Pole Dancing with the Stars

A few years ago I received this photo from my cousin, Doug, who at the time was living at Casey Station, Antarctica. Doug is a communications technician with the Australian Antarctic Division. Over the past decade he has mostly lived and worked at one or another of the four A.A.D. research bases. This year he is at Macquarie Island. He sends a weekly newsletter, adorned with magnificent photos of pristine icy landscapes, extraordinary wildlife and colourful and mind-blowing captures of the night sky that include Aroura Australis and time-lapse star-trails like the photograph here.

I find all his stories and photography amazing, but the mathematician in me drew special interest in this South Pole time-lapse specimen. There is no set point in the picture that identifies exactly where the south celestial pole (SCP) lies, but it’s not too difficult to pose a guess when considering the circle centre from all these arcs. The arcs themselves are quite interesting, because they are the actual stars, with their movement recorded over a slice of time. From our perspective, it would seem that any given star would complete a full circle around the SCP in 24 hours. However, we know that what’s really rotating is our Earth against the fixed background of stars. Here then comes the obvious maths problem: For how long was the camera shutter open in order to take this photo?

Here’s how I did it:

  1. I started by importing the photo to a Graphs page of my TI-Nspire CAS.
  2. I then moved the axes to place the origin at where I estimated the SCP to be.
  3. Next I selected one of the star-trails. You can see that my selection is towards the lower-left of the photo, but really any of them would do.
  4. I graphed f1(x)=1 and then used the line-rotation feature until the line ran across one end of the star-trail arc (blue line).
  5. I graphed f2(x)=1 and used the line-rotation feature again until the line ran across the other end of the star-trail arc (red line).
  6. The CAS indicates the equations of the two lines and I extracted the gradient of each into a Notes page.
  7. Continuing on the Notes page I used the two gradients and a known formula to compute the angle of the arc. (Note that my document is set to degrees)
  8. This angle as a fraction of 360 degrees equates to the exposure time as a fraction of a full day. I have made my calculation of the exposure time in seconds further down the Notes page. (1593 s in this example – about 26.5 mins)
Photograph credit: Doug McVeigh. Australian Antarctic Division, Casey Station 2015

And now the best part of it all: I can check my result another way! Remember that my cousin Doug had sent me this digital photo, which as a JPG file, I can not only view it, import it into calculator software, but I also have the original metadata. Here is the details page for the file. Note that among bountiful information, the exposure time is indicated: 1652 s. My calculation was but 59 s out.  

Want to see more classroom resources from the deep south? Classroom Antarctica is a comprehensive online teaching resource produced by the Australian Antarctic Division, with lesson plans aimed at grades 3 to 8. Ideas contained in Classroom Antarctica will stimulate your students’ interest in real-world applications for science, mathematics and studies of society and environment, inspiring and engaging your students in learning.

MAV Conference 5 & 6 December

Making Connections Mathematics Numeracy

Visit the TI Booth at the Conference

TI Australian Team will be there to answer all your questions, drop by the booth and mention code word: TEXAS to receive a gift!

Workshops using TI Technology

Rover Will Find the Solution Presenters: Rodney Anderson, Jim Lowe

The Art of Mathematics  Presenter: John Bament

Making Music with Maths  Presenter: John Bament

Complex Numbers, Polynomial Equations and Polygons Presenter: Yew
Fook Chan

Lights, Music and the TI-Innovator  Presenters: Raymond Rozen, Shane Dempsey

Bringing VCE Maths to Life with TI-Nspire  Presenter: Stephen Crouch

Rock N Rover  Presenter: Jody Crothers

Cartesian Coordinates Come to Life  Presenter: Jody Crothers

CAS in Specialist Mathematics Classroom  Presenter: Bozenna Graham

Mathematical Methods Unit 3: Introducing Discrete Random Variables  Presenter: Peter Flynn

Wowed by Widgets – The Directors Cut  Presenters: Chris Ireson, Len Bedier

Widgets and UDFs in the classroom using TI-Nspire  Presenter: James Mott

Geometry + Technology = Proof Presenter: Irina Lyublinskaya

Mathematical Methods: Probability enhanced with TI-Nspire  Presenter: Frank Moya

Maths and Music – play me a tune on your calculator  Presenter:  Brian Lannen

Mathematical Investigations for the new VCE Structure  Presenter: Brian Lannen

Function Junction – Exploring functions, graphing and coordinate geometry  Presenter: Roger Wander

