Year 9 Mathematics Study Program - Assumption...

ASSUMPTION COLLEGE KILMORE

Year 9 Mathematics Study Program

Helping Create the Independent Learner

Faculty of Mathematics

2014

This document is designed to help students to develop study techniques and create their own individual learning plan for Mathematics. The strategies outlined coincide with the Year 9 General Mathematics learning outcomes and can be readily applied at home.

Table of Contents

Introduction ............................................................................................................................................................................ 2

Purpose ................................................................................................................................................................................... 2

Contacts .................................................................................................................................................................................. 2

Part 1 - Getting Organised ...................................................................................................................................................... 3

Part 2 - Suggested Home Study .............................................................................................................................................. 4

Completing questions from the exercise ............................................................................................................................ 4

Class notes .......................................................................................................................................................................... 5

Assignments ........................................................................................................................................................................ 5

Examination Preparation .................................................................................................................................................... 5

MathsOnline ....................................................................................................................................................................... 5

Part 3 - Expectations ............................................................................................................................................................... 6

Maintaining a Mathematics Workbook .............................................................................................................................. 6

Showing Working Out ......................................................................................................................................................... 7

Part 4 - Need Help? ................................................................................................................................................................. 8

Mathematics Teachers ....................................................................................................................................................... 8

AIMS Program ..................................................................................................................................................................... 8

Part 5 - The Work Program ..................................................................................................................................................... 9

The Timeline ....................................................................................................................................................................... 9

Work Program ................................................................................................................................................................... 10

Part 6 – Preparing for Tests and Examinations ..................................................................................................................... 18

Suggestions for Students .................................................................................................................................................. 18

Suggestions for Parents/Guardians .................................................................................................................................. 19

2 | Y e a r 9 M a t h e m a t i c s S t u d y P r o g r a m 2 0 1 4

Introduction Learning Mathematics in Australia is not only fundamental for our daily lives but also ensures that our students excel in

their chosen life after school careers. The Australian Curriculum: Mathematics provides students with essential

mathematical skills and knowledge in Number and Algebra, Measurement and Geometry, and Statistics and Probability1.

The Australian Curriculum has been designed to ensure that all students:

are able to link and relate real-life situations/scenarios to skills and knowledge obtained ensuring that they are

creative and confident

acquire a fluent understanding of all concepts and processes learnt in order to find solutions in all areas: Number

and Algebra, Measurement and Geometry and Statistics and Probability

comprehend and are able to make connections with other subject areas strengthening their appreciation for the

Mathematics discipline

Purpose The purpose of this document is to help Year 9 Mathematics students develop independent learning skills and home

study plans. We aim to help all students develop a positive attitude towards their mathematics allowing each child a

chance to accomplish a sense of achievement and success.

We hope to encourage all Year 9 students to develop an independent study routine ensuring they are keeping on top of

their studies as well as extending themselves mathematically.

We encourage students to take active responsibility for their home study throughout each unit of study with

consideration given to the following proficiency strands:

1. Understanding: knowledge obtained previously will help establish whether students are able to

establish a link connecting the ‘why’ and ‘how’ of mathematical concepts

2. Fluency: the development of skills, knowledge and concepts helping carry out procedures and

methods where answering problems

3. Problem Solving: modelling is used here to link the skills obtained with real-life scenarios

4. Reasoning: the development of solutions to sophisticated situations.

These proficiency strands, which underpin the Australian Curriculum, are designed as a set of ‘stepping stones’ towards

mathematical proficiency and understanding for each unit studied.

Contacts If there are any questions or concerns at any stage of the year please feel free to contact the school any time.

Narelle Collins Learning Area Coordinator - Junior Mathematics

(03) 5782 1422 [email protected]

Laila Sarraf Learning Area Coordinator - Senior Mathematics

(03) 5782 1422 [email protected]

We hope the partnership between school and home continues to grow ensuring each student obtains a strong

mathematical future.

1 http://ausvels.vcaa.vic.edu.au/Mathematics/Overview/Rationale-and-Aims

Part 1 - Getting Organised All students are to ensure there is a quiet and fully equipped study area/space for nightly homework. The materials that

each student is required to have readily available for Mathematics studies are as follows:

1

Workbook: where all worked calculations and solutions are recorded. This workbook is to be kept neat and tidy at all times. Under no circumstances are students permitted to tear pages out of their workbooks.

