To keep this intro bit short, I was generally impressed by the online (and physical) resources that were curated by the Financial Mathematics Unit of Study (UoS) websites.
A refresher for how these Resources For posts works: under each heading (e.g. Stage 4), I list some of the resources that were featured from the particular UoS website, as well as add some comments and personal observations. Note that these resources may still be useful in other stages, sub-strands, or just in general as a teaching tool.
Stage 4
Mentimeter (Host)/Menti (Audience)
- Used in this UoS to poll students’ initial understanding of percentages.
- Note: Mentimeter requires students to have access to laptops or their mobile devices to submit responses (as well as a screen or projector to display students’ responses).
- Outside of polling, I have also used Mentimeter (and similar online tools, see below) for quizzing students on content.
- In theory, if you had students conducting presentations, you could encourage or mandate them to include a short quiz at the end of their presentation in order to test how much the class was able to learn.
- Make sure to supplement each question with time for students to discuss the reasoning behind their responses (this works well if there are conflicting answers).
Similar: AhaSlides, Socrative, Poll Everywhere, DirectPoll
Everyday Items
- Catalogues – this particular UoS suggested using physical JB Hi-Fi catalogues; it’s a great idea to give students experience with navigating actual catalogues and performing discount calculations.
- I would go a step further and also demonstrate to students how to navigate online catalogues and shopping websites (particularly, how to quickly compare prices across different stores, discounts included).
- See here for direct links to shopping comparison websites you could get students to browse either at school or home. Also featured on that link is a homework task about ticket pricing that I think you should consider.
- Grocery Receipts – the main purpose of using these would be to give students experience with locating the total cost and the GST included.
- It may be useful to hide the GST included and allow students to perform the calculation themselves (using the total cost of taxable items marked on the receipts with % or * symbols).
Dueling Discounts by Dan Meyer
- This resource is an example of one of Dan Meyer’s ‘Three-Act Maths‘ activities (it should be noted that Dueling Discounts only has two acts, but many examples to work with).
- Students are asked to argue if and when they should use either ‘$x off’ or ‘y% off’ coupons.
- I would encourage you to take photos/video of yourself shopping for items and giving students the time to discuss amongst themselves/as a class which voucher they think would work best. Get students to also estimate the price of items before showing them the actual price.
- It would also be interesting to get students to design their own vouchers (that they think are fair and aren’t just ‘get five items for free’).
Grocery Unit Prices by ACCC (Australian Competition & Consumer Commission)
- Some general, useful information about unit pricing and the standard amounts used to define units of particular item types (e.g. those supplied by volume versus weight).
- Also featured on the website is a list of exempted products (i.e. items that do not need to carry unit prices), as well as tips for using unit pricing when shopping.
- Beyond Unit Pricing, I think the ACCC website (especially the Consumers section) is highly underrated and should be introduced to your students.
- They should, at the very least, visit the website if they ever have consumer complaints, or need help with online shopping or choosing mobile phone plans. Students should also learn their consumer rights & guarantees. Warranties are especially tricky.
- Also, shout-out to The Checkout (ABC Consumer Affairs TV Show). The ABC may have cut the show, but segments from their show are still watchable on Youtube.
- Featured Segments: The Price of Convenience & Serving Size Me.
Stage 5.1
Job-searching Websites
- This particular UoS features Seek – the intended purpose for its inclusion is to have students search for jobs and identify their “pay rates, penalty rates and award conditions”.
- I’m not too sure you’ll be able to find all of this information using Seek. However, the website is useful for other purposes, such as researching different careers, then calculating yearly tax based on their salaries.
- Students would almost definitely need a demonstration for how to navigate these kinds of websites before you set them any research tasks to complete independently.
Similar: CareerOne, Indeed, Jora
Tax Table & Simple Tax Calculator by ATO (Australian Taxation Office)
- Tax Table – Resident tax rates can be found here (note that students will need to separately apply the 2% Medicare levy, on top of the tax paid on taxable income).
- Older tax tables can be found here; it could be worth spending time discussing why these are regularly updated, as well as what taxes are generally used for.
- Simple Tax Calculator – This tool allows students to determine how much tax they would have to pay for a certain taxable income amount.
- Note that this also does not account for medicare levy. Working is also not shown, so the tool should only be used to confirm students’ own calculations.
- To access the calculator, scroll to the bottom on the ATO page, or click here.
Modelling Compound Interest (Desmos) by MathsLinks & Compound Interest (GeoGebra) by shanlee
- Modelling Compound Interest – graph that plots the amount earned against time (years) using the compound interest formula; P (principal) and r (interest rate) serve as free parameters.
- Consider deriving the formula and plotting points before showing students the graph/equation on Desmos.
- If you are looking for a collection of web-links to online mathematics resources for teachers, give MathsLinks some of your browsing time.
- Compound Interest – animated table that demonstrates how $5000 is compounded over 5 years according to different time periods (showing yearly balances).
- I would supplement this by getting students to also graph the results of the compounding.
