Best wishes for your future Mathematics and Statistics learning and achievements.

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getting started information how this course is delivered

MX1000 is a blended course with some print-based material, that can be downloaded from the online teaching and learning environment (OTLE), and an interactive online component in OTLE. You will receive an email explaining how to log in to OTLE. This email includes a link to set your password if you have not logged into the OTLE before. You can access OTLE by clicking on www.tekura.school.nz/login. It is recommended that you bookmark this site in your browser. This will take you to a page with links to your courses. Your username and initial password is your Te Kura student ID number. You will be asked to set a new password when you first log in. After that, if you need to reset your password you can click on the ‘Forgot password’ link on the login page. If you have difficulties logging in, please email: helpdesk.otle@tekura.school.nz

organising your study Plan a regular time to study. Some people learn best from frequent short sessions while others do better with fewer, longer sessions. It is important to have a plan or a timetable and to keep to it. There is a suggested planner in the back of this guide for you to plan your programme of study. You may wish to consult with your subject teacher to help you decide on your plan. Getting your study underway is very important. Your first return of work should be two weeks after you first enrol. If you have any issues returning your work within this time please contact your subject teacher. For more information on how to study successfully, refer to the Student Guide to Years 11–13 (www.tekura.school.nz).

te kura codes Your course code is: MX1000. MX is the code for Mathematics and Statistics and 1000 refers to Level 1. ‘MX1011’ refers to a booklet that covers a particular learning topic in the MX1000 course. ‘MX1013Y1’ refers to the first assessment for an achievement standard (AS91026). ‘AS’ is the code for achievement standard.

mathematical equipment You will need to have quad paper (or book), refill paper, and a scientific or graphics calculator to work with. You will also need access to a computer with some mathematical software installed. You will need a ruler and may need a protractor and drawing equipment (a pair of compasses).

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getting started information

teacher support You will be assigned a Mathematics and Statistics teacher. It is important to contact him/her if you have any queries about your work. He/she can assist you with your learning and also in tailoring your programme to suit your needs.

self-marking Many assessment activities are self-marked. You’ll find an Answer guide in each resource. Use these answers to mark your own work and make corrections where necessary. Self-marking is very important as it gives you instant feedback on how well you understand the ideas, concepts or information that has been covered.

assessment There are self-assessments contained within the booklets. Please check your work as you progress through each resource and make contact with your Mathematics and Statistics teacher if you require help along your learning journey. You are required to send in your self-marked activities and the teacher-assessed review answers. Your teacher will return your work with feedback in each resource that you complete. The internal achievement standard tasks will be sent to you when you have submitted the work from the last unit of work in the series that relates to the particular standard you are working towards. The detailed criteria for achievement standards are given in the relevant booklets. They can also be found by searching the subject and level in the NCEA part of the NZQA website (www.nzqa.govt.nz) and then finding the relevant standard(s). If there are two assessment opportunities, one is called ‘Y1’ for an achievement standard and the other is called ‘Y2’. For example, MX1013Y1 is the first assessment for AS91026 and MX1013Y2 is the second assessment opportunity. External assessment preparation includes: • practice external assessments • Te Kura practice examinations. There are no reassessment opportunities for externally assessed standards.

normal pace of learning A normal pace of learning is similar to what a student does at school. As a guide, expect to do at least five hours work per week. This means completing four to six booklets each term so that you complete the course before the end of year external examinations and the end of the school year.

time commitment There is a lot of flexibility for you to design a course that will suit your needs at NCEA Level 1. Each booklet indicates how many study hours it is likely to require. For example, booklet MX1011 may take 10 hours of work to complete at the normal pace, representing about two weeks work. There are 28 booklets that make up the content of this course, but you are not expected to complete them all. 6

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getting started information

Before deciding on the pace of learning, ask yourself the following: • How much time can I set aside for study each week? • Will I be able to keep a steady pace of five hours of study each week? • What do I want to do next year? How many credits will I need to do this? • Will I be doing externally and internally assessed standards? • Do I intend to sit the external examination at the end of the year? • Do I need specific external or internal credits as a prerequisite for next year’s study or work?

flexible pace of learning If you have less than a year because you start later or need to finish earlier, you can decide the pace at which you work. You could still complete the whole course by devoting more time and effort to it.