2

Work book: where notes and worked examples taken in class are recorded. Students are to ensure that this is kept up to date – if a student is absent from class it is his or her responsibility to catch up.

3

Textbook: The textbook is required to ensure that students are able to complete the assigned problems. The textbook should also be used as a resource to obtain worked examples as well as consolidate classroom based learning.

4

Calculator (Scientific): ensures that students are able to proceed with most mathematical worked solutions. Practice with the calculator also ensures that students are familiar with adjusting certain settings for certain units/topics studied. Teachers will not be able to assist with adjusting or showing how to work the calculator in a test or examination.

5

Writing Materials: correct materials are used to guarantee that the workbook is kept presentable. The ruler should be used to rule margins and for all graphing. Graphing should always be done using a lead pencil.

6

MathsOnline: every student is able to access MathsOnline – an online mathematics resource. The program contains many online tutorials with a step by step guide through examples as well as additional worksheets to help consolidate understanding.

7

Student Diary (or alternative): will help keep track of tasks, questions and assignments that need to be completed.

8

iPad: while pen and paper study techniques remain critical to successful learning in Mathematics, the iPad is an engaging tool that can support a student’s study program if used effectively.


Part 2 - Suggested Home Study These general guidelines are provided to support students in developing individual home study plans and techniques

that allow them to perform at their best throughout Year 9 and future years.

The Suggested Home Study Options include practical activities that students can undertake to manage their studies.

While these activities are suggested to support students in their home study, it is important that students realise that

they are ultimately responsible for investing time and effort into developing and fulfilling their personal study plan.

Completing questions from the exercise 1. Ensure that all questions set by the teacher are complete.

2. Students should endeavour to complete a range of questions from the four proficiency strands: Understanding,

Fluency, Problem Solving and Reasoning. These are located with each exercise in the text book:

2

The textbook also contains example references beside certain questions that can be used. The calculator icon

indicates when the calculator is recommended.

Finally, enrichment tasks can be used as extension questions for those willing to extend their learning.

Students are advised to correct their work as they work through the set tasks to ensure they have the right

mathematical procedures in place.

Any difficulties in completing the work accurately may be due to a lack of understanding or problems in following

the procedures involved. If students are unable to resolve the difficulties they are advised to seek assistance from

their teacher as soon as possible.

2 Greenwood et al. (2011) Essential Mathematics Year 9: For the Australian Curriculum Cambridge University Press, Australia

Class notes 1. Students should ensure that class notes are up to date.

2. Read over the notes taken in class to check their understanding of what was taught in class.

3. Where understanding is not there, students are encouraged to follow up with their

teacher, ask questions and ask for help.

4. Even if students’ have understood the classroom based learning, they are encouraged to

add diagrams, colour (highlighting) and side notes to ensure that they understand their

class notes if they were to read them again, for example, in two weeks’ time.

Assignments 1. All assignments need to be done over 2-3 nights. Students should never begin an assignment the night before it

is due!

2. When working through an assignment, students should ensure that they are setting out their solutions neatly

and that are referring to notes for guidance.

3. All diagrams and graphs need to be drawn neatly with a ruler and in pencil. The assignment needs to be

completed neatly on loose leaf paper (unless otherwise stated) NOT on a piece of paper torn from an exercise

book.

Examination Preparation 1. Exam preparation needs to begin during the semester - NOT right before the examination day. Preparation for

the mid-year examination needs to begin in term 1. Preparation for the end of year examination needs to begin

in term 3.

2. Prepare summary notes and reference sheets and refer to them regularly.

3. Study and review the mathematical concepts learned in class every week – whether revision homework has

been set or not. (Use the Work Program outlined in this booklet to help).

4. Complete randomly selected questions (from exercises, chapter review or MathsOnline) using the reference

sheets which will give a good indication of whether the reference sheets will be useful in the examination.

