## TI Australia

## Live Student Webinars

## FREE Student Term 1 Revision Webinars starting 8th April!

This program has been developed to assist students consolidate Term 1 concepts, whilst also demonstrating how their TI-Nspire™ CAS technology can assist in efficiently answering exam style questions.

Students will have the opportunity to ask the presenter questions and will receive a revision worksheet to practice concepts covered in each webinar.

### VCE **Further Mathematics Program**

**8th April – Univariate data analysis: SAC and exam smarts**

**9th April – Bivariate data analysis: SAC and exam smarts**

**9th April – Univariate & Bivariate Data analysis: SAC and exam smarts**

Teachers are welcome to attend!

## Watch On Demand

YouTube video will be available 48 hours after the live event.

## Live Webinars

### FREE Student Term 1 Revision Webinars

Students will have the opportunity to ask the presenter questions and will receive a revision worksheet to practice concepts covered in each webinar.

**Specialist Mathematics Program**

**Monday 6th April 2020**

**10am – Complex Numbers (Part 2)**

We will explore how to convert between Cartesian and Polar form, how to apply De Moivre’;s Theorem, how to see connections between various representations of a complex number and their graphical equivalents. Your CAS calculator can easily convert a complex equation into a Cartesian relation and graph it on the Argand diagram as rays, lines and circles.

**11am – Vectors (Part 1)**

We will show how vectors can be entered into the CAS, as well as ways that CAS can be used to effectively deal with operations between two vectors, such as addition/subtraction, dot product and angles between vectors.

**Tuesday 7th April 2020**

**10am – Vectors (Part 2)**

We will show how CAS can be used for more advanced vector analysis, such as projections (scalar and vector), linear dependence/independence and geometry proofs.

**11am – Calculus (Part 1)**

We will review how to find a second derivative using your CAS calculator, along with points of inflection, what they are and how to find them using your CAS calculator, and how they relate to Concavity. We will look at ways of using your TI Nspire CAS Calculator in Exam 2 to efficiently approach questions that involve Differential Calculus.

**Wednesday 8th April**

**10am – Calculus (Part 2)**

We will review how to analyse, interpret and approach Related Rates questions, including differentiating parametric equations using your TI Nspire CAS calculator. We will also explore how to efficiently use your calculator to perform implicit differentiation in Exam 2.

**11am – Graph Sketching (Part 1)**

We will explore the graphs of absolute value functions and various composite functions, where the modulus is involved. Further on, we will consider piecewise functions and how your CAS calculator can be used effectively for piecewise functions: to graph, solve equations and determine continuity and differentiability.

**Thursday 9th April 2020**

**11am – Graph Sketching (Part 2)**

We will show how reciprocal and rational functions can be sketched, including analysis of axes intercepts, asymptotes and stationary & inflection points.

### Watch On Demand

YouTube video will be available 48 hours after the live event.

**Inverse and Reciprocal Trigonometric Functions**

**Complex Numbers (Part 1)**

## Activity

## Flattening the Curve: How You Can Learn to Stay Healthy With STEM

Everyone is scrambling to figure out how to keep the learning going. Teachers are being asked to create online content and lessons for students to use at home. COVID-19 has had a significant impact on schools, teachers and students. But what is COVID-19, and why is it affecting everyone in such dramatic ways? Why didn’t past viruses, such as SARS, MERS, H1N1 and others cause schools to shut down?

COVID-19, according to Johns Hopkins medicine, is a coronavirus similar to SARS (severe acute respiratory syndrome). In fact, COVID-19 has been officially named severe acute respiratory syndrome coronavirus 2 or SARS-CoV-2. Unlike epidemics/pandemics in the past, COVID-19 symptoms aren’t as severe and, thus, not as easy to identify right away. The time it takes before an infected person may show signs can be between two to 14 days. COVID-19 also seems to be more transmissible than past viruses and has spread across the globe quickly as a result.

The World Health Organization and the Centers for Disease Control have recommended social distancing to “flatten the curve” — an effort to reduce the potential for transmitting the virus from one person to another and hopefully keep more people healthy. As a result, we’ve seen schools, organizations and businesses asking their students, employees and participants to work/study from home, if possible. To better understand what “flattening the curve” means, and to explore how epidemics/pandemics can happen, we can use models and simulations.

A mathematical model is a useful tool for describing natural phenomena, such as the epidemiology of the COVID-19 pandemic. Some mathematical models are empirically based, while others are theoretically based. Empirical models are built from after-the-fact observations, for example, fitting a polynomial regression to a set of observed COVID-19 cases. Empirical models are justified solely by how well they extrapolate and predict future values. This type of model has several weaknesses. They are only as good as the data they are based on, there could be odd mathematical behavior outside of the dataset that has no meaning to the phenomenon, and importantly, they lend no insight into the phenomenon.

Alternatively, a theoretical mathematical model is based on a currently accepted theory. Historically, theoretical models have made considerable advances in the sciences. Theoretical models can predict a phenomenon before it is ever observed. Examples include the existence of Neptune, anti-mater, the cosmic microwave background, and the Higgs boson, to name just a few.

Some phenomena have a random component, for example, rolling dice, radioactive decay and evolution. A Monte-Carlo mathematical model is one way to describe and predict this type of phenomenon. The model used in “Flattening the Curve” is a Monte-Carlo simulation. The hectic motion of the particles models the random interactions people could have while shopping at a crowded store.

Social distancing, R0, and self-quarantine can be simulated by changing the way the particles interact. Since the “Flattening the Curve” simulation is Monte-Carlo, the data is never precisely the same each time, which is the way a real pandemic spreads.

Run the simulation several times using different parameters, and note the effect on the graphs on the following pages.