Classic Geometric Constructions  Presenter: Neale Woods

Creating Widgets for Senior Mathematics  Presenter: Neale Woods

Tips for using TI Nspire CAS effectively in Further Mathematics  Presenter: Danijela Draskovic

Conceptualise and understand Mathematics with Geometry  Presenters: Sanjeev Meston

Taking conceptual understanding to the next level in Mathematical Methods  Presenters: Sanjeev Meston

Maximum fun with calculus  Presenter: Peter Fox

Avoiding the RHS  Presenter: Peter Fox

What’s New with CX II? Exploring TI-Nspire  Presenter: Peter Fox

Engineered for Education

I have witnessed and participated in in many changes in the educational landscape over my almost four decades in the business. Expressions such as flipped classroom, teacher-centred, student-centred, instructor, facilitator, coach, mentor, project-based learning, explicit teaching and more have contributed to the vocabulary used to describe this evolutionary process.

Through it all however, I believe an important constant to recognise is that teachers and students have different roles to play in education.

Subsequently, I have found the perfect technology solution for my maths classroom to be the marriage of TI-Nspire CAS software for me and handheld units for my students. OK, I also have the luxury of a Navigator system, but that’s really the icing on the cake. And sure, I’m also a big fan of the vast offerings from full computer technologies; laptops, tablets and phones with access to endless data via internet connectivity. I have reflected on this again while reading the VCE Mathematics Review and associated background papers. However, I find myself returning to the proven model of TI software/handheld partnership and conclude that the reason for this is that these are specific built-for-purpose tools rather than high-powered, but generic computing machines. It comes back to that difference in roles of teacher and student and, corresponding with that, a difference in tools. I have heard the argument of ‘why should students use a technology in their schooling that they are unlikely to use in their later working life’. The answer is because it is specifically designed for their schooling.

At every stage in the development of TI educational technologies, the engineers, designers and managers consult established educational research and seek feedback from practicing teachers. The happy tech model that I conveniently employ in my classroom is not just a lucky accident, but the result of careful design. 

For me, the TI-Nspire Premium Teacher Software is simply the best. I use it for demonstrating, generating discussion and collecting student assessment data (with the help of TI-Navigator). I also use it to distribute files to students and collect files and screen-shots back from them. Although the software is my primary tool-of-trade, I still use my handheld unit for straight out portability about the classroom. My standard lesson generally consists of some whole-class instruction (Teacher Software) followed by individual and small-group assistance about the classroom as students work on their assigned exercises (Handheld  unit). I also know that, although students primarily use their handheld units, they also utilise the student software, mostly in their home study, collecting screen-shots for their notes. I have seen this feature to be especially useful for students studying by distance education as they can screen-shot evidence of their working and paste into assignments.

I absolutely believe that the principal role of educational technology is for the enhancement of student learning. However, I also know from experience that what has become the defining factor for most schools and school systems is whatever technology is or isn’t permitted for use in senior exams. Here again, the handheld unit is the best solution (though as I have stated its educational value extends way beyond that of simply being an exam tool). Handheld calculators do NOT have student to student connectivity other than via a physical link cable. Even their capacity for Wi-Fi connectivity (TI-Navigator system) requires fitting a bright yellow Wi-Fi adaptor and communication is only between individual students and the teacher. Further yet, in jurisdictions that specify the lockdown of specified calculator functions for exams, the TI engineers have installed a ‘Press-to-Test’ mode especially for such situations. The point is that the calculators are deliberately designed for this. Computers are not. I have seen situations where schools have tried to use computers for exams – with disastrous consequences. School computer technicians have been challenged to lockdown laptops to prevent students from communicating with each other or the broader internet. The worst I’ve seen is where students tried to access online exams, with the school server collapsing under the stress and panic-stricken invigilators needing to quickly organise paper copies of the exams.

Yes, computers are more powerful machines than calculators, but they are not more powerful in this situation, because they are not primarily designed for the task. The conclusion is very simple – if you seek to incorporate a technology for education, select one that is specifically engineered for education. Want to know more?      https://education.ti.com/en-au        

LEC Melbourne IB 2019

Learn.Energise.Connect.

IB Mathematics Free Mini Conference, Melbourne 2019

Venue: Mantra Bell City, 215 Bell St Preston (Parking included).