MathsOnline All students in Year 9 have access to MathsOnline using their unique login and password details. The web-based

software provides example driven, online tutorials that guide students in the processes involved in solving standard

problems associated with the given topic. Students are advised to:

1. Visit MathsOnline to assist in revising the work learned in class.

2. Watch tutorials of topics that are currently being covered in class. Complete the worksheets that are linked to

the tutorials to consolidate skills in the mathematical processes, gain more practice on a wider range of

problems (not just those in the text book) and gain feedback on where errors may be arising.

3. To help with examination preparation, choose a topic of difficulty and watch the tutorials, practice the skills and

read the feedback.


Part 3 - Expectations

Maintaining a Mathematics Workbook It is vital that all students take pride in their work.

Some students very easily fall into the trap of leaving blank pages between exercises, tearing out messy pages (causing

their exercise book to fall apart) and scribbling out work.

It is recommended that students set up and maintain their exercise book in a neat and well-ordered manner.

Below are two options that can be taken:

Exercise book with two (2) columns Exercise book with no columns

Showing Working Out Students must always show working out before writing down their answer to any problem.

Simply writing an answer down to a question does not meet the required standard at year 9.

Students must set out all calculations in a clear and concise manner. An example (to compare):

Correct set-out

Incorrect set-out

Example: Find the value of the pronumeral. Express your answer correct to two decimal places.

Example: Find the value of the pronumeral. Express your answer correct to two decimal places.

Label your diagram:

Write out the formula you need to use (where applicable):

𝑐2 = 𝑎2 + 𝑏2 𝑎2 = 𝑐2 − 𝑏2

Substitute in the values then calculate: 𝑎2 = (12)2 − (4)2

𝑎2 = 144 − 16

𝑎 = √144 − 16

𝑎 = √128 = 11.3137 Write your answer to two decimal places:

𝑎 = 11.31 (units)

Most students will skip important steps:

𝑎2 = 𝑐2 + 𝑏2 𝑎2 = 144 + 16

𝑎 = 128

Firstly, the equation wasn’t written down correctly resulting with a poor start. It shows that the student has attempted to solve the problem using the calculator and not working through the correct process.

Student work must always resemble the set-out in the first column (above).

All tests, assignments and the examination have marks allocated for both set-out and the correct answer.

Students who do not practice the correct setting-out jeopardise their chances of obtaining the best possible mark.

DON’T THROW AWAY MARKS – SHOW ALL WORKING OUT!


Part 4 - Need Help?

Mathematics Teachers The first person to contact is a student finds him or herself struggling or falling behind with their work is their

mathematics teacher. The year 9 mathematics team are listed below:

Teacher Class Office Location Email

Mr M Egan 9A/B (Accelerated) 216 [email protected]

Mr A Langdon 9A/B 217 [email protected]

Mr D Coonan 9C and 9E 661 [email protected]

Mr M Johnson 9D Gonzales Centre [email protected]

Mr J Weber 9F 107 [email protected]

Mr K Edwards 9G 526 [email protected]

Ms T Frost LEC LEC [email protected]

Mrs N Collins LAC – Jnr Maths 334 [email protected]

Ms L Sarraf LAC– Snr Maths 526 [email protected]

AIMS Program The AIMS (Academics in Mathematics and Science) Program is a tutorial session held in the library every Wednesday

after school. The purpose of the program is to help all students with troubles they may be experiencing with their

Mathematics (and Science) work.

Any student who feels the need for extra one-on-one help with Mathematics homework or a study routine is

encouraged to make the most of this resource. Contact the library for more information.

mailto:[email protected]









Part 5 - The Work Program

The Timeline The timeline is a yearly planner that will show an overview of the topics covered over the year.

Term Chapter/Unit Assessment

Terms 1 and 2

Chapter 1: Reviewing Number and Financial Mathematics Test Chapter 6: Indices Test Chapter 3: Pythagoras’ Theorem & Trigonometry Test and Assignment

--End of Semester 1-- Examination

Terms 3 and 4

Chapter 5: Measurement Test and Assignment Chapter 2: Algebraic Expressions and Linear Equations Test Chapter 4: Linear and Non-Linear Modelling Test Chapter 9: Probability Test

--End of Semester 2-- Examination

Work Program The following sets of tables are a list of work that must be completed by students. The tables are divided into sections allowing students to see the advancement and difficulty

level of questions. The Understanding and Fluency questions indicate questions at a standard level in year 9. The Problem Solving column shows questions that require

students to link the real-life scenario with the skills that have been learned and the Reasoning column relates to the questions that will extend students wanting to advance.

