Assessment conditions:

Part 1 is to be completed in pairs outside of class. It must be submitted as a single Google Doc to the Google Classroom; anything you want marked, including photos of working done by hand, should be   inserted into this Doc. Only one member of the pair needs to submit a file, but the file should be

renamed to include the names of both group members.

Part 2 is to be completed individually. Part 2 is a validation task that will be completed under test

conditions. The purpose of the validation is to make sure you understood the concepts in the take-     home component, and to confirm you contributed to your group’s submission. A student whose result

in the validation is significantly different to their take-home component may have their work investigated for academic integrity, and their result for Part 1 may be reduced.

A note on extensions:

Unless otherwise specified by your Engagement Advisor, extensions granted to one student apply to their work. In this case, that means they will have an extension on the validation and your group will have an

extension on Part 1 only; other group members will be expected to complete the validation on 25th August. Please speak with your classroom teacher as soon as possible if this is an issue for you.

Overall marks for this Assignment will be out of 80, which is (Part 1+Part 2). Grades will be awarded    based on the Achievement Standards, which you can find on the Unit Outline. Grades will be awarded on the proviso that you have made a reasonable attempt at both parts of this task. Teachers will

consider, when allocating grades, the degree to which students demonstrate their ability to complete and submit tasks within a specified time frame; late penalties will affect your grade for this task.

TASK OVERVIEW

In this task, you will use exponential functions to model an issue related to biosecurity in Australia.

Note: The mathematical concepts assessed in both parts of this assignment are covered in Ex 14I of the textbook.

Part 1 (15%):

More detailed instructions and the marking scheme are given on the following pages, but you are required to:

During the validation, you will be required to:

o Determine an exponential equation that can be used to model the growth of a certain population

o Algebraically determine future population and/or time values

o Briefly (about 2-3 sentences) explain what issue you investigated in Part 1 and one

method you tried when you were developing your third equation in the Analysis section

o Write a very brief comment about the effectiveness of the collaboration and time management within your group

o Identify one thing you can do to care for Dhawura Ngunnawal (Ngunnawal Country)

Part 1: Take-home component

Living in Canberra, it is easy to take for granted the fact we live on beautiful, bushy Country. Nature  Reserves, parks, and trees lining almost every road are so commonplace that it’s easy to forget how privileged we are to live in a city that values the land so highly. This land we live on is Ngunnawal

Country, and it would not be the place we know today without their knowledge and respect for the land.

We all have a role to play in making sure future generations can enjoy this Country as much as we do.

Bruce Ridge, Ngunnawal Country. Image credit: Emily Hathaway

Make sure you’re constantly referring to the rubric on the final page to ensure you include everything.

Achievement Standards assessed in this task:

.    critically applies mathematical concepts in a variety of complex contexts to routine and non-routine problems

.    selects and applies advanced mathematical techniques to solve complex problems in a variety of contexts

.    constructs, selects and applies complex mathematical models to routine and non-routine problems in a variety of contexts

.    uses digital technologies efficiently to solve routine and non-routine problems in a variety of contexts

.     represents complex mathematical concepts in numerical, graphical and symbolic form in routine and non-routine problems in a variety of contexts

.    communicates mathematical judgements and arguments in oral, written and/or multimodal forms, which are succinct and well-reasoned, using appropriate and accurate language

.    evaluates the reasonableness of solutions to routine and non-routine problems in a variety of contexts

.     reflects with insight on their own thinking and that of others and evaluates planning, time management, use of appropriate strategies to work independently and collaboratively

.    evaluates the potential of Mathematics to generate knowledge in the public good

Unit Goals assessed in this task:

.      understand the concepts and techniques used in algebra and exponential functions

.      solve problems in algebra and exponential functions

.      apply reasoning skills in algebra and exponential functions

.      interpret and evaluate mathematical and statistical information and ascertain the reasonableness of solutions to problems

.      communicate arguments and strategies when solving problems

Stories about Country[1] : Biodiversity threats

Background research

(About ½ - 1 page of writing)

Find a biosecurity/biodiversity issue with an invasive species currently affecting some part of Australia. Examples that have been in the news recently include fire antsorvarroa mites.

Note on which Country your issue is happening (e.g. most of Canberra is Ngunnawal Country, on the NSW South Coast is Yuin Country, etc). (If you’re unsure, you can check the AIATSIS map:

https://aiatsis.gov.au/explore/map-indigenous-australia)

.    What is the issue?

o What is it affecting? (E.g. farmland, invading habitat of native wildlife, killing native wildlife, etc.)

o Where is this issue taking place? What Australian First Nation’s Country is this?

o How is it spreading? (E.g. on trucks, down rivers, general population growth.)

.     How is it being managed?

o What is being done to try to slow its progress/eradicate it completely?

o Do people who work on this issue think that these strategies are working?

o Are there any competing ethical issues? (E.g. does one strategy involve an animal cull etc?)