Date: Wednesday 4th December 2019 – 8:30am – 4:15pm

The main objective of the mini conference is to introduce quality ways of using TI-Nspire™ Technology in the teaching of some key topics in the two new SL and HL Mathematics courses. In addition, HL teachers will have an opportunity to consider ways of preparing their students for the new Paper 3.

7:45am – 8:25am               Registration                                       

8:30am – 9:00am               Welcome                                            

9.30am – 10.30am              Session 1       

Workshop 1: Introducing TI-Nspire CX II and the 5.0 Software              

Come along and find out what’s new with the TI-Nspire CX II and the 5.0 software and how they both relate to the new IB Mathematics courses. This informative and collaborative session is designed to help IB Mathematics teachers decide on which calculator that best suits their teachers and students moving forward.

10:40am – 12.25pm Session 2

Workshop 2A: Teaching Calculus in Analysis and Approaches

The new Mathematics: Analysis and Approaches subject demands a strong and rigorous approach towards the teaching and learning of calculus at the SL and HL levels. In this session, we will show how TI-Nspire technology can be used to explore, visualise and help explain some important calculus concepts in the SL and HL courses.  Topics covered include limits, graphical interpretation of first and second derivatives, optimisation, kinematics, L’Hopital’s rule and Euler’s method.

Workshop 2B: Modelling in Applications and Interpretation   

The new Mathematics: Applications and Interpretation subject places a strong emphasis on developing, applying and interpreting results derived from a variety of mathematical models at the SL and HL levels. In this session, we will use TI-Nspire technology and real-life data to develop and use a variety of mathematical models from the new course. A central focus of the session is to explore and understand how parameters affect the behaviour of a function.

1:20pm – 2.50pm               Session 3

Workshop 3A: Teaching Finance and More Advanced Graphing in Analysis and Approaches    

The new Mathematics: Analysis and Approaches contains a section on financial applications of geometric sequences and series including compound interest and annual depreciation. In the first part of this session we will use TI Nspire technology to solve some problems in financial mathematics. In the remainder of the session, we will introduce and use some more advanced graphing skills relevant to the new course.

Workshop 3B: Teaching Statistics and Matrices in Applications and Interpretation

The new Mathematics: Applications and Interpretation course has a strong focus on the teaching and learning of statistics and matrices at the SL and HL levels. In this session, we will show how TI-Nspire technology can be used to teach important statistical and matrix concepts in the SL and HL courses. The two main areas covered are bivariate data analysis including various forms of regression and transition matrices.

3:00pm – 4:15pm               Session 4

Workshop 4A: Paper 3 in Applications and Interpretation HL     

The new Mathematics: Applications and Interpretation course has a Paper 3 which is very different in structure and assessment objectives from the current Paper 3. The new Paper 3 will aim to assess a student’s ability to apply their mathematical knowledge in context with a strong emphasis on interpretation and explanation of mathematical results. In this session, we will use TI-Nspire technology to work through some Paper 3 style question parts. Towards the end of the session, we will briefly discuss and share ideas for resources on how to best prepare our students for this paper.

Workshop 4B: Paper 3 in Analysis and Approaches HL

The new Mathematics: Analysis and Approaches course has a Paper 3 which is very different in structure and assessment objectives from the current Paper 3. The new Paper 3 will aim to assess a student’s ability to apply their mathematical knowledge in situations often requiring exploration leading to generalisation. In this session, we will use TI-Nspire technology to work through some Paper 3 style question parts. Towards the end of the session, we will briefly discuss and share ideas for resources on how to best prepare our students for this paper.

Certificate of Participation will be provided.

Catering will be provided, Halal, Vegan & Gluten Free options will be available.

Please contact pdrego@list.ti.com or call 1300 138 140 for further information.

LEC Brisbane 2019

Learn.Energise.Connect. Brisbane 2019

FREE PD EVENT

Venue: Novotel Brisbane, 200 Creek Street, Brisbane

Date: Friday 29th November 2019 – 8:30am – 3:45pm

Come along to a full day of workshops focusing on Mathematical Methods and Specialist Mathematics courses, including PSMT and Exam preparation!