choosing topics and standards You may wish to do only some topics. For example, you may only want to do internal standards in this course. You should discuss this with your learning advisor and Mathematics and Statistics teacher. You should consider how well this will meet your learning goals and whether it will meet the specific course entry requirements for tertiary institutions or any future study and whether you will be able to gain enough credits to achieve your NCEA. To be awarded NCEA Level 1, you will need to gain a minimum of 80 credits at Level 1 (or above) including the 10 credits for literacy and the 10 credits for numeracy. A list of achievement standards from levels 1, 2 and 3 that count towards Level 1 literacy and numeracy can be accessed from: www.nzqa.govt.nz/about-us/our-role/legislation/nzqa-rules/secondary-schools-supportinginformation/level-1-literacy-and-numeracy-requirements/

cover sheets The back cover of the booklet is called the cover sheet. You must fill it in and sign it before sending your work back to Te Kura. Your supervisor, if applicable, must also sign this sheet as part of our authenticity requirements. All students are encouraged to submit as much as possible of their work online via the OTLE Dropbox. When work requires authentication, students will follow the instructions provided in OTLE.

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mx1000 course outline and assessment summary This table shows the standards offered and the learning material associated with them. It also gives a suggested time to complete the learning. title

item code

title

AS91026 4 credits Internal

Apply numeric reasoning in solving problems

MX1011 MX1012 MX1013

Decimals, fractions, percentages Powers, standard form, rounding Rate, ratio, proportion

5

AS91027 4 credits External

Apply algebraic proceedures in solving problems

MX1021 MX1022 MX1023

Basic algebra skills Quadratics and further skills Exponential & simultaneous equations

7

AS91028 4 credits External

Investigate relationships between tables, equations and graphs

MX1021 MX1043 MX1033

Basic algebra skills Linear patterns & graphs Exponential & quadratic patterns

7

AS91029 3 credits Internal

Apply linear algebra in solving problems

MX1021 MX1043

Basic algebra skills Linear patterns & graphs

4

AS91030 3 credits Internal

Apply measurement in solving problems

MX1051 MX1052

Area, volume, time Rate, capacity, surface area

4

AS91031 4 credits External

Apply geometric reasoning in solving problems

MX1061 MX1062 MX1063 MX1064

Pythagoras; similar triangles Trigonometry – basic skills Angles, bearings & proofs Circle geometry

7

AS91032 3 credits Internal

Apply right angled triangles in solving problems

MX1061 MX1062 MX1073 MX1074

Pythagoras; similar triangles Trigonometry – basic skills Trigonometry in 3D (i) Trigonometry in 3D (ii)

6

AS91033 3 credits Internal

Apply knowledge of geometric representations in solving problems

MX1081 MX1082 MX1083

Scale, bearings, nets Constructions & loci Describing loci

6

AS91034 2 credits Internal

Apply transformation geometry in solving problems

MX1091 MX1092

Transformations – concepts Multiple transformations

4

AS91035 4 credits Internal

Investigate a given multivariate data set using the statistical enquiry cycle

MX1101 MX1102 MX1103

Sampling, displaying data Investigations Multivariate data

7

AS91036 3 credits Internal

Investigate bivariate numerical data using the statistical enquiry cycle

MX1101 MX1102 MX1113

Sampling, displaying data Investigations Bivariate data

7

AS91037 4 credits External

Demonstrate understanding MX1122 of chance and data

MX1101

Sampling, displaying data Probability (i) Probability (ii)

6

standard

8

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time (weeks)

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mx1000 course outline and assessment summary

AS91038 3 credits Internal

Investigate a situation involving elements of chance

MX1101 MX1122 MX1133

Sampling, displaying data Probability (i) Simulation

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conditions of assessment for some achievement standards Assessment of the standards could include, but is not restricted to, a written test, an extended task or an investigation. In all cases authenticity needs to be assured. Internal assessment provides considerable flexibility in collection of evidence. Care is taken to give you opportunities to present your best evidence against the standard at all levels of achievement. Holistic decisions may be used in awarding of a grade by reference to the achievement criteria. Partial solutions can provide evidence. Access to appropriate technology is expected except when conditions state that they cannot be used.