The Reasoning questions are particularly challenging but will support students in developing a deeper understanding of the concepts being studied. The final column gives

students the lesson number of the related MathsOnline lesson. Each lesson incorporates an animation, summary and activities for skills practice.

Chapter 1: Reviewing Number and Financial Mathematics

Topic Understanding (ALL) Fluency (ALL)

Problem Solving (SELECTED)

Reasoning Complete?

Student / Teacher

MathsOnline Reference

(Lesson Number)

Less

on

1

1.1 Integer Operations

Exercise 1A (p 6)

1, 2, 3 4, 5, 6, 7, 8 9, 10, 11 14, 15

#8136

Less

on

2

1.2 Decimals and Rounding

Exercise 1B (p 12)

1, 2, 3 4, 5, 6, 7, 8, 9

10, 11, 12 14, 15, 16

#4184 #8138

Less

on

3

1.3 Rational Numbers

Exercise 1C (p 17)

1, 2, 3, 4 5, 6, 7, 8, 9, 10

11, 12, 13 15, 16

Less

on

4

1.4 Operations with Fractions

Exercise 1D (p 22)

1, 2, 3 4, 5, 6, 7, 8, 9, 10

11, 12, 14, 15 17, 18

#8137

Less

on

5

1.10 Simple Interest

Exercise 1J (p56)

1, 2 3, 4, 5, 6, 7, 8

9, 10, 11, 12 13, 14

#3200

Chapter 6: Indices



Reasoning Complete?

Student / Teacher


(Lesson Number)

Less

on

1

6.1 Index Notation

Exercise 6A (p 329) 1, 2, 3, 4

5, 6, 7, 8, 9, 10, 11

12, 13, 14 16, 17, 18

Less

on

2

6.2 Index Laws 1 and 2

Exercise 6B (p 334)

1, 2, 3 4, 5, 6,

7, 8 9, 10, 11 12, 13, 14

#4135 #4136

Less

on

3

6.3 Index Law 3 and the zero power

Exercise 6C (p 339)

1, 2, 3 4, 5, 6, 7, 8 9, 10 12, 13

#4137 #4138

Less

on

4

6.4 Index Laws 4 and 5

Exercise 6D (p 344)

1, 2 3, 4, 5, 6

7, 8 9, 10

#4139

Less

on

5

6.5 Negative Indices

Exercise 6E (349)

1, 2 3, 4, 5, 6 7, 8, 9 10, 11

#4140

Less

on

6

6.6 Scientific Notation

Exercise 6F (p354) 1, 2, 3 4, 5, 6, 7, 8 9, 10, 11 15

#4100 #4101


Chapter 3: Pythagoras’ Theorem



Reasoning Complete?

Student / Teacher


(Lesson Number)

Less

on

1

3.1 Pythagoras’ Theorem

Exercise 3A (p 135) 1, 2, 3

4, 5, 6, 7, 8

9, 10, 11, 12 15, 16, 17

Less

on

2

3.2 Finding the Shorter Sides

Exercise 3B (p 140)

1, 2

3, 4, 5, 6

7, 8, 9, 10 12, 13

Less

on

3 3.3 Applying

Pythagoras’ Theorem

Exercise 3C (p 144) 1 2, 3, 4, 5, 6 7, 8, 9 11, 12

Less

on

4

3.4 Pythagoras in 3D

Exercise 3D (p 150) 1

2, 3, 4, 5, 6

7, 8 10, 11

Chapter 3: Trigonometry (continued)



Reasoning Complete?