Analyze the data by fitting an empirical model to the simulated data during the exponential phase of growth. What changes in the simulation will flatten this curve?

This simulation is a model of a very complicated phenomenon. The model is not complete and is not based on, nor uses, actual COVID-19 case data. This model assumes everyone who is sick will recover; regrettably, this is false. This feature was purposeful to be sensitive, not to be misleading. The intent of the simulation is to have a discussion on how a pandemic spreads and the mathematics of modeling and to also understand how personal behaviors can help to reduce the spread of the disease. Please use the free student software and companion file, “Flattening the Curve” to enrich your classes’ distance learning experience. Help your students learn how to “flatten the curve” and to stay healthy.

**About the author**: *Fred Fotsch is a retired high school science teacher who now works as the STEM education manager at Texas Instruments.*

## Live Webinars

### FREE Student Term 1 Revision Webinars

Students will have the opportunity to ask the presenter questions and will receive a revision worksheet to practice concepts covered in each webinar.

**Specialist Mathematics Program**

**Friday 3rd April 2020**

**10am – Inverse and Reciprocal Trigonometric Functions**

We will review inverse and reciprocal trigonometric functions; what they are, how to sketch them, how to find maximal domain, and how to solve trigonometric equations using your TI Nspire CAS Calculator.

**11am – Complex Numbers (Part 1)**

We will explore the conjugate root theorem and show how your CAS calculator can be used effectively in exam type questions. In particular, we will illustrate, with examples, when to use cSolve versus cZeros or cFactor; how to use expand and other Algebra features to save you time in Exam 2 multiple choice and extended response section.

**Monday 6th April 2020**

**10am – Complex Numbers (Part 2)**

We will explore how to convert between Cartesian and Polar form, how to apply De Moivre’;s Theorem, how to see connections between various representations of a complex number and their graphical equivalents. Your CAS calculator can easily convert a complex equation into a Cartesian relation and graph it on the Argand diagram as rays, lines and circles.

**11am – Vectors (Part 1)**

We will show how vectors can be entered into the CAS, as well as ways that CAS can be used to effectively deal with operations between two vectors, such as addition/subtraction, dot product and angles between vectors.

**Tuesday 7th April 2020**

**10am – Vectors (Part 2)**

We will show how CAS can be used for more advanced vector analysis, such as projections (scalar and vector), linear dependence/independence and geometry proofs.

**11am – Calculus (Part 1)**

We will review how to find a second derivative using your CAS calculator, along with points of inflection, what they are and how to find them using your CAS calculator, and how they relate to Concavity. We will look at ways of using your TI Nspire CAS Calculator in Exam 2 to efficiently approach questions that involve Differential Calculus.

**Wednesday 8th April**

**10am – Calculus (Part 2)**

We will review how to analyse, interpret and approach Related Rates questions, including differentiating parametric equations using your TI Nspire CAS calculator. We will also explore how to efficiently use your calculator to perform implicit differentiation in Exam 2.

**11am – Graph Sketching (Part 1)**

We will explore the graphs of absolute value functions and various composite functions, where the modulus is involved. Further on, we will consider piecewise functions and how your CAS calculator can be used effectively for piecewise functions: to graph, solve equations and determine continuity and differentiability.

**Thursday 9th April 2020**

**11am – Graph Sketching (Part 2)**

We will show how reciprocal and rational functions can be sketched, including analysis of axes intercepts, asymptotes and stationary & inflection points.

### Watch On Demand

YouTube video will be available 48 hours after the live event.

## Differentiation from First Principles – with TI-nspire CX and TI-nspire CX CAS

## Creating Digital Content for On Line Lessons

As we transition to online learning for schools, this video contains some suggestions, ideas and solutions for teachers and students.

## Live Webinars

## FREE Student Term 1 Revision Webinars starting this Friday, 3rd April!

This program has been developed to assist Unit 3 students consolidate term 1 concepts, whilst also demonstrating how their TI-Nspire™ CAS technology can assist in efficiently answering exam style questions.

**Specialist Mathematics Program**

**3rd April – Inverse and Reciprocal Trigonometric Functions**

**3rd April – Complex Numbers (Part 1)**

**6th April – Complex Numbers (Part 2)**

**6th April – Vectors (Part 1)**

**7th April – Vectors (Part 2)**

**7th April – Calculus (Part 1)**

**8th April – Calculus (Part 2)**

**8th April – Graph Sketching (Part 1)**

**9th April – Graph Sketching (Part 2)**

Further Mathematics and Mathematical Methods Programs will be posted later this week.

Please share the registration link with your students. Teachers are welcome to attend!

### Free software for students and teachers

We are pleased to offer all students and teachers free, six-month software licenses for the following:

- TI-Nspire
^{TM }CX CAS and TI-Nspire^{TM }CX Student Software - TI-Nspire
^{TM }CX Premium Teacher Software - TI-Smartview
^{TM}CE emulator software for the TI-84 Plus graphing family - TI-30XB scientific calculator Smartview
^{TM}emulator

In addition, we have made the TI-Nspire™ CAS App for iPad® and TI-Nspire™ App for iPad® free for download through April 2020.

## Increasing and decreasing functions with TI-nspire

## COVID-19 support

Due to a heightened need for online resources as a result of the coronavirus, we are offering several free resources to help students and teachers continue teaching and learning remotely.

## Available resources

#### Computer software: Free six-month subscriptions

### iPad^{®} solution

We have temporarily made the TI-Nspire™ App for iPad^{®} and TI-Nspire™ CAS App for iPad^{®} free for download in the app store until the end of April 2020.

iPad is a trademark of Apple Inc., registered in the U.S. and other countries. Chromebook™ is a trademark of Google LLC.