- Assuming your students do not know much about compound interest, it might also be interesting to get them to ‘bet’ on different accounts, e.g. an account with a high-ish interest rate that compounds annually versus other accounts with lower interest rates but compounds much more quickly.
Side Note: This UoS features many interesting ideas for activities, including one that involves history, studying primary & secondary sources and the ABS, as well as another activity involving Pinterest. I’d be curious to hear back from anyone who decides to give these a shot in the classroom.
Stage 5.2
Word Association: Compound Interest (Padlet) by Miss Gard
- Padlet is a freemium* online bulletin board service where you can invite students to post text, images, videos, links to other websites, and document files. These are then shared and made visible to anyone who has the link to the bulletin board.
- In this UoS, Padlet has been used as part of a vocabulary exercise; students add what they know about the terms ‘compound’, ‘interest’ & ‘compound interest’ under separate columns.
- Another use for Padlet can include encouraging students to find and collect real-world examples of things discussed in Mathematics, such as shapes & solids, bank savings accounts, etc.
- *If you want to use Padlet in the classroom, you’ll most likely need to consider whether the premium version is appropriate for you. Consider the alternatives below:
Similar: Dotstorming, Lino, Wakelet
Desmos Activities
- Graphing Compound Interest – template, requires you to insert table data; students try their best to match a linear equation to compound interest data.
- Graphing Compound Interest Example – same thing as above but with data inserted.
- If the curve is not obvious, I suggest adding more data, or get students to match the linear equation to the first two points.
- Graphing Compound Interest 2 – a more complicated graph of compound interest with three different equations; students select which best matches the compound interest data.
- Who Wants To Be A Millionaire? (Code: sqmu5f)
- Not quite sure how this is meant to work, but the ideas are worth taking a look at. Consider remaking this yourself in Desmos.
- Straight-line Depreciation Worksheet – graphing activity to model depreciation using a linear function; it also has accompanying questions.
- This would probably work better as a Desmos classroom activity.
- Car Declining Balance – Blank – depreciation model (of the decreasing value of a car years after its purchase).
- Using the graph given, I find it easiest to insert y values into the blank table after first inserting vertical lines (x = 0 to 5). This allows you to select the points of intersection between the vertical lines and the function.
- This pre-prepared activity also showcases the regression model feature available on Desmos. Learn more here.
- Simple vs Compound Interest – graphing model that does a fantastic job of demonstrating the difference between simple and compound interest growth.
- The activity also gives you the option to change the principal amount and the interest rate per time period parameters.
- Each of the activity features are accompanied with helpful comments that are worth reading to better understand the relevant parameters.
- Generating Compound Interest Formula – pre-prepared tables that demonstrate how principal amounts grow over 12 years through simple or compound interest
- The second sheet demonstrates how the simple and compound interests can be derived via a table.
- Monthly vs Yearly Compound Interest – this is similarly formatted to the Google Sheet above; it provides an example of the difference between yearly and monthly-based compound interest (over a 12-year period).
- To best demonstrate this effect to students, I would recommend showing them the accompanying graphs. On the tens of thousands scale, the differences between the two amounts are slight but can be easily seen, advantaging the monthly compounding.
- Depreciation – this sheet provides example data to demonstrate how compounding depreciation and straight-line depreciation works over a long time period.
- The second sheet also provides example data for yearly vs monthly compounding depreciation, and similar looking graphs to the sheet above.
High Rollers Game
- Dice-rolling game (requires a d20, d12, d4 and a percentile die; if you don’t have these available, see Roll The Dice, or use Google’s Roll Dice tool).
- Each die is used to roll a certain parameter; e.g. the d12 is used to determine the interest rate (as a % per annum).
- After rolling and computing the interest earned, students have the option to change the value of any of the parameters;
- With this, students are able to experiment with changing the values and identify/explain which has the greatest impact on the final interest earned.
Paper Folding (Exponentials) by Riehlt/MathWeCanUse
- I’d recommend reading the blog post for further details; it’s about paper folding and how it connects to exponential growth (check this MythBusters clip for background information).
- Available on the post is a Desmos Classroom Activity, as well as some other activity/project files the author has developed.
Game of Life (Simulation)
- Note: Not to be confused with Conway’s Game of Life or the Hasbro board game The Game of Life (one of these are iconic; the other is a slightly more complicated Candy Land).
- This activity should be done in conjunction with the Investment Plan Research resources (but you could also prepare example interest rates if students do not have access to the Internet or computer/mobile devices).
- The blue cards represent the principal amount students invest, while the green cards represent the time period students invest their money for.
- After deciding on some life commitments (e.g. purchasing a car) and waiting a 5 year period, students take a red card. These represent different financial scenarios or events. With these new changes, students need to reassess their financial situations, particularly in regards to the commitments they made prior to receiving the red cards.
- Overall, this seems like a fun activity to get students thinking about how they should plan and invest for their future as working adults.
That’s all for the Financial Mathematics sub-strand. My next Resource For post will be about the Ratio & Rates sub-strand. Before that though, I will also be throwing up a post for a new series, as well as starting some drafts for other topics.
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