Student / Teacher


(Lesson Number)

Less

on

1

3.5 Trigonometric Ratios

Exercise 3E (p 155) 1, 2, 3

4, 5, 6

8, 9, 10 12, 13, 14

#4253

Less

on

2

3.6 Finding side lengths

Exercise 3F (p 161)

1, 2, 3

4, 5

6, 7, 8 10, 11

#4254 #4255

Less

on

3

3.7 Solving for the denominator

Exercise 3G (p 165)

1, 2 3, 4 5, 6, 7, 8 9

#4256

Less

on

4

3.8 Finding and Angle

Exercise 3H (p 169)

1, 2, 3, 4

5, 6, 7

8, 9, 10, 11 13, 14, 15

#4257


Chapter 5: Measurement

Topic

Understanding (ALL)

Fluency (ALL) Problem Solving

(SELECTED) Reasoning

Complete? Student / Teacher


(Lesson Number)

Less

on

1

5.1 Length

Exercise 5A (p 267)

1, 2, 3, 4 5, 6, 7, 8 9, 10, 11 13, 14, 15

#4279

Less

on

2 5.2 Circumference

and perimeter of a sector

Exercise 5B (p 272)

1, 2, 3, 4 5, 6, 7, 8 9, 10, 11 13, 14

#8164 #8165

Less

on

3

5.3 Area

Exercise 5C (p 279) 1, 2, 3

4, 5, 6, 7, 8, 9

10, 11, 12, 13 16, 17

#8166 #8167

Less

on

4

5.4 Composite shapes

Exercise 5D (p 285)

1, 2 3, 4, 5, 6, 7 8, 9, 10 12, 13, 14

#8168

Less

on

5 5.5 Surface area of

prisms and pyramids

Exercise 5E (p291) 1, 2 3, 4, 5, 6 7, 8, 9 11, 12

#8171 #8172 #4308

Less

on

6

5.7 Volume (and Capacity)

Exercise 5G (p301) 1, 2

3, 4, 5, 6, 7, 8

9, 10, 11, 12 15, 16

#8169 #4300

Chapter 2: Algebraic Expressions and Linear Equations

Topic Understanding (ALL) Fluency (ALL) Problem Solving




(Lesson Number)

Less

on

1

2.1 Algebraic expressions

Exercise 2A (p 75) 1, 2, 3 4, 5, 6, 7 8, 9 11, 12, 13

#4182 #4183

Less

on

2 2.2 Simplifying

algebraic expressions

Exercise 2B (p 80)

1, 2, 3 4, 5, 6, 7, 8,

9, 10, 11 12, 13 16, 17

#4175 #4176

Less

on

3 2.3 Expanding

algebraic expressions

Exercise 2C (p 84) 1, 2 3, 4, 5, 6, 7 8, 9, 10 12, 13

#8142 #8143 #8144

Less

on

4

2.4 Solving linear equations

Exercise 2D (p 88) 1, 2, 3 4, 5, 6, 7, 8 9 10, 11

#4172 #4173

Less

on

5 8.1 Expanding

binomial products

Exercise 8A (p448)

1, 2, 3 4, 5, 6 7, 8 10, 11

#4143 #4144


Chapter 4: Linear and Non-Linear Relations

Topic

Understanding (ALL)





(Lesson Number)

Less

on

1

4.1 Introduction to linear relations

Exercise 4A (p 198)

1, 2, 3 4, 5, 6 7, 8, 9 10, 11, 12

#8150 #8151

Less

on

2 4.2 Graphing

straight lines with intercepts

Exercise 4B (p 204) 1, 2, 3, 4 5, 6, 7 8, 9 11, 12, 13

#4194

Less

on

3

4.3 Lines with one intercept

Exercise 4C (p 208) 1, 2, 3 4, 5, 6, 7 8, 9, 11 13, 14, 15

Less

on

4

4.4 Gradient

Exercise 4D (p 215) 1, 2 3, 4, 5 6, 7 10, 11

#4191

Less

on

5 4.5 Gradient and

direct proportion

Exercise 4E (p221)

1, 2 3, 4, 5, 6 7, 8, 9 11, 12, 13, 14

Less

on

6

4.6 Gradient intercept form

Exercise 4F (p227) 1, 2, 3 4, 5, 6, 7, 8 9, 10, 11 13, 14, 15

Less

on

7 4.7 Finding the

equation of a line

Exercise 4G (p231) 1, 2 3, 4, 5 6, 7, 9 11, 12, 13

#4192 #4193 #4203

Less

on

8

4.10 Linear modelling

Exercise 4J (p244) 1, 2, 3 4, 5, 6, 7 8, 9 11, 12

#8152

Chapter 9: Probability

Topic

Understanding (ALL)