Program:

Registration: 7:45am to    8:25am Collect Attendee Gifts.
Welcome: 8:30am to    9:00am Prize Draw!
Morning Tea 9:00am to 9:30am Catered
Session 1: 9:30am to 10:45am Workshops: A, B C or D
Session 2: 10:55am to 12:15pm Workshops: E, F, G or H
Lunch: 12:15pm to 12:55pm Catered
Session 3: 1:00pm to 2:15pm Workshops: I, J, K & L
Session 4: 2:25pm to 3:45pm Workshops: M, N,O & P

There will be 16 Workshops to choose from on the day.

Workshop Choices

A:  TI-Nspire™ Fundamentals

Are you new to TI-Nspire™?  Learning the basics will give you confidence to use the technology in your classroom and provide students with the basic skills they need to use it efficiently in their courses. In this session we will explore the many features of the Calculator and Graph applications. You will find answers to your questions and are sure to leave saying: “I did not know it could do that”.   Level: ALL  Technology: TI-Nspire™

B:  Tips & Tricks with TI-Nspire™

TI-Nspire is much more than a platform used to generate graphs and execute computations. Incorporating other applications such as Lists and Spreadsheets, Geometry and Statistics is when efficiency transforms into effective. In this session participants will see how to use sliders, dynamically link to Spreadsheets, Geometry and Statistics applications to create a complete learning environment. Examples applicable to both Methods and Specialist will be covered.    Level: ALL  Technology: TI-Nspire™

C:  TI-84PlusCE™ Fundamentals

Are you new to the TI-84PlusCE™?  Learning the basics will give you confidence to use the technology in your classroom and provide students with the basic skills they need to use it efficiently in their courses. In this session we will explore the basic features, commands and navigation. You will find answers to your questions and are sure to leave saying: “I did not know it could do that”.    Level: ALL  Technology: TI-84PlusCE™

D:  Tips & Tricks with TI-84PlusCE™

From graphing functions and derivatives to saving files and settings, there are so many powerful ways to use the TI-84Plus CE.  Participants in this session will see how to use Group files, Graphical Data Bases and Apps to enable students can use their calculator efficiently in the classroom, between classes and in examinations.   Level: ALL  Technology: TI-84PlusCE™

E:  To Infinity and Beyond – What a Buzz! Who says “Calculus can’t be fun”? 

In this session you will see and experience ways to energise the teaching of Calculus and turn it from a feared topic to one that your students will rave about. Unleash the power of TI-Nspire™ and see how to take it to the limit!  Level: Mathematical Methods  Technology: TI-Nspire™

F: TI-84Plus CE™ – Know your Limit              

Teaching functions and calculus with the TI-84PlusCE is limited only by your imagination. Functions, composite functions, derivatives, dynamic derivatives, numerical integration and solving problems will be explored in this workshop. We’ll maximise our time to minimise yours.   Level: Mathematical Methods  Technology: TI-84PlusCE™

G:  Integrating Significant Change

In this session we will investigate the tools required for Unit 3 and 4 Specialist Mathematics. Some applications of integration and rates of change will be investigated. Use of the complex number and statistical inference tools will also be included, so be prepared to integrate significant change into your classroom teaching.  Level: Specialist Mathematics  Technology: TI-Nspire™

H:  Integrating Significant Change            

Differential and integral calculus, applications of differential equations and more, you’ll see how to rise and not run when it comes to the appropriate use of TI technology in your Specialist Mathematics class. We’re 95% confident that you will be smarter when you finish this session.   Level: Specialist Mathematics  Technology: TI-84PlusCE™

I:  Efficient and Effective use of TI-Nspire™ in the Specialist Mathematics Exam

In this session we will look at questions from the QCAA Specialist Mathematics Sample Technology Active Examination and demonstrate the ways in which users of the TI-Nspire calculator can benefit and save time in reaching solutions and checking answers. Participants will explore how to efficiently utilise features of the TI-Nspire to answer typical examination questions.  Level: Specialist Mathematics  Technology: TI-Nspire™

J:  Efficient and Effective use of TI-84PlusCE™ in the Specialist Mathematics Exam

In this session we will look at questions from the QCAA Specialist Mathematics Sample Technology Active Examination and demonstrate the ways in which users of the TI-84PlusCE calculators can benefit and save time in reaching solutions and checking answers. Participants will explore how to efficiently utilise features of the TI-84PlusCE to answer typical examination questions.  Level: Specialist Mathematics  Technology: TI-84PlusCE™