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assessment information standards

The National Qualifications Framework has two types of national standards: achievement and unit standards. Credits from both achievement standards and unit standards count towards NCEA. Please refer to our Student Guide to National Certificates or Te Kura (www.tekura.school.nz) and NZQA websites (www.nzqa.govt.nz) for more information about National Certificates of Educational Achievement, and assessment.

internal assessment Some achievement standards and unit standards are internally assessed. This means that the teachers set and mark your assessments at the school.

external assessment External assessment means that someone outside the school marks your work. This may be through NZQA examinations at the end of the year. You will be able to complete practice assessments and Te Kura examinations for external standards.

te kura practice examinations You should complete the Te Kura practice examinations for any external standards with an end of year examination that you have entered. If for some reason, such as illness, you are unable to sit the examinations at the end of the year you will only be eligible for consideration for a derived grade (compassionate consideration) if you have completed the practice examinations.

further assessment opportunities for internal assessments For some standards, you will be able to complete a second assessment called a ‘further assessment opportunity’ to improve your results. These standards are indicated in the course outline. You should take this opportunity where it is available.

resubmissions If you have made a small mistake in your assessment, your teacher may offer you a resubmission. This means you have made an error that you are capable of discovering and correcting by yourself. A resubmission allows you to improve your result.

authenticity Authenticity means students complete and submit work that is their own. When you submit work to Te Kura you sign an authentication declaration that the work you are submitting is your own work and was done under the required assessment conditions. Your supervisor signs this declaration to confirm this (where applicable). When submitting work online via the OTLE Dropbox, if it requires authentication, students must follow the instructions provided in OTLE.

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assessment information

derived grades (compassionate consideration)

If for any unexpected reason you are not able to sit your end of year examination or to submit final work towards an external standard (portfolios or projects), you may be eligible for a derived grade. Please refer to the Student Guide to National Certificates and contact your learning advisor as soon as possible to find out more should you feel this is necessary.

appeals You have the right to query an assessment result if you want further clarification or disagree with the result. If you are still not satisfied, you may appeal. Refer to the Student Guide to National Certificates for more information. You can also appeal any other decisions, procedures or policies about assessments. Contact your teacher or learning advisor if you wish to appeal. More information and a form that students can use to appeal is available on the Te Kura website in the Student toolkit area (www.tekura.school.nz and go to Student toolkit).

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suggested programme plan There are many pathways through MX1000. Most of them start with Number, MX1011, which you can access through OTLE. This, along with other learning material, leads to the Achievement Standard 91026 (internal). If you think that your plan should not include MX1011, contact your teacher immediately to discuss a more appropriate start. You might like to design your own course by writing item numbers on the Personal pathway line. Some topics are essential if you plan to continue on to NCEA Level 2 Mathematics and Statistics. You should discuss this with your teacher.

Personal pathway (You can list the items you will need – use the course outline and assessment summary on page 8)

Statistics

*

**

**

*

**

*

**

 

**

*

*

**

*

*

**

*

*

**

*

**

*

*

*

**

**

Probability

Trigonometry

Statistics focus

Geometry

Mathematics focus

Measurement

Service industries Social and community services

Algebra

Primary and secondary industries e.g. construction, technology

Number

Possible career path:

Introduction

It is recommended that you return one item every two weeks.

All students receive the course guide MX1000CA, and MX1061, an introduction to trigonometry and geometry.

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Key: ** These strands are very important for the career path – some topics are essential. * These strands can be useful for the career path – some topics are recommended.

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my mathematics and statistics level 1 assessment record (mx1000) You can keep track of your progress in this course by filling in this table each time you gain a standard. Standard Number

Assessment Details

Credits

Grade Awarded

Exam/ Assessment

AS91026

Internal – Closed book assessment on number

4

AS91027

External (CAT) – Apply algebraic methods in solving problems

4

September exam*

AS91028

External – Investigate relationships between tables, equations and graphs

4

November exam*

Practice Te Kura examination AS91029

Internal – Closed book assessment on linear algebra

3

AS91030

Internal – Closed book assessment on measurement

3

AS91031

External – Apply geometric reasoning in solving problems

4

November exam*

Practice Te Kura Examination AS91032

Internal – Closed book assessment on right-angled triangles

3

AS91033

Internal – Closed book assessment on geometrical reasoning

3

AS91034

Internal – Open book assessment on transformation geometry

2

AS91035

Internal – Open book assessment on multivatiate data analysis

4

AS91036

Internal – Open book assessment on bivariate data analysis

3

AS91037

External – Demonstrate understanding of chance and data

4

November exam*

Practice Te Kura examination AS91038

Internal – Open book assessment on probability simulations

3

Indicates external standard with NZQA Nov/Dec examination or CAT results available in January.

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MX1000CA 2015