(Lesson Number)

Less

on

1

9.1 Probability review

Exercise 9A (p 267)

1, 2, 3 4, 5, 6, 7, 8 9, 10, 11 14, 15

#4337

Less

on

2

9.2 Venn diagrams and two-way

tables

Exercise 9B (p 272)

1, 2, 3 4, 5, 6, 7 9, 11 14, 15, 16

#8175 #4332

Less

on

3

9.3 Using set notation

Exercise 9C (p 279) 1, 2, 3 4, 5, 6, 7 8, 9 11, 13, 15

Less

on

4

9.4 Multiple events using tables

Exercise 9D (p 285)

1, 2, 3 4, 5, 6, 7 8, 9 13, 14, 15

Less

on

5

9.5 Tree diagrams Exercise 9E

(p291) 1, 2 3, 4, 5, 6, 7 8, 9 11, 12

#8174

Less

on

6

9.6 Experimental probability

Exercise 9F (p531) 1, 2, 3 4, 5, 6 7, 8, 9 12, 13, 14

#8173

Part 6 – Preparing for Tests and Examinations

Suggestions for Students Preparation for tests, assignments and examinations can be achieved with a good plan and a steady study

routine. The schedule that students set for themselves leading up to tests and examinations is also

important. It is never a good idea to begin revision or study the night before a test or examination. The

following is a suggested timeline as well as activities to support preparation for tests and examinations.

Test Examination Suggested start: at least one (1) week before the scheduled test.

Suggested start: the term before (term 2 examination – start in term 1 and term 4 examination start in term 3)

** Read through your notes and make sure they are a complete set. If you find there are notes missing see your teacher to catch up immediately.

** Read through the entirety of your notes! Identify the area(s) that you struggled with throughout the semester.

Day 1:

Read through the entirety of your notes and try and make connections with the different concepts. Aim to understand the concepts involved.

Step 1: Summary Sheets

Review your summary sheets that were used for the different topics. Review each topic test and see if your summary sheet was sufficient enough to help you. If not, create a new summary sheet making sure that it covers questions and concepts that you had the most difficulty.

Day 2:

Write out a summary sheet to take in to your test/exam. Make sure you read through your notes to work out what to include. Also include:

Definitions

Formulae

Key ideas

Examples

Diagrams and Graphs (where necessary)

Day 3:

Practice some basic questions with your summary notes by your side. Add things to your summary notes if need be.

Step 2: Concepts

You have already learned everything that will be assessed on the exam. Start to go over all your tests as a whole and write down concepts that you struggled with across all topics – this could be simply showing steps to questions.

Day 4:

At this stage you should be reviewing your summary notes and ensuring that it helps you. If you are finding it hard to locate things use colour to help.

Day 5:

Complete practice questions with your summary notes. Time yourself. Make a list of questions that you struggle with and seek assistance from your teacher.

Step 3: Practice, Practice, Practice!

Complete as many practice questions as possible. Use MathsOnline to obtain even more questions to practice with during your study time. Also, it is vital that you seek assistance whenever you are unsure of key ideas and concepts.

Days 6 and 7:

Complete more practice questions. Seek further assistance if necessary.

Suggestions for Parents/Guardians Teachers usually find that most students ask for assistance right before a test or examination leaving

little to no time to help them. Alternatively students do not ask for help at all.

We encourage all students to ask for help as soon as they recognise they are falling behind, not

understanding the concepts being studied or even if they wish to extend themselves further.

Parents are encouraged to contact their child’s mathematics teacher any time during the course of the year particularly

if they are struggling with their mathematics.

Due to the nature of the subject, we find students can quickly switch off and give up so any assistance that parents can

provide is greatly appreciated.

The partnership between teacher and parent/guardian is vital to ensure all students achieve success in mathematics

now and into the future.

Year 9 Mathematics Study Program - Assumption...

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