K:  Wine Glasses and Roller Coasters – PSMT with TI-Nspire™    

What do wine glasses and roller coasters have in common you ask? They are both great practical applications on which to base a Problem Solving and Modelling Task. Participants in this session will explore these and other great ideas where students can use a range of technology including data logging, TI-Innovator™ Rover, images and the TI-Nspire to apply mathematical concepts and techniques, evaluate reasonableness of solutions and communicate mathematical ideas.  Level: Mathematical Methods    Technology: TI-Nspire™

L:  Wine Glasses and Roller Coasters – PSMT with TI-84PlusCE™

What do wine glasses and roller coasters have in common you ask? They are both great practical applications on which to base a Problem Solving and Modelling Task. Participants in this session will explore these and other great ideas where students can use a range of technology including data logging, TI-Innovator Rover, images and the TI-84PlusCE to apply mathematical concepts and techniques, evaluate reasonableness of solutions and communicate mathematical ideas.  Level: Mathematical Methods    Technology: TI-84PlusCE™

M :  Efficient and Effective use of the TI-Nspire™ in the Mathematical Methods Exam

In this session we will look at questions from the QCAA Mathematical Methods Sample Technology Active Examination and demonstrate the ways in which users of the TI-Nspire calculator can benefit and save time in reaching solutions and checking answers. Participants will explore how to efficiently utilise features of the TI-Nspire to answer typical examination questions.  Level: Mathematical Methods    Technology: TI-Nspire™

N:  Efficient and Effective use of the TI-84PlusCE™ in the Mathematical

Methods Exam  In this session we will look at questions from the QCAA Mathematical Methods Sample Technology Active Examination and demonstrate the ways in which users of the TI-84PlusCE calculators can benefit and save time in reaching solutions and checking answers. Participants will explore how to efficiently utilise features of the TI-84PlusCE to answer typical examination questions.  Level: Mathematical Methods    Technology: TI-84PlusCE™

O:  What’s your Vector Victor? – Flying High with PSMT & TI-Nspire™

There are so many wonderful applications of Vectors, it’s hard to go past them as a focus for the Problem Solving and Modelling Task in Unit 1. Participants in this session will explore ways that the TI-Nspire can be used to apply mathematical concepts and techniques, evaluate reasonableness of solutions and communicate mathematical ideas to enhance the PSMT.   Note: Ideas for Unit 3 PSMT will also be discussed.  Level: Specialist Mathematics   Technology: TI-Nspire™

P:  What’s your Vector Victor? – Flying High with PSMT & TI-84PlusCE™ 

There are so many wonderful applications of Vectors, it’s hard to go past them as a focus for the Problem Solving and Modelling Task in Unit 1. Participants in this session will explore ways that the TI-84PlusCE  can be used to apply mathematical concepts and techniques, evaluate reasonableness of solutions and communicate mathematical ideas to enhance the PSMT.   Note: Ideas for Unit 3  SMT will also be discussed.  Level: Specialist Mathematics      Technology: TI-84PlusCE™

Certificate of Participation will be provided.

Catering will be provided, Halal, Vegan & Gluten Free options will be available.

Please contact pdrego@list.ti.com or call 1300 138 140 for further information.

LEC Melbourne 2019

Learn.Energise.Connect. Melbourne 2019

FREE PD EVENT

Venue: Mantra Bell City, 215 Bell St Preston (FREE Parking included).

Date: Wednesday 4th December 2019 – 8:30am – 3:45pm

Come along to a full day of workshops including General/Further Maths, Mathematical Methods and Specialist Mathematics, Learning and Assessment, STEM using Texas Instruments Technology.

There will be 24 Workshops to choose from on the day, no need to pre book your workshop selections just register for the day and attend the workshops you desire. Download the program to view the workshops on offer!

Certificate of Participation will be provided.

Catering will be provided, Halal, Vegan & Gluten Free options will be available.

Please contact pdrego@list.ti.com or call 1300 138 140 for further information.

MAWA Conference 18 & 19 November

Making Maths Matter

Visit the TI Booth at the Conference

TI Australian Team will be there to answer all your questions, drop by the booth and mention code word: TEXAS to receive a gift!

Workshops using TI Technology

Crashing Robot Cars Presenter: Brian Lannen

Cubic Polynomials Presenter: Peter Flynn

7th Heaven Presenter: Jody Crothers

Mathemagicians Exposed Presenter: Peter Fox

Lessons from CAS Presenter: Peter Fox

Robots vs Maths Presenter: Jody Crothers

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