.     How quickly is it spreading?

o When did it start?

o How large an area did it initially affect?

o How large an area does it currently affect?

(Note: you probably won’t be able to find exact values here, so make sure you explain any approximations and assumptions you’ve made and cite your

references using in-text referencing.)

Queensland Governmentelectric antsmanagement sign, Kuku Yalanji Country. Image credit: Emily Hathaway

Mathematical calculations

The following calculations can be either handwritten or typed using the Equation editor in Docs. It is recommended that you insert the final values/equations into the body of your report and include the detailed calculations in appendices at the end.

.     Using the information about the time and area above, algebraically develop an exponential equation that describes the approximate growth of this population.

.     Research to find how quickly this species’ population would grow if no interventions had been   put in place. Algebraically develop a second equation that describes this ideal growth scenario.

.     Using Google Sheets or Desmos, plot these equations on the same set of axes. Copy/screenshot this graph and insert it into the body of your assignment.

.     For both equations above, algebraically determine how large the population would be in the year 2030.

.     For both equations above, algebraically determine how long it would take for the population to cover an area the size of the ACT.

o (Note: you will need to make some approximations and assumptions here as well, so make sure you justify your values and cite your references using in-text referencing.)

.    Determine the average rate of change for each of these equations over 5 equal time periods.

o Divide the total time you have above into 5 equal sections, and calculate the average    rate of change over each of those time periods. (For example, if the data I had showed the species being introduced to Australia in the year 2003, I would break the data into time periods 2003-2007, 2007-2011, 2011-2015, 2015-2019, and 2019-2023.)

Butterflies on yellow weed, Yuin Country. Image credit: Emily Hathaway

Mathematical analysis

(About ½ - 1 page of writing, plus relevant graphs or equations)

Compare the two models above.

.     Do your equations suggest that the strategies mentioned in the “Background research” section are effective? Justify your answer.

.    What do the rates of change calculated above tell you about your species?

.     Research to find a governmental goal for the population management (e.g. to keep the population below …, to reduce the population to … by the year … , etc).

o What is the goal?

o Based on your equations, are they on track to achieve this goal? How far off are they?

.    Create a new equation that will allow the government’s goal to be reached.

o What effect would some of the proposed measures mentioned in the “Background research” section have on the population?

o Experiment with the parameters e.g. instead of applying fertility treatments to 20% of the population, what happens if you increase it to 40%?

(Note: there will be a lot of trial and error here, and you should use Desmos and/or Sheets to help with any calculations. There are a lot of possible solutions to this question. Start by modelling some of the proposed management strategies you mentioned in the “Background research” section and adjust

some of the parameters. You are not expected to come up with your own solutions, but make sure your equations include realistic goals e.g. reducing the population to 15% by September is probably not realistic.

.    Make a note of the different equations and parameters you change, and discuss how you settled on your final equation

Stories of Country: Dhawura Ngunnawal (Ngunnawal Country)

Mulligans Flat, Ngunnawal Country. Image credit: Emily Hathaway

Your own On Country reflection[2]

Now focus on the Country on which we live and learn: Ngunnawal Country.

Individually and/or with your group member, take some time to be outside, without talking, without

looking at your phone, and trying not to be distracted by other things. This could be in your own

backyard, on your way to school, on a walk/ride in a nature reserve, on the school oval, or any other   place outside. Try to become immersed in the natural world around you. The longer you can spend in this location the better but aim to be there for at least 20-25 minutes.

What can you see? Are there different kinds of plants and birds and insects? What can you hear? Can you feel the sun or a breeze, or is it cool and shady and still?

.     Every member of the group should complete the following sentences:

o Something I thought about when out on Ngunnawal Country today was …

o Something I noticed about the Country around me today was …

Once you’ve started talking again, take a photo of a plant or animal that is NOT native to Ngunnawal   Country. It does not have to be an artistic photo, but it does have to be something taken by a member of your group.

.     Insert the photo into your document. Does this plant or animal pose a threat to the native wildlife? What do you need to do to make sure it doesn’t become a threat[3]?

Note: Being an introduced species doesn’t necessarily make it bad e.g. there are a lot of benefits to a pet dog or a vegetable garden or a plant that connects someone to their own cultural identity. It is,

however, still important to make sure it doesn’t become a problem for the native wildlife.

Cows, Ngunnawal Country. Image credit: Emily Hathaway

[2] Townsend, M., & Weerasuriya, R. (2010). Beyond Blue to Green.

https://www.deakin.edu.au/    data/assets/pdf_file/0004/310747/Beyond-Blue-To-Green-Literature-Review.pdf

[3] Caring for Dhawura Ngunnawal A natural resource plan for the ACT. (2022).https://hdp-au-prod-app-act-yoursay- files.s3.ap-southeast-

2.amazonaws.com/5316/6451/7165/2022_NRM_Draft_Plan_Caring_for_Dhuwura_Ngunnawal_access_V